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prodejna/qdecimal/decnumber/decNumber.c

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/* ------------------------------------------------------------------ */
/* Decimal Number arithmetic module */
/* ------------------------------------------------------------------ */
/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */
/* */
/* This software is made available under the terms of the */
/* ICU License -- ICU 1.8.1 and later. */
/* */
/* The description and User's Guide ("The decNumber C Library") for */
/* this software is called decNumber.pdf. This document is */
/* available, together with arithmetic and format specifications, */
/* testcases, and Web links, on the General Decimal Arithmetic page. */
/* */
/* Please send comments, suggestions, and corrections to the author: */
/* mfc@uk.ibm.com */
/* Mike Cowlishaw, IBM Fellow */
/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for arbitrary-precision General */
/* Decimal Arithmetic as defined in the specification which may be */
/* found on the General Decimal Arithmetic pages. It implements both */
/* the full ('extended') arithmetic and the simpler ('subset') */
/* arithmetic. */
/* */
/* Usage notes: */
/* */
/* 1. This code is ANSI C89 except: */
/* */
/* a) C99 line comments (double forward slash) are used. (Most C */
/* compilers accept these. If yours does not, a simple script */
/* can be used to convert them to ANSI C comments.) */
/* */
/* b) Types from C99 stdint.h are used. If you do not have this */
/* header file, see the User's Guide section of the decNumber */
/* documentation; this lists the necessary definitions. */
/* */
/* c) If DECDPUN>4 or DECUSE64=1, the C99 64-bit int64_t and */
/* uint64_t types may be used. To avoid these, set DECUSE64=0 */
/* and DECDPUN<=4 (see documentation). */
/* */
/* The code also conforms to C99 restrictions; in particular, */
/* strict aliasing rules are observed. */
/* */
/* 2. The decNumber format which this library uses is optimized for */
/* efficient processing of relatively short numbers; in particular */
/* it allows the use of fixed sized structures and minimizes copy */
/* and move operations. It does, however, support arbitrary */
/* precision (up to 999,999,999 digits) and arbitrary exponent */
/* range (Emax in the range 0 through 999,999,999 and Emin in the */
/* range -999,999,999 through 0). Mathematical functions (for */
/* example decNumberExp) as identified below are restricted more */
/* tightly: digits, emax, and -emin in the context must be <= */
/* DEC_MAX_MATH (999999), and their operand(s) must be within */
/* these bounds. */
/* */
/* 3. Logical functions are further restricted; their operands must */
/* be finite, positive, have an exponent of zero, and all digits */
/* must be either 0 or 1. The result will only contain digits */
/* which are 0 or 1 (and will have exponent=0 and a sign of 0). */
/* */
/* 4. Operands to operator functions are never modified unless they */
/* are also specified to be the result number (which is always */
/* permitted). Other than that case, operands must not overlap. */
/* */
/* 5. Error handling: the type of the error is ORed into the status */
/* flags in the current context (decContext structure). The */
/* SIGFPE signal is then raised if the corresponding trap-enabler */
/* flag in the decContext is set (is 1). */
/* */
/* It is the responsibility of the caller to clear the status */
/* flags as required. */
/* */
/* The result of any routine which returns a number will always */
/* be a valid number (which may be a special value, such as an */
/* Infinity or NaN). */
/* */
/* 6. The decNumber format is not an exchangeable concrete */
/* representation as it comprises fields which may be machine- */
/* dependent (packed or unpacked, or special length, for example). */
/* Canonical conversions to and from strings are provided; other */
/* conversions are available in separate modules. */
/* */
/* 7. Normally, input operands are assumed to be valid. Set DECCHECK */
/* to 1 for extended operand checking (including NULL operands). */
/* Results are undefined if a badly-formed structure (or a NULL */
/* pointer to a structure) is provided, though with DECCHECK */
/* enabled the operator routines are protected against exceptions. */
/* (Except if the result pointer is NULL, which is unrecoverable.) */
/* */
/* However, the routines will never cause exceptions if they are */
/* given well-formed operands, even if the value of the operands */
/* is inappropriate for the operation and DECCHECK is not set. */
/* (Except for SIGFPE, as and where documented.) */
/* */
/* 8. Subset arithmetic is available only if DECSUBSET is set to 1. */
/* ------------------------------------------------------------------ */
/* Implementation notes for maintenance of this module: */
/* */
/* 1. Storage leak protection: Routines which use malloc are not */
/* permitted to use return for fastpath or error exits (i.e., */
/* they follow strict structured programming conventions). */
/* Instead they have a do{}while(0); construct surrounding the */
/* code which is protected -- break may be used to exit this. */
/* Other routines can safely use the return statement inline. */
/* */
/* Storage leak accounting can be enabled using DECALLOC. */
/* */
/* 2. All loops use the for(;;) construct. Any do construct does */
/* not loop; it is for allocation protection as just described. */
/* */
/* 3. Setting status in the context must always be the very last */
/* action in a routine, as non-0 status may raise a trap and hence */
/* the call to set status may not return (if the handler uses long */
/* jump). Therefore all cleanup must be done first. In general, */
/* to achieve this status is accumulated and is only applied just */
/* before return by calling decContextSetStatus (via decStatus). */
/* */
/* Routines which allocate storage cannot, in general, use the */
/* 'top level' routines which could cause a non-returning */
/* transfer of control. The decXxxxOp routines are safe (do not */
/* call decStatus even if traps are set in the context) and should */
/* be used instead (they are also a little faster). */
/* */
/* 4. Exponent checking is minimized by allowing the exponent to */
/* grow outside its limits during calculations, provided that */
/* the decFinalize function is called later. Multiplication and */
/* division, and intermediate calculations in exponentiation, */
/* require more careful checks because of the risk of 31-bit */
/* overflow (the most negative valid exponent is -1999999997, for */
/* a 999999999-digit number with adjusted exponent of -999999999). */
/* */
/* 5. Rounding is deferred until finalization of results, with any */
/* 'off to the right' data being represented as a single digit */
/* residue (in the range -1 through 9). This avoids any double- */
/* rounding when more than one shortening takes place (for */
/* example, when a result is subnormal). */
/* */
/* 6. The digits count is allowed to rise to a multiple of DECDPUN */
/* during many operations, so whole Units are handled and exact */
/* accounting of digits is not needed. The correct digits value */
/* is found by decGetDigits, which accounts for leading zeros. */
/* This must be called before any rounding if the number of digits */
/* is not known exactly. */
/* */
/* 7. The multiply-by-reciprocal 'trick' is used for partitioning */
/* numbers up to four digits, using appropriate constants. This */
/* is not useful for longer numbers because overflow of 32 bits */
/* would lead to 4 multiplies, which is almost as expensive as */
/* a divide (unless a floating-point or 64-bit multiply is */
/* assumed to be available). */
/* */
/* 8. Unusual abbreviations that may be used in the commentary: */
/* lhs -- left hand side (operand, of an operation) */
/* lsd -- least significant digit (of coefficient) */
/* lsu -- least significant Unit (of coefficient) */
/* msd -- most significant digit (of coefficient) */
/* msi -- most significant item (in an array) */
/* msu -- most significant Unit (of coefficient) */
/* rhs -- right hand side (operand, of an operation) */
/* +ve -- positive */
/* -ve -- negative */
/* ** -- raise to the power */
/* ------------------------------------------------------------------ */
#include <stdlib.h> // for malloc, free, etc.
#include <stdio.h> // for printf [if needed]
#include <string.h> // for strcpy
#include <ctype.h> // for lower
#include "decNumber.h" // base number library
#include "decNumberLocal.h" // decNumber local types, etc.
/* Constants */
// Public lookup table used by the D2U macro
const uByte d2utable[DECMAXD2U+1]=D2UTABLE;
#define DECVERB 1 // set to 1 for verbose DECCHECK
#define powers DECPOWERS // old internal name
// Local constants
#define DIVIDE 0x80 // Divide operators
#define REMAINDER 0x40 // ..
#define DIVIDEINT 0x20 // ..
#define REMNEAR 0x10 // ..
#define COMPARE 0x01 // Compare operators
#define COMPMAX 0x02 // ..
#define COMPMIN 0x03 // ..
#define COMPTOTAL 0x04 // ..
#define COMPNAN 0x05 // .. [NaN processing]
#define COMPSIG 0x06 // .. [signaling COMPARE]
#define COMPMAXMAG 0x07 // ..
#define COMPMINMAG 0x08 // ..
#define DEC_sNaN 0x40000000 // local status: sNaN signal
#define BADINT (Int)0x80000000 // most-negative Int; error indicator
// Next two indicate an integer >= 10**6, and its parity (bottom bit)
#define BIGEVEN (Int)0x80000002
#define BIGODD (Int)0x80000003
static Unit uarrone[1]={1}; // Unit array of 1, used for incrementing
/* Granularity-dependent code */
#if DECDPUN<=4
#define eInt Int // extended integer
#define ueInt uInt // unsigned extended integer
// Constant multipliers for divide-by-power-of five using reciprocal
// multiply, after removing powers of 2 by shifting, and final shift
// of 17 [we only need up to **4]
static const uInt multies[]={131073, 26215, 5243, 1049, 210};
// QUOT10 -- macro to return the quotient of unit u divided by 10**n
#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
#else
// For DECDPUN>4 non-ANSI-89 64-bit types are needed.
#if !DECUSE64
#error decNumber.c: DECUSE64 must be 1 when DECDPUN>4
#endif
#define eInt Long // extended integer
#define ueInt uLong // unsigned extended integer
#endif
/* Local routines */
static decNumber * decAddOp(decNumber *, const decNumber *, const decNumber *,
decContext *, uByte, uInt *);
static Flag decBiStr(const char *, const char *, const char *);
static uInt decCheckMath(const decNumber *, decContext *, uInt *);
static void decApplyRound(decNumber *, decContext *, Int, uInt *);
static Int decCompare(const decNumber *lhs, const decNumber *rhs, Flag);
static decNumber * decCompareOp(decNumber *, const decNumber *,
const decNumber *, decContext *,
Flag, uInt *);
static void decCopyFit(decNumber *, const decNumber *, decContext *,
Int *, uInt *);
static decNumber * decDecap(decNumber *, Int);
static decNumber * decDivideOp(decNumber *, const decNumber *,
const decNumber *, decContext *, Flag, uInt *);
static decNumber * decExpOp(decNumber *, const decNumber *,
decContext *, uInt *);
static void decFinalize(decNumber *, decContext *, Int *, uInt *);
static Int decGetDigits(Unit *, Int);
static Int decGetInt(const decNumber *);
static decNumber * decLnOp(decNumber *, const decNumber *,
decContext *, uInt *);
static decNumber * decMultiplyOp(decNumber *, const decNumber *,
const decNumber *, decContext *,
uInt *);
static decNumber * decNaNs(decNumber *, const decNumber *,
const decNumber *, decContext *, uInt *);
static decNumber * decQuantizeOp(decNumber *, const decNumber *,
const decNumber *, decContext *, Flag,
uInt *);
static void decReverse(Unit *, Unit *);
static void decSetCoeff(decNumber *, decContext *, const Unit *,
Int, Int *, uInt *);
static void decSetMaxValue(decNumber *, decContext *);
static void decSetOverflow(decNumber *, decContext *, uInt *);
static void decSetSubnormal(decNumber *, decContext *, Int *, uInt *);
static Int decShiftToLeast(Unit *, Int, Int);
static Int decShiftToMost(Unit *, Int, Int);
static void decStatus(decNumber *, uInt, decContext *);
static void decToString(const decNumber *, char[], Flag);
static decNumber * decTrim(decNumber *, decContext *, Flag, Flag, Int *);
static Int decUnitAddSub(const Unit *, Int, const Unit *, Int, Int,
Unit *, Int);
static Int decUnitCompare(const Unit *, Int, const Unit *, Int, Int);
#if !DECSUBSET
/* decFinish == decFinalize when no subset arithmetic needed */
#define decFinish(a,b,c,d) decFinalize(a,b,c,d)
#else
static void decFinish(decNumber *, decContext *, Int *, uInt *);
static decNumber * decRoundOperand(const decNumber *, decContext *, uInt *);
#endif
/* Local macros */
// masked special-values bits
#define SPECIALARG (rhs->bits & DECSPECIAL)
#define SPECIALARGS ((lhs->bits | rhs->bits) & DECSPECIAL)
/* Diagnostic macros, etc. */
#if DECALLOC
// Handle malloc/free accounting. If enabled, our accountable routines
// are used; otherwise the code just goes straight to the system malloc
// and free routines.
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
#define DECFENCE 0x5a // corruption detector
// 'Our' malloc and free:
static void *decMalloc(size_t);
static void decFree(void *);
uInt decAllocBytes=0; // count of bytes allocated
// Note that DECALLOC code only checks for storage buffer overflow.
// To check for memory leaks, the decAllocBytes variable must be
// checked to be 0 at appropriate times (e.g., after the test
// harness completes a set of tests). This checking may be unreliable
// if the testing is done in a multi-thread environment.
#endif
#if DECCHECK
// Optional checking routines. Enabling these means that decNumber
// and decContext operands to operator routines are checked for
// correctness. This roughly doubles the execution time of the
// fastest routines (and adds 600+ bytes), so should not normally be
// used in 'production'.
// decCheckInexact is used to check that inexact results have a full
// complement of digits (where appropriate -- this is not the case
// for Quantize, for example)
#define DECUNRESU ((decNumber *)(void *)0xffffffff)
#define DECUNUSED ((const decNumber *)(void *)0xffffffff)
#define DECUNCONT ((decContext *)(void *)(0xffffffff))
static Flag decCheckOperands(decNumber *, const decNumber *,
const decNumber *, decContext *);
static Flag decCheckNumber(const decNumber *);
static void decCheckInexact(const decNumber *, decContext *);
#endif
#if DECTRACE || DECCHECK
// Optional trace/debugging routines (may or may not be used)
void decNumberShow(const decNumber *); // displays the components of a number
static void decDumpAr(char, const Unit *, Int);
#endif
/* ================================================================== */
/* Conversions */
/* ================================================================== */
/* ------------------------------------------------------------------ */
/* from-int32 -- conversion from Int or uInt */
/* */
/* dn is the decNumber to receive the integer */
/* in or uin is the integer to be converted */
/* returns dn */
/* */
/* No error is possible. */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromInt32(decNumber *dn, Int in) {
uInt unsig;
if (in>=0) unsig=in;
else { // negative (possibly BADINT)
if (in==BADINT) unsig=(uInt)1073741824*2; // special case
else unsig=-in; // invert
}
// in is now positive
decNumberFromUInt32(dn, unsig);
if (in<0) dn->bits=DECNEG; // sign needed
return dn;
} // decNumberFromInt32
decNumber * decNumberFromUInt32(decNumber *dn, uInt uin) {
Unit *up; // work pointer
decNumberZero(dn); // clean
if (uin==0) return dn; // [or decGetDigits bad call]
for (up=dn->lsu; uin>0; up++) {
*up=(Unit)(uin%(DECDPUNMAX+1));
uin=uin/(DECDPUNMAX+1);
}
dn->digits=decGetDigits(dn->lsu, up-dn->lsu);
return dn;
} // decNumberFromUInt32
/* ------------------------------------------------------------------ */
/* to-int32 -- conversion to Int or uInt */
/* */
/* dn is the decNumber to convert */
/* set is the context for reporting errors */
/* returns the converted decNumber, or 0 if Invalid is set */
/* */
/* Invalid is set if the decNumber does not have exponent==0 or if */
/* it is a NaN, Infinite, or out-of-range. */
/* ------------------------------------------------------------------ */
Int decNumberToInt32(const decNumber *dn, decContext *set) {
#if DECCHECK
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
#endif
// special or too many digits, or bad exponent
if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0) ; // bad
else { // is a finite integer with 10 or fewer digits
Int d; // work
const Unit *up; // ..
uInt hi=0, lo; // ..
up=dn->lsu; // -> lsu
lo=*up; // get 1 to 9 digits
#if DECDPUN>1 // split to higher
hi=lo/10;
lo=lo%10;
#endif
up++;
// collect remaining Units, if any, into hi
for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
// now low has the lsd, hi the remainder
if (hi>214748364 || (hi==214748364 && lo>7)) { // out of range?
// most-negative is a reprieve
if (dn->bits&DECNEG && hi==214748364 && lo==8) return 0x80000000;
// bad -- drop through
}
else { // in-range always
Int i=X10(hi)+lo;
if (dn->bits&DECNEG) return -i;
return i;
}
} // integer
decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
return 0;
} // decNumberToInt32
uInt decNumberToUInt32(const decNumber *dn, decContext *set) {
#if DECCHECK
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
#endif
// special or too many digits, or bad exponent, or negative (<0)
if (dn->bits&DECSPECIAL || dn->digits>10 || dn->exponent!=0
|| (dn->bits&DECNEG && !ISZERO(dn))); // bad
else { // is a finite integer with 10 or fewer digits
Int d; // work
const Unit *up; // ..
uInt hi=0, lo; // ..
up=dn->lsu; // -> lsu
lo=*up; // get 1 to 9 digits
#if DECDPUN>1 // split to higher
hi=lo/10;
lo=lo%10;
#endif
up++;
// collect remaining Units, if any, into hi
for (d=DECDPUN; d<dn->digits; up++, d+=DECDPUN) hi+=*up*powers[d-1];
// now low has the lsd, hi the remainder
if (hi>429496729 || (hi==429496729 && lo>5)) ; // no reprieve possible
else return X10(hi)+lo;
} // integer
decContextSetStatus(set, DEC_Invalid_operation); // [may not return]
return 0;
} // decNumberToUInt32
/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string */
/* to-engineering-string -- conversion to numeric string */
/* */
/* decNumberToString(dn, string); */
/* decNumberToEngString(dn, string); */
/* */
/* dn is the decNumber to convert */
/* string is the string where the result will be laid out */
/* */
/* string must be at least dn->digits+14 characters long */
/* */
/* No error is possible, and no status can be set. */
/* ------------------------------------------------------------------ */
char * decNumberToString(const decNumber *dn, char *string){
decToString(dn, string, 0);
return string;
} // DecNumberToString
char * decNumberToEngString(const decNumber *dn, char *string){
decToString(dn, string, 1);
return string;
} // DecNumberToEngString
/* ------------------------------------------------------------------ */
/* to-number -- conversion from numeric string */
/* */
/* decNumberFromString -- convert string to decNumber */
/* dn -- the number structure to fill */
/* chars[] -- the string to convert ('\0' terminated) */
/* set -- the context used for processing any error, */
/* determining the maximum precision available */
/* (set.digits), determining the maximum and minimum */
/* exponent (set.emax and set.emin), determining if */
/* extended values are allowed, and checking the */
/* rounding mode if overflow occurs or rounding is */
/* needed. */
/* */
/* The length of the coefficient and the size of the exponent are */
/* checked by this routine, so the correct error (Underflow or */
/* Overflow) can be reported or rounding applied, as necessary. */
/* */
/* If bad syntax is detected, the result will be a quiet NaN. */
/* ------------------------------------------------------------------ */
decNumber * decNumberFromString(decNumber *dn, const char chars[],
decContext *set) {
Int exponent=0; // working exponent [assume 0]
uByte bits=0; // working flags [assume +ve]
Unit *res; // where result will be built
Unit resbuff[SD2U(DECBUFFER+9)];// local buffer in case need temporary
// [+9 allows for ln() constants]
Unit *allocres=NULL; // -> allocated result, iff allocated
Int d=0; // count of digits found in decimal part
const char *dotchar=NULL; // where dot was found
const char *cfirst=chars; // -> first character of decimal part
const char *last=NULL; // -> last digit of decimal part
const char *c; // work
Unit *up; // ..
#if DECDPUN>1
Int cut, out; // ..
#endif
Int residue; // rounding residue
uInt status=0; // error code
#if DECCHECK
if (decCheckOperands(DECUNRESU, DECUNUSED, DECUNUSED, set))
return decNumberZero(dn);
#endif
do { // status & malloc protection
for (c=chars;; c++) { // -> input character
if (*c>='0' && *c<='9') { // test for Arabic digit
last=c;
d++; // count of real digits
continue; // still in decimal part
}
if (*c=='.' && dotchar==NULL) { // first '.'
dotchar=c; // record offset into decimal part
if (c==cfirst) cfirst++; // first digit must follow
continue;}
if (c==chars) { // first in string...
if (*c=='-') { // valid - sign
cfirst++;
bits=DECNEG;
continue;}
if (*c=='+') { // valid + sign
cfirst++;
continue;}
}
// *c is not a digit, or a valid +, -, or '.'
break;
} // c
if (last==NULL) { // no digits yet
status=DEC_Conversion_syntax;// assume the worst
if (*c=='\0') break; // and no more to come...
#if DECSUBSET
// if subset then infinities and NaNs are not allowed
if (!set->extended) break; // hopeless
#endif
// Infinities and NaNs are possible, here
if (dotchar!=NULL) break; // .. unless had a dot
decNumberZero(dn); // be optimistic
if (decBiStr(c, "infinity", "INFINITY")
|| decBiStr(c, "inf", "INF")) {
dn->bits=bits | DECINF;
status=0; // is OK
break; // all done
}
// a NaN expected
// 2003.09.10 NaNs are now permitted to have a sign
dn->bits=bits | DECNAN; // assume simple NaN
if (*c=='s' || *c=='S') { // looks like an sNaN
c++;
dn->bits=bits | DECSNAN;
}
if (*c!='n' && *c!='N') break; // check caseless "NaN"
c++;
if (*c!='a' && *c!='A') break; // ..
c++;
if (*c!='n' && *c!='N') break; // ..
c++;
// now either nothing, or nnnn payload, expected
// -> start of integer and skip leading 0s [including plain 0]
for (cfirst=c; *cfirst=='0';) cfirst++;
if (*cfirst=='\0') { // "NaN" or "sNaN", maybe with all 0s
status=0; // it's good
break; // ..
}
// something other than 0s; setup last and d as usual [no dots]
for (c=cfirst;; c++, d++) {
if (*c<'0' || *c>'9') break; // test for Arabic digit
last=c;
}
if (*c!='\0') break; // not all digits
if (d>set->digits-1) {
// [NB: payload in a decNumber can be full length unless
// clamped, in which case can only be digits-1]
if (set->clamp) break;
if (d>set->digits) break;
} // too many digits?
// good; drop through to convert the integer to coefficient
status=0; // syntax is OK
bits=dn->bits; // for copy-back
} // last==NULL
else if (*c!='\0') { // more to process...
// had some digits; exponent is only valid sequence now
Flag nege; // 1=negative exponent
const char *firstexp; // -> first significant exponent digit
status=DEC_Conversion_syntax;// assume the worst
if (*c!='e' && *c!='E') break;
/* Found 'e' or 'E' -- now process explicit exponent */
// 1998.07.11: sign no longer required
nege=0;
c++; // to (possible) sign
if (*c=='-') {nege=1; c++;}
else if (*c=='+') c++;
if (*c=='\0') break;
for (; *c=='0' && *(c+1)!='\0';) c++; // strip insignificant zeros
firstexp=c; // save exponent digit place
for (; ;c++) {
if (*c<'0' || *c>'9') break; // not a digit
exponent=X10(exponent)+(Int)*c-(Int)'0';
} // c
// if not now on a '\0', *c must not be a digit
if (*c!='\0') break;
// (this next test must be after the syntax checks)
// if it was too long the exponent may have wrapped, so check
// carefully and set it to a certain overflow if wrap possible
if (c>=firstexp+9+1) {
if (c>firstexp+9+1 || *firstexp>'1') exponent=DECNUMMAXE*2;
// [up to 1999999999 is OK, for example 1E-1000000998]
}
if (nege) exponent=-exponent; // was negative
status=0; // is OK
} // stuff after digits
// Here when whole string has been inspected; syntax is good
// cfirst->first digit (never dot), last->last digit (ditto)
// strip leading zeros/dot [leave final 0 if all 0's]
if (*cfirst=='0') { // [cfirst has stepped over .]
for (c=cfirst; c<last; c++, cfirst++) {
if (*c=='.') continue; // ignore dots
if (*c!='0') break; // non-zero found
d--; // 0 stripped
} // c
#if DECSUBSET
// make a rapid exit for easy zeros if !extended
if (*cfirst=='0' && !set->extended) {
decNumberZero(dn); // clean result
break; // [could be return]
}
#endif
} // at least one leading 0
// Handle decimal point...
if (dotchar!=NULL && dotchar<last) // non-trailing '.' found?
exponent-=(last-dotchar); // adjust exponent
// [we can now ignore the .]
// OK, the digits string is good. Assemble in the decNumber, or in
// a temporary units array if rounding is needed
if (d<=set->digits) res=dn->lsu; // fits into supplied decNumber
else { // rounding needed
Int needbytes=D2U(d)*sizeof(Unit);// bytes needed
res=resbuff; // assume use local buffer
if (needbytes>(Int)sizeof(resbuff)) { // too big for local
allocres=(Unit *)malloc(needbytes);
if (allocres==NULL) {status|=DEC_Insufficient_storage; break;}
res=allocres;
}
}
// res now -> number lsu, buffer, or allocated storage for Unit array
// Place the coefficient into the selected Unit array
// [this is often 70% of the cost of this function when DECDPUN>1]
#if DECDPUN>1
out=0; // accumulator
up=res+D2U(d)-1; // -> msu
cut=d-(up-res)*DECDPUN; // digits in top unit
for (c=cfirst;; c++) { // along the digits
if (*c=='.') continue; // ignore '.' [don't decrement cut]
out=X10(out)+(Int)*c-(Int)'0';
if (c==last) break; // done [never get to trailing '.']
cut--;
if (cut>0) continue; // more for this unit
*up=(Unit)out; // write unit
up--; // prepare for unit below..
cut=DECDPUN; // ..
out=0; // ..
} // c
*up=(Unit)out; // write lsu
#else
// DECDPUN==1
up=res; // -> lsu
for (c=last; c>=cfirst; c--) { // over each character, from least
if (*c=='.') continue; // ignore . [don't step up]
*up=(Unit)((Int)*c-(Int)'0');
up++;
} // c
#endif
dn->bits=bits;
dn->exponent=exponent;
dn->digits=d;
// if not in number (too long) shorten into the number
if (d>set->digits) {
residue=0;
decSetCoeff(dn, set, res, d, &residue, &status);
// always check for overflow or subnormal and round as needed
decFinalize(dn, set, &residue, &status);
}
else { // no rounding, but may still have overflow or subnormal
// [these tests are just for performance; finalize repeats them]
if ((dn->exponent-1<set->emin-dn->digits)
|| (dn->exponent-1>set->emax-set->digits)) {
residue=0;
decFinalize(dn, set, &residue, &status);
}
}
// decNumberShow(dn);
} while(0); // [for break]
if (allocres!=NULL) free(allocres); // drop any storage used
if (status!=0) decStatus(dn, status, set);
return dn;
} /* decNumberFromString */
/* ================================================================== */
/* Operators */
/* ================================================================== */
/* ------------------------------------------------------------------ */
/* decNumberAbs -- absolute value operator */
/* */
/* This computes C = abs(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context */
/* */
/* See also decNumberCopyAbs for a quiet bitwise version of this. */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* This has the same effect as decNumberPlus unless A is negative, */
/* in which case it has the same effect as decNumberMinus. */
/* ------------------------------------------------------------------ */
decNumber * decNumberAbs(decNumber *res, const decNumber *rhs,
decContext *set) {
decNumber dzero; // for 0
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
decNumberZero(&dzero); // set 0
dzero.exponent=rhs->exponent; // [no coefficient expansion]
decAddOp(res, &dzero, rhs, set, (uByte)(rhs->bits & DECNEG), &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberAbs
/* ------------------------------------------------------------------ */
/* decNumberAdd -- add two Numbers */
/* */
/* This computes C = A + B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* This just calls the routine shared with Subtract */
decNumber * decNumberAdd(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decAddOp(res, lhs, rhs, set, 0, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberAdd
/* ------------------------------------------------------------------ */
/* decNumberAnd -- AND two Numbers, digitwise */
/* */
/* This computes C = A & B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X&X) */
/* lhs is A */
/* rhs is B */
/* set is the context (used for result length and error report) */
/* */
/* C must have space for set->digits digits. */
/* */
/* Logical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* ------------------------------------------------------------------ */
decNumber * decNumberAnd(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
const Unit *ua, *ub; // -> operands
const Unit *msua, *msub; // -> operand msus
Unit *uc, *msuc; // -> result and its msu
Int msudigs; // digits in res msu
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
// operands are valid
ua=lhs->lsu; // bottom-up
ub=rhs->lsu; // ..
uc=res->lsu; // ..
msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
msuc=uc+D2U(set->digits)-1; // -> msu of result
msudigs=MSUDIGITS(set->digits); // [faster than remainder]
for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
Unit a, b; // extract units
if (ua>msua) a=0;
else a=*ua;
if (ub>msub) b=0;
else b=*ub;
*uc=0; // can now write back
if (a|b) { // maybe 1 bits to examine
Int i, j;
*uc=0; // can now write back
// This loop could be unrolled and/or use BIN2BCD tables
for (i=0; i<DECDPUN; i++) {
if (a&b&1) *uc=*uc+(Unit)powers[i]; // effect AND
j=a%10;
a=a/10;
j|=b%10;
b=b/10;
if (j>1) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
if (uc==msuc && i==msudigs-1) break; // just did final digit
} // each digit
} // both OK
} // each unit
// [here uc-1 is the msu of the result]
res->digits=decGetDigits(res->lsu, uc-res->lsu);
res->exponent=0; // integer
res->bits=0; // sign=0
return res; // [no status to set]
} // decNumberAnd
/* ------------------------------------------------------------------ */
/* decNumberCompare -- compare two Numbers */
/* */
/* This computes C = A ? B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for one digit (or NaN). */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompare(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPARE, &status);
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberCompare
/* ------------------------------------------------------------------ */
/* decNumberCompareSignal -- compare, signalling on all NaNs */
/* */
/* This computes C = A ? B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for one digit (or NaN). */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareSignal(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPSIG, &status);
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberCompareSignal
/* ------------------------------------------------------------------ */
/* decNumberCompareTotal -- compare two Numbers, using total ordering */
/* */
/* This computes C = A ? B, under total ordering */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for one digit; the result will always be one of */
/* -1, 0, or 1. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotal(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberCompareTotal
/* ------------------------------------------------------------------ */
/* decNumberCompareTotalMag -- compare, total ordering of magnitudes */
/* */
/* This computes C = |A| ? |B|, under total ordering */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for one digit; the result will always be one of */
/* -1, 0, or 1. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCompareTotalMag(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
uInt needbytes; // for space calculations
decNumber bufa[D2N(DECBUFFER+1)];// +1 in case DECBUFFER=0
decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
decNumber bufb[D2N(DECBUFFER+1)];
decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
decNumber *a, *b; // temporary pointers
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
do { // protect allocated storage
// if either is negative, take a copy and absolute
if (decNumberIsNegative(lhs)) { // lhs<0
a=bufa;
needbytes=sizeof(decNumber)+(D2U(lhs->digits)-1)*sizeof(Unit);
if (needbytes>sizeof(bufa)) { // need malloc space
allocbufa=(decNumber *)malloc(needbytes);
if (allocbufa==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
a=allocbufa; // use the allocated space
}
decNumberCopy(a, lhs); // copy content
a->bits&=~DECNEG; // .. and clear the sign
lhs=a; // use copy from here on
}
if (decNumberIsNegative(rhs)) { // rhs<0
b=bufb;
needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
if (needbytes>sizeof(bufb)) { // need malloc space
allocbufb=(decNumber *)malloc(needbytes);
if (allocbufb==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
b=allocbufb; // use the allocated space
}
decNumberCopy(b, rhs); // copy content
b->bits&=~DECNEG; // .. and clear the sign
rhs=b; // use copy from here on
}
decCompareOp(res, lhs, rhs, set, COMPTOTAL, &status);
} while(0); // end protected
if (allocbufa!=NULL) free(allocbufa); // drop any storage used
if (allocbufb!=NULL) free(allocbufb); // ..
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberCompareTotalMag
/* ------------------------------------------------------------------ */
/* decNumberDivide -- divide one number by another */
/* */
/* This computes C = A / B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivide(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decDivideOp(res, lhs, rhs, set, DIVIDE, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberDivide
/* ------------------------------------------------------------------ */
/* decNumberDivideInteger -- divide and return integer quotient */
/* */
/* This computes C = A # B, where # is the integer divide operator */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X#X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberDivideInteger(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decDivideOp(res, lhs, rhs, set, DIVIDEINT, &status);
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberDivideInteger
/* ------------------------------------------------------------------ */
/* decNumberExp -- exponentiation */
/* */
/* This computes C = exp(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context; note that rounding mode has no effect */
/* */
/* C must have space for set->digits digits. */
/* */
/* Mathematical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* */
/* Finite results will always be full precision and Inexact, except */
/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
/* */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
/* almost always be correctly rounded, but may be up to 1 ulp in */
/* error in rare cases. */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decExpOp which can handle the slightly wider */
/* (double) range needed by Ln (which has to be able to calculate */
/* exp(-a) where a can be the tiniest number (Ntiny). */
/* ------------------------------------------------------------------ */
decNumber * decNumberExp(decNumber *res, const decNumber *rhs,
decContext *set) {
uInt status=0; // accumulator
#if DECSUBSET
decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
#endif
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// Check restrictions; these restrictions ensure that if h=8 (see
// decExpOp) then the result will either overflow or underflow to 0.
// Other math functions restrict the input range, too, for inverses.
// If not violated then carry out the operation.
if (!decCheckMath(rhs, set, &status)) do { // protect allocation
#if DECSUBSET
if (!set->extended) {
// reduce operand and set lostDigits status, as needed
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, &status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
decExpOp(res, rhs, set, &status);
} while(0); // end protected
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); // drop any storage used
#endif
// apply significant status
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberExp
/* ------------------------------------------------------------------ */
/* decNumberFMA -- fused multiply add */
/* */
/* This computes D = (A * B) + C with only one rounding */
/* */
/* res is D, the result. D may be A or B or C (e.g., X=FMA(X,X,X)) */
/* lhs is A */
/* rhs is B */
/* fhs is C [far hand side] */
/* set is the context */
/* */
/* Mathematical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberFMA(decNumber *res, const decNumber *lhs,
const decNumber *rhs, const decNumber *fhs,
decContext *set) {
uInt status=0; // accumulator
decContext dcmul; // context for the multiplication
uInt needbytes; // for space calculations
decNumber bufa[D2N(DECBUFFER*2+1)];
decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
decNumber *acc; // accumulator pointer
decNumber dzero; // work
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
if (decCheckOperands(res, fhs, DECUNUSED, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) { // [undefined if subset]
status|=DEC_Invalid_operation;
break;}
#endif
// Check math restrictions [these ensure no overflow or underflow]
if ((!decNumberIsSpecial(lhs) && decCheckMath(lhs, set, &status))
|| (!decNumberIsSpecial(rhs) && decCheckMath(rhs, set, &status))
|| (!decNumberIsSpecial(fhs) && decCheckMath(fhs, set, &status))) break;
// set up context for multiply
dcmul=*set;
dcmul.digits=lhs->digits+rhs->digits; // just enough
// [The above may be an over-estimate for subset arithmetic, but that's OK]
dcmul.emax=DEC_MAX_EMAX; // effectively unbounded ..
dcmul.emin=DEC_MIN_EMIN; // [thanks to Math restrictions]
// set up decNumber space to receive the result of the multiply
acc=bufa; // may fit
needbytes=sizeof(decNumber)+(D2U(dcmul.digits)-1)*sizeof(Unit);
if (needbytes>sizeof(bufa)) { // need malloc space
allocbufa=(decNumber *)malloc(needbytes);
if (allocbufa==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
acc=allocbufa; // use the allocated space
}
// multiply with extended range and necessary precision
//printf("emin=%ld\n", dcmul.emin);
decMultiplyOp(acc, lhs, rhs, &dcmul, &status);
// Only Invalid operation (from sNaN or Inf * 0) is possible in
// status; if either is seen than ignore fhs (in case it is
// another sNaN) and set acc to NaN unless we had an sNaN
// [decMultiplyOp leaves that to caller]
// Note sNaN has to go through addOp to shorten payload if
// necessary
if ((status&DEC_Invalid_operation)!=0) {
if (!(status&DEC_sNaN)) { // but be true invalid
decNumberZero(res); // acc not yet set
res->bits=DECNAN;
break;
}
decNumberZero(&dzero); // make 0 (any non-NaN would do)
fhs=&dzero; // use that
}
#if DECCHECK
else { // multiply was OK
if (status!=0) printf("Status=%08lx after FMA multiply\n", (LI)status);
}
#endif
// add the third operand and result -> res, and all is done
decAddOp(res, acc, fhs, set, 0, &status);
} while(0); // end protected
if (allocbufa!=NULL) free(allocbufa); // drop any storage used
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberFMA
/* ------------------------------------------------------------------ */
/* decNumberInvert -- invert a Number, digitwise */
/* */
/* This computes C = ~A */
/* */
/* res is C, the result. C may be A (e.g., X=~X) */
/* rhs is A */
/* set is the context (used for result length and error report) */
/* */
/* C must have space for set->digits digits. */
/* */
/* Logical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* ------------------------------------------------------------------ */
decNumber * decNumberInvert(decNumber *res, const decNumber *rhs,
decContext *set) {
const Unit *ua, *msua; // -> operand and its msu
Unit *uc, *msuc; // -> result and its msu
Int msudigs; // digits in res msu
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
if (rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
// operand is valid
ua=rhs->lsu; // bottom-up
uc=res->lsu; // ..
msua=ua+D2U(rhs->digits)-1; // -> msu of rhs
msuc=uc+D2U(set->digits)-1; // -> msu of result
msudigs=MSUDIGITS(set->digits); // [faster than remainder]
for (; uc<=msuc; ua++, uc++) { // Unit loop
Unit a; // extract unit
Int i, j; // work
if (ua>msua) a=0;
else a=*ua;
*uc=0; // can now write back
// always need to examine all bits in rhs
// This loop could be unrolled and/or use BIN2BCD tables
for (i=0; i<DECDPUN; i++) {
if ((~a)&1) *uc=*uc+(Unit)powers[i]; // effect INVERT
j=a%10;
a=a/10;
if (j>1) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
if (uc==msuc && i==msudigs-1) break; // just did final digit
} // each digit
} // each unit
// [here uc-1 is the msu of the result]
res->digits=decGetDigits(res->lsu, uc-res->lsu);
res->exponent=0; // integer
res->bits=0; // sign=0
return res; // [no status to set]
} // decNumberInvert
/* ------------------------------------------------------------------ */
/* decNumberLn -- natural logarithm */
/* */
/* This computes C = ln(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context; note that rounding mode has no effect */
/* */
/* C must have space for set->digits digits. */
/* */
/* Notable cases: */
/* A<0 -> Invalid */
/* A=0 -> -Infinity (Exact) */
/* A=+Infinity -> +Infinity (Exact) */
/* A=1 exactly -> 0 (Exact) */
/* */
/* Mathematical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
/* almost always be correctly rounded, but may be up to 1 ulp in */
/* error in rare cases. */
/* ------------------------------------------------------------------ */
/* This is a wrapper for decLnOp which can handle the slightly wider */
/* (+11) range needed by Ln, Log10, etc. (which may have to be able */
/* to calculate at p+e+2). */
/* ------------------------------------------------------------------ */
decNumber * decNumberLn(decNumber *res, const decNumber *rhs,
decContext *set) {
uInt status=0; // accumulator
#if DECSUBSET
decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
#endif
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// Check restrictions; this is a math function; if not violated
// then carry out the operation.
if (!decCheckMath(rhs, set, &status)) do { // protect allocation
#if DECSUBSET
if (!set->extended) {
// reduce operand and set lostDigits status, as needed
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, &status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
// special check in subset for rhs=0
if (ISZERO(rhs)) { // +/- zeros -> error
status|=DEC_Invalid_operation;
break;}
} // extended=0
#endif
decLnOp(res, rhs, set, &status);
} while(0); // end protected
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); // drop any storage used
#endif
// apply significant status
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberLn
/* ------------------------------------------------------------------ */
/* decNumberLogB - get adjusted exponent, by 754 rules */
/* */
/* This computes C = adjustedexponent(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context, used only for digits and status */
/* */
/* For an unrounded result, digits may need to be 10 (A might have */
/* 10**9 digits and an exponent of +999999999, or one digit and an */
/* exponent of -1999999999). */
/* */
/* This returns the adjusted exponent of A after (in theory) padding */
/* with zeros on the right to set->digits digits while keeping the */
/* same value. The exponent is not limited by emin/emax. */
/* */
/* Notable cases: */
/* A<0 -> Use |A| */
/* A=0 -> -Infinity (Division by zero) */
/* A=Infinite -> +Infinity (Exact) */
/* A=1 exactly -> 0 (Exact) */
/* NaNs are propagated as usual */
/* ------------------------------------------------------------------ */
decNumber * decNumberLogB(decNumber *res, const decNumber *rhs,
decContext *set) {
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// NaNs as usual; Infinities return +Infinity; 0->oops
if (decNumberIsNaN(rhs)) decNaNs(res, rhs, NULL, set, &status);
else if (decNumberIsInfinite(rhs)) decNumberCopyAbs(res, rhs);
else if (decNumberIsZero(rhs)) {
decNumberZero(res); // prepare for Infinity
res->bits=DECNEG|DECINF; // -Infinity
status|=DEC_Division_by_zero; // as per 754
}
else { // finite non-zero
Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
if (set->digits>=10) decNumberFromInt32(res, ae); // lay it out
else {
decNumber buft[D2N(10)]; // temporary number
decNumber *t=buft; // ..
decNumberFromInt32(t, ae); // lay it out
decNumberPlus(res, t, set); // round as necessary
}
}
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberLogB
/* ------------------------------------------------------------------ */
/* decNumberLog10 -- logarithm in base 10 */
/* */
/* This computes C = log10(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context; note that rounding mode has no effect */
/* */
/* C must have space for set->digits digits. */
/* */
/* Notable cases: */
/* A<0 -> Invalid */
/* A=0 -> -Infinity (Exact) */
/* A=+Infinity -> +Infinity (Exact) */
/* A=10**n (if n is an integer) -> n (Exact) */
/* */
/* Mathematical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* */
/* An Inexact result is rounded using DEC_ROUND_HALF_EVEN; it will */
/* almost always be correctly rounded, but may be up to 1 ulp in */
/* error in rare cases. */
/* ------------------------------------------------------------------ */
/* This calculates ln(A)/ln(10) using appropriate precision. For */
/* ln(A) this is the max(p, rhs->digits + t) + 3, where p is the */
/* requested digits and t is the number of digits in the exponent */
/* (maximum 6). For ln(10) it is p + 3; this is often handled by the */
/* fastpath in decLnOp. The final division is done to the requested */
/* precision. */
/* ------------------------------------------------------------------ */
decNumber * decNumberLog10(decNumber *res, const decNumber *rhs,
decContext *set) {
uInt status=0, ignore=0; // status accumulators
uInt needbytes; // for space calculations
Int p; // working precision
Int t; // digits in exponent of A
// buffers for a and b working decimals
// (adjustment calculator, same size)
decNumber bufa[D2N(DECBUFFER+2)];
decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
decNumber *a=bufa; // temporary a
decNumber bufb[D2N(DECBUFFER+2)];
decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
decNumber *b=bufb; // temporary b
decNumber bufw[D2N(10)]; // working 2-10 digit number
decNumber *w=bufw; // ..
#if DECSUBSET
decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
#endif
decContext aset; // working context
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// Check restrictions; this is a math function; if not violated
// then carry out the operation.
if (!decCheckMath(rhs, set, &status)) do { // protect malloc
#if DECSUBSET
if (!set->extended) {
// reduce operand and set lostDigits status, as needed
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, &status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
// special check in subset for rhs=0
if (ISZERO(rhs)) { // +/- zeros -> error
status|=DEC_Invalid_operation;
break;}
} // extended=0
#endif
decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
// handle exact powers of 10; only check if +ve finite
if (!(rhs->bits&(DECNEG|DECSPECIAL)) && !ISZERO(rhs)) {
Int residue=0; // (no residue)
uInt copystat=0; // clean status
// round to a single digit...
aset.digits=1;
decCopyFit(w, rhs, &aset, &residue, &copystat); // copy & shorten
// if exact and the digit is 1, rhs is a power of 10
if (!(copystat&DEC_Inexact) && w->lsu[0]==1) {
// the exponent, conveniently, is the power of 10; making
// this the result needs a little care as it might not fit,
// so first convert it into the working number, and then move
// to res
decNumberFromInt32(w, w->exponent);
residue=0;
decCopyFit(res, w, set, &residue, &status); // copy & round
decFinish(res, set, &residue, &status); // cleanup/set flags
break;
} // not a power of 10
} // not a candidate for exact
// simplify the information-content calculation to use 'total
// number of digits in a, including exponent' as compared to the
// requested digits, as increasing this will only rarely cost an
// iteration in ln(a) anyway
t=6; // it can never be >6
// allocate space when needed...
p=(rhs->digits+t>set->digits?rhs->digits+t:set->digits)+3;
needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
if (needbytes>sizeof(bufa)) { // need malloc space
allocbufa=(decNumber *)malloc(needbytes);
if (allocbufa==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
a=allocbufa; // use the allocated space
}
aset.digits=p; // as calculated
aset.emax=DEC_MAX_MATH; // usual bounds
aset.emin=-DEC_MAX_MATH; // ..
aset.clamp=0; // and no concrete format
decLnOp(a, rhs, &aset, &status); // a=ln(rhs)
// skip the division if the result so far is infinite, NaN, or
// zero, or there was an error; note NaN from sNaN needs copy
if (status&DEC_NaNs && !(status&DEC_sNaN)) break;
if (a->bits&DECSPECIAL || ISZERO(a)) {
decNumberCopy(res, a); // [will fit]
break;}
// for ln(10) an extra 3 digits of precision are needed
p=set->digits+3;
needbytes=sizeof(decNumber)+(D2U(p)-1)*sizeof(Unit);
if (needbytes>sizeof(bufb)) { // need malloc space
allocbufb=(decNumber *)malloc(needbytes);
if (allocbufb==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
b=allocbufb; // use the allocated space
}
decNumberZero(w); // set up 10...
#if DECDPUN==1
w->lsu[1]=1; w->lsu[0]=0; // ..
#else
w->lsu[0]=10; // ..
#endif
w->digits=2; // ..
aset.digits=p;
decLnOp(b, w, &aset, &ignore); // b=ln(10)
aset.digits=set->digits; // for final divide
decDivideOp(res, a, b, &aset, DIVIDE, &status); // into result
} while(0); // [for break]
if (allocbufa!=NULL) free(allocbufa); // drop any storage used
if (allocbufb!=NULL) free(allocbufb); // ..
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); // ..
#endif
// apply significant status
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberLog10
/* ------------------------------------------------------------------ */
/* decNumberMax -- compare two Numbers and return the maximum */
/* */
/* This computes C = A ? B, returning the maximum by 754 rules */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberMax(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPMAX, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberMax
/* ------------------------------------------------------------------ */
/* decNumberMaxMag -- compare and return the maximum by magnitude */
/* */
/* This computes C = A ? B, returning the maximum by 754 rules */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberMaxMag(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPMAXMAG, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberMaxMag
/* ------------------------------------------------------------------ */
/* decNumberMin -- compare two Numbers and return the minimum */
/* */
/* This computes C = A ? B, returning the minimum by 754 rules */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberMin(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPMIN, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberMin
/* ------------------------------------------------------------------ */
/* decNumberMinMag -- compare and return the minimum by magnitude */
/* */
/* This computes C = A ? B, returning the minimum by 754 rules */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinMag(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decCompareOp(res, lhs, rhs, set, COMPMINMAG, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberMinMag
/* ------------------------------------------------------------------ */
/* decNumberMinus -- prefix minus operator */
/* */
/* This computes C = 0 - A */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context */
/* */
/* See also decNumberCopyNegate for a quiet bitwise version of this. */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* Simply use AddOp for the subtract, which will do the necessary. */
/* ------------------------------------------------------------------ */
decNumber * decNumberMinus(decNumber *res, const decNumber *rhs,
decContext *set) {
decNumber dzero;
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
decNumberZero(&dzero); // make 0
dzero.exponent=rhs->exponent; // [no coefficient expansion]
decAddOp(res, &dzero, rhs, set, DECNEG, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberMinus
/* ------------------------------------------------------------------ */
/* decNumberNextMinus -- next towards -Infinity */
/* */
/* This computes C = A - infinitesimal, rounded towards -Infinity */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context */
/* */
/* This is a generalization of 754 NextDown. */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextMinus(decNumber *res, const decNumber *rhs,
decContext *set) {
decNumber dtiny; // constant
decContext workset=*set; // work
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// +Infinity is the special case
if ((rhs->bits&(DECINF|DECNEG))==DECINF) {
decSetMaxValue(res, set); // is +ve
// there is no status to set
return res;
}
decNumberZero(&dtiny); // start with 0
dtiny.lsu[0]=1; // make number that is ..
dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
workset.round=DEC_ROUND_FLOOR;
decAddOp(res, rhs, &dtiny, &workset, DECNEG, &status);
status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberNextMinus
/* ------------------------------------------------------------------ */
/* decNumberNextPlus -- next towards +Infinity */
/* */
/* This computes C = A + infinitesimal, rounded towards +Infinity */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context */
/* */
/* This is a generalization of 754 NextUp. */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextPlus(decNumber *res, const decNumber *rhs,
decContext *set) {
decNumber dtiny; // constant
decContext workset=*set; // work
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// -Infinity is the special case
if ((rhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
decSetMaxValue(res, set);
res->bits=DECNEG; // negative
// there is no status to set
return res;
}
decNumberZero(&dtiny); // start with 0
dtiny.lsu[0]=1; // make number that is ..
dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
workset.round=DEC_ROUND_CEILING;
decAddOp(res, rhs, &dtiny, &workset, 0, &status);
status&=DEC_Invalid_operation|DEC_sNaN; // only sNaN Invalid please
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberNextPlus
/* ------------------------------------------------------------------ */
/* decNumberNextToward -- next towards rhs */
/* */
/* This computes C = A +/- infinitesimal, rounded towards */
/* +/-Infinity in the direction of B, as per 754-1985 nextafter */
/* modified during revision but dropped from 754-2008. */
/* */
/* res is C, the result. C may be A or B. */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* This is a generalization of 754-1985 NextAfter. */
/* ------------------------------------------------------------------ */
decNumber * decNumberNextToward(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
decNumber dtiny; // constant
decContext workset=*set; // work
Int result; // ..
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) {
decNaNs(res, lhs, rhs, set, &status);
}
else { // Is numeric, so no chance of sNaN Invalid, etc.
result=decCompare(lhs, rhs, 0); // sign matters
if (result==BADINT) status|=DEC_Insufficient_storage; // rare
else { // valid compare
if (result==0) decNumberCopySign(res, lhs, rhs); // easy
else { // differ: need NextPlus or NextMinus
uByte sub; // add or subtract
if (result<0) { // lhs<rhs, do nextplus
// -Infinity is the special case
if ((lhs->bits&(DECINF|DECNEG))==(DECINF|DECNEG)) {
decSetMaxValue(res, set);
res->bits=DECNEG; // negative
return res; // there is no status to set
}
workset.round=DEC_ROUND_CEILING;
sub=0; // add, please
} // plus
else { // lhs>rhs, do nextminus
// +Infinity is the special case
if ((lhs->bits&(DECINF|DECNEG))==DECINF) {
decSetMaxValue(res, set);
return res; // there is no status to set
}
workset.round=DEC_ROUND_FLOOR;
sub=DECNEG; // subtract, please
} // minus
decNumberZero(&dtiny); // start with 0
dtiny.lsu[0]=1; // make number that is ..
dtiny.exponent=DEC_MIN_EMIN-1; // .. smaller than tiniest
decAddOp(res, lhs, &dtiny, &workset, sub, &status); // + or -
// turn off exceptions if the result is a normal number
// (including Nmin), otherwise let all status through
if (decNumberIsNormal(res, set)) status=0;
} // unequal
} // compare OK
} // numeric
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberNextToward
/* ------------------------------------------------------------------ */
/* decNumberOr -- OR two Numbers, digitwise */
/* */
/* This computes C = A | B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X|X) */
/* lhs is A */
/* rhs is B */
/* set is the context (used for result length and error report) */
/* */
/* C must have space for set->digits digits. */
/* */
/* Logical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* ------------------------------------------------------------------ */
decNumber * decNumberOr(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
const Unit *ua, *ub; // -> operands
const Unit *msua, *msub; // -> operand msus
Unit *uc, *msuc; // -> result and its msu
Int msudigs; // digits in res msu
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
// operands are valid
ua=lhs->lsu; // bottom-up
ub=rhs->lsu; // ..
uc=res->lsu; // ..
msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
msuc=uc+D2U(set->digits)-1; // -> msu of result
msudigs=MSUDIGITS(set->digits); // [faster than remainder]
for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
Unit a, b; // extract units
if (ua>msua) a=0;
else a=*ua;
if (ub>msub) b=0;
else b=*ub;
*uc=0; // can now write back
if (a|b) { // maybe 1 bits to examine
Int i, j;
// This loop could be unrolled and/or use BIN2BCD tables
for (i=0; i<DECDPUN; i++) {
if ((a|b)&1) *uc=*uc+(Unit)powers[i]; // effect OR
j=a%10;
a=a/10;
j|=b%10;
b=b/10;
if (j>1) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
if (uc==msuc && i==msudigs-1) break; // just did final digit
} // each digit
} // non-zero
} // each unit
// [here uc-1 is the msu of the result]
res->digits=decGetDigits(res->lsu, uc-res->lsu);
res->exponent=0; // integer
res->bits=0; // sign=0
return res; // [no status to set]
} // decNumberOr
/* ------------------------------------------------------------------ */
/* decNumberPlus -- prefix plus operator */
/* */
/* This computes C = 0 + A */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context */
/* */
/* See also decNumberCopy for a quiet bitwise version of this. */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* This simply uses AddOp; Add will take fast path after preparing A. */
/* Performance is a concern here, as this routine is often used to */
/* check operands and apply rounding and overflow/underflow testing. */
/* ------------------------------------------------------------------ */
decNumber * decNumberPlus(decNumber *res, const decNumber *rhs,
decContext *set) {
decNumber dzero;
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
decNumberZero(&dzero); // make 0
dzero.exponent=rhs->exponent; // [no coefficient expansion]
decAddOp(res, &dzero, rhs, set, 0, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberPlus
/* ------------------------------------------------------------------ */
/* decNumberMultiply -- multiply two Numbers */
/* */
/* This computes C = A x B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberMultiply(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decMultiplyOp(res, lhs, rhs, set, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberMultiply
/* ------------------------------------------------------------------ */
/* decNumberPower -- raise a number to a power */
/* */
/* This computes C = A ** B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X**X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* Mathematical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* */
/* However, if 1999999997<=B<=999999999 and B is an integer then the */
/* restrictions on A and the context are relaxed to the usual bounds, */
/* for compatibility with the earlier (integer power only) version */
/* of this function. */
/* */
/* When B is an integer, the result may be exact, even if rounded. */
/* */
/* The final result is rounded according to the context; it will */
/* almost always be correctly rounded, but may be up to 1 ulp in */
/* error in rare cases. */
/* ------------------------------------------------------------------ */
decNumber * decNumberPower(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
#if DECSUBSET
decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
decNumber *allocrhs=NULL; // .., rhs
#endif
decNumber *allocdac=NULL; // -> allocated acc buffer, iff used
decNumber *allocinv=NULL; // -> allocated 1/x buffer, iff used
Int reqdigits=set->digits; // requested DIGITS
Int n; // rhs in binary
Flag rhsint=0; // 1 if rhs is an integer
Flag useint=0; // 1 if can use integer calculation
Flag isoddint=0; // 1 if rhs is an integer and odd
Int i; // work
#if DECSUBSET
Int dropped; // ..
#endif
uInt needbytes; // buffer size needed
Flag seenbit; // seen a bit while powering
Int residue=0; // rounding residue
uInt status=0; // accumulators
uByte bits=0; // result sign if errors
decContext aset; // working context
decNumber dnOne; // work value 1...
// local accumulator buffer [a decNumber, with digits+elength+1 digits]
decNumber dacbuff[D2N(DECBUFFER+9)];
decNumber *dac=dacbuff; // -> result accumulator
// same again for possible 1/lhs calculation
decNumber invbuff[D2N(DECBUFFER+9)];
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) { // reduce operands and set status, as needed
if (lhs->digits>reqdigits) {
alloclhs=decRoundOperand(lhs, set, &status);
if (alloclhs==NULL) break;
lhs=alloclhs;
}
if (rhs->digits>reqdigits) {
allocrhs=decRoundOperand(rhs, set, &status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
// handle NaNs and rhs Infinity (lhs infinity is harder)
if (SPECIALARGS) {
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs)) { // NaNs
decNaNs(res, lhs, rhs, set, &status);
break;}
if (decNumberIsInfinite(rhs)) { // rhs Infinity
Flag rhsneg=rhs->bits&DECNEG; // save rhs sign
if (decNumberIsNegative(lhs) // lhs<0
&& !decNumberIsZero(lhs)) // ..
status|=DEC_Invalid_operation;
else { // lhs >=0
decNumberZero(&dnOne); // set up 1
dnOne.lsu[0]=1;
decNumberCompare(dac, lhs, &dnOne, set); // lhs ? 1
decNumberZero(res); // prepare for 0/1/Infinity
if (decNumberIsNegative(dac)) { // lhs<1
if (rhsneg) res->bits|=DECINF; // +Infinity [else is +0]
}
else if (dac->lsu[0]==0) { // lhs=1
// 1**Infinity is inexact, so return fully-padded 1.0000
Int shift=set->digits-1;
*res->lsu=1; // was 0, make int 1
res->digits=decShiftToMost(res->lsu, 1, shift);
res->exponent=-shift; // make 1.0000...
status|=DEC_Inexact|DEC_Rounded; // deemed inexact
}
else { // lhs>1
if (!rhsneg) res->bits|=DECINF; // +Infinity [else is +0]
}
} // lhs>=0
break;}
// [lhs infinity drops through]
} // specials
// Original rhs may be an integer that fits and is in range
n=decGetInt(rhs);
if (n!=BADINT) { // it is an integer
rhsint=1; // record the fact for 1**n
isoddint=(Flag)n&1; // [works even if big]
if (n!=BIGEVEN && n!=BIGODD) // can use integer path?
useint=1; // looks good
}
if (decNumberIsNegative(lhs) // -x ..
&& isoddint) bits=DECNEG; // .. to an odd power
// handle LHS infinity
if (decNumberIsInfinite(lhs)) { // [NaNs already handled]
uByte rbits=rhs->bits; // save
decNumberZero(res); // prepare
if (n==0) *res->lsu=1; // [-]Inf**0 => 1
else {
// -Inf**nonint -> error
if (!rhsint && decNumberIsNegative(lhs)) {
status|=DEC_Invalid_operation; // -Inf**nonint is error
break;}
if (!(rbits & DECNEG)) bits|=DECINF; // was not a **-n
// [otherwise will be 0 or -0]
res->bits=bits;
}
break;}
// similarly handle LHS zero
if (decNumberIsZero(lhs)) {
if (n==0) { // 0**0 => Error
#if DECSUBSET
if (!set->extended) { // [unless subset]
decNumberZero(res);
*res->lsu=1; // return 1
break;}
#endif
status|=DEC_Invalid_operation;
}
else { // 0**x
uByte rbits=rhs->bits; // save
if (rbits & DECNEG) { // was a 0**(-n)
#if DECSUBSET
if (!set->extended) { // [bad if subset]
status|=DEC_Invalid_operation;
break;}
#endif
bits|=DECINF;
}
decNumberZero(res); // prepare
// [otherwise will be 0 or -0]
res->bits=bits;
}
break;}
// here both lhs and rhs are finite; rhs==0 is handled in the
// integer path. Next handle the non-integer cases
if (!useint) { // non-integral rhs
// any -ve lhs is bad, as is either operand or context out of
// bounds
if (decNumberIsNegative(lhs)) {
status|=DEC_Invalid_operation;
break;}
if (decCheckMath(lhs, set, &status)
|| decCheckMath(rhs, set, &status)) break; // variable status
decContextDefault(&aset, DEC_INIT_DECIMAL64); // clean context
aset.emax=DEC_MAX_MATH; // usual bounds
aset.emin=-DEC_MAX_MATH; // ..
aset.clamp=0; // and no concrete format
// calculate the result using exp(ln(lhs)*rhs), which can
// all be done into the accumulator, dac. The precision needed
// is enough to contain the full information in the lhs (which
// is the total digits, including exponent), or the requested
// precision, if larger, + 4; 6 is used for the exponent
// maximum length, and this is also used when it is shorter
// than the requested digits as it greatly reduces the >0.5 ulp
// cases at little cost (because Ln doubles digits each
// iteration so a few extra digits rarely causes an extra
// iteration)
aset.digits=MAXI(lhs->digits, set->digits)+6+4;
} // non-integer rhs
else { // rhs is in-range integer
if (n==0) { // x**0 = 1
// (0**0 was handled above)
decNumberZero(res); // result=1
*res->lsu=1; // ..
break;}
// rhs is a non-zero integer
if (n<0) n=-n; // use abs(n)
aset=*set; // clone the context
aset.round=DEC_ROUND_HALF_EVEN; // internally use balanced
// calculate the working DIGITS
aset.digits=reqdigits+(rhs->digits+rhs->exponent)+2;
#if DECSUBSET
if (!set->extended) aset.digits--; // use classic precision
#endif
// it's an error if this is more than can be handled
if (aset.digits>DECNUMMAXP) {status|=DEC_Invalid_operation; break;}
} // integer path
// aset.digits is the count of digits for the accumulator needed
// if accumulator is too long for local storage, then allocate
needbytes=sizeof(decNumber)+(D2U(aset.digits)-1)*sizeof(Unit);
// [needbytes also used below if 1/lhs needed]
if (needbytes>sizeof(dacbuff)) {
allocdac=(decNumber *)malloc(needbytes);
if (allocdac==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
dac=allocdac; // use the allocated space
}
// here, aset is set up and accumulator is ready for use
if (!useint) { // non-integral rhs
// x ** y; special-case x=1 here as it will otherwise always
// reduce to integer 1; decLnOp has a fastpath which detects
// the case of x=1
decLnOp(dac, lhs, &aset, &status); // dac=ln(lhs)
// [no error possible, as lhs 0 already handled]
if (ISZERO(dac)) { // x==1, 1.0, etc.
// need to return fully-padded 1.0000 etc., but rhsint->1
*dac->lsu=1; // was 0, make int 1
if (!rhsint) { // add padding
Int shift=set->digits-1;
dac->digits=decShiftToMost(dac->lsu, 1, shift);
dac->exponent=-shift; // make 1.0000...
status|=DEC_Inexact|DEC_Rounded; // deemed inexact
}
}
else {
decMultiplyOp(dac, dac, rhs, &aset, &status); // dac=dac*rhs
decExpOp(dac, dac, &aset, &status); // dac=exp(dac)
}
// and drop through for final rounding
} // non-integer rhs
else { // carry on with integer
decNumberZero(dac); // acc=1
*dac->lsu=1; // ..
// if a negative power the constant 1 is needed, and if not subset
// invert the lhs now rather than inverting the result later
if (decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]
decNumber *inv=invbuff; // asssume use fixed buffer
decNumberCopy(&dnOne, dac); // dnOne=1; [needed now or later]
#if DECSUBSET
if (set->extended) { // need to calculate 1/lhs
#endif
// divide lhs into 1, putting result in dac [dac=1/dac]
decDivideOp(dac, &dnOne, lhs, &aset, DIVIDE, &status);
// now locate or allocate space for the inverted lhs
if (needbytes>sizeof(invbuff)) {
allocinv=(decNumber *)malloc(needbytes);
if (allocinv==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
inv=allocinv; // use the allocated space
}
// [inv now points to big-enough buffer or allocated storage]
decNumberCopy(inv, dac); // copy the 1/lhs
decNumberCopy(dac, &dnOne); // restore acc=1
lhs=inv; // .. and go forward with new lhs
#if DECSUBSET
}
#endif
}
// Raise-to-the-power loop...
seenbit=0; // set once a 1-bit is encountered
for (i=1;;i++){ // for each bit [top bit ignored]
// abandon if had overflow or terminal underflow
if (status & (DEC_Overflow|DEC_Underflow)) { // interesting?
if (status&DEC_Overflow || ISZERO(dac)) break;
}
// [the following two lines revealed an optimizer bug in a C++
// compiler, with symptom: 5**3 -> 25, when n=n+n was used]
n=n<<1; // move next bit to testable position
if (n<0) { // top bit is set
seenbit=1; // OK, significant bit seen
decMultiplyOp(dac, dac, lhs, &aset, &status); // dac=dac*x
}
if (i==31) break; // that was the last bit
if (!seenbit) continue; // no need to square 1
decMultiplyOp(dac, dac, dac, &aset, &status); // dac=dac*dac [square]
} /*i*/ // 32 bits
// complete internal overflow or underflow processing
if (status & (DEC_Overflow|DEC_Underflow)) {
#if DECSUBSET
// If subset, and power was negative, reverse the kind of -erflow
// [1/x not yet done]
if (!set->extended && decNumberIsNegative(rhs)) {
if (status & DEC_Overflow)
status^=DEC_Overflow | DEC_Underflow | DEC_Subnormal;
else { // trickier -- Underflow may or may not be set
status&=~(DEC_Underflow | DEC_Subnormal); // [one or both]
status|=DEC_Overflow;
}
}
#endif
dac->bits=(dac->bits & ~DECNEG) | bits; // force correct sign
// round subnormals [to set.digits rather than aset.digits]
// or set overflow result similarly as required
decFinalize(dac, set, &residue, &status);
decNumberCopy(res, dac); // copy to result (is now OK length)
break;
}
#if DECSUBSET
if (!set->extended && // subset math
decNumberIsNegative(rhs)) { // was a **-n [hence digits>0]
// so divide result into 1 [dac=1/dac]
decDivideOp(dac, &dnOne, dac, &aset, DIVIDE, &status);
}
#endif
} // rhs integer path
// reduce result to the requested length and copy to result
decCopyFit(res, dac, set, &residue, &status);
decFinish(res, set, &residue, &status); // final cleanup
#if DECSUBSET
if (!set->extended) decTrim(res, set, 0, 1, &dropped); // trailing zeros
#endif
} while(0); // end protected
if (allocdac!=NULL) free(allocdac); // drop any storage used
if (allocinv!=NULL) free(allocinv); // ..
#if DECSUBSET
if (alloclhs!=NULL) free(alloclhs); // ..
if (allocrhs!=NULL) free(allocrhs); // ..
#endif
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberPower
/* ------------------------------------------------------------------ */
/* decNumberQuantize -- force exponent to requested value */
/* */
/* This computes C = op(A, B), where op adjusts the coefficient */
/* of C (by rounding or shifting) such that the exponent (-scale) */
/* of C has exponent of B. The numerical value of C will equal A, */
/* except for the effects of any rounding that occurred. */
/* */
/* res is C, the result. C may be A or B */
/* lhs is A, the number to adjust */
/* rhs is B, the number with exponent to match */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* Unless there is an error or the result is infinite, the exponent */
/* after the operation is guaranteed to be equal to that of B. */
/* ------------------------------------------------------------------ */
decNumber * decNumberQuantize(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decQuantizeOp(res, lhs, rhs, set, 1, &status);
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberQuantize
/* ------------------------------------------------------------------ */
/* decNumberReduce -- remove trailing zeros */
/* */
/* This computes C = 0 + A, and normalizes the result */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
// Previously known as Normalize
decNumber * decNumberNormalize(decNumber *res, const decNumber *rhs,
decContext *set) {
return decNumberReduce(res, rhs, set);
} // decNumberNormalize
decNumber * decNumberReduce(decNumber *res, const decNumber *rhs,
decContext *set) {
#if DECSUBSET
decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
#endif
uInt status=0; // as usual
Int residue=0; // as usual
Int dropped; // work
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operand and set lostDigits status, as needed
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, &status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
// Infinities copy through; NaNs need usual treatment
if (decNumberIsNaN(rhs)) {
decNaNs(res, rhs, NULL, set, &status);
break;
}
// reduce result to the requested length and copy to result
decCopyFit(res, rhs, set, &residue, &status); // copy & round
decFinish(res, set, &residue, &status); // cleanup/set flags
decTrim(res, set, 1, 0, &dropped); // normalize in place
// [may clamp]
} while(0); // end protected
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); // ..
#endif
if (status!=0) decStatus(res, status, set);// then report status
return res;
} // decNumberReduce
/* ------------------------------------------------------------------ */
/* decNumberRescale -- force exponent to requested value */
/* */
/* This computes C = op(A, B), where op adjusts the coefficient */
/* of C (by rounding or shifting) such that the exponent (-scale) */
/* of C has the value B. The numerical value of C will equal A, */
/* except for the effects of any rounding that occurred. */
/* */
/* res is C, the result. C may be A or B */
/* lhs is A, the number to adjust */
/* rhs is B, the requested exponent */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* Unless there is an error or the result is infinite, the exponent */
/* after the operation is guaranteed to be equal to B. */
/* ------------------------------------------------------------------ */
decNumber * decNumberRescale(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decQuantizeOp(res, lhs, rhs, set, 0, &status);
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberRescale
/* ------------------------------------------------------------------ */
/* decNumberRemainder -- divide and return remainder */
/* */
/* This computes C = A % B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainder(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decDivideOp(res, lhs, rhs, set, REMAINDER, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberRemainder
/* ------------------------------------------------------------------ */
/* decNumberRemainderNear -- divide and return remainder from nearest */
/* */
/* This computes C = A % B, where % is the IEEE remainder operator */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X%X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberRemainderNear(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decDivideOp(res, lhs, rhs, set, REMNEAR, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberRemainderNear
/* ------------------------------------------------------------------ */
/* decNumberRotate -- rotate the coefficient of a Number left/right */
/* */
/* This computes C = A rot B (in base ten and rotating set->digits */
/* digits). */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=XrotX) */
/* lhs is A */
/* rhs is B, the number of digits to rotate (-ve to right) */
/* set is the context */
/* */
/* The digits of the coefficient of A are rotated to the left (if B */
/* is positive) or to the right (if B is negative) without adjusting */
/* the exponent or the sign of A. If lhs->digits is less than */
/* set->digits the coefficient is padded with zeros on the left */
/* before the rotate. Any leading zeros in the result are removed */
/* as usual. */
/* */
/* B must be an integer (q=0) and in the range -set->digits through */
/* +set->digits. */
/* C must have space for set->digits digits. */
/* NaNs are propagated as usual. Infinities are unaffected (but */
/* B must be valid). No status is set unless B is invalid or an */
/* operand is an sNaN. */
/* ------------------------------------------------------------------ */
decNumber * decNumberRotate(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
Int rotate; // rhs as an Int
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
// NaNs propagate as normal
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
decNaNs(res, lhs, rhs, set, &status);
// rhs must be an integer
else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
status=DEC_Invalid_operation;
else { // both numeric, rhs is an integer
rotate=decGetInt(rhs); // [cannot fail]
if (rotate==BADINT // something bad ..
|| rotate==BIGODD || rotate==BIGEVEN // .. very big ..
|| abs(rotate)>set->digits) // .. or out of range
status=DEC_Invalid_operation;
else { // rhs is OK
decNumberCopy(res, lhs);
// convert -ve rotate to equivalent positive rotation
if (rotate<0) rotate=set->digits+rotate;
if (rotate!=0 && rotate!=set->digits // zero or full rotation
&& !decNumberIsInfinite(res)) { // lhs was infinite
// left-rotate to do; 0 < rotate < set->digits
uInt units, shift; // work
uInt msudigits; // digits in result msu
Unit *msu=res->lsu+D2U(res->digits)-1; // current msu
Unit *msumax=res->lsu+D2U(set->digits)-1; // rotation msu
for (msu++; msu<=msumax; msu++) *msu=0; // ensure high units=0
res->digits=set->digits; // now full-length
msudigits=MSUDIGITS(res->digits); // actual digits in msu
// rotation here is done in-place, in three steps
// 1. shift all to least up to one unit to unit-align final
// lsd [any digits shifted out are rotated to the left,
// abutted to the original msd (which may require split)]
//
// [if there are no whole units left to rotate, the
// rotation is now complete]
//
// 2. shift to least, from below the split point only, so that
// the final msd is in the right place in its Unit [any
// digits shifted out will fit exactly in the current msu,
// left aligned, no split required]
//
// 3. rotate all the units by reversing left part, right
// part, and then whole
//
// example: rotate right 8 digits (2 units + 2), DECDPUN=3.
//
// start: 00a bcd efg hij klm npq
//
// 1a 000 0ab cde fgh|ijk lmn [pq saved]
// 1b 00p qab cde fgh|ijk lmn
//
// 2a 00p qab cde fgh|00i jkl [mn saved]
// 2b mnp qab cde fgh|00i jkl
//
// 3a fgh cde qab mnp|00i jkl
// 3b fgh cde qab mnp|jkl 00i
// 3c 00i jkl mnp qab cde fgh
// Step 1: amount to shift is the partial right-rotate count
rotate=set->digits-rotate; // make it right-rotate
units=rotate/DECDPUN; // whole units to rotate
shift=rotate%DECDPUN; // left-over digits count
if (shift>0) { // not an exact number of units
uInt save=res->lsu[0]%powers[shift]; // save low digit(s)
decShiftToLeast(res->lsu, D2U(res->digits), shift);
if (shift>msudigits) { // msumax-1 needs >0 digits
uInt rem=save%powers[shift-msudigits];// split save
*msumax=(Unit)(save/powers[shift-msudigits]); // and insert
*(msumax-1)=*(msumax-1)
+(Unit)(rem*powers[DECDPUN-(shift-msudigits)]); // ..
}
else { // all fits in msumax
*msumax=*msumax+(Unit)(save*powers[msudigits-shift]); // [maybe *1]
}
} // digits shift needed
// If whole units to rotate...
if (units>0) { // some to do
// Step 2: the units to touch are the whole ones in rotate,
// if any, and the shift is DECDPUN-msudigits (which may be
// 0, again)
shift=DECDPUN-msudigits;
if (shift>0) { // not an exact number of units
uInt save=res->lsu[0]%powers[shift]; // save low digit(s)
decShiftToLeast(res->lsu, units, shift);
*msumax=*msumax+(Unit)(save*powers[msudigits]);
} // partial shift needed
// Step 3: rotate the units array using triple reverse
// (reversing is easy and fast)
decReverse(res->lsu+units, msumax); // left part
decReverse(res->lsu, res->lsu+units-1); // right part
decReverse(res->lsu, msumax); // whole
} // whole units to rotate
// the rotation may have left an undetermined number of zeros
// on the left, so true length needs to be calculated
res->digits=decGetDigits(res->lsu, msumax-res->lsu+1);
} // rotate needed
} // rhs OK
} // numerics
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberRotate
/* ------------------------------------------------------------------ */
/* decNumberSameQuantum -- test for equal exponents */
/* */
/* res is the result number, which will contain either 0 or 1 */
/* lhs is a number to test */
/* rhs is the second (usually a pattern) */
/* */
/* No errors are possible and no context is needed. */
/* ------------------------------------------------------------------ */
decNumber * decNumberSameQuantum(decNumber *res, const decNumber *lhs,
const decNumber *rhs) {
Unit ret=0; // return value
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, DECUNCONT)) return res;
#endif
if (SPECIALARGS) {
if (decNumberIsNaN(lhs) && decNumberIsNaN(rhs)) ret=1;
else if (decNumberIsInfinite(lhs) && decNumberIsInfinite(rhs)) ret=1;
// [anything else with a special gives 0]
}
else if (lhs->exponent==rhs->exponent) ret=1;
decNumberZero(res); // OK to overwrite an operand now
*res->lsu=ret;
return res;
} // decNumberSameQuantum
/* ------------------------------------------------------------------ */
/* decNumberScaleB -- multiply by a power of 10 */
/* */
/* This computes C = A x 10**B where B is an integer (q=0) with */
/* maximum magnitude 2*(emax+digits) */
/* */
/* res is C, the result. C may be A or B */
/* lhs is A, the number to adjust */
/* rhs is B, the requested power of ten to use */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* */
/* The result may underflow or overflow. */
/* ------------------------------------------------------------------ */
decNumber * decNumberScaleB(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
Int reqexp; // requested exponent change [B]
uInt status=0; // accumulator
Int residue; // work
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
// Handle special values except lhs infinite
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
decNaNs(res, lhs, rhs, set, &status);
// rhs must be an integer
else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
status=DEC_Invalid_operation;
else {
// lhs is a number; rhs is a finite with q==0
reqexp=decGetInt(rhs); // [cannot fail]
// maximum range is larger than getInt can handle, so this is
// more restrictive than the specification
if (reqexp==BADINT // something bad ..
|| reqexp==BIGODD || reqexp==BIGEVEN // it was huge
|| (abs(reqexp)+1)/2>(set->digits+set->emax)) // .. or out of range
status=DEC_Invalid_operation;
else { // rhs is OK
decNumberCopy(res, lhs); // all done if infinite lhs
if (!decNumberIsInfinite(res)) { // prepare to scale
Int exp=res->exponent; // save for overflow test
res->exponent+=reqexp; // adjust the exponent
if (((exp^reqexp)>=0) // same sign ...
&& ((exp^res->exponent)<0)) { // .. but result had different
// the calculation overflowed, so force right treatment
if (exp<0) res->exponent=DEC_MIN_EMIN-DEC_MAX_DIGITS;
else res->exponent=DEC_MAX_EMAX+1;
}
residue=0;
decFinalize(res, set, &residue, &status); // final check
} // finite LHS
} // rhs OK
} // rhs finite
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberScaleB
/* ------------------------------------------------------------------ */
/* decNumberShift -- shift the coefficient of a Number left or right */
/* */
/* This computes C = A << B or C = A >> -B (in base ten). */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X<<X) */
/* lhs is A */
/* rhs is B, the number of digits to shift (-ve to right) */
/* set is the context */
/* */
/* The digits of the coefficient of A are shifted to the left (if B */
/* is positive) or to the right (if B is negative) without adjusting */
/* the exponent or the sign of A. */
/* */
/* B must be an integer (q=0) and in the range -set->digits through */
/* +set->digits. */
/* C must have space for set->digits digits. */
/* NaNs are propagated as usual. Infinities are unaffected (but */
/* B must be valid). No status is set unless B is invalid or an */
/* operand is an sNaN. */
/* ------------------------------------------------------------------ */
decNumber * decNumberShift(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
Int shift; // rhs as an Int
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
// NaNs propagate as normal
if (decNumberIsNaN(lhs) || decNumberIsNaN(rhs))
decNaNs(res, lhs, rhs, set, &status);
// rhs must be an integer
else if (decNumberIsInfinite(rhs) || rhs->exponent!=0)
status=DEC_Invalid_operation;
else { // both numeric, rhs is an integer
shift=decGetInt(rhs); // [cannot fail]
if (shift==BADINT // something bad ..
|| shift==BIGODD || shift==BIGEVEN // .. very big ..
|| abs(shift)>set->digits) // .. or out of range
status=DEC_Invalid_operation;
else { // rhs is OK
decNumberCopy(res, lhs);
if (shift!=0 && !decNumberIsInfinite(res)) { // something to do
if (shift>0) { // to left
if (shift==set->digits) { // removing all
*res->lsu=0; // so place 0
res->digits=1; // ..
}
else { //
// first remove leading digits if necessary
if (res->digits+shift>set->digits) {
decDecap(res, res->digits+shift-set->digits);
// that updated res->digits; may have gone to 1 (for a
// single digit or for zero
}
if (res->digits>1 || *res->lsu) // if non-zero..
res->digits=decShiftToMost(res->lsu, res->digits, shift);
} // partial left
} // left
else { // to right
if (-shift>=res->digits) { // discarding all
*res->lsu=0; // so place 0
res->digits=1; // ..
}
else {
decShiftToLeast(res->lsu, D2U(res->digits), -shift);
res->digits-=(-shift);
}
} // to right
} // non-0 non-Inf shift
} // rhs OK
} // numerics
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberShift
/* ------------------------------------------------------------------ */
/* decNumberSquareRoot -- square root operator */
/* */
/* This computes C = squareroot(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context; note that rounding mode has no effect */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
/* This uses the following varying-precision algorithm in: */
/* */
/* Properly Rounded Variable Precision Square Root, T. E. Hull and */
/* A. Abrham, ACM Transactions on Mathematical Software, Vol 11 #3, */
/* pp229-237, ACM, September 1985. */
/* */
/* The square-root is calculated using Newton's method, after which */
/* a check is made to ensure the result is correctly rounded. */
/* */
/* % [Reformatted original Numerical Turing source code follows.] */
/* function sqrt(x : real) : real */
/* % sqrt(x) returns the properly rounded approximation to the square */
/* % root of x, in the precision of the calling environment, or it */
/* % fails if x < 0. */
/* % t e hull and a abrham, august, 1984 */
/* if x <= 0 then */
/* if x < 0 then */
/* assert false */
/* else */
/* result 0 */
/* end if */
/* end if */
/* var f := setexp(x, 0) % fraction part of x [0.1 <= x < 1] */
/* var e := getexp(x) % exponent part of x */
/* var approx : real */
/* if e mod 2 = 0 then */
/* approx := .259 + .819 * f % approx to root of f */
/* else */
/* f := f/l0 % adjustments */
/* e := e + 1 % for odd */
/* approx := .0819 + 2.59 * f % exponent */
/* end if */
/* */
/* var p:= 3 */
/* const maxp := currentprecision + 2 */
/* loop */
/* p := min(2*p - 2, maxp) % p = 4,6,10, . . . , maxp */
/* precision p */
/* approx := .5 * (approx + f/approx) */
/* exit when p = maxp */
/* end loop */
/* */
/* % approx is now within 1 ulp of the properly rounded square root */
/* % of f; to ensure proper rounding, compare squares of (approx - */
/* % l/2 ulp) and (approx + l/2 ulp) with f. */
/* p := currentprecision */
/* begin */
/* precision p + 2 */
/* const approxsubhalf := approx - setexp(.5, -p) */
/* if mulru(approxsubhalf, approxsubhalf) > f then */
/* approx := approx - setexp(.l, -p + 1) */
/* else */
/* const approxaddhalf := approx + setexp(.5, -p) */
/* if mulrd(approxaddhalf, approxaddhalf) < f then */
/* approx := approx + setexp(.l, -p + 1) */
/* end if */
/* end if */
/* end */
/* result setexp(approx, e div 2) % fix exponent */
/* end sqrt */
/* ------------------------------------------------------------------ */
decNumber * decNumberSquareRoot(decNumber *res, const decNumber *rhs,
decContext *set) {
decContext workset, approxset; // work contexts
decNumber dzero; // used for constant zero
Int maxp; // largest working precision
Int workp; // working precision
Int residue=0; // rounding residue
uInt status=0, ignore=0; // status accumulators
uInt rstatus; // ..
Int exp; // working exponent
Int ideal; // ideal (preferred) exponent
Int needbytes; // work
Int dropped; // ..
#if DECSUBSET
decNumber *allocrhs=NULL; // non-NULL if rounded rhs allocated
#endif
// buffer for f [needs +1 in case DECBUFFER 0]
decNumber buff[D2N(DECBUFFER+1)];
// buffer for a [needs +2 to match likely maxp]
decNumber bufa[D2N(DECBUFFER+2)];
// buffer for temporary, b [must be same size as a]
decNumber bufb[D2N(DECBUFFER+2)];
decNumber *allocbuff=NULL; // -> allocated buff, iff allocated
decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
decNumber *allocbufb=NULL; // -> allocated bufb, iff allocated
decNumber *f=buff; // reduced fraction
decNumber *a=bufa; // approximation to result
decNumber *b=bufb; // intermediate result
// buffer for temporary variable, up to 3 digits
decNumber buft[D2N(3)];
decNumber *t=buft; // up-to-3-digit constant or work
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operand and set lostDigits status, as needed
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, &status);
if (allocrhs==NULL) break;
// [Note: 'f' allocation below could reuse this buffer if
// used, but as this is rare they are kept separate for clarity.]
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
// handle infinities and NaNs
if (SPECIALARG) {
if (decNumberIsInfinite(rhs)) { // an infinity
if (decNumberIsNegative(rhs)) status|=DEC_Invalid_operation;
else decNumberCopy(res, rhs); // +Infinity
}
else decNaNs(res, rhs, NULL, set, &status); // a NaN
break;
}
// calculate the ideal (preferred) exponent [floor(exp/2)]
// [It would be nicer to write: ideal=rhs->exponent>>1, but this
// generates a compiler warning. Generated code is the same.]
ideal=(rhs->exponent&~1)/2; // target
// handle zeros
if (ISZERO(rhs)) {
decNumberCopy(res, rhs); // could be 0 or -0
res->exponent=ideal; // use the ideal [safe]
// use decFinish to clamp any out-of-range exponent, etc.
decFinish(res, set, &residue, &status);
break;
}
// any other -x is an oops
if (decNumberIsNegative(rhs)) {
status|=DEC_Invalid_operation;
break;
}
// space is needed for three working variables
// f -- the same precision as the RHS, reduced to 0.01->0.99...
// a -- Hull's approximation -- precision, when assigned, is
// currentprecision+1 or the input argument precision,
// whichever is larger (+2 for use as temporary)
// b -- intermediate temporary result (same size as a)
// if any is too long for local storage, then allocate
workp=MAXI(set->digits+1, rhs->digits); // actual rounding precision
workp=MAXI(workp, 7); // at least 7 for low cases
maxp=workp+2; // largest working precision
needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
if (needbytes>(Int)sizeof(buff)) {
allocbuff=(decNumber *)malloc(needbytes);
if (allocbuff==NULL) { // hopeless -- abandon
status|=DEC_Insufficient_storage;
break;}
f=allocbuff; // use the allocated space
}
// a and b both need to be able to hold a maxp-length number
needbytes=sizeof(decNumber)+(D2U(maxp)-1)*sizeof(Unit);
if (needbytes>(Int)sizeof(bufa)) { // [same applies to b]
allocbufa=(decNumber *)malloc(needbytes);
allocbufb=(decNumber *)malloc(needbytes);
if (allocbufa==NULL || allocbufb==NULL) { // hopeless
status|=DEC_Insufficient_storage;
break;}
a=allocbufa; // use the allocated spaces
b=allocbufb; // ..
}
// copy rhs -> f, save exponent, and reduce so 0.1 <= f < 1
decNumberCopy(f, rhs);
exp=f->exponent+f->digits; // adjusted to Hull rules
f->exponent=-(f->digits); // to range
// set up working context
decContextDefault(&workset, DEC_INIT_DECIMAL64);
workset.emax=DEC_MAX_EMAX;
workset.emin=DEC_MIN_EMIN;
// [Until further notice, no error is possible and status bits
// (Rounded, etc.) should be ignored, not accumulated.]
// Calculate initial approximation, and allow for odd exponent
workset.digits=workp; // p for initial calculation
t->bits=0; t->digits=3;
a->bits=0; a->digits=3;
if ((exp & 1)==0) { // even exponent
// Set t=0.259, a=0.819
t->exponent=-3;
a->exponent=-3;
#if DECDPUN>=3
t->lsu[0]=259;
a->lsu[0]=819;
#elif DECDPUN==2
t->lsu[0]=59; t->lsu[1]=2;
a->lsu[0]=19; a->lsu[1]=8;
#else
t->lsu[0]=9; t->lsu[1]=5; t->lsu[2]=2;
a->lsu[0]=9; a->lsu[1]=1; a->lsu[2]=8;
#endif
}
else { // odd exponent
// Set t=0.0819, a=2.59
f->exponent--; // f=f/10
exp++; // e=e+1
t->exponent=-4;
a->exponent=-2;
#if DECDPUN>=3
t->lsu[0]=819;
a->lsu[0]=259;
#elif DECDPUN==2
t->lsu[0]=19; t->lsu[1]=8;
a->lsu[0]=59; a->lsu[1]=2;
#else
t->lsu[0]=9; t->lsu[1]=1; t->lsu[2]=8;
a->lsu[0]=9; a->lsu[1]=5; a->lsu[2]=2;
#endif
}
decMultiplyOp(a, a, f, &workset, &ignore); // a=a*f
decAddOp(a, a, t, &workset, 0, &ignore); // ..+t
// [a is now the initial approximation for sqrt(f), calculated with
// currentprecision, which is also a's precision.]
// the main calculation loop
decNumberZero(&dzero); // make 0
decNumberZero(t); // set t = 0.5
t->lsu[0]=5; // ..
t->exponent=-1; // ..
workset.digits=3; // initial p
for (; workset.digits<maxp;) {
// set p to min(2*p - 2, maxp) [hence 3; or: 4, 6, 10, ... , maxp]
workset.digits=MINI(workset.digits*2-2, maxp);
// a = 0.5 * (a + f/a)
// [calculated at p then rounded to currentprecision]
decDivideOp(b, f, a, &workset, DIVIDE, &ignore); // b=f/a
decAddOp(b, b, a, &workset, 0, &ignore); // b=b+a
decMultiplyOp(a, b, t, &workset, &ignore); // a=b*0.5
} // loop
// Here, 0.1 <= a < 1 [Hull], and a has maxp digits
// now reduce to length, etc.; this needs to be done with a
// having the correct exponent so as to handle subnormals
// correctly
approxset=*set; // get emin, emax, etc.
approxset.round=DEC_ROUND_HALF_EVEN;
a->exponent+=exp/2; // set correct exponent
rstatus=0; // clear status
residue=0; // .. and accumulator
decCopyFit(a, a, &approxset, &residue, &rstatus); // reduce (if needed)
decFinish(a, &approxset, &residue, &rstatus); // clean and finalize
// Overflow was possible if the input exponent was out-of-range,
// in which case quit
if (rstatus&DEC_Overflow) {
status=rstatus; // use the status as-is
decNumberCopy(res, a); // copy to result
break;
}
// Preserve status except Inexact/Rounded
status|=(rstatus & ~(DEC_Rounded|DEC_Inexact));
// Carry out the Hull correction
a->exponent-=exp/2; // back to 0.1->1
// a is now at final precision and within 1 ulp of the properly
// rounded square root of f; to ensure proper rounding, compare
// squares of (a - l/2 ulp) and (a + l/2 ulp) with f.
// Here workset.digits=maxp and t=0.5, and a->digits determines
// the ulp
workset.digits--; // maxp-1 is OK now
t->exponent=-a->digits-1; // make 0.5 ulp
decAddOp(b, a, t, &workset, DECNEG, &ignore); // b = a - 0.5 ulp
workset.round=DEC_ROUND_UP;
decMultiplyOp(b, b, b, &workset, &ignore); // b = mulru(b, b)
decCompareOp(b, f, b, &workset, COMPARE, &ignore); // b ? f, reversed
if (decNumberIsNegative(b)) { // f < b [i.e., b > f]
// this is the more common adjustment, though both are rare
t->exponent++; // make 1.0 ulp
t->lsu[0]=1; // ..
decAddOp(a, a, t, &workset, DECNEG, &ignore); // a = a - 1 ulp
// assign to approx [round to length]
approxset.emin-=exp/2; // adjust to match a
approxset.emax-=exp/2;
decAddOp(a, &dzero, a, &approxset, 0, &ignore);
}
else {
decAddOp(b, a, t, &workset, 0, &ignore); // b = a + 0.5 ulp
workset.round=DEC_ROUND_DOWN;
decMultiplyOp(b, b, b, &workset, &ignore); // b = mulrd(b, b)
decCompareOp(b, b, f, &workset, COMPARE, &ignore); // b ? f
if (decNumberIsNegative(b)) { // b < f
t->exponent++; // make 1.0 ulp
t->lsu[0]=1; // ..
decAddOp(a, a, t, &workset, 0, &ignore); // a = a + 1 ulp
// assign to approx [round to length]
approxset.emin-=exp/2; // adjust to match a
approxset.emax-=exp/2;
decAddOp(a, &dzero, a, &approxset, 0, &ignore);
}
}
// [no errors are possible in the above, and rounding/inexact during
// estimation are irrelevant, so status was not accumulated]
// Here, 0.1 <= a < 1 (still), so adjust back
a->exponent+=exp/2; // set correct exponent
// count droppable zeros [after any subnormal rounding] by
// trimming a copy
decNumberCopy(b, a);
decTrim(b, set, 1, 1, &dropped); // [drops trailing zeros]
// Set Inexact and Rounded. The answer can only be exact if
// it is short enough so that squaring it could fit in workp
// digits, so this is the only (relatively rare) condition that
// a careful check is needed
if (b->digits*2-1 > workp) { // cannot fit
status|=DEC_Inexact|DEC_Rounded;
}
else { // could be exact/unrounded
uInt mstatus=0; // local status
decMultiplyOp(b, b, b, &workset, &mstatus); // try the multiply
if (mstatus&DEC_Overflow) { // result just won't fit
status|=DEC_Inexact|DEC_Rounded;
}
else { // plausible
decCompareOp(t, b, rhs, &workset, COMPARE, &mstatus); // b ? rhs
if (!ISZERO(t)) status|=DEC_Inexact|DEC_Rounded; // not equal
else { // is Exact
// here, dropped is the count of trailing zeros in 'a'
// use closest exponent to ideal...
Int todrop=ideal-a->exponent; // most that can be dropped
if (todrop<0) status|=DEC_Rounded; // ideally would add 0s
else { // unrounded
// there are some to drop, but emax may not allow all
Int maxexp=set->emax-set->digits+1;
Int maxdrop=maxexp-a->exponent;
if (todrop>maxdrop && set->clamp) { // apply clamping
todrop=maxdrop;
status|=DEC_Clamped;
}
if (dropped<todrop) { // clamp to those available
todrop=dropped;
status|=DEC_Clamped;
}
if (todrop>0) { // have some to drop
decShiftToLeast(a->lsu, D2U(a->digits), todrop);
a->exponent+=todrop; // maintain numerical value
a->digits-=todrop; // new length
}
}
}
}
}
// double-check Underflow, as perhaps the result could not have
// been subnormal (initial argument too big), or it is now Exact
if (status&DEC_Underflow) {
Int ae=rhs->exponent+rhs->digits-1; // adjusted exponent
// check if truly subnormal
#if DECEXTFLAG // DEC_Subnormal too
if (ae>=set->emin*2) status&=~(DEC_Subnormal|DEC_Underflow);
#else
if (ae>=set->emin*2) status&=~DEC_Underflow;
#endif
// check if truly inexact
if (!(status&DEC_Inexact)) status&=~DEC_Underflow;
}
decNumberCopy(res, a); // a is now the result
} while(0); // end protected
if (allocbuff!=NULL) free(allocbuff); // drop any storage used
if (allocbufa!=NULL) free(allocbufa); // ..
if (allocbufb!=NULL) free(allocbufb); // ..
#if DECSUBSET
if (allocrhs !=NULL) free(allocrhs); // ..
#endif
if (status!=0) decStatus(res, status, set);// then report status
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberSquareRoot
/* ------------------------------------------------------------------ */
/* decNumberSubtract -- subtract two Numbers */
/* */
/* This computes C = A - B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X-X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* */
/* C must have space for set->digits digits. */
/* ------------------------------------------------------------------ */
decNumber * decNumberSubtract(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
uInt status=0; // accumulator
decAddOp(res, lhs, rhs, set, DECNEG, &status);
if (status!=0) decStatus(res, status, set);
#if DECCHECK
decCheckInexact(res, set);
#endif
return res;
} // decNumberSubtract
/* ------------------------------------------------------------------ */
/* decNumberToIntegralExact -- round-to-integral-value with InExact */
/* decNumberToIntegralValue -- round-to-integral-value */
/* */
/* res is the result */
/* rhs is input number */
/* set is the context */
/* */
/* res must have space for any value of rhs. */
/* */
/* This implements the IEEE special operators and therefore treats */
/* special values as valid. For finite numbers it returns */
/* rescale(rhs, 0) if rhs->exponent is <0. */
/* Otherwise the result is rhs (so no error is possible, except for */
/* sNaN). */
/* */
/* The context is used for rounding mode and status after sNaN, but */
/* the digits setting is ignored. The Exact version will signal */
/* Inexact if the result differs numerically from rhs; the other */
/* never signals Inexact. */
/* ------------------------------------------------------------------ */
decNumber * decNumberToIntegralExact(decNumber *res, const decNumber *rhs,
decContext *set) {
decNumber dn;
decContext workset; // working context
uInt status=0; // accumulator
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
// handle infinities and NaNs
if (SPECIALARG) {
if (decNumberIsInfinite(rhs)) decNumberCopy(res, rhs); // an Infinity
else decNaNs(res, rhs, NULL, set, &status); // a NaN
}
else { // finite
// have a finite number; no error possible (res must be big enough)
if (rhs->exponent>=0) return decNumberCopy(res, rhs);
// that was easy, but if negative exponent there is work to do...
workset=*set; // clone rounding, etc.
workset.digits=rhs->digits; // no length rounding
workset.traps=0; // no traps
decNumberZero(&dn); // make a number with exponent 0
decNumberQuantize(res, rhs, &dn, &workset);
status|=workset.status;
}
if (status!=0) decStatus(res, status, set);
return res;
} // decNumberToIntegralExact
decNumber * decNumberToIntegralValue(decNumber *res, const decNumber *rhs,
decContext *set) {
decContext workset=*set; // working context
workset.traps=0; // no traps
decNumberToIntegralExact(res, rhs, &workset);
// this never affects set, except for sNaNs; NaN will have been set
// or propagated already, so no need to call decStatus
set->status|=workset.status&DEC_Invalid_operation;
return res;
} // decNumberToIntegralValue
/* ------------------------------------------------------------------ */
/* decNumberXor -- XOR two Numbers, digitwise */
/* */
/* This computes C = A ^ B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X^X) */
/* lhs is A */
/* rhs is B */
/* set is the context (used for result length and error report) */
/* */
/* C must have space for set->digits digits. */
/* */
/* Logical function restrictions apply (see above); a NaN is */
/* returned with Invalid_operation if a restriction is violated. */
/* ------------------------------------------------------------------ */
decNumber * decNumberXor(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
const Unit *ua, *ub; // -> operands
const Unit *msua, *msub; // -> operand msus
Unit *uc, *msuc; // -> result and its msu
Int msudigs; // digits in res msu
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
if (lhs->exponent!=0 || decNumberIsSpecial(lhs) || decNumberIsNegative(lhs)
|| rhs->exponent!=0 || decNumberIsSpecial(rhs) || decNumberIsNegative(rhs)) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
// operands are valid
ua=lhs->lsu; // bottom-up
ub=rhs->lsu; // ..
uc=res->lsu; // ..
msua=ua+D2U(lhs->digits)-1; // -> msu of lhs
msub=ub+D2U(rhs->digits)-1; // -> msu of rhs
msuc=uc+D2U(set->digits)-1; // -> msu of result
msudigs=MSUDIGITS(set->digits); // [faster than remainder]
for (; uc<=msuc; ua++, ub++, uc++) { // Unit loop
Unit a, b; // extract units
if (ua>msua) a=0;
else a=*ua;
if (ub>msub) b=0;
else b=*ub;
*uc=0; // can now write back
if (a|b) { // maybe 1 bits to examine
Int i, j;
// This loop could be unrolled and/or use BIN2BCD tables
for (i=0; i<DECDPUN; i++) {
if ((a^b)&1) *uc=*uc+(Unit)powers[i]; // effect XOR
j=a%10;
a=a/10;
j|=b%10;
b=b/10;
if (j>1) {
decStatus(res, DEC_Invalid_operation, set);
return res;
}
if (uc==msuc && i==msudigs-1) break; // just did final digit
} // each digit
} // non-zero
} // each unit
// [here uc-1 is the msu of the result]
res->digits=decGetDigits(res->lsu, uc-res->lsu);
res->exponent=0; // integer
res->bits=0; // sign=0
return res; // [no status to set]
} // decNumberXor
/* ================================================================== */
/* Utility routines */
/* ================================================================== */
/* ------------------------------------------------------------------ */
/* decNumberClass -- return the decClass of a decNumber */
/* dn -- the decNumber to test */
/* set -- the context to use for Emin */
/* returns the decClass enum */
/* ------------------------------------------------------------------ */
enum decClass decNumberClass(const decNumber *dn, decContext *set) {
if (decNumberIsSpecial(dn)) {
if (decNumberIsQNaN(dn)) return DEC_CLASS_QNAN;
if (decNumberIsSNaN(dn)) return DEC_CLASS_SNAN;
// must be an infinity
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_INF;
return DEC_CLASS_POS_INF;
}
// is finite
if (decNumberIsNormal(dn, set)) { // most common
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_NORMAL;
return DEC_CLASS_POS_NORMAL;
}
// is subnormal or zero
if (decNumberIsZero(dn)) { // most common
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_ZERO;
return DEC_CLASS_POS_ZERO;
}
if (decNumberIsNegative(dn)) return DEC_CLASS_NEG_SUBNORMAL;
return DEC_CLASS_POS_SUBNORMAL;
} // decNumberClass
/* ------------------------------------------------------------------ */
/* decNumberClassToString -- convert decClass to a string */
/* */
/* eclass is a valid decClass */
/* returns a constant string describing the class (max 13+1 chars) */
/* ------------------------------------------------------------------ */
const char *decNumberClassToString(enum decClass eclass) {
if (eclass==DEC_CLASS_POS_NORMAL) return DEC_ClassString_PN;
if (eclass==DEC_CLASS_NEG_NORMAL) return DEC_ClassString_NN;
if (eclass==DEC_CLASS_POS_ZERO) return DEC_ClassString_PZ;
if (eclass==DEC_CLASS_NEG_ZERO) return DEC_ClassString_NZ;
if (eclass==DEC_CLASS_POS_SUBNORMAL) return DEC_ClassString_PS;
if (eclass==DEC_CLASS_NEG_SUBNORMAL) return DEC_ClassString_NS;
if (eclass==DEC_CLASS_POS_INF) return DEC_ClassString_PI;
if (eclass==DEC_CLASS_NEG_INF) return DEC_ClassString_NI;
if (eclass==DEC_CLASS_QNAN) return DEC_ClassString_QN;
if (eclass==DEC_CLASS_SNAN) return DEC_ClassString_SN;
return DEC_ClassString_UN; // Unknown
} // decNumberClassToString
/* ------------------------------------------------------------------ */
/* decNumberCopy -- copy a number */
/* */
/* dest is the target decNumber */
/* src is the source decNumber */
/* returns dest */
/* */
/* (dest==src is allowed and is a no-op) */
/* All fields are updated as required. This is a utility operation, */
/* so special values are unchanged and no error is possible. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopy(decNumber *dest, const decNumber *src) {
#if DECCHECK
if (src==NULL) return decNumberZero(dest);
#endif
if (dest==src) return dest; // no copy required
// Use explicit assignments here as structure assignment could copy
// more than just the lsu (for small DECDPUN). This would not affect
// the value of the results, but could disturb test harness spill
// checking.
dest->bits=src->bits;
dest->exponent=src->exponent;
dest->digits=src->digits;
dest->lsu[0]=src->lsu[0];
if (src->digits>DECDPUN) { // more Units to come
const Unit *smsup, *s; // work
Unit *d; // ..
// memcpy for the remaining Units would be safe as they cannot
// overlap. However, this explicit loop is faster in short cases.
d=dest->lsu+1; // -> first destination
smsup=src->lsu+D2U(src->digits); // -> source msu+1
for (s=src->lsu+1; s<smsup; s++, d++) *d=*s;
}
return dest;
} // decNumberCopy
/* ------------------------------------------------------------------ */
/* decNumberCopyAbs -- quiet absolute value operator */
/* */
/* This sets C = abs(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* */
/* C must have space for set->digits digits. */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberAbs for a checking version of this. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyAbs(decNumber *res, const decNumber *rhs) {
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
#endif
decNumberCopy(res, rhs);
res->bits&=~DECNEG; // turn off sign
return res;
} // decNumberCopyAbs
/* ------------------------------------------------------------------ */
/* decNumberCopyNegate -- quiet negate value operator */
/* */
/* This sets C = negate(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* */
/* C must have space for set->digits digits. */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* See also decNumberMinus for a checking version of this. */
/* ------------------------------------------------------------------ */
decNumber * decNumberCopyNegate(decNumber *res, const decNumber *rhs) {
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
#endif
decNumberCopy(res, rhs);
res->bits^=DECNEG; // invert the sign
return res;
} // decNumberCopyNegate
/* ------------------------------------------------------------------ */
/* decNumberCopySign -- quiet copy and set sign operator */
/* */
/* This sets C = A with the sign of B */
/* */
/* res is C, the result. C may be A */
/* lhs is A */
/* rhs is B */
/* */
/* C must have space for set->digits digits. */
/* No exception or error can occur; this is a quiet bitwise operation.*/
/* ------------------------------------------------------------------ */
decNumber * decNumberCopySign(decNumber *res, const decNumber *lhs,
const decNumber *rhs) {
uByte sign; // rhs sign
#if DECCHECK
if (decCheckOperands(res, DECUNUSED, rhs, DECUNCONT)) return res;
#endif
sign=rhs->bits & DECNEG; // save sign bit
decNumberCopy(res, lhs);
res->bits&=~DECNEG; // clear the sign
res->bits|=sign; // set from rhs
return res;
} // decNumberCopySign
/* ------------------------------------------------------------------ */
/* decNumberGetBCD -- get the coefficient in BCD8 */
/* dn is the source decNumber */
/* bcd is the uInt array that will receive dn->digits BCD bytes, */
/* most-significant at offset 0 */
/* returns bcd */
/* */
/* bcd must have at least dn->digits bytes. No error is possible; if */
/* dn is a NaN or Infinite, digits must be 1 and the coefficient 0. */
/* ------------------------------------------------------------------ */
uByte * decNumberGetBCD(const decNumber *dn, uByte *bcd) {
uByte *ub=bcd+dn->digits-1; // -> lsd
const Unit *up=dn->lsu; // Unit pointer, -> lsu
#if DECDPUN==1 // trivial simple copy
for (; ub>=bcd; ub--, up++) *ub=*up;
#else // chopping needed
uInt u=*up; // work
uInt cut=DECDPUN; // downcounter through unit
for (; ub>=bcd; ub--) {
*ub=(uByte)(u%10); // [*6554 trick inhibits, here]
u=u/10;
cut--;
if (cut>0) continue; // more in this unit
up++;
u=*up;
cut=DECDPUN;
}
#endif
return bcd;
} // decNumberGetBCD
/* ------------------------------------------------------------------ */
/* decNumberSetBCD -- set (replace) the coefficient from BCD8 */
/* dn is the target decNumber */
/* bcd is the uInt array that will source n BCD bytes, most- */
/* significant at offset 0 */
/* n is the number of digits in the source BCD array (bcd) */
/* returns dn */
/* */
/* dn must have space for at least n digits. No error is possible; */
/* if dn is a NaN, or Infinite, or is to become a zero, n must be 1 */
/* and bcd[0] zero. */
/* ------------------------------------------------------------------ */
decNumber * decNumberSetBCD(decNumber *dn, const uByte *bcd, uInt n) {
Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [target pointer]
const uByte *ub=bcd; // -> source msd
#if DECDPUN==1 // trivial simple copy
for (; ub<bcd+n; ub++, up--) *up=*ub;
#else // some assembly needed
// calculate how many digits in msu, and hence first cut
Int cut=MSUDIGITS(n); // [faster than remainder]
for (;up>=dn->lsu; up--) { // each Unit from msu
*up=0; // will take <=DECDPUN digits
for (; cut>0; ub++, cut--) *up=X10(*up)+*ub;
cut=DECDPUN; // next Unit has all digits
}
#endif
dn->digits=n; // set digit count
return dn;
} // decNumberSetBCD
/* ------------------------------------------------------------------ */
/* decNumberIsNormal -- test normality of a decNumber */
/* dn is the decNumber to test */
/* set is the context to use for Emin */
/* returns 1 if |dn| is finite and >=Nmin, 0 otherwise */
/* ------------------------------------------------------------------ */
Int decNumberIsNormal(const decNumber *dn, decContext *set) {
Int ae; // adjusted exponent
#if DECCHECK
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
#endif
if (decNumberIsSpecial(dn)) return 0; // not finite
if (decNumberIsZero(dn)) return 0; // not non-zero
ae=dn->exponent+dn->digits-1; // adjusted exponent
if (ae<set->emin) return 0; // is subnormal
return 1;
} // decNumberIsNormal
/* ------------------------------------------------------------------ */
/* decNumberIsSubnormal -- test subnormality of a decNumber */
/* dn is the decNumber to test */
/* set is the context to use for Emin */
/* returns 1 if |dn| is finite, non-zero, and <Nmin, 0 otherwise */
/* ------------------------------------------------------------------ */
Int decNumberIsSubnormal(const decNumber *dn, decContext *set) {
Int ae; // adjusted exponent
#if DECCHECK
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, set)) return 0;
#endif
if (decNumberIsSpecial(dn)) return 0; // not finite
if (decNumberIsZero(dn)) return 0; // not non-zero
ae=dn->exponent+dn->digits-1; // adjusted exponent
if (ae<set->emin) return 1; // is subnormal
return 0;
} // decNumberIsSubnormal
/* ------------------------------------------------------------------ */
/* decNumberTrim -- remove insignificant zeros */
/* */
/* dn is the number to trim */
/* returns dn */
/* */
/* All fields are updated as required. This is a utility operation, */
/* so special values are unchanged and no error is possible. The */
/* zeros are removed unconditionally. */
/* ------------------------------------------------------------------ */
decNumber * decNumberTrim(decNumber *dn) {
Int dropped; // work
decContext set; // ..
#if DECCHECK
if (decCheckOperands(DECUNRESU, DECUNUSED, dn, DECUNCONT)) return dn;
#endif
decContextDefault(&set, DEC_INIT_BASE); // clamp=0
return decTrim(dn, &set, 0, 1, &dropped);
} // decNumberTrim
/* ------------------------------------------------------------------ */
/* decNumberVersion -- return the name and version of this module */
/* */
/* No error is possible. */
/* ------------------------------------------------------------------ */
const char * decNumberVersion(void) {
return DECVERSION;
} // decNumberVersion
/* ------------------------------------------------------------------ */
/* decNumberZero -- set a number to 0 */
/* */
/* dn is the number to set, with space for one digit */
/* returns dn */
/* */
/* No error is possible. */
/* ------------------------------------------------------------------ */
// Memset is not used as it is much slower in some environments.
decNumber * decNumberZero(decNumber *dn) {
#if DECCHECK
if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
#endif
dn->bits=0;
dn->exponent=0;
dn->digits=1;
dn->lsu[0]=0;
return dn;
} // decNumberZero
/* ================================================================== */
/* Local routines */
/* ================================================================== */
/* ------------------------------------------------------------------ */
/* decToString -- lay out a number into a string */
/* */
/* dn is the number to lay out */
/* string is where to lay out the number */
/* eng is 1 if Engineering, 0 if Scientific */
/* */
/* string must be at least dn->digits+14 characters long */
/* No error is possible. */
/* */
/* Note that this routine can generate a -0 or 0.000. These are */
/* never generated in subset to-number or arithmetic, but can occur */
/* in non-subset arithmetic (e.g., -1*0 or 1.234-1.234). */
/* ------------------------------------------------------------------ */
// If DECCHECK is enabled the string "?" is returned if a number is
// invalid.
static void decToString(const decNumber *dn, char *string, Flag eng) {
Int exp=dn->exponent; // local copy
Int e; // E-part value
Int pre; // digits before the '.'
Int cut; // for counting digits in a Unit
char *c=string; // work [output pointer]
const Unit *up=dn->lsu+D2U(dn->digits)-1; // -> msu [input pointer]
uInt u, pow; // work
#if DECCHECK
if (decCheckOperands(DECUNRESU, dn, DECUNUSED, DECUNCONT)) {
strcpy(string, "?");
return;}
#endif
if (decNumberIsNegative(dn)) { // Negatives get a minus
*c='-';
c++;
}
if (dn->bits&DECSPECIAL) { // Is a special value
if (decNumberIsInfinite(dn)) {
strcpy(c, "Inf");
strcpy(c+3, "inity");
return;}
// a NaN
if (dn->bits&DECSNAN) { // signalling NaN
*c='s';
c++;
}
strcpy(c, "NaN");
c+=3; // step past
// if not a clean non-zero coefficient, that's all there is in a
// NaN string
if (exp!=0 || (*dn->lsu==0 && dn->digits==1)) return;
// [drop through to add integer]
}
// calculate how many digits in msu, and hence first cut
cut=MSUDIGITS(dn->digits); // [faster than remainder]
cut--; // power of ten for digit
if (exp==0) { // simple integer [common fastpath]
for (;up>=dn->lsu; up--) { // each Unit from msu
u=*up; // contains DECDPUN digits to lay out
for (; cut>=0; c++, cut--) TODIGIT(u, cut, c, pow);
cut=DECDPUN-1; // next Unit has all digits
}
*c='\0'; // terminate the string
return;}
/* non-0 exponent -- assume plain form */
pre=dn->digits+exp; // digits before '.'
e=0; // no E
if ((exp>0) || (pre<-5)) { // need exponential form
e=exp+dn->digits-1; // calculate E value
pre=1; // assume one digit before '.'
if (eng && (e!=0)) { // engineering: may need to adjust
Int adj; // adjustment
// The C remainder operator is undefined for negative numbers, so
// a positive remainder calculation must be used here
if (e<0) {
adj=(-e)%3;
if (adj!=0) adj=3-adj;
}
else { // e>0
adj=e%3;
}
e=e-adj;
// if dealing with zero still produce an exponent which is a
// multiple of three, as expected, but there will only be the
// one zero before the E, still. Otherwise note the padding.
if (!ISZERO(dn)) pre+=adj;
else { // is zero
if (adj!=0) { // 0.00Esnn needed
e=e+3;
pre=-(2-adj);
}
} // zero
} // eng
} // need exponent
/* lay out the digits of the coefficient, adding 0s and . as needed */
u=*up;
if (pre>0) { // xxx.xxx or xx00 (engineering) form
Int n=pre;
for (; pre>0; pre--, c++, cut--) {
if (cut<0) { // need new Unit
if (up==dn->lsu) break; // out of input digits (pre>digits)
up--;
cut=DECDPUN-1;
u=*up;
}
TODIGIT(u, cut, c, pow);
}
if (n<dn->digits) { // more to come, after '.'
*c='.'; c++;
for (;; c++, cut--) {
if (cut<0) { // need new Unit
if (up==dn->lsu) break; // out of input digits
up--;
cut=DECDPUN-1;
u=*up;
}
TODIGIT(u, cut, c, pow);
}
}
else for (; pre>0; pre--, c++) *c='0'; // 0 padding (for engineering) needed
}
else { // 0.xxx or 0.000xxx form
*c='0'; c++;
*c='.'; c++;
for (; pre<0; pre++, c++) *c='0'; // add any 0's after '.'
for (; ; c++, cut--) {
if (cut<0) { // need new Unit
if (up==dn->lsu) break; // out of input digits
up--;
cut=DECDPUN-1;
u=*up;
}
TODIGIT(u, cut, c, pow);
}
}
/* Finally add the E-part, if needed. It will never be 0, has a
base maximum and minimum of +999999999 through -999999999, but
could range down to -1999999998 for anormal numbers */
if (e!=0) {
Flag had=0; // 1=had non-zero
*c='E'; c++;
*c='+'; c++; // assume positive
u=e; // ..
if (e<0) {
*(c-1)='-'; // oops, need -
u=-e; // uInt, please
}
// lay out the exponent [_itoa or equivalent is not ANSI C]
for (cut=9; cut>=0; cut--) {
TODIGIT(u, cut, c, pow);
if (*c=='0' && !had) continue; // skip leading zeros
had=1; // had non-0
c++; // step for next
} // cut
}
*c='\0'; // terminate the string (all paths)
return;
} // decToString
/* ------------------------------------------------------------------ */
/* decAddOp -- add/subtract operation */
/* */
/* This computes C = A + B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X+X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* negate is DECNEG if rhs should be negated, or 0 otherwise */
/* status accumulates status for the caller */
/* */
/* C must have space for set->digits digits. */
/* Inexact in status must be 0 for correct Exact zero sign in result */
/* ------------------------------------------------------------------ */
/* If possible, the coefficient is calculated directly into C. */
/* However, if: */
/* -- a digits+1 calculation is needed because the numbers are */
/* unaligned and span more than set->digits digits */
/* -- a carry to digits+1 digits looks possible */
/* -- C is the same as A or B, and the result would destructively */
/* overlap the A or B coefficient */
/* then the result must be calculated into a temporary buffer. In */
/* this case a local (stack) buffer is used if possible, and only if */
/* too long for that does malloc become the final resort. */
/* */
/* Misalignment is handled as follows: */
/* Apad: (AExp>BExp) Swap operands and proceed as for BExp>AExp. */
/* BPad: Apply the padding by a combination of shifting (whole */
/* units) and multiplication (part units). */
/* */
/* Addition, especially x=x+1, is speed-critical. */
/* The static buffer is larger than might be expected to allow for */
/* calls from higher-level funtions (notable exp). */
/* ------------------------------------------------------------------ */
static decNumber * decAddOp(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set,
uByte negate, uInt *status) {
#if DECSUBSET
decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
decNumber *allocrhs=NULL; // .., rhs
#endif
Int rhsshift; // working shift (in Units)
Int maxdigits; // longest logical length
Int mult; // multiplier
Int residue; // rounding accumulator
uByte bits; // result bits
Flag diffsign; // non-0 if arguments have different sign
Unit *acc; // accumulator for result
Unit accbuff[SD2U(DECBUFFER*2+20)]; // local buffer [*2+20 reduces many
// allocations when called from
// other operations, notable exp]
Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated
Int reqdigits=set->digits; // local copy; requested DIGITS
Int padding; // work
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operands and set lostDigits status, as needed
if (lhs->digits>reqdigits) {
alloclhs=decRoundOperand(lhs, set, status);
if (alloclhs==NULL) break;
lhs=alloclhs;
}
if (rhs->digits>reqdigits) {
allocrhs=decRoundOperand(rhs, set, status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
// note whether signs differ [used all paths]
diffsign=(Flag)((lhs->bits^rhs->bits^negate)&DECNEG);
// handle infinities and NaNs
if (SPECIALARGS) { // a special bit set
if (SPECIALARGS & (DECSNAN | DECNAN)) // a NaN
decNaNs(res, lhs, rhs, set, status);
else { // one or two infinities
if (decNumberIsInfinite(lhs)) { // LHS is infinity
// two infinities with different signs is invalid
if (decNumberIsInfinite(rhs) && diffsign) {
*status|=DEC_Invalid_operation;
break;
}
bits=lhs->bits & DECNEG; // get sign from LHS
}
else bits=(rhs->bits^negate) & DECNEG;// RHS must be Infinity
bits|=DECINF;
decNumberZero(res);
res->bits=bits; // set +/- infinity
} // an infinity
break;
}
// Quick exit for add 0s; return the non-0, modified as need be
if (ISZERO(lhs)) {
Int adjust; // work
Int lexp=lhs->exponent; // save in case LHS==RES
bits=lhs->bits; // ..
residue=0; // clear accumulator
decCopyFit(res, rhs, set, &residue, status); // copy (as needed)
res->bits^=negate; // flip if rhs was negated
#if DECSUBSET
if (set->extended) { // exponents on zeros count
#endif
// exponent will be the lower of the two
adjust=lexp-res->exponent; // adjustment needed [if -ve]
if (ISZERO(res)) { // both 0: special IEEE 754 rules
if (adjust<0) res->exponent=lexp; // set exponent
// 0-0 gives +0 unless rounding to -infinity, and -0-0 gives -0
if (diffsign) {
if (set->round!=DEC_ROUND_FLOOR) res->bits=0;
else res->bits=DECNEG; // preserve 0 sign
}
}
else { // non-0 res
if (adjust<0) { // 0-padding needed
if ((res->digits-adjust)>set->digits) {
adjust=res->digits-set->digits; // to fit exactly
*status|=DEC_Rounded; // [but exact]
}
res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
res->exponent+=adjust; // set the exponent.
}
} // non-0 res
#if DECSUBSET
} // extended
#endif
decFinish(res, set, &residue, status); // clean and finalize
break;}
if (ISZERO(rhs)) { // [lhs is non-zero]
Int adjust; // work
Int rexp=rhs->exponent; // save in case RHS==RES
bits=rhs->bits; // be clean
residue=0; // clear accumulator
decCopyFit(res, lhs, set, &residue, status); // copy (as needed)
#if DECSUBSET
if (set->extended) { // exponents on zeros count
#endif
// exponent will be the lower of the two
// [0-0 case handled above]
adjust=rexp-res->exponent; // adjustment needed [if -ve]
if (adjust<0) { // 0-padding needed
if ((res->digits-adjust)>set->digits) {
adjust=res->digits-set->digits; // to fit exactly
*status|=DEC_Rounded; // [but exact]
}
res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
res->exponent+=adjust; // set the exponent.
}
#if DECSUBSET
} // extended
#endif
decFinish(res, set, &residue, status); // clean and finalize
break;}
// [NB: both fastpath and mainpath code below assume these cases
// (notably 0-0) have already been handled]
// calculate the padding needed to align the operands
padding=rhs->exponent-lhs->exponent;
// Fastpath cases where the numbers are aligned and normal, the RHS
// is all in one unit, no operand rounding is needed, and no carry,
// lengthening, or borrow is needed
if (padding==0
&& rhs->digits<=DECDPUN
&& rhs->exponent>=set->emin // [some normals drop through]
&& rhs->exponent<=set->emax-set->digits+1 // [could clamp]
&& rhs->digits<=reqdigits
&& lhs->digits<=reqdigits) {
Int partial=*lhs->lsu;
if (!diffsign) { // adding
partial+=*rhs->lsu;
if ((partial<=DECDPUNMAX) // result fits in unit
&& (lhs->digits>=DECDPUN || // .. and no digits-count change
partial<(Int)powers[lhs->digits])) { // ..
if (res!=lhs) decNumberCopy(res, lhs); // not in place
*res->lsu=(Unit)partial; // [copy could have overwritten RHS]
break;
}
// else drop out for careful add
}
else { // signs differ
partial-=*rhs->lsu;
if (partial>0) { // no borrow needed, and non-0 result
if (res!=lhs) decNumberCopy(res, lhs); // not in place
*res->lsu=(Unit)partial;
// this could have reduced digits [but result>0]
res->digits=decGetDigits(res->lsu, D2U(res->digits));
break;
}
// else drop out for careful subtract
}
}
// Now align (pad) the lhs or rhs so they can be added or
// subtracted, as necessary. If one number is much larger than
// the other (that is, if in plain form there is a least one
// digit between the lowest digit of one and the highest of the
// other) padding with up to DIGITS-1 trailing zeros may be
// needed; then apply rounding (as exotic rounding modes may be
// affected by the residue).
rhsshift=0; // rhs shift to left (padding) in Units
bits=lhs->bits; // assume sign is that of LHS
mult=1; // likely multiplier
// [if padding==0 the operands are aligned; no padding is needed]
if (padding!=0) {
// some padding needed; always pad the RHS, as any required
// padding can then be effected by a simple combination of
// shifts and a multiply
Flag swapped=0;
if (padding<0) { // LHS needs the padding
const decNumber *t;
padding=-padding; // will be +ve
bits=(uByte)(rhs->bits^negate); // assumed sign is now that of RHS
t=lhs; lhs=rhs; rhs=t;
swapped=1;
}
// If, after pad, rhs would be longer than lhs by digits+1 or
// more then lhs cannot affect the answer, except as a residue,
// so only need to pad up to a length of DIGITS+1.
if (rhs->digits+padding > lhs->digits+reqdigits+1) {
// The RHS is sufficient
// for residue use the relative sign indication...
Int shift=reqdigits-rhs->digits; // left shift needed
residue=1; // residue for rounding
if (diffsign) residue=-residue; // signs differ
// copy, shortening if necessary
decCopyFit(res, rhs, set, &residue, status);
// if it was already shorter, then need to pad with zeros
if (shift>0) {
res->digits=decShiftToMost(res->lsu, res->digits, shift);
res->exponent-=shift; // adjust the exponent.
}
// flip the result sign if unswapped and rhs was negated
if (!swapped) res->bits^=negate;
decFinish(res, set, &residue, status); // done
break;}
// LHS digits may affect result
rhsshift=D2U(padding+1)-1; // this much by Unit shift ..
mult=powers[padding-(rhsshift*DECDPUN)]; // .. this by multiplication
} // padding needed
if (diffsign) mult=-mult; // signs differ
// determine the longer operand
maxdigits=rhs->digits+padding; // virtual length of RHS
if (lhs->digits>maxdigits) maxdigits=lhs->digits;
// Decide on the result buffer to use; if possible place directly
// into result.
acc=res->lsu; // assume add direct to result
// If destructive overlap, or the number is too long, or a carry or
// borrow to DIGITS+1 might be possible, a buffer must be used.
// [Might be worth more sophisticated tests when maxdigits==reqdigits]
if ((maxdigits>=reqdigits) // is, or could be, too large
|| (res==rhs && rhsshift>0)) { // destructive overlap
// buffer needed, choose it; units for maxdigits digits will be
// needed, +1 Unit for carry or borrow
Int need=D2U(maxdigits)+1;
acc=accbuff; // assume use local buffer
if (need*sizeof(Unit)>sizeof(accbuff)) {
// printf("malloc add %ld %ld\n", need, sizeof(accbuff));
allocacc=(Unit *)malloc(need*sizeof(Unit));
if (allocacc==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
acc=allocacc;
}
}
res->bits=(uByte)(bits&DECNEG); // it's now safe to overwrite..
res->exponent=lhs->exponent; // .. operands (even if aliased)
#if DECTRACE
decDumpAr('A', lhs->lsu, D2U(lhs->digits));
decDumpAr('B', rhs->lsu, D2U(rhs->digits));
printf(" :h: %ld %ld\n", rhsshift, mult);
#endif
// add [A+B*m] or subtract [A+B*(-m)]
res->digits=decUnitAddSub(lhs->lsu, D2U(lhs->digits),
rhs->lsu, D2U(rhs->digits),
rhsshift, acc, mult)
*DECDPUN; // [units -> digits]
if (res->digits<0) { // borrowed...
res->digits=-res->digits;
res->bits^=DECNEG; // flip the sign
}
#if DECTRACE
decDumpAr('+', acc, D2U(res->digits));
#endif
// If a buffer was used the result must be copied back, possibly
// shortening. (If no buffer was used then the result must have
// fit, so can't need rounding and residue must be 0.)
residue=0; // clear accumulator
if (acc!=res->lsu) {
#if DECSUBSET
if (set->extended) { // round from first significant digit
#endif
// remove leading zeros that were added due to rounding up to
// integral Units -- before the test for rounding.
if (res->digits>reqdigits)
res->digits=decGetDigits(acc, D2U(res->digits));
decSetCoeff(res, set, acc, res->digits, &residue, status);
#if DECSUBSET
}
else { // subset arithmetic rounds from original significant digit
// May have an underestimate. This only occurs when both
// numbers fit in DECDPUN digits and are padding with a
// negative multiple (-10, -100...) and the top digit(s) become
// 0. (This only matters when using X3.274 rules where the
// leading zero could be included in the rounding.)
if (res->digits<maxdigits) {
*(acc+D2U(res->digits))=0; // ensure leading 0 is there
res->digits=maxdigits;
}
else {
// remove leading zeros that added due to rounding up to
// integral Units (but only those in excess of the original
// maxdigits length, unless extended) before test for rounding.
if (res->digits>reqdigits) {
res->digits=decGetDigits(acc, D2U(res->digits));
if (res->digits<maxdigits) res->digits=maxdigits;
}
}
decSetCoeff(res, set, acc, res->digits, &residue, status);
// Now apply rounding if needed before removing leading zeros.
// This is safe because subnormals are not a possibility
if (residue!=0) {
decApplyRound(res, set, residue, status);
residue=0; // did what needed to be done
}
} // subset
#endif
} // used buffer
// strip leading zeros [these were left on in case of subset subtract]
res->digits=decGetDigits(res->lsu, D2U(res->digits));
// apply checks and rounding
decFinish(res, set, &residue, status);
// "When the sum of two operands with opposite signs is exactly
// zero, the sign of that sum shall be '+' in all rounding modes
// except round toward -Infinity, in which mode that sign shall be
// '-'." [Subset zeros also never have '-', set by decFinish.]
if (ISZERO(res) && diffsign
#if DECSUBSET
&& set->extended
#endif
&& (*status&DEC_Inexact)==0) {
if (set->round==DEC_ROUND_FLOOR) res->bits|=DECNEG; // sign -
else res->bits&=~DECNEG; // sign +
}
} while(0); // end protected
if (allocacc!=NULL) free(allocacc); // drop any storage used
#if DECSUBSET
if (allocrhs!=NULL) free(allocrhs); // ..
if (alloclhs!=NULL) free(alloclhs); // ..
#endif
return res;
} // decAddOp
/* ------------------------------------------------------------------ */
/* decDivideOp -- division operation */
/* */
/* This routine performs the calculations for all four division */
/* operators (divide, divideInteger, remainder, remainderNear). */
/* */
/* C=A op B */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X/X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* op is DIVIDE, DIVIDEINT, REMAINDER, or REMNEAR respectively. */
/* status is the usual accumulator */
/* */
/* C must have space for set->digits digits. */
/* */
/* ------------------------------------------------------------------ */
/* The underlying algorithm of this routine is the same as in the */
/* 1981 S/370 implementation, that is, non-restoring long division */
/* with bi-unit (rather than bi-digit) estimation for each unit */
/* multiplier. In this pseudocode overview, complications for the */
/* Remainder operators and division residues for exact rounding are */
/* omitted for clarity. */
/* */
/* Prepare operands and handle special values */
/* Test for x/0 and then 0/x */
/* Exp =Exp1 - Exp2 */
/* Exp =Exp +len(var1) -len(var2) */
/* Sign=Sign1 * Sign2 */
/* Pad accumulator (Var1) to double-length with 0's (pad1) */
/* Pad Var2 to same length as Var1 */
/* msu2pair/plus=1st 2 or 1 units of var2, +1 to allow for round */
/* have=0 */
/* Do until (have=digits+1 OR residue=0) */
/* if exp<0 then if integer divide/residue then leave */
/* this_unit=0 */
/* Do forever */
/* compare numbers */
/* if <0 then leave inner_loop */
/* if =0 then (* quick exit without subtract *) do */
/* this_unit=this_unit+1; output this_unit */
/* leave outer_loop; end */
/* Compare lengths of numbers (mantissae): */
/* If same then tops2=msu2pair -- {units 1&2 of var2} */
/* else tops2=msu2plus -- {0, unit 1 of var2} */
/* tops1=first_unit_of_Var1*10**DECDPUN +second_unit_of_var1 */
/* mult=tops1/tops2 -- Good and safe guess at divisor */
/* if mult=0 then mult=1 */
/* this_unit=this_unit+mult */
/* subtract */
/* end inner_loop */
/* if have\=0 | this_unit\=0 then do */
/* output this_unit */
/* have=have+1; end */
/* var2=var2/10 */
/* exp=exp-1 */
/* end outer_loop */
/* exp=exp+1 -- set the proper exponent */
/* if have=0 then generate answer=0 */
/* Return (Result is defined by Var1) */
/* */
/* ------------------------------------------------------------------ */
/* Two working buffers are needed during the division; one (digits+ */
/* 1) to accumulate the result, and the other (up to 2*digits+1) for */
/* long subtractions. These are acc and var1 respectively. */
/* var1 is a copy of the lhs coefficient, var2 is the rhs coefficient.*/
/* The static buffers may be larger than might be expected to allow */
/* for calls from higher-level funtions (notable exp). */
/* ------------------------------------------------------------------ */
static decNumber * decDivideOp(decNumber *res,
const decNumber *lhs, const decNumber *rhs,
decContext *set, Flag op, uInt *status) {
#if DECSUBSET
decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
decNumber *allocrhs=NULL; // .., rhs
#endif
Unit accbuff[SD2U(DECBUFFER+DECDPUN+10)]; // local buffer
Unit *acc=accbuff; // -> accumulator array for result
Unit *allocacc=NULL; // -> allocated buffer, iff allocated
Unit *accnext; // -> where next digit will go
Int acclength; // length of acc needed [Units]
Int accunits; // count of units accumulated
Int accdigits; // count of digits accumulated
Unit varbuff[SD2U(DECBUFFER*2+DECDPUN)]; // buffer for var1
Unit *var1=varbuff; // -> var1 array for long subtraction
Unit *varalloc=NULL; // -> allocated buffer, iff used
Unit *msu1; // -> msu of var1
const Unit *var2; // -> var2 array
const Unit *msu2; // -> msu of var2
Int msu2plus; // msu2 plus one [does not vary]
eInt msu2pair; // msu2 pair plus one [does not vary]
Int var1units, var2units; // actual lengths
Int var2ulen; // logical length (units)
Int var1initpad=0; // var1 initial padding (digits)
Int maxdigits; // longest LHS or required acc length
Int mult; // multiplier for subtraction
Unit thisunit; // current unit being accumulated
Int residue; // for rounding
Int reqdigits=set->digits; // requested DIGITS
Int exponent; // working exponent
Int maxexponent=0; // DIVIDE maximum exponent if unrounded
uByte bits; // working sign
Unit *target; // work
const Unit *source; // ..
uInt const *pow; // ..
Int shift, cut; // ..
#if DECSUBSET
Int dropped; // work
#endif
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operands and set lostDigits status, as needed
if (lhs->digits>reqdigits) {
alloclhs=decRoundOperand(lhs, set, status);
if (alloclhs==NULL) break;
lhs=alloclhs;
}
if (rhs->digits>reqdigits) {
allocrhs=decRoundOperand(rhs, set, status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
bits=(lhs->bits^rhs->bits)&DECNEG; // assumed sign for divisions
// handle infinities and NaNs
if (SPECIALARGS) { // a special bit set
if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
decNaNs(res, lhs, rhs, set, status);
break;
}
// one or two infinities
if (decNumberIsInfinite(lhs)) { // LHS (dividend) is infinite
if (decNumberIsInfinite(rhs) || // two infinities are invalid ..
op & (REMAINDER | REMNEAR)) { // as is remainder of infinity
*status|=DEC_Invalid_operation;
break;
}
// [Note that infinity/0 raises no exceptions]
decNumberZero(res);
res->bits=bits|DECINF; // set +/- infinity
break;
}
else { // RHS (divisor) is infinite
residue=0;
if (op&(REMAINDER|REMNEAR)) {
// result is [finished clone of] lhs
decCopyFit(res, lhs, set, &residue, status);
}
else { // a division
decNumberZero(res);
res->bits=bits; // set +/- zero
// for DIVIDEINT the exponent is always 0. For DIVIDE, result
// is a 0 with infinitely negative exponent, clamped to minimum
if (op&DIVIDE) {
res->exponent=set->emin-set->digits+1;
*status|=DEC_Clamped;
}
}
decFinish(res, set, &residue, status);
break;
}
}
// handle 0 rhs (x/0)
if (ISZERO(rhs)) { // x/0 is always exceptional
if (ISZERO(lhs)) {
decNumberZero(res); // [after lhs test]
*status|=DEC_Division_undefined;// 0/0 will become NaN
}
else {
decNumberZero(res);
if (op&(REMAINDER|REMNEAR)) *status|=DEC_Invalid_operation;
else {
*status|=DEC_Division_by_zero; // x/0
res->bits=bits|DECINF; // .. is +/- Infinity
}
}
break;}
// handle 0 lhs (0/x)
if (ISZERO(lhs)) { // 0/x [x!=0]
#if DECSUBSET
if (!set->extended) decNumberZero(res);
else {
#endif
if (op&DIVIDE) {
residue=0;
exponent=lhs->exponent-rhs->exponent; // ideal exponent
decNumberCopy(res, lhs); // [zeros always fit]
res->bits=bits; // sign as computed
res->exponent=exponent; // exponent, too
decFinalize(res, set, &residue, status); // check exponent
}
else if (op&DIVIDEINT) {
decNumberZero(res); // integer 0
res->bits=bits; // sign as computed
}
else { // a remainder
exponent=rhs->exponent; // [save in case overwrite]
decNumberCopy(res, lhs); // [zeros always fit]
if (exponent<res->exponent) res->exponent=exponent; // use lower
}
#if DECSUBSET
}
#endif
break;}
// Precalculate exponent. This starts off adjusted (and hence fits
// in 31 bits) and becomes the usual unadjusted exponent as the
// division proceeds. The order of evaluation is important, here,
// to avoid wrap.
exponent=(lhs->exponent+lhs->digits)-(rhs->exponent+rhs->digits);
// If the working exponent is -ve, then some quick exits are
// possible because the quotient is known to be <1
// [for REMNEAR, it needs to be < -1, as -0.5 could need work]
if (exponent<0 && !(op==DIVIDE)) {
if (op&DIVIDEINT) {
decNumberZero(res); // integer part is 0
#if DECSUBSET
if (set->extended)
#endif
res->bits=bits; // set +/- zero
break;}
// fastpath remainders so long as the lhs has the smaller
// (or equal) exponent
if (lhs->exponent<=rhs->exponent) {
if (op&REMAINDER || exponent<-1) {
// It is REMAINDER or safe REMNEAR; result is [finished
// clone of] lhs (r = x - 0*y)
residue=0;
decCopyFit(res, lhs, set, &residue, status);
decFinish(res, set, &residue, status);
break;
}
// [unsafe REMNEAR drops through]
}
} // fastpaths
/* Long (slow) division is needed; roll up the sleeves... */
// The accumulator will hold the quotient of the division.
// If it needs to be too long for stack storage, then allocate.
acclength=D2U(reqdigits+DECDPUN); // in Units
if (acclength*sizeof(Unit)>sizeof(accbuff)) {
// printf("malloc dvacc %ld units\n", acclength);
allocacc=(Unit *)malloc(acclength*sizeof(Unit));
if (allocacc==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
acc=allocacc; // use the allocated space
}
// var1 is the padded LHS ready for subtractions.
// If it needs to be too long for stack storage, then allocate.
// The maximum units needed for var1 (long subtraction) is:
// Enough for
// (rhs->digits+reqdigits-1) -- to allow full slide to right
// or (lhs->digits) -- to allow for long lhs
// whichever is larger
// +1 -- for rounding of slide to right
// +1 -- for leading 0s
// +1 -- for pre-adjust if a remainder or DIVIDEINT
// [Note: unused units do not participate in decUnitAddSub data]
maxdigits=rhs->digits+reqdigits-1;
if (lhs->digits>maxdigits) maxdigits=lhs->digits;
var1units=D2U(maxdigits)+2;
// allocate a guard unit above msu1 for REMAINDERNEAR
if (!(op&DIVIDE)) var1units++;
if ((var1units+1)*sizeof(Unit)>sizeof(varbuff)) {
// printf("malloc dvvar %ld units\n", var1units+1);
varalloc=(Unit *)malloc((var1units+1)*sizeof(Unit));
if (varalloc==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
var1=varalloc; // use the allocated space
}
// Extend the lhs and rhs to full long subtraction length. The lhs
// is truly extended into the var1 buffer, with 0 padding, so a
// subtract in place is always possible. The rhs (var2) has
// virtual padding (implemented by decUnitAddSub).
// One guard unit was allocated above msu1 for rem=rem+rem in
// REMAINDERNEAR.
msu1=var1+var1units-1; // msu of var1
source=lhs->lsu+D2U(lhs->digits)-1; // msu of input array
for (target=msu1; source>=lhs->lsu; source--, target--) *target=*source;
for (; target>=var1; target--) *target=0;
// rhs (var2) is left-aligned with var1 at the start
var2ulen=var1units; // rhs logical length (units)
var2units=D2U(rhs->digits); // rhs actual length (units)
var2=rhs->lsu; // -> rhs array
msu2=var2+var2units-1; // -> msu of var2 [never changes]
// now set up the variables which will be used for estimating the
// multiplication factor. If these variables are not exact, add
// 1 to make sure that the multiplier is never overestimated.
msu2plus=*msu2; // it's value ..
if (var2units>1) msu2plus++; // .. +1 if any more
msu2pair=(eInt)*msu2*(DECDPUNMAX+1);// top two pair ..
if (var2units>1) { // .. [else treat 2nd as 0]
msu2pair+=*(msu2-1); // ..
if (var2units>2) msu2pair++; // .. +1 if any more
}
// The calculation is working in units, which may have leading zeros,
// but the exponent was calculated on the assumption that they are
// both left-aligned. Adjust the exponent to compensate: add the
// number of leading zeros in var1 msu and subtract those in var2 msu.
// [This is actually done by counting the digits and negating, as
// lead1=DECDPUN-digits1, and similarly for lead2.]
for (pow=&powers[1]; *msu1>=*pow; pow++) exponent--;
for (pow=&powers[1]; *msu2>=*pow; pow++) exponent++;
// Now, if doing an integer divide or remainder, ensure that
// the result will be Unit-aligned. To do this, shift the var1
// accumulator towards least if need be. (It's much easier to
// do this now than to reassemble the residue afterwards, if
// doing a remainder.) Also ensure the exponent is not negative.
if (!(op&DIVIDE)) {
Unit *u; // work
// save the initial 'false' padding of var1, in digits
var1initpad=(var1units-D2U(lhs->digits))*DECDPUN;
// Determine the shift to do.
if (exponent<0) cut=-exponent;
else cut=DECDPUN-exponent%DECDPUN;
decShiftToLeast(var1, var1units, cut);
exponent+=cut; // maintain numerical value
var1initpad-=cut; // .. and reduce padding
// clean any most-significant units which were just emptied
for (u=msu1; cut>=DECDPUN; cut-=DECDPUN, u--) *u=0;
} // align
else { // is DIVIDE
maxexponent=lhs->exponent-rhs->exponent; // save
// optimization: if the first iteration will just produce 0,
// preadjust to skip it [valid for DIVIDE only]
if (*msu1<*msu2) {
var2ulen--; // shift down
exponent-=DECDPUN; // update the exponent
}
}
// ---- start the long-division loops ------------------------------
accunits=0; // no units accumulated yet
accdigits=0; // .. or digits
accnext=acc+acclength-1; // -> msu of acc [NB: allows digits+1]
for (;;) { // outer forever loop
thisunit=0; // current unit assumed 0
// find the next unit
for (;;) { // inner forever loop
// strip leading zero units [from either pre-adjust or from
// subtract last time around]. Leave at least one unit.
for (; *msu1==0 && msu1>var1; msu1--) var1units--;
if (var1units<var2ulen) break; // var1 too low for subtract
if (var1units==var2ulen) { // unit-by-unit compare needed
// compare the two numbers, from msu
const Unit *pv1, *pv2;
Unit v2; // units to compare
pv2=msu2; // -> msu
for (pv1=msu1; ; pv1--, pv2--) {
// v1=*pv1 -- always OK
v2=0; // assume in padding
if (pv2>=var2) v2=*pv2; // in range
if (*pv1!=v2) break; // no longer the same
if (pv1==var1) break; // done; leave pv1 as is
}
// here when all inspected or a difference seen
if (*pv1<v2) break; // var1 too low to subtract
if (*pv1==v2) { // var1 == var2
// reach here if var1 and var2 are identical; subtraction
// would increase digit by one, and the residue will be 0 so
// the calculation is done; leave the loop with residue=0.
thisunit++; // as though subtracted
*var1=0; // set var1 to 0
var1units=1; // ..
break; // from inner
} // var1 == var2
// *pv1>v2. Prepare for real subtraction; the lengths are equal
// Estimate the multiplier (there's always a msu1-1)...
// Bring in two units of var2 to provide a good estimate.
mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2pair);
} // lengths the same
else { // var1units > var2ulen, so subtraction is safe
// The var2 msu is one unit towards the lsu of the var1 msu,
// so only one unit for var2 can be used.
mult=(Int)(((eInt)*msu1*(DECDPUNMAX+1)+*(msu1-1))/msu2plus);
}
if (mult==0) mult=1; // must always be at least 1
// subtraction needed; var1 is > var2
thisunit=(Unit)(thisunit+mult); // accumulate
// subtract var1-var2, into var1; only the overlap needs
// processing, as this is an in-place calculation
shift=var2ulen-var2units;
#if DECTRACE
decDumpAr('1', &var1[shift], var1units-shift);
decDumpAr('2', var2, var2units);
printf("m=%ld\n", -mult);
#endif
decUnitAddSub(&var1[shift], var1units-shift,
var2, var2units, 0,
&var1[shift], -mult);
#if DECTRACE
decDumpAr('#', &var1[shift], var1units-shift);
#endif
// var1 now probably has leading zeros; these are removed at the
// top of the inner loop.
} // inner loop
// The next unit has been calculated in full; unless it's a
// leading zero, add to acc
if (accunits!=0 || thisunit!=0) { // is first or non-zero
*accnext=thisunit; // store in accumulator
// account exactly for the new digits
if (accunits==0) {
accdigits++; // at least one
for (pow=&powers[1]; thisunit>=*pow; pow++) accdigits++;
}
else accdigits+=DECDPUN;
accunits++; // update count
accnext--; // ready for next
if (accdigits>reqdigits) break; // have enough digits
}
// if the residue is zero, the operation is done (unless divide
// or divideInteger and still not enough digits yet)
if (*var1==0 && var1units==1) { // residue is 0
if (op&(REMAINDER|REMNEAR)) break;
if ((op&DIVIDE) && (exponent<=maxexponent)) break;
// [drop through if divideInteger]
}
// also done enough if calculating remainder or integer
// divide and just did the last ('units') unit
if (exponent==0 && !(op&DIVIDE)) break;
// to get here, var1 is less than var2, so divide var2 by the per-
// Unit power of ten and go for the next digit
var2ulen--; // shift down
exponent-=DECDPUN; // update the exponent
} // outer loop
// ---- division is complete ---------------------------------------
// here: acc has at least reqdigits+1 of good results (or fewer
// if early stop), starting at accnext+1 (its lsu)
// var1 has any residue at the stopping point
// accunits is the number of digits collected in acc
if (accunits==0) { // acc is 0
accunits=1; // show have a unit ..
accdigits=1; // ..
*accnext=0; // .. whose value is 0
}
else accnext++; // back to last placed
// accnext now -> lowest unit of result
residue=0; // assume no residue
if (op&DIVIDE) {
// record the presence of any residue, for rounding
if (*var1!=0 || var1units>1) residue=1;
else { // no residue
// Had an exact division; clean up spurious trailing 0s.
// There will be at most DECDPUN-1, from the final multiply,
// and then only if the result is non-0 (and even) and the
// exponent is 'loose'.
#if DECDPUN>1
Unit lsu=*accnext;
if (!(lsu&0x01) && (lsu!=0)) {
// count the trailing zeros
Int drop=0;
for (;; drop++) { // [will terminate because lsu!=0]
if (exponent>=maxexponent) break; // don't chop real 0s
#if DECDPUN<=4
if ((lsu-QUOT10(lsu, drop+1)
*powers[drop+1])!=0) break; // found non-0 digit
#else
if (lsu%powers[drop+1]!=0) break; // found non-0 digit
#endif
exponent++;
}
if (drop>0) {
accunits=decShiftToLeast(accnext, accunits, drop);
accdigits=decGetDigits(accnext, accunits);
accunits=D2U(accdigits);
// [exponent was adjusted in the loop]
}
} // neither odd nor 0
#endif
} // exact divide
} // divide
else /* op!=DIVIDE */ {
// check for coefficient overflow
if (accdigits+exponent>reqdigits) {
*status|=DEC_Division_impossible;
break;
}
if (op & (REMAINDER|REMNEAR)) {
// [Here, the exponent will be 0, because var1 was adjusted
// appropriately.]
Int postshift; // work
Flag wasodd=0; // integer was odd
Unit *quotlsu; // for save
Int quotdigits; // ..
bits=lhs->bits; // remainder sign is always as lhs
// Fastpath when residue is truly 0 is worthwhile [and
// simplifies the code below]
if (*var1==0 && var1units==1) { // residue is 0
Int exp=lhs->exponent; // save min(exponents)
if (rhs->exponent<exp) exp=rhs->exponent;
decNumberZero(res); // 0 coefficient
#if DECSUBSET
if (set->extended)
#endif
res->exponent=exp; // .. with proper exponent
res->bits=(uByte)(bits&DECNEG); // [cleaned]
decFinish(res, set, &residue, status); // might clamp
break;
}
// note if the quotient was odd
if (*accnext & 0x01) wasodd=1; // acc is odd
quotlsu=accnext; // save in case need to reinspect
quotdigits=accdigits; // ..
// treat the residue, in var1, as the value to return, via acc
// calculate the unused zero digits. This is the smaller of:
// var1 initial padding (saved above)
// var2 residual padding, which happens to be given by:
postshift=var1initpad+exponent-lhs->exponent+rhs->exponent;
// [the 'exponent' term accounts for the shifts during divide]
if (var1initpad<postshift) postshift=var1initpad;
// shift var1 the requested amount, and adjust its digits
var1units=decShiftToLeast(var1, var1units, postshift);
accnext=var1;
accdigits=decGetDigits(var1, var1units);
accunits=D2U(accdigits);
exponent=lhs->exponent; // exponent is smaller of lhs & rhs
if (rhs->exponent<exponent) exponent=rhs->exponent;
// Now correct the result if doing remainderNear; if it
// (looking just at coefficients) is > rhs/2, or == rhs/2 and
// the integer was odd then the result should be rem-rhs.
if (op&REMNEAR) {
Int compare, tarunits; // work
Unit *up; // ..
// calculate remainder*2 into the var1 buffer (which has
// 'headroom' of an extra unit and hence enough space)
// [a dedicated 'double' loop would be faster, here]
tarunits=decUnitAddSub(accnext, accunits, accnext, accunits,
0, accnext, 1);
// decDumpAr('r', accnext, tarunits);
// Here, accnext (var1) holds tarunits Units with twice the
// remainder's coefficient, which must now be compared to the
// RHS. The remainder's exponent may be smaller than the RHS's.
compare=decUnitCompare(accnext, tarunits, rhs->lsu, D2U(rhs->digits),
rhs->exponent-exponent);
if (compare==BADINT) { // deep trouble
*status|=DEC_Insufficient_storage;
break;}
// now restore the remainder by dividing by two; the lsu
// is known to be even.
for (up=accnext; up<accnext+tarunits; up++) {
Int half; // half to add to lower unit
half=*up & 0x01;
*up/=2; // [shift]
if (!half) continue;
*(up-1)+=(DECDPUNMAX+1)/2;
}
// [accunits still describes the original remainder length]
if (compare>0 || (compare==0 && wasodd)) { // adjustment needed
Int exp, expunits, exprem; // work
// This is effectively causing round-up of the quotient,
// so if it was the rare case where it was full and all
// nines, it would overflow and hence division-impossible
// should be raised
Flag allnines=0; // 1 if quotient all nines
if (quotdigits==reqdigits) { // could be borderline
for (up=quotlsu; ; up++) {
if (quotdigits>DECDPUN) {
if (*up!=DECDPUNMAX) break;// non-nines
}
else { // this is the last Unit
if (*up==powers[quotdigits]-1) allnines=1;
break;
}
quotdigits-=DECDPUN; // checked those digits
} // up
} // borderline check
if (allnines) {
*status|=DEC_Division_impossible;
break;}
// rem-rhs is needed; the sign will invert. Again, var1
// can safely be used for the working Units array.
exp=rhs->exponent-exponent; // RHS padding needed
// Calculate units and remainder from exponent.
expunits=exp/DECDPUN;
exprem=exp%DECDPUN;
// subtract [A+B*(-m)]; the result will always be negative
accunits=-decUnitAddSub(accnext, accunits,
rhs->lsu, D2U(rhs->digits),
expunits, accnext, -(Int)powers[exprem]);
accdigits=decGetDigits(accnext, accunits); // count digits exactly
accunits=D2U(accdigits); // and recalculate the units for copy
// [exponent is as for original remainder]
bits^=DECNEG; // flip the sign
}
} // REMNEAR
} // REMAINDER or REMNEAR
} // not DIVIDE
// Set exponent and bits
res->exponent=exponent;
res->bits=(uByte)(bits&DECNEG); // [cleaned]
// Now the coefficient.
decSetCoeff(res, set, accnext, accdigits, &residue, status);
decFinish(res, set, &residue, status); // final cleanup
#if DECSUBSET
// If a divide then strip trailing zeros if subset [after round]
if (!set->extended && (op==DIVIDE)) decTrim(res, set, 0, 1, &dropped);
#endif
} while(0); // end protected
if (varalloc!=NULL) free(varalloc); // drop any storage used
if (allocacc!=NULL) free(allocacc); // ..
#if DECSUBSET
if (allocrhs!=NULL) free(allocrhs); // ..
if (alloclhs!=NULL) free(alloclhs); // ..
#endif
return res;
} // decDivideOp
/* ------------------------------------------------------------------ */
/* decMultiplyOp -- multiplication operation */
/* */
/* This routine performs the multiplication C=A x B. */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X*X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* status is the usual accumulator */
/* */
/* C must have space for set->digits digits. */
/* */
/* ------------------------------------------------------------------ */
/* 'Classic' multiplication is used rather than Karatsuba, as the */
/* latter would give only a minor improvement for the short numbers */
/* expected to be handled most (and uses much more memory). */
/* */
/* There are two major paths here: the general-purpose ('old code') */
/* path which handles all DECDPUN values, and a fastpath version */
/* which is used if 64-bit ints are available, DECDPUN<=4, and more */
/* than two calls to decUnitAddSub would be made. */
/* */
/* The fastpath version lumps units together into 8-digit or 9-digit */
/* chunks, and also uses a lazy carry strategy to minimise expensive */
/* 64-bit divisions. The chunks are then broken apart again into */
/* units for continuing processing. Despite this overhead, the */
/* fastpath can speed up some 16-digit operations by 10x (and much */
/* more for higher-precision calculations). */
/* */
/* A buffer always has to be used for the accumulator; in the */
/* fastpath, buffers are also always needed for the chunked copies of */
/* of the operand coefficients. */
/* Static buffers are larger than needed just for multiply, to allow */
/* for calls from other operations (notably exp). */
/* ------------------------------------------------------------------ */
#define FASTMUL (DECUSE64 && DECDPUN<5)
static decNumber * decMultiplyOp(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set,
uInt *status) {
Int accunits; // Units of accumulator in use
Int exponent; // work
Int residue=0; // rounding residue
uByte bits; // result sign
Unit *acc; // -> accumulator Unit array
Int needbytes; // size calculator
void *allocacc=NULL; // -> allocated accumulator, iff allocated
Unit accbuff[SD2U(DECBUFFER*4+1)]; // buffer (+1 for DECBUFFER==0,
// *4 for calls from other operations)
const Unit *mer, *mermsup; // work
Int madlength; // Units in multiplicand
Int shift; // Units to shift multiplicand by
#if FASTMUL
// if DECDPUN is 1 or 3 work in base 10**9, otherwise
// (DECDPUN is 2 or 4) then work in base 10**8
#if DECDPUN & 1 // odd
#define FASTBASE 1000000000 // base
#define FASTDIGS 9 // digits in base
#define FASTLAZY 18 // carry resolution point [1->18]
#else
#define FASTBASE 100000000
#define FASTDIGS 8
#define FASTLAZY 1844 // carry resolution point [1->1844]
#endif
// three buffers are used, two for chunked copies of the operands
// (base 10**8 or base 10**9) and one base 2**64 accumulator with
// lazy carry evaluation
uInt zlhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
uInt *zlhi=zlhibuff; // -> lhs array
uInt *alloclhi=NULL; // -> allocated buffer, iff allocated
uInt zrhibuff[(DECBUFFER*2+1)/8+1]; // buffer (+1 for DECBUFFER==0)
uInt *zrhi=zrhibuff; // -> rhs array
uInt *allocrhi=NULL; // -> allocated buffer, iff allocated
uLong zaccbuff[(DECBUFFER*2+1)/4+2]; // buffer (+1 for DECBUFFER==0)
// [allocacc is shared for both paths, as only one will run]
uLong *zacc=zaccbuff; // -> accumulator array for exact result
#if DECDPUN==1
Int zoff; // accumulator offset
#endif
uInt *lip, *rip; // item pointers
uInt *lmsi, *rmsi; // most significant items
Int ilhs, irhs, iacc; // item counts in the arrays
Int lazy; // lazy carry counter
uLong lcarry; // uLong carry
uInt carry; // carry (NB not uLong)
Int count; // work
const Unit *cup; // ..
Unit *up; // ..
uLong *lp; // ..
Int p; // ..
#endif
#if DECSUBSET
decNumber *alloclhs=NULL; // -> allocated buffer, iff allocated
decNumber *allocrhs=NULL; // -> allocated buffer, iff allocated
#endif
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
// precalculate result sign
bits=(uByte)((lhs->bits^rhs->bits)&DECNEG);
// handle infinities and NaNs
if (SPECIALARGS) { // a special bit set
if (SPECIALARGS & (DECSNAN | DECNAN)) { // one or two NaNs
decNaNs(res, lhs, rhs, set, status);
return res;}
// one or two infinities; Infinity * 0 is invalid
if (((lhs->bits & DECINF)==0 && ISZERO(lhs))
||((rhs->bits & DECINF)==0 && ISZERO(rhs))) {
*status|=DEC_Invalid_operation;
return res;}
decNumberZero(res);
res->bits=bits|DECINF; // infinity
return res;}
// For best speed, as in DMSRCN [the original Rexx numerics
// module], use the shorter number as the multiplier (rhs) and
// the longer as the multiplicand (lhs) to minimise the number of
// adds (partial products)
if (lhs->digits<rhs->digits) { // swap...
const decNumber *hold=lhs;
lhs=rhs;
rhs=hold;
}
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operands and set lostDigits status, as needed
if (lhs->digits>set->digits) {
alloclhs=decRoundOperand(lhs, set, status);
if (alloclhs==NULL) break;
lhs=alloclhs;
}
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
#if FASTMUL // fastpath can be used
// use the fast path if there are enough digits in the shorter
// operand to make the setup and takedown worthwhile
#define NEEDTWO (DECDPUN*2) // within two decUnitAddSub calls
if (rhs->digits>NEEDTWO) { // use fastpath...
// calculate the number of elements in each array
ilhs=(lhs->digits+FASTDIGS-1)/FASTDIGS; // [ceiling]
irhs=(rhs->digits+FASTDIGS-1)/FASTDIGS; // ..
iacc=ilhs+irhs;
// allocate buffers if required, as usual
needbytes=ilhs*sizeof(uInt);
if (needbytes>(Int)sizeof(zlhibuff)) {
alloclhi=(uInt *)malloc(needbytes);
zlhi=alloclhi;}
needbytes=irhs*sizeof(uInt);
if (needbytes>(Int)sizeof(zrhibuff)) {
allocrhi=(uInt *)malloc(needbytes);
zrhi=allocrhi;}
// Allocating the accumulator space needs a special case when
// DECDPUN=1 because when converting the accumulator to Units
// after the multiplication each 8-byte item becomes 9 1-byte
// units. Therefore iacc extra bytes are needed at the front
// (rounded up to a multiple of 8 bytes), and the uLong
// accumulator starts offset the appropriate number of units
// to the right to avoid overwrite during the unchunking.
needbytes=iacc*sizeof(uLong);
#if DECDPUN==1
zoff=(iacc+7)/8; // items to offset by
needbytes+=zoff*8;
#endif
if (needbytes>(Int)sizeof(zaccbuff)) {
allocacc=(uLong *)malloc(needbytes);
zacc=(uLong *)allocacc;}
if (zlhi==NULL||zrhi==NULL||zacc==NULL) {
*status|=DEC_Insufficient_storage;
break;}
acc=(Unit *)zacc; // -> target Unit array
#if DECDPUN==1
zacc+=zoff; // start uLong accumulator to right
#endif
// assemble the chunked copies of the left and right sides
for (count=lhs->digits, cup=lhs->lsu, lip=zlhi; count>0; lip++)
for (p=0, *lip=0; p<FASTDIGS && count>0;
p+=DECDPUN, cup++, count-=DECDPUN)
*lip+=*cup*powers[p];
lmsi=lip-1; // save -> msi
for (count=rhs->digits, cup=rhs->lsu, rip=zrhi; count>0; rip++)
for (p=0, *rip=0; p<FASTDIGS && count>0;
p+=DECDPUN, cup++, count-=DECDPUN)
*rip+=*cup*powers[p];
rmsi=rip-1; // save -> msi
// zero the accumulator
for (lp=zacc; lp<zacc+iacc; lp++) *lp=0;
/* Start the multiplication */
// Resolving carries can dominate the cost of accumulating the
// partial products, so this is only done when necessary.
// Each uLong item in the accumulator can hold values up to
// 2**64-1, and each partial product can be as large as
// (10**FASTDIGS-1)**2. When FASTDIGS=9, this can be added to
// itself 18.4 times in a uLong without overflowing, so during
// the main calculation resolution is carried out every 18th
// add -- every 162 digits. Similarly, when FASTDIGS=8, the
// partial products can be added to themselves 1844.6 times in
// a uLong without overflowing, so intermediate carry
// resolution occurs only every 14752 digits. Hence for common
// short numbers usually only the one final carry resolution
// occurs.
// (The count is set via FASTLAZY to simplify experiments to
// measure the value of this approach: a 35% improvement on a
// [34x34] multiply.)
lazy=FASTLAZY; // carry delay count
for (rip=zrhi; rip<=rmsi; rip++) { // over each item in rhs
lp=zacc+(rip-zrhi); // where to add the lhs
for (lip=zlhi; lip<=lmsi; lip++, lp++) { // over each item in lhs
*lp+=(uLong)(*lip)*(*rip); // [this should in-line]
} // lip loop
lazy--;
if (lazy>0 && rip!=rmsi) continue;
lazy=FASTLAZY; // reset delay count
// spin up the accumulator resolving overflows
for (lp=zacc; lp<zacc+iacc; lp++) {
if (*lp<FASTBASE) continue; // it fits
lcarry=*lp/FASTBASE; // top part [slow divide]
// lcarry can exceed 2**32-1, so check again; this check
// and occasional extra divide (slow) is well worth it, as
// it allows FASTLAZY to be increased to 18 rather than 4
// in the FASTDIGS=9 case
if (lcarry<FASTBASE) carry=(uInt)lcarry; // [usual]
else { // two-place carry [fairly rare]
uInt carry2=(uInt)(lcarry/FASTBASE); // top top part
*(lp+2)+=carry2; // add to item+2
*lp-=((uLong)FASTBASE*FASTBASE*carry2); // [slow]
carry=(uInt)(lcarry-((uLong)FASTBASE*carry2)); // [inline]
}
*(lp+1)+=carry; // add to item above [inline]
*lp-=((uLong)FASTBASE*carry); // [inline]
} // carry resolution
} // rip loop
// The multiplication is complete; time to convert back into
// units. This can be done in-place in the accumulator and in
// 32-bit operations, because carries were resolved after the
// final add. This needs N-1 divides and multiplies for
// each item in the accumulator (which will become up to N
// units, where 2<=N<=9).
for (lp=zacc, up=acc; lp<zacc+iacc; lp++) {
uInt item=(uInt)*lp; // decapitate to uInt
for (p=0; p<FASTDIGS-DECDPUN; p+=DECDPUN, up++) {
uInt part=item/(DECDPUNMAX+1);
*up=(Unit)(item-(part*(DECDPUNMAX+1)));
item=part;
} // p
*up=(Unit)item; up++; // [final needs no division]
} // lp
accunits=up-acc; // count of units
}
else { // here to use units directly, without chunking ['old code']
#endif
// if accumulator will be too long for local storage, then allocate
acc=accbuff; // -> assume buffer for accumulator
needbytes=(D2U(lhs->digits)+D2U(rhs->digits))*sizeof(Unit);
if (needbytes>(Int)sizeof(accbuff)) {
allocacc=(Unit *)malloc(needbytes);
if (allocacc==NULL) {*status|=DEC_Insufficient_storage; break;}
acc=(Unit *)allocacc; // use the allocated space
}
/* Now the main long multiplication loop */
// Unlike the equivalent in the IBM Java implementation, there
// is no advantage in calculating from msu to lsu. So, do it
// by the book, as it were.
// Each iteration calculates ACC=ACC+MULTAND*MULT
accunits=1; // accumulator starts at '0'
*acc=0; // .. (lsu=0)
shift=0; // no multiplicand shift at first
madlength=D2U(lhs->digits); // this won't change
mermsup=rhs->lsu+D2U(rhs->digits); // -> msu+1 of multiplier
for (mer=rhs->lsu; mer<mermsup; mer++) {
// Here, *mer is the next Unit in the multiplier to use
// If non-zero [optimization] add it...
if (*mer!=0) accunits=decUnitAddSub(&acc[shift], accunits-shift,
lhs->lsu, madlength, 0,
&acc[shift], *mer)
+ shift;
else { // extend acc with a 0; it will be used shortly
*(acc+accunits)=0; // [this avoids length of <=0 later]
accunits++;
}
// multiply multiplicand by 10**DECDPUN for next Unit to left
shift++; // add this for 'logical length'
} // n
#if FASTMUL
} // unchunked units
#endif
// common end-path
#if DECTRACE
decDumpAr('*', acc, accunits); // Show exact result
#endif
// acc now contains the exact result of the multiplication,
// possibly with a leading zero unit; build the decNumber from
// it, noting if any residue
res->bits=bits; // set sign
res->digits=decGetDigits(acc, accunits); // count digits exactly
// There can be a 31-bit wrap in calculating the exponent.
// This can only happen if both input exponents are negative and
// both their magnitudes are large. If there was a wrap, set a
// safe very negative exponent, from which decFinalize() will
// raise a hard underflow shortly.
exponent=lhs->exponent+rhs->exponent; // calculate exponent
if (lhs->exponent<0 && rhs->exponent<0 && exponent>0)
exponent=-2*DECNUMMAXE; // force underflow
res->exponent=exponent; // OK to overwrite now
// Set the coefficient. If any rounding, residue records
decSetCoeff(res, set, acc, res->digits, &residue, status);
decFinish(res, set, &residue, status); // final cleanup
} while(0); // end protected
if (allocacc!=NULL) free(allocacc); // drop any storage used
#if DECSUBSET
if (allocrhs!=NULL) free(allocrhs); // ..
if (alloclhs!=NULL) free(alloclhs); // ..
#endif
#if FASTMUL
if (allocrhi!=NULL) free(allocrhi); // ..
if (alloclhi!=NULL) free(alloclhi); // ..
#endif
return res;
} // decMultiplyOp
/* ------------------------------------------------------------------ */
/* decExpOp -- effect exponentiation */
/* */
/* This computes C = exp(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context; note that rounding mode has no effect */
/* */
/* C must have space for set->digits digits. status is updated but */
/* not set. */
/* */
/* Restrictions: */
/* */
/* digits, emax, and -emin in the context must be less than */
/* 2*DEC_MAX_MATH (1999998), and the rhs must be within these */
/* bounds or a zero. This is an internal routine, so these */
/* restrictions are contractual and not enforced. */
/* */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
/* almost always be correctly rounded, but may be up to 1 ulp in */
/* error in rare cases. */
/* */
/* Finite results will always be full precision and Inexact, except */
/* when A is a zero or -Infinity (giving 1 or 0 respectively). */
/* ------------------------------------------------------------------ */
/* This approach used here is similar to the algorithm described in */
/* */
/* Variable Precision Exponential Function, T. E. Hull and */
/* A. Abrham, ACM Transactions on Mathematical Software, Vol 12 #2, */
/* pp79-91, ACM, June 1986. */
/* */
/* with the main difference being that the iterations in the series */
/* evaluation are terminated dynamically (which does not require the */
/* extra variable-precision variables which are expensive in this */
/* context). */
/* */
/* The error analysis in Hull & Abrham's paper applies except for the */
/* round-off error accumulation during the series evaluation. This */
/* code does not precalculate the number of iterations and so cannot */
/* use Horner's scheme. Instead, the accumulation is done at double- */
/* precision, which ensures that the additions of the terms are exact */
/* and do not accumulate round-off (and any round-off errors in the */
/* terms themselves move 'to the right' faster than they can */
/* accumulate). This code also extends the calculation by allowing, */
/* in the spirit of other decNumber operators, the input to be more */
/* precise than the result (the precision used is based on the more */
/* precise of the input or requested result). */
/* */
/* Implementation notes: */
/* */
/* 1. This is separated out as decExpOp so it can be called from */
/* other Mathematical functions (notably Ln) with a wider range */
/* than normal. In particular, it can handle the slightly wider */
/* (double) range needed by Ln (which has to be able to calculate */
/* exp(-x) where x can be the tiniest number (Ntiny). */
/* */
/* 2. Normalizing x to be <=0.1 (instead of <=1) reduces loop */
/* iterations by appoximately a third with additional (although */
/* diminishing) returns as the range is reduced to even smaller */
/* fractions. However, h (the power of 10 used to correct the */
/* result at the end, see below) must be kept <=8 as otherwise */
/* the final result cannot be computed. Hence the leverage is a */
/* sliding value (8-h), where potentially the range is reduced */
/* more for smaller values. */
/* */
/* The leverage that can be applied in this way is severely */
/* limited by the cost of the raise-to-the power at the end, */
/* which dominates when the number of iterations is small (less */
/* than ten) or when rhs is short. As an example, the adjustment */
/* x**10,000,000 needs 31 multiplications, all but one full-width. */
/* */
/* 3. The restrictions (especially precision) could be raised with */
/* care, but the full decNumber range seems very hard within the */
/* 32-bit limits. */
/* */
/* 4. The working precisions for the static buffers are twice the */
/* obvious size to allow for calls from decNumberPower. */
/* ------------------------------------------------------------------ */
decNumber * decExpOp(decNumber *res, const decNumber *rhs,
decContext *set, uInt *status) {
uInt ignore=0; // working status
Int h; // adjusted exponent for 0.xxxx
Int p; // working precision
Int residue; // rounding residue
uInt needbytes; // for space calculations
const decNumber *x=rhs; // (may point to safe copy later)
decContext aset, tset, dset; // working contexts
Int comp; // work
// the argument is often copied to normalize it, so (unusually) it
// is treated like other buffers, using DECBUFFER, +1 in case
// DECBUFFER is 0
decNumber bufr[D2N(DECBUFFER*2+1)];
decNumber *allocrhs=NULL; // non-NULL if rhs buffer allocated
// the working precision will be no more than set->digits+8+1
// so for on-stack buffers DECBUFFER+9 is used, +1 in case DECBUFFER
// is 0 (and twice that for the accumulator)
// buffer for t, term (working precision plus)
decNumber buft[D2N(DECBUFFER*2+9+1)];
decNumber *allocbuft=NULL; // -> allocated buft, iff allocated
decNumber *t=buft; // term
// buffer for a, accumulator (working precision * 2), at least 9
decNumber bufa[D2N(DECBUFFER*4+18+1)];
decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
decNumber *a=bufa; // accumulator
// decNumber for the divisor term; this needs at most 9 digits
// and so can be fixed size [16 so can use standard context]
decNumber bufd[D2N(16)];
decNumber *d=bufd; // divisor
decNumber numone; // constant 1
#if DECCHECK
Int iterations=0; // for later sanity check
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
do { // protect allocated storage
if (SPECIALARG) { // handle infinities and NaNs
if (decNumberIsInfinite(rhs)) { // an infinity
if (decNumberIsNegative(rhs)) // -Infinity -> +0
decNumberZero(res);
else decNumberCopy(res, rhs); // +Infinity -> self
}
else decNaNs(res, rhs, NULL, set, status); // a NaN
break;}
if (ISZERO(rhs)) { // zeros -> exact 1
decNumberZero(res); // make clean 1
*res->lsu=1; // ..
break;} // [no status to set]
// e**x when 0 < x < 0.66 is < 1+3x/2, hence can fast-path
// positive and negative tiny cases which will result in inexact
// 1. This also allows the later add-accumulate to always be
// exact (because its length will never be more than twice the
// working precision).
// The comparator (tiny) needs just one digit, so use the
// decNumber d for it (reused as the divisor, etc., below); its
// exponent is such that if x is positive it will have
// set->digits-1 zeros between the decimal point and the digit,
// which is 4, and if x is negative one more zero there as the
// more precise result will be of the form 0.9999999 rather than
// 1.0000001. Hence, tiny will be 0.0000004 if digits=7 and x>0
// or 0.00000004 if digits=7 and x<0. If RHS not larger than
// this then the result will be 1.000000
decNumberZero(d); // clean
*d->lsu=4; // set 4 ..
d->exponent=-set->digits; // * 10**(-d)
if (decNumberIsNegative(rhs)) d->exponent--; // negative case
comp=decCompare(d, rhs, 1); // signless compare
if (comp==BADINT) {
*status|=DEC_Insufficient_storage;
break;}
if (comp>=0) { // rhs < d
Int shift=set->digits-1;
decNumberZero(res); // set 1
*res->lsu=1; // ..
res->digits=decShiftToMost(res->lsu, 1, shift);
res->exponent=-shift; // make 1.0000...
*status|=DEC_Inexact | DEC_Rounded; // .. inexactly
break;} // tiny
// set up the context to be used for calculating a, as this is
// used on both paths below
decContextDefault(&aset, DEC_INIT_DECIMAL64);
// accumulator bounds are as requested (could underflow)
aset.emax=set->emax; // usual bounds
aset.emin=set->emin; // ..
aset.clamp=0; // and no concrete format
// calculate the adjusted (Hull & Abrham) exponent (where the
// decimal point is just to the left of the coefficient msd)
h=rhs->exponent+rhs->digits;
// if h>8 then 10**h cannot be calculated safely; however, when
// h=8 then exp(|rhs|) will be at least exp(1E+7) which is at
// least 6.59E+4342944, so (due to the restriction on Emax/Emin)
// overflow (or underflow to 0) is guaranteed -- so this case can
// be handled by simply forcing the appropriate excess
if (h>8) { // overflow/underflow
// set up here so Power call below will over or underflow to
// zero; set accumulator to either 2 or 0.02
// [stack buffer for a is always big enough for this]
decNumberZero(a);
*a->lsu=2; // not 1 but < exp(1)
if (decNumberIsNegative(rhs)) a->exponent=-2; // make 0.02
h=8; // clamp so 10**h computable
p=9; // set a working precision
}
else { // h<=8
Int maxlever=(rhs->digits>8?1:0);
// [could/should increase this for precisions >40 or so, too]
// if h is 8, cannot normalize to a lower upper limit because
// the final result will not be computable (see notes above),
// but leverage can be applied whenever h is less than 8.
// Apply as much as possible, up to a MAXLEVER digits, which
// sets the tradeoff against the cost of the later a**(10**h).
// As h is increased, the working precision below also
// increases to compensate for the "constant digits at the
// front" effect.
Int lever=MINI(8-h, maxlever); // leverage attainable
Int use=-rhs->digits-lever; // exponent to use for RHS
h+=lever; // apply leverage selected
if (h<0) { // clamp
use+=h; // [may end up subnormal]
h=0;
}
// Take a copy of RHS if it needs normalization (true whenever x>=1)
if (rhs->exponent!=use) {
decNumber *newrhs=bufr; // assume will fit on stack
needbytes=sizeof(decNumber)+(D2U(rhs->digits)-1)*sizeof(Unit);
if (needbytes>sizeof(bufr)) { // need malloc space
allocrhs=(decNumber *)malloc(needbytes);
if (allocrhs==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
newrhs=allocrhs; // use the allocated space
}
decNumberCopy(newrhs, rhs); // copy to safe space
newrhs->exponent=use; // normalize; now <1
x=newrhs; // ready for use
// decNumberShow(x);
}
// Now use the usual power series to evaluate exp(x). The
// series starts as 1 + x + x^2/2 ... so prime ready for the
// third term by setting the term variable t=x, the accumulator
// a=1, and the divisor d=2.
// First determine the working precision. From Hull & Abrham
// this is set->digits+h+2. However, if x is 'over-precise' we
// need to allow for all its digits to potentially participate
// (consider an x where all the excess digits are 9s) so in
// this case use x->digits+h+2
p=MAXI(x->digits, set->digits)+h+2; // [h<=8]
// a and t are variable precision, and depend on p, so space
// must be allocated for them if necessary
// the accumulator needs to be able to hold 2p digits so that
// the additions on the second and subsequent iterations are
// sufficiently exact.
needbytes=sizeof(decNumber)+(D2U(p*2)-1)*sizeof(Unit);
if (needbytes>sizeof(bufa)) { // need malloc space
allocbufa=(decNumber *)malloc(needbytes);
if (allocbufa==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
a=allocbufa; // use the allocated space
}
// the term needs to be able to hold p digits (which is
// guaranteed to be larger than x->digits, so the initial copy
// is safe); it may also be used for the raise-to-power
// calculation below, which needs an extra two digits
needbytes=sizeof(decNumber)+(D2U(p+2)-1)*sizeof(Unit);
if (needbytes>sizeof(buft)) { // need malloc space
allocbuft=(decNumber *)malloc(needbytes);
if (allocbuft==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
t=allocbuft; // use the allocated space
}
decNumberCopy(t, x); // term=x
decNumberZero(a); *a->lsu=1; // accumulator=1
decNumberZero(d); *d->lsu=2; // divisor=2
decNumberZero(&numone); *numone.lsu=1; // constant 1 for increment
// set up the contexts for calculating a, t, and d
decContextDefault(&tset, DEC_INIT_DECIMAL64);
dset=tset;
// accumulator bounds are set above, set precision now
aset.digits=p*2; // double
// term bounds avoid any underflow or overflow
tset.digits=p;
tset.emin=DEC_MIN_EMIN; // [emax is plenty]
// [dset.digits=16, etc., are sufficient]
// finally ready to roll
for (;;) {
#if DECCHECK
iterations++;
#endif
// only the status from the accumulation is interesting
// [but it should remain unchanged after first add]
decAddOp(a, a, t, &aset, 0, status); // a=a+t
decMultiplyOp(t, t, x, &tset, &ignore); // t=t*x
decDivideOp(t, t, d, &tset, DIVIDE, &ignore); // t=t/d
// the iteration ends when the term cannot affect the result,
// if rounded to p digits, which is when its value is smaller
// than the accumulator by p+1 digits. There must also be
// full precision in a.
if (((a->digits+a->exponent)>=(t->digits+t->exponent+p+1))
&& (a->digits>=p)) break;
decAddOp(d, d, &numone, &dset, 0, &ignore); // d=d+1
} // iterate
#if DECCHECK
// just a sanity check; comment out test to show always
if (iterations>p+3)
printf("Exp iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
(LI)iterations, (LI)*status, (LI)p, (LI)x->digits);
#endif
} // h<=8
// apply postconditioning: a=a**(10**h) -- this is calculated
// at a slightly higher precision than Hull & Abrham suggest
if (h>0) {
Int seenbit=0; // set once a 1-bit is seen
Int i; // counter
Int n=powers[h]; // always positive
aset.digits=p+2; // sufficient precision
// avoid the overhead and many extra digits of decNumberPower
// as all that is needed is the short 'multipliers' loop; here
// accumulate the answer into t
decNumberZero(t); *t->lsu=1; // acc=1
for (i=1;;i++){ // for each bit [top bit ignored]
// abandon if have had overflow or terminal underflow
if (*status & (DEC_Overflow|DEC_Underflow)) { // interesting?
if (*status&DEC_Overflow || ISZERO(t)) break;}
n=n<<1; // move next bit to testable position
if (n<0) { // top bit is set
seenbit=1; // OK, have a significant bit
decMultiplyOp(t, t, a, &aset, status); // acc=acc*x
}
if (i==31) break; // that was the last bit
if (!seenbit) continue; // no need to square 1
decMultiplyOp(t, t, t, &aset, status); // acc=acc*acc [square]
} /*i*/ // 32 bits
// decNumberShow(t);
a=t; // and carry on using t instead of a
}
// Copy and round the result to res
residue=1; // indicate dirt to right ..
if (ISZERO(a)) residue=0; // .. unless underflowed to 0
aset.digits=set->digits; // [use default rounding]
decCopyFit(res, a, &aset, &residue, status); // copy & shorten
decFinish(res, set, &residue, status); // cleanup/set flags
} while(0); // end protected
if (allocrhs !=NULL) free(allocrhs); // drop any storage used
if (allocbufa!=NULL) free(allocbufa); // ..
if (allocbuft!=NULL) free(allocbuft); // ..
// [status is handled by caller]
return res;
} // decExpOp
/* ------------------------------------------------------------------ */
/* Initial-estimate natural logarithm table */
/* */
/* LNnn -- 90-entry 16-bit table for values from .10 through .99. */
/* The result is a 4-digit encode of the coefficient (c=the */
/* top 14 bits encoding 0-9999) and a 2-digit encode of the */
/* exponent (e=the bottom 2 bits encoding 0-3) */
/* */
/* The resulting value is given by: */
/* */
/* v = -c * 10**(-e-3) */
/* */
/* where e and c are extracted from entry k = LNnn[x-10] */
/* where x is truncated (NB) into the range 10 through 99, */
/* and then c = k>>2 and e = k&3. */
/* ------------------------------------------------------------------ */
const uShort LNnn[90]={9016, 8652, 8316, 8008, 7724, 7456, 7208,
6972, 6748, 6540, 6340, 6148, 5968, 5792, 5628, 5464, 5312,
5164, 5020, 4884, 4748, 4620, 4496, 4376, 4256, 4144, 4032,
39233, 38181, 37157, 36157, 35181, 34229, 33297, 32389, 31501, 30629,
29777, 28945, 28129, 27329, 26545, 25777, 25021, 24281, 23553, 22837,
22137, 21445, 20769, 20101, 19445, 18801, 18165, 17541, 16925, 16321,
15721, 15133, 14553, 13985, 13421, 12865, 12317, 11777, 11241, 10717,
10197, 9685, 9177, 8677, 8185, 7697, 7213, 6737, 6269, 5801,
5341, 4889, 4437, 39930, 35534, 31186, 26886, 22630, 18418, 14254,
10130, 6046, 20055};
/* ------------------------------------------------------------------ */
/* decLnOp -- effect natural logarithm */
/* */
/* This computes C = ln(A) */
/* */
/* res is C, the result. C may be A */
/* rhs is A */
/* set is the context; note that rounding mode has no effect */
/* */
/* C must have space for set->digits digits. */
/* */
/* Notable cases: */
/* A<0 -> Invalid */
/* A=0 -> -Infinity (Exact) */
/* A=+Infinity -> +Infinity (Exact) */
/* A=1 exactly -> 0 (Exact) */
/* */
/* Restrictions (as for Exp): */
/* */
/* digits, emax, and -emin in the context must be less than */
/* DEC_MAX_MATH+11 (1000010), and the rhs must be within these */
/* bounds or a zero. This is an internal routine, so these */
/* restrictions are contractual and not enforced. */
/* */
/* A finite result is rounded using DEC_ROUND_HALF_EVEN; it will */
/* almost always be correctly rounded, but may be up to 1 ulp in */
/* error in rare cases. */
/* ------------------------------------------------------------------ */
/* The result is calculated using Newton's method, with each */
/* iteration calculating a' = a + x * exp(-a) - 1. See, for example, */
/* Epperson 1989. */
/* */
/* The iteration ends when the adjustment x*exp(-a)-1 is tiny enough. */
/* This has to be calculated at the sum of the precision of x and the */
/* working precision. */
/* */
/* Implementation notes: */
/* */
/* 1. This is separated out as decLnOp so it can be called from */
/* other Mathematical functions (e.g., Log 10) with a wider range */
/* than normal. In particular, it can handle the slightly wider */
/* (+9+2) range needed by a power function. */
/* */
/* 2. The speed of this function is about 10x slower than exp, as */
/* it typically needs 4-6 iterations for short numbers, and the */
/* extra precision needed adds a squaring effect, twice. */
/* */
/* 3. Fastpaths are included for ln(10) and ln(2), up to length 40, */
/* as these are common requests. ln(10) is used by log10(x). */
/* */
/* 4. An iteration might be saved by widening the LNnn table, and */
/* would certainly save at least one if it were made ten times */
/* bigger, too (for truncated fractions 0.100 through 0.999). */
/* However, for most practical evaluations, at least four or five */
/* iterations will be neede -- so this would only speed up by */
/* 20-25% and that probably does not justify increasing the table */
/* size. */
/* */
/* 5. The static buffers are larger than might be expected to allow */
/* for calls from decNumberPower. */
/* ------------------------------------------------------------------ */
decNumber * decLnOp(decNumber *res, const decNumber *rhs,
decContext *set, uInt *status) {
uInt ignore=0; // working status accumulator
uInt needbytes; // for space calculations
Int residue; // rounding residue
Int r; // rhs=f*10**r [see below]
Int p; // working precision
Int pp; // precision for iteration
Int t; // work
// buffers for a (accumulator, typically precision+2) and b
// (adjustment calculator, same size)
decNumber bufa[D2N(DECBUFFER+12)];
decNumber *allocbufa=NULL; // -> allocated bufa, iff allocated
decNumber *a=bufa; // accumulator/work
decNumber bufb[D2N(DECBUFFER*2+2)];
decNumber *allocbufb=NULL; // -> allocated bufa, iff allocated
decNumber *b=bufb; // adjustment/work
decNumber numone; // constant 1
decNumber cmp; // work
decContext aset, bset; // working contexts
#if DECCHECK
Int iterations=0; // for later sanity check
if (decCheckOperands(res, DECUNUSED, rhs, set)) return res;
#endif
do { // protect allocated storage
if (SPECIALARG) { // handle infinities and NaNs
if (decNumberIsInfinite(rhs)) { // an infinity
if (decNumberIsNegative(rhs)) // -Infinity -> error
*status|=DEC_Invalid_operation;
else decNumberCopy(res, rhs); // +Infinity -> self
}
else decNaNs(res, rhs, NULL, set, status); // a NaN
break;}
if (ISZERO(rhs)) { // +/- zeros -> -Infinity
decNumberZero(res); // make clean
res->bits=DECINF|DECNEG; // set - infinity
break;} // [no status to set]
// Non-zero negatives are bad...
if (decNumberIsNegative(rhs)) { // -x -> error
*status|=DEC_Invalid_operation;
break;}
// Here, rhs is positive, finite, and in range
// lookaside fastpath code for ln(2) and ln(10) at common lengths
if (rhs->exponent==0 && set->digits<=40) {
#if DECDPUN==1
if (rhs->lsu[0]==0 && rhs->lsu[1]==1 && rhs->digits==2) { // ln(10)
#else
if (rhs->lsu[0]==10 && rhs->digits==2) { // ln(10)
#endif
aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
#define LN10 "2.302585092994045684017991454684364207601"
decNumberFromString(res, LN10, &aset);
*status|=(DEC_Inexact | DEC_Rounded); // is inexact
break;}
if (rhs->lsu[0]==2 && rhs->digits==1) { // ln(2)
aset=*set; aset.round=DEC_ROUND_HALF_EVEN;
#define LN2 "0.6931471805599453094172321214581765680755"
decNumberFromString(res, LN2, &aset);
*status|=(DEC_Inexact | DEC_Rounded);
break;}
} // integer and short
// Determine the working precision. This is normally the
// requested precision + 2, with a minimum of 9. However, if
// the rhs is 'over-precise' then allow for all its digits to
// potentially participate (consider an rhs where all the excess
// digits are 9s) so in this case use rhs->digits+2.
p=MAXI(rhs->digits, MAXI(set->digits, 7))+2;
// Allocate space for the accumulator and the high-precision
// adjustment calculator, if necessary. The accumulator must
// be able to hold p digits, and the adjustment up to
// rhs->digits+p digits. They are also made big enough for 16
// digits so that they can be used for calculating the initial
// estimate.
needbytes=sizeof(decNumber)+(D2U(MAXI(p,16))-1)*sizeof(Unit);
if (needbytes>sizeof(bufa)) { // need malloc space
allocbufa=(decNumber *)malloc(needbytes);
if (allocbufa==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
a=allocbufa; // use the allocated space
}
pp=p+rhs->digits;
needbytes=sizeof(decNumber)+(D2U(MAXI(pp,16))-1)*sizeof(Unit);
if (needbytes>sizeof(bufb)) { // need malloc space
allocbufb=(decNumber *)malloc(needbytes);
if (allocbufb==NULL) { // hopeless -- abandon
*status|=DEC_Insufficient_storage;
break;}
b=allocbufb; // use the allocated space
}
// Prepare an initial estimate in acc. Calculate this by
// considering the coefficient of x to be a normalized fraction,
// f, with the decimal point at far left and multiplied by
// 10**r. Then, rhs=f*10**r and 0.1<=f<1, and
// ln(x) = ln(f) + ln(10)*r
// Get the initial estimate for ln(f) from a small lookup
// table (see above) indexed by the first two digits of f,
// truncated.
decContextDefault(&aset, DEC_INIT_DECIMAL64); // 16-digit extended
r=rhs->exponent+rhs->digits; // 'normalised' exponent
decNumberFromInt32(a, r); // a=r
decNumberFromInt32(b, 2302585); // b=ln(10) (2.302585)
b->exponent=-6; // ..
decMultiplyOp(a, a, b, &aset, &ignore); // a=a*b
// now get top two digits of rhs into b by simple truncate and
// force to integer
residue=0; // (no residue)
aset.digits=2; aset.round=DEC_ROUND_DOWN;
decCopyFit(b, rhs, &aset, &residue, &ignore); // copy & shorten
b->exponent=0; // make integer
t=decGetInt(b); // [cannot fail]
if (t<10) t=X10(t); // adjust single-digit b
t=LNnn[t-10]; // look up ln(b)
decNumberFromInt32(b, t>>2); // b=ln(b) coefficient
b->exponent=-(t&3)-3; // set exponent
b->bits=DECNEG; // ln(0.10)->ln(0.99) always -ve
aset.digits=16; aset.round=DEC_ROUND_HALF_EVEN; // restore
decAddOp(a, a, b, &aset, 0, &ignore); // acc=a+b
// the initial estimate is now in a, with up to 4 digits correct.
// When rhs is at or near Nmax the estimate will be low, so we
// will approach it from below, avoiding overflow when calling exp.
decNumberZero(&numone); *numone.lsu=1; // constant 1 for adjustment
// accumulator bounds are as requested (could underflow, but
// cannot overflow)
aset.emax=set->emax;
aset.emin=set->emin;
aset.clamp=0; // no concrete format
// set up a context to be used for the multiply and subtract
bset=aset;
bset.emax=DEC_MAX_MATH*2; // use double bounds for the
bset.emin=-DEC_MAX_MATH*2; // adjustment calculation
// [see decExpOp call below]
// for each iteration double the number of digits to calculate,
// up to a maximum of p
pp=9; // initial precision
// [initially 9 as then the sequence starts 7+2, 16+2, and
// 34+2, which is ideal for standard-sized numbers]
aset.digits=pp; // working context
bset.digits=pp+rhs->digits; // wider context
for (;;) { // iterate
#if DECCHECK
iterations++;
if (iterations>24) break; // consider 9 * 2**24
#endif
// calculate the adjustment (exp(-a)*x-1) into b. This is a
// catastrophic subtraction but it really is the difference
// from 1 that is of interest.
// Use the internal entry point to Exp as it allows the double
// range for calculating exp(-a) when a is the tiniest subnormal.
a->bits^=DECNEG; // make -a
decExpOp(b, a, &bset, &ignore); // b=exp(-a)
a->bits^=DECNEG; // restore sign of a
// now multiply by rhs and subtract 1, at the wider precision
decMultiplyOp(b, b, rhs, &bset, &ignore); // b=b*rhs
decAddOp(b, b, &numone, &bset, DECNEG, &ignore); // b=b-1
// the iteration ends when the adjustment cannot affect the
// result by >=0.5 ulp (at the requested digits), which
// is when its value is smaller than the accumulator by
// set->digits+1 digits (or it is zero) -- this is a looser
// requirement than for Exp because all that happens to the
// accumulator after this is the final rounding (but note that
// there must also be full precision in a, or a=0).
if (decNumberIsZero(b) ||
(a->digits+a->exponent)>=(b->digits+b->exponent+set->digits+1)) {
if (a->digits==p) break;
if (decNumberIsZero(a)) {
decCompareOp(&cmp, rhs, &numone, &aset, COMPARE, &ignore); // rhs=1 ?
if (cmp.lsu[0]==0) a->exponent=0; // yes, exact 0
else *status|=(DEC_Inexact | DEC_Rounded); // no, inexact
break;
}
// force padding if adjustment has gone to 0 before full length
if (decNumberIsZero(b)) b->exponent=a->exponent-p;
}
// not done yet ...
decAddOp(a, a, b, &aset, 0, &ignore); // a=a+b for next estimate
if (pp==p) continue; // precision is at maximum
// lengthen the next calculation
pp=pp*2; // double precision
if (pp>p) pp=p; // clamp to maximum
aset.digits=pp; // working context
bset.digits=pp+rhs->digits; // wider context
} // Newton's iteration
#if DECCHECK
// just a sanity check; remove the test to show always
if (iterations>24)
printf("Ln iterations=%ld, status=%08lx, p=%ld, d=%ld\n",
(LI)iterations, (LI)*status, (LI)p, (LI)rhs->digits);
#endif
// Copy and round the result to res
residue=1; // indicate dirt to right
if (ISZERO(a)) residue=0; // .. unless underflowed to 0
aset.digits=set->digits; // [use default rounding]
decCopyFit(res, a, &aset, &residue, status); // copy & shorten
decFinish(res, set, &residue, status); // cleanup/set flags
} while(0); // end protected
if (allocbufa!=NULL) free(allocbufa); // drop any storage used
if (allocbufb!=NULL) free(allocbufb); // ..
// [status is handled by caller]
return res;
} // decLnOp
/* ------------------------------------------------------------------ */
/* decQuantizeOp -- force exponent to requested value */
/* */
/* This computes C = op(A, B), where op adjusts the coefficient */
/* of C (by rounding or shifting) such that the exponent (-scale) */
/* of C has the value B or matches the exponent of B. */
/* The numerical value of C will equal A, except for the effects of */
/* any rounding that occurred. */
/* */
/* res is C, the result. C may be A or B */
/* lhs is A, the number to adjust */
/* rhs is B, the requested exponent */
/* set is the context */
/* quant is 1 for quantize or 0 for rescale */
/* status is the status accumulator (this can be called without */
/* risk of control loss) */
/* */
/* C must have space for set->digits digits. */
/* */
/* Unless there is an error or the result is infinite, the exponent */
/* after the operation is guaranteed to be that requested. */
/* ------------------------------------------------------------------ */
static decNumber * decQuantizeOp(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set,
Flag quant, uInt *status) {
#if DECSUBSET
decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
decNumber *allocrhs=NULL; // .., rhs
#endif
const decNumber *inrhs=rhs; // save original rhs
Int reqdigits=set->digits; // requested DIGITS
Int reqexp; // requested exponent [-scale]
Int residue=0; // rounding residue
Int etiny=set->emin-(reqdigits-1);
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operands and set lostDigits status, as needed
if (lhs->digits>reqdigits) {
alloclhs=decRoundOperand(lhs, set, status);
if (alloclhs==NULL) break;
lhs=alloclhs;
}
if (rhs->digits>reqdigits) { // [this only checks lostDigits]
allocrhs=decRoundOperand(rhs, set, status);
if (allocrhs==NULL) break;
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
// Handle special values
if (SPECIALARGS) {
// NaNs get usual processing
if (SPECIALARGS & (DECSNAN | DECNAN))
decNaNs(res, lhs, rhs, set, status);
// one infinity but not both is bad
else if ((lhs->bits ^ rhs->bits) & DECINF)
*status|=DEC_Invalid_operation;
// both infinity: return lhs
else decNumberCopy(res, lhs); // [nop if in place]
break;
}
// set requested exponent
if (quant) reqexp=inrhs->exponent; // quantize -- match exponents
else { // rescale -- use value of rhs
// Original rhs must be an integer that fits and is in range,
// which could be from -1999999997 to +999999999, thanks to
// subnormals
reqexp=decGetInt(inrhs); // [cannot fail]
}
#if DECSUBSET
if (!set->extended) etiny=set->emin; // no subnormals
#endif
if (reqexp==BADINT // bad (rescale only) or ..
|| reqexp==BIGODD || reqexp==BIGEVEN // very big (ditto) or ..
|| (reqexp<etiny) // < lowest
|| (reqexp>set->emax)) { // > emax
*status|=DEC_Invalid_operation;
break;}
// the RHS has been processed, so it can be overwritten now if necessary
if (ISZERO(lhs)) { // zero coefficient unchanged
decNumberCopy(res, lhs); // [nop if in place]
res->exponent=reqexp; // .. just set exponent
#if DECSUBSET
if (!set->extended) res->bits=0; // subset specification; no -0
#endif
}
else { // non-zero lhs
Int adjust=reqexp-lhs->exponent; // digit adjustment needed
// if adjusted coefficient will definitely not fit, give up now
if ((lhs->digits-adjust)>reqdigits) {
*status|=DEC_Invalid_operation;
break;
}
if (adjust>0) { // increasing exponent
// this will decrease the length of the coefficient by adjust
// digits, and must round as it does so
decContext workset; // work
workset=*set; // clone rounding, etc.
workset.digits=lhs->digits-adjust; // set requested length
// [note that the latter can be <1, here]
decCopyFit(res, lhs, &workset, &residue, status); // fit to result
decApplyRound(res, &workset, residue, status); // .. and round
residue=0; // [used]
// If just rounded a 999s case, exponent will be off by one;
// adjust back (after checking space), if so.
if (res->exponent>reqexp) {
// re-check needed, e.g., for quantize(0.9999, 0.001) under
// set->digits==3
if (res->digits==reqdigits) { // cannot shift by 1
*status&=~(DEC_Inexact | DEC_Rounded); // [clean these]
*status|=DEC_Invalid_operation;
break;
}
res->digits=decShiftToMost(res->lsu, res->digits, 1); // shift
res->exponent--; // (re)adjust the exponent.
}
#if DECSUBSET
if (ISZERO(res) && !set->extended) res->bits=0; // subset; no -0
#endif
} // increase
else /* adjust<=0 */ { // decreasing or = exponent
// this will increase the length of the coefficient by -adjust
// digits, by adding zero or more trailing zeros; this is
// already checked for fit, above
decNumberCopy(res, lhs); // [it will fit]
// if padding needed (adjust<0), add it now...
if (adjust<0) {
res->digits=decShiftToMost(res->lsu, res->digits, -adjust);
res->exponent+=adjust; // adjust the exponent
}
} // decrease
} // non-zero
// Check for overflow [do not use Finalize in this case, as an
// overflow here is a "don't fit" situation]
if (res->exponent>set->emax-res->digits+1) { // too big
*status|=DEC_Invalid_operation;
break;
}
else {
decFinalize(res, set, &residue, status); // set subnormal flags
*status&=~DEC_Underflow; // suppress Underflow [as per 754]
}
} while(0); // end protected
#if DECSUBSET
if (allocrhs!=NULL) free(allocrhs); // drop any storage used
if (alloclhs!=NULL) free(alloclhs); // ..
#endif
return res;
} // decQuantizeOp
/* ------------------------------------------------------------------ */
/* decCompareOp -- compare, min, or max two Numbers */
/* */
/* This computes C = A ? B and carries out one of four operations: */
/* COMPARE -- returns the signum (as a number) giving the */
/* result of a comparison unless one or both */
/* operands is a NaN (in which case a NaN results) */
/* COMPSIG -- as COMPARE except that a quiet NaN raises */
/* Invalid operation. */
/* COMPMAX -- returns the larger of the operands, using the */
/* 754 maxnum operation */
/* COMPMAXMAG -- ditto, comparing absolute values */
/* COMPMIN -- the 754 minnum operation */
/* COMPMINMAG -- ditto, comparing absolute values */
/* COMTOTAL -- returns the signum (as a number) giving the */
/* result of a comparison using 754 total ordering */
/* */
/* res is C, the result. C may be A and/or B (e.g., X=X?X) */
/* lhs is A */
/* rhs is B */
/* set is the context */
/* op is the operation flag */
/* status is the usual accumulator */
/* */
/* C must have space for one digit for COMPARE or set->digits for */
/* COMPMAX, COMPMIN, COMPMAXMAG, or COMPMINMAG. */
/* ------------------------------------------------------------------ */
/* The emphasis here is on speed for common cases, and avoiding */
/* coefficient comparison if possible. */
/* ------------------------------------------------------------------ */
decNumber * decCompareOp(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set,
Flag op, uInt *status) {
#if DECSUBSET
decNumber *alloclhs=NULL; // non-NULL if rounded lhs allocated
decNumber *allocrhs=NULL; // .., rhs
#endif
Int result=0; // default result value
uByte merged; // work
#if DECCHECK
if (decCheckOperands(res, lhs, rhs, set)) return res;
#endif
do { // protect allocated storage
#if DECSUBSET
if (!set->extended) {
// reduce operands and set lostDigits status, as needed
if (lhs->digits>set->digits) {
alloclhs=decRoundOperand(lhs, set, status);
if (alloclhs==NULL) {result=BADINT; break;}
lhs=alloclhs;
}
if (rhs->digits>set->digits) {
allocrhs=decRoundOperand(rhs, set, status);
if (allocrhs==NULL) {result=BADINT; break;}
rhs=allocrhs;
}
}
#endif
// [following code does not require input rounding]
// If total ordering then handle differing signs 'up front'
if (op==COMPTOTAL) { // total ordering
if (decNumberIsNegative(lhs) & !decNumberIsNegative(rhs)) {
result=-1;
break;
}
if (!decNumberIsNegative(lhs) & decNumberIsNegative(rhs)) {
result=+1;
break;
}
}
// handle NaNs specially; let infinities drop through
// This assumes sNaN (even just one) leads to NaN.
merged=(lhs->bits | rhs->bits) & (DECSNAN | DECNAN);
if (merged) { // a NaN bit set
if (op==COMPARE); // result will be NaN
else if (op==COMPSIG) // treat qNaN as sNaN
*status|=DEC_Invalid_operation | DEC_sNaN;
else if (op==COMPTOTAL) { // total ordering, always finite
// signs are known to be the same; compute the ordering here
// as if the signs are both positive, then invert for negatives
if (!decNumberIsNaN(lhs)) result=-1;
else if (!decNumberIsNaN(rhs)) result=+1;
// here if both NaNs
else if (decNumberIsSNaN(lhs) && decNumberIsQNaN(rhs)) result=-1;
else if (decNumberIsQNaN(lhs) && decNumberIsSNaN(rhs)) result=+1;
else { // both NaN or both sNaN
// now it just depends on the payload
result=decUnitCompare(lhs->lsu, D2U(lhs->digits),
rhs->lsu, D2U(rhs->digits), 0);
// [Error not possible, as these are 'aligned']
} // both same NaNs
if (decNumberIsNegative(lhs)) result=-result;
break;
} // total order
else if (merged & DECSNAN); // sNaN -> qNaN
else { // here if MIN or MAX and one or two quiet NaNs
// min or max -- 754 rules ignore single NaN
if (!decNumberIsNaN(lhs) || !decNumberIsNaN(rhs)) {
// just one NaN; force choice to be the non-NaN operand
op=COMPMAX;
if (lhs->bits & DECNAN) result=-1; // pick rhs
else result=+1; // pick lhs
break;
}
} // max or min
op=COMPNAN; // use special path
decNaNs(res, lhs, rhs, set, status); // propagate NaN
break;
}
// have numbers
if (op==COMPMAXMAG || op==COMPMINMAG) result=decCompare(lhs, rhs, 1);
else result=decCompare(lhs, rhs, 0); // sign matters
} while(0); // end protected
if (result==BADINT) *status|=DEC_Insufficient_storage; // rare
else {
if (op==COMPARE || op==COMPSIG ||op==COMPTOTAL) { // returning signum
if (op==COMPTOTAL && result==0) {
// operands are numerically equal or same NaN (and same sign,
// tested first); if identical, leave result 0
if (lhs->exponent!=rhs->exponent) {
if (lhs->exponent<rhs->exponent) result=-1;
else result=+1;
if (decNumberIsNegative(lhs)) result=-result;
} // lexp!=rexp
} // total-order by exponent
decNumberZero(res); // [always a valid result]
if (result!=0) { // must be -1 or +1
*res->lsu=1;
if (result<0) res->bits=DECNEG;
}
}
else if (op==COMPNAN); // special, drop through
else { // MAX or MIN, non-NaN result
Int residue=0; // rounding accumulator
// choose the operand for the result
const decNumber *choice;
if (result==0) { // operands are numerically equal
// choose according to sign then exponent (see 754)
uByte slhs=(lhs->bits & DECNEG);
uByte srhs=(rhs->bits & DECNEG);
#if DECSUBSET
if (!set->extended) { // subset: force left-hand
op=COMPMAX;
result=+1;
}
else
#endif
if (slhs!=srhs) { // signs differ
if (slhs) result=-1; // rhs is max
else result=+1; // lhs is max
}
else if (slhs && srhs) { // both negative
if (lhs->exponent<rhs->exponent) result=+1;
else result=-1;
// [if equal, use lhs, technically identical]
}
else { // both positive
if (lhs->exponent>rhs->exponent) result=+1;
else result=-1;
// [ditto]
}
} // numerically equal
// here result will be non-0; reverse if looking for MIN
if (op==COMPMIN || op==COMPMINMAG) result=-result;
choice=(result>0 ? lhs : rhs); // choose
// copy chosen to result, rounding if need be
decCopyFit(res, choice, set, &residue, status);
decFinish(res, set, &residue, status);
}
}
#if DECSUBSET
if (allocrhs!=NULL) free(allocrhs); // free any storage used
if (alloclhs!=NULL) free(alloclhs); // ..
#endif
return res;
} // decCompareOp
/* ------------------------------------------------------------------ */
/* decCompare -- compare two decNumbers by numerical value */
/* */
/* This routine compares A ? B without altering them. */
/* */
/* Arg1 is A, a decNumber which is not a NaN */
/* Arg2 is B, a decNumber which is not a NaN */
/* Arg3 is 1 for a sign-independent compare, 0 otherwise */
/* */
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
/* (the only possible failure is an allocation error) */
/* ------------------------------------------------------------------ */
static Int decCompare(const decNumber *lhs, const decNumber *rhs,
Flag abs) {
Int result; // result value
Int sigr; // rhs signum
Int compare; // work
result=1; // assume signum(lhs)
if (ISZERO(lhs)) result=0;
if (abs) {
if (ISZERO(rhs)) return result; // LHS wins or both 0
// RHS is non-zero
if (result==0) return -1; // LHS is 0; RHS wins
// [here, both non-zero, result=1]
}
else { // signs matter
if (result && decNumberIsNegative(lhs)) result=-1;
sigr=1; // compute signum(rhs)
if (ISZERO(rhs)) sigr=0;
else if (decNumberIsNegative(rhs)) sigr=-1;
if (result > sigr) return +1; // L > R, return 1
if (result < sigr) return -1; // L < R, return -1
if (result==0) return 0; // both 0
}
// signums are the same; both are non-zero
if ((lhs->bits | rhs->bits) & DECINF) { // one or more infinities
if (decNumberIsInfinite(rhs)) {
if (decNumberIsInfinite(lhs)) result=0;// both infinite
else result=-result; // only rhs infinite
}
return result;
}
// must compare the coefficients, allowing for exponents
if (lhs->exponent>rhs->exponent) { // LHS exponent larger
// swap sides, and sign
const decNumber *temp=lhs;
lhs=rhs;
rhs=temp;
result=-result;
}
compare=decUnitCompare(lhs->lsu, D2U(lhs->digits),
rhs->lsu, D2U(rhs->digits),
rhs->exponent-lhs->exponent);
if (compare!=BADINT) compare*=result; // comparison succeeded
return compare;
} // decCompare
/* ------------------------------------------------------------------ */
/* decUnitCompare -- compare two >=0 integers in Unit arrays */
/* */
/* This routine compares A ? B*10**E where A and B are unit arrays */
/* A is a plain integer */
/* B has an exponent of E (which must be non-negative) */
/* */
/* Arg1 is A first Unit (lsu) */
/* Arg2 is A length in Units */
/* Arg3 is B first Unit (lsu) */
/* Arg4 is B length in Units */
/* Arg5 is E (0 if the units are aligned) */
/* */
/* returns -1, 0, or 1 for A<B, A==B, or A>B, or BADINT if failure */
/* (the only possible failure is an allocation error, which can */
/* only occur if E!=0) */
/* ------------------------------------------------------------------ */
static Int decUnitCompare(const Unit *a, Int alength,
const Unit *b, Int blength, Int exp) {
Unit *acc; // accumulator for result
Unit accbuff[SD2U(DECBUFFER*2+1)]; // local buffer
Unit *allocacc=NULL; // -> allocated acc buffer, iff allocated
Int accunits, need; // units in use or needed for acc
const Unit *l, *r, *u; // work
Int expunits, exprem, result; // ..
if (exp==0) { // aligned; fastpath
if (alength>blength) return 1;
if (alength<blength) return -1;
// same number of units in both -- need unit-by-unit compare
l=a+alength-1;
r=b+alength-1;
for (;l>=a; l--, r--) {
if (*l>*r) return 1;
if (*l<*r) return -1;
}
return 0; // all units match
} // aligned
// Unaligned. If one is >1 unit longer than the other, padded
// approximately, then can return easily
if (alength>blength+(Int)D2U(exp)) return 1;
if (alength+1<blength+(Int)D2U(exp)) return -1;
// Need to do a real subtract. For this, a result buffer is needed
// even though only the sign is of interest. Its length needs
// to be the larger of alength and padded blength, +2
need=blength+D2U(exp); // maximum real length of B
if (need<alength) need=alength;
need+=2;
acc=accbuff; // assume use local buffer
if (need*sizeof(Unit)>sizeof(accbuff)) {
allocacc=(Unit *)malloc(need*sizeof(Unit));
if (allocacc==NULL) return BADINT; // hopeless -- abandon
acc=allocacc;
}
// Calculate units and remainder from exponent.
expunits=exp/DECDPUN;
exprem=exp%DECDPUN;
// subtract [A+B*(-m)]
accunits=decUnitAddSub(a, alength, b, blength, expunits, acc,
-(Int)powers[exprem]);
// [UnitAddSub result may have leading zeros, even on zero]
if (accunits<0) result=-1; // negative result
else { // non-negative result
// check units of the result before freeing any storage
for (u=acc; u<acc+accunits-1 && *u==0;) u++;
result=(*u==0 ? 0 : +1);
}
// clean up and return the result
if (allocacc!=NULL) free(allocacc); // drop any storage used
return result;
} // decUnitCompare
/* ------------------------------------------------------------------ */
/* decUnitAddSub -- add or subtract two >=0 integers in Unit arrays */
/* */
/* This routine performs the calculation: */
/* */
/* C=A+(B*M) */
/* */
/* Where M is in the range -DECDPUNMAX through +DECDPUNMAX. */
/* */
/* A may be shorter or longer than B. */
/* */
/* Leading zeros are not removed after a calculation. The result is */
/* either the same length as the longer of A and B (adding any */
/* shift), or one Unit longer than that (if a Unit carry occurred). */
/* */
/* A and B content are not altered unless C is also A or B. */
/* C may be the same array as A or B, but only if no zero padding is */
/* requested (that is, C may be B only if bshift==0). */
/* C is filled from the lsu; only those units necessary to complete */
/* the calculation are referenced. */
/* */
/* Arg1 is A first Unit (lsu) */
/* Arg2 is A length in Units */
/* Arg3 is B first Unit (lsu) */
/* Arg4 is B length in Units */
/* Arg5 is B shift in Units (>=0; pads with 0 units if positive) */
/* Arg6 is C first Unit (lsu) */
/* Arg7 is M, the multiplier */
/* */
/* returns the count of Units written to C, which will be non-zero */
/* and negated if the result is negative. That is, the sign of the */
/* returned Int is the sign of the result (positive for zero) and */
/* the absolute value of the Int is the count of Units. */
/* */
/* It is the caller's responsibility to make sure that C size is */
/* safe, allowing space if necessary for a one-Unit carry. */
/* */
/* This routine is severely performance-critical; *any* change here */
/* must be measured (timed) to assure no performance degradation. */
/* In particular, trickery here tends to be counter-productive, as */
/* increased complexity of code hurts register optimizations on */
/* register-poor architectures. Avoiding divisions is nearly */
/* always a Good Idea, however. */
/* */
/* Special thanks to Rick McGuire (IBM Cambridge, MA) and Dave Clark */
/* (IBM Warwick, UK) for some of the ideas used in this routine. */
/* ------------------------------------------------------------------ */
static Int decUnitAddSub(const Unit *a, Int alength,
const Unit *b, Int blength, Int bshift,
Unit *c, Int m) {
const Unit *alsu=a; // A lsu [need to remember it]
Unit *clsu=c; // C ditto
Unit *minC; // low water mark for C
Unit *maxC; // high water mark for C
eInt carry=0; // carry integer (could be Long)
Int add; // work
#if DECDPUN<=4 // myriadal, millenary, etc.
Int est; // estimated quotient
#endif
#if DECTRACE
if (alength<1 || blength<1)
printf("decUnitAddSub: alen blen m %ld %ld [%ld]\n", alength, blength, m);
#endif
maxC=c+alength; // A is usually the longer
minC=c+blength; // .. and B the shorter
if (bshift!=0) { // B is shifted; low As copy across
minC+=bshift;
// if in place [common], skip copy unless there's a gap [rare]
if (a==c && bshift<=alength) {
c+=bshift;
a+=bshift;
}
else for (; c<clsu+bshift; a++, c++) { // copy needed
if (a<alsu+alength) *c=*a;
else *c=0;
}
}
if (minC>maxC) { // swap
Unit *hold=minC;
minC=maxC;
maxC=hold;
}
// For speed, do the addition as two loops; the first where both A
// and B contribute, and the second (if necessary) where only one or
// other of the numbers contribute.
// Carry handling is the same (i.e., duplicated) in each case.
for (; c<minC; c++) {
carry+=*a;
a++;
carry+=((eInt)*b)*m; // [special-casing m=1/-1
b++; // here is not a win]
// here carry is new Unit of digits; it could be +ve or -ve
if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX
*c=(Unit)carry;
carry=0;
continue;
}
#if DECDPUN==4 // use divide-by-multiply
if (carry>=0) {
est=(((ueInt)carry>>11)*53687)>>18;
*c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
carry=est; // likely quotient [89%]
if (*c<DECDPUNMAX+1) continue; // estimate was correct
carry++;
*c-=DECDPUNMAX+1;
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
est=(((ueInt)carry>>11)*53687)>>18;
*c=(Unit)(carry-est*(DECDPUNMAX+1));
carry=est-(DECDPUNMAX+1); // correctly negative
if (*c<DECDPUNMAX+1) continue; // was OK
carry++;
*c-=DECDPUNMAX+1;
#elif DECDPUN==3
if (carry>=0) {
est=(((ueInt)carry>>3)*16777)>>21;
*c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
carry=est; // likely quotient [99%]
if (*c<DECDPUNMAX+1) continue; // estimate was correct
carry++;
*c-=DECDPUNMAX+1;
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
est=(((ueInt)carry>>3)*16777)>>21;
*c=(Unit)(carry-est*(DECDPUNMAX+1));
carry=est-(DECDPUNMAX+1); // correctly negative
if (*c<DECDPUNMAX+1) continue; // was OK
carry++;
*c-=DECDPUNMAX+1;
#elif DECDPUN<=2
// Can use QUOT10 as carry <= 4 digits
if (carry>=0) {
est=QUOT10(carry, DECDPUN);
*c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
carry=est; // quotient
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
est=QUOT10(carry, DECDPUN);
*c=(Unit)(carry-est*(DECDPUNMAX+1));
carry=est-(DECDPUNMAX+1); // correctly negative
#else
// remainder operator is undefined if negative, so must test
if ((ueInt)carry<(DECDPUNMAX+1)*2) { // fastpath carry +1
*c=(Unit)(carry-(DECDPUNMAX+1)); // [helps additions]
carry=1;
continue;
}
if (carry>=0) {
*c=(Unit)(carry%(DECDPUNMAX+1));
carry=carry/(DECDPUNMAX+1);
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
*c=(Unit)(carry%(DECDPUNMAX+1));
carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
#endif
} // c
// now may have one or other to complete
// [pretest to avoid loop setup/shutdown]
if (c<maxC) for (; c<maxC; c++) {
if (a<alsu+alength) { // still in A
carry+=*a;
a++;
}
else { // inside B
carry+=((eInt)*b)*m;
b++;
}
// here carry is new Unit of digits; it could be +ve or -ve and
// magnitude up to DECDPUNMAX squared
if ((ueInt)carry<=DECDPUNMAX) { // fastpath 0-DECDPUNMAX
*c=(Unit)carry;
carry=0;
continue;
}
// result for this unit is negative or >DECDPUNMAX
#if DECDPUN==4 // use divide-by-multiply
if (carry>=0) {
est=(((ueInt)carry>>11)*53687)>>18;
*c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
carry=est; // likely quotient [79.7%]
if (*c<DECDPUNMAX+1) continue; // estimate was correct
carry++;
*c-=DECDPUNMAX+1;
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
est=(((ueInt)carry>>11)*53687)>>18;
*c=(Unit)(carry-est*(DECDPUNMAX+1));
carry=est-(DECDPUNMAX+1); // correctly negative
if (*c<DECDPUNMAX+1) continue; // was OK
carry++;
*c-=DECDPUNMAX+1;
#elif DECDPUN==3
if (carry>=0) {
est=(((ueInt)carry>>3)*16777)>>21;
*c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
carry=est; // likely quotient [99%]
if (*c<DECDPUNMAX+1) continue; // estimate was correct
carry++;
*c-=DECDPUNMAX+1;
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
est=(((ueInt)carry>>3)*16777)>>21;
*c=(Unit)(carry-est*(DECDPUNMAX+1));
carry=est-(DECDPUNMAX+1); // correctly negative
if (*c<DECDPUNMAX+1) continue; // was OK
carry++;
*c-=DECDPUNMAX+1;
#elif DECDPUN<=2
if (carry>=0) {
est=QUOT10(carry, DECDPUN);
*c=(Unit)(carry-est*(DECDPUNMAX+1)); // remainder
carry=est; // quotient
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
est=QUOT10(carry, DECDPUN);
*c=(Unit)(carry-est*(DECDPUNMAX+1));
carry=est-(DECDPUNMAX+1); // correctly negative
#else
if ((ueInt)carry<(DECDPUNMAX+1)*2){ // fastpath carry 1
*c=(Unit)(carry-(DECDPUNMAX+1));
carry=1;
continue;
}
// remainder operator is undefined if negative, so must test
if (carry>=0) {
*c=(Unit)(carry%(DECDPUNMAX+1));
carry=carry/(DECDPUNMAX+1);
continue;
}
// negative case
carry=carry+(eInt)(DECDPUNMAX+1)*(DECDPUNMAX+1); // make positive
*c=(Unit)(carry%(DECDPUNMAX+1));
carry=carry/(DECDPUNMAX+1)-(DECDPUNMAX+1);
#endif
} // c
// OK, all A and B processed; might still have carry or borrow
// return number of Units in the result, negated if a borrow
if (carry==0) return c-clsu; // no carry, so no more to do
if (carry>0) { // positive carry
*c=(Unit)carry; // place as new unit
c++; // ..
return c-clsu;
}
// -ve carry: it's a borrow; complement needed
add=1; // temporary carry...
for (c=clsu; c<maxC; c++) {
add=DECDPUNMAX+add-*c;
if (add<=DECDPUNMAX) {
*c=(Unit)add;
add=0;
}
else {
*c=0;
add=1;
}
}
// add an extra unit iff it would be non-zero
#if DECTRACE
printf("UAS borrow: add %ld, carry %ld\n", add, carry);
#endif
if ((add-carry-1)!=0) {
*c=(Unit)(add-carry-1);
c++; // interesting, include it
}
return clsu-c; // -ve result indicates borrowed
} // decUnitAddSub
/* ------------------------------------------------------------------ */
/* decTrim -- trim trailing zeros or normalize */
/* */
/* dn is the number to trim or normalize */
/* set is the context to use to check for clamp */
/* all is 1 to remove all trailing zeros, 0 for just fraction ones */
/* noclamp is 1 to unconditional (unclamped) trim */
/* dropped returns the number of discarded trailing zeros */
/* returns dn */
/* */
/* If clamp is set in the context then the number of zeros trimmed */
/* may be limited if the exponent is high. */
/* All fields are updated as required. This is a utility operation, */
/* so special values are unchanged and no error is possible. */
/* ------------------------------------------------------------------ */
static decNumber * decTrim(decNumber *dn, decContext *set, Flag all,
Flag noclamp, Int *dropped) {
Int d, exp; // work
uInt cut; // ..
Unit *up; // -> current Unit
#if DECCHECK
if (decCheckOperands(dn, DECUNUSED, DECUNUSED, DECUNCONT)) return dn;
#endif
*dropped=0; // assume no zeros dropped
if ((dn->bits & DECSPECIAL) // fast exit if special ..
|| (*dn->lsu & 0x01)) return dn; // .. or odd
if (ISZERO(dn)) { // .. or 0
dn->exponent=0; // (sign is preserved)
return dn;
}
// have a finite number which is even
exp=dn->exponent;
cut=1; // digit (1-DECDPUN) in Unit
up=dn->lsu; // -> current Unit
for (d=0; d<dn->digits-1; d++) { // [don't strip the final digit]
// slice by powers
#if DECDPUN<=4
uInt quot=QUOT10(*up, cut);
if ((*up-quot*powers[cut])!=0) break; // found non-0 digit
#else
if (*up%powers[cut]!=0) break; // found non-0 digit
#endif
// have a trailing 0
if (!all) { // trimming
// [if exp>0 then all trailing 0s are significant for trim]
if (exp<=0) { // if digit might be significant
if (exp==0) break; // then quit
exp++; // next digit might be significant
}
}
cut++; // next power
if (cut>DECDPUN) { // need new Unit
up++;
cut=1;
}
} // d
if (d==0) return dn; // none to drop
// may need to limit drop if clamping
if (set->clamp && !noclamp) {
Int maxd=set->emax-set->digits+1-dn->exponent;
if (maxd<=0) return dn; // nothing possible
if (d>maxd) d=maxd;
}
// effect the drop
decShiftToLeast(dn->lsu, D2U(dn->digits), d);
dn->exponent+=d; // maintain numerical value
dn->digits-=d; // new length
*dropped=d; // report the count
return dn;
} // decTrim
/* ------------------------------------------------------------------ */
/* decReverse -- reverse a Unit array in place */
/* */
/* ulo is the start of the array */
/* uhi is the end of the array (highest Unit to include) */
/* */
/* The units ulo through uhi are reversed in place (if the number */
/* of units is odd, the middle one is untouched). Note that the */
/* digit(s) in each unit are unaffected. */
/* ------------------------------------------------------------------ */
static void decReverse(Unit *ulo, Unit *uhi) {
Unit temp;
for (; ulo<uhi; ulo++, uhi--) {
temp=*ulo;
*ulo=*uhi;
*uhi=temp;
}
return;
} // decReverse
/* ------------------------------------------------------------------ */
/* decShiftToMost -- shift digits in array towards most significant */
/* */
/* uar is the array */
/* digits is the count of digits in use in the array */
/* shift is the number of zeros to pad with (least significant); */
/* it must be zero or positive */
/* */
/* returns the new length of the integer in the array, in digits */
/* */
/* No overflow is permitted (that is, the uar array must be known to */
/* be large enough to hold the result, after shifting). */
/* ------------------------------------------------------------------ */
static Int decShiftToMost(Unit *uar, Int digits, Int shift) {
Unit *target, *source, *first; // work
Int cut; // odd 0's to add
uInt next; // work
if (shift==0) return digits; // [fastpath] nothing to do
if ((digits+shift)<=DECDPUN) { // [fastpath] single-unit case
*uar=(Unit)(*uar*powers[shift]);
return digits+shift;
}
next=0; // all paths
source=uar+D2U(digits)-1; // where msu comes from
target=source+D2U(shift); // where upper part of first cut goes
cut=DECDPUN-MSUDIGITS(shift); // where to slice
if (cut==0) { // unit-boundary case
for (; source>=uar; source--, target--) *target=*source;
}
else {
first=uar+D2U(digits+shift)-1; // where msu of source will end up
for (; source>=uar; source--, target--) {
// split the source Unit and accumulate remainder for next
#if DECDPUN<=4
uInt quot=QUOT10(*source, cut);
uInt rem=*source-quot*powers[cut];
next+=quot;
#else
uInt rem=*source%powers[cut];
next+=*source/powers[cut];
#endif
if (target<=first) *target=(Unit)next; // write to target iff valid
next=rem*powers[DECDPUN-cut]; // save remainder for next Unit
}
} // shift-move
// propagate any partial unit to one below and clear the rest
for (; target>=uar; target--) {
*target=(Unit)next;
next=0;
}
return digits+shift;
} // decShiftToMost
/* ------------------------------------------------------------------ */
/* decShiftToLeast -- shift digits in array towards least significant */
/* */
/* uar is the array */
/* units is length of the array, in units */
/* shift is the number of digits to remove from the lsu end; it */
/* must be zero or positive and <= than units*DECDPUN. */
/* */
/* returns the new length of the integer in the array, in units */
/* */
/* Removed digits are discarded (lost). Units not required to hold */
/* the final result are unchanged. */
/* ------------------------------------------------------------------ */
static Int decShiftToLeast(Unit *uar, Int units, Int shift) {
Unit *target, *up; // work
Int cut, count; // work
Int quot, rem; // for division
if (shift==0) return units; // [fastpath] nothing to do
if (shift==units*DECDPUN) { // [fastpath] little to do
*uar=0; // all digits cleared gives zero
return 1; // leaves just the one
}
target=uar; // both paths
cut=MSUDIGITS(shift);
if (cut==DECDPUN) { // unit-boundary case; easy
up=uar+D2U(shift);
for (; up<uar+units; target++, up++) *target=*up;
return target-uar;
}
// messier
up=uar+D2U(shift-cut); // source; correct to whole Units
count=units*DECDPUN-shift; // the maximum new length
#if DECDPUN<=4
quot=QUOT10(*up, cut);
#else
quot=*up/powers[cut];
#endif
for (; ; target++) {
*target=(Unit)quot;
count-=(DECDPUN-cut);
if (count<=0) break;
up++;
quot=*up;
#if DECDPUN<=4
quot=QUOT10(quot, cut);
rem=*up-quot*powers[cut];
#else
rem=quot%powers[cut];
quot=quot/powers[cut];
#endif
*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
count-=cut;
if (count<=0) break;
}
return target-uar+1;
} // decShiftToLeast
#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decRoundOperand -- round an operand [used for subset only] */
/* */
/* dn is the number to round (dn->digits is > set->digits) */
/* set is the relevant context */
/* status is the status accumulator */
/* */
/* returns an allocated decNumber with the rounded result. */
/* */
/* lostDigits and other status may be set by this. */
/* */
/* Since the input is an operand, it must not be modified. */
/* Instead, return an allocated decNumber, rounded as required. */
/* It is the caller's responsibility to free the allocated storage. */
/* */
/* If no storage is available then the result cannot be used, so NULL */
/* is returned. */
/* ------------------------------------------------------------------ */
static decNumber *decRoundOperand(const decNumber *dn, decContext *set,
uInt *status) {
decNumber *res; // result structure
uInt newstatus=0; // status from round
Int residue=0; // rounding accumulator
// Allocate storage for the returned decNumber, big enough for the
// length specified by the context
res=(decNumber *)malloc(sizeof(decNumber)
+(D2U(set->digits)-1)*sizeof(Unit));
if (res==NULL) {
*status|=DEC_Insufficient_storage;
return NULL;
}
decCopyFit(res, dn, set, &residue, &newstatus);
decApplyRound(res, set, residue, &newstatus);
// If that set Inexact then "lost digits" is raised...
if (newstatus & DEC_Inexact) newstatus|=DEC_Lost_digits;
*status|=newstatus;
return res;
} // decRoundOperand
#endif
/* ------------------------------------------------------------------ */
/* decCopyFit -- copy a number, truncating the coefficient if needed */
/* */
/* dest is the target decNumber */
/* src is the source decNumber */
/* set is the context [used for length (digits) and rounding mode] */
/* residue is the residue accumulator */
/* status contains the current status to be updated */
/* */
/* (dest==src is allowed and will be a no-op if fits) */
/* All fields are updated as required. */
/* ------------------------------------------------------------------ */
static void decCopyFit(decNumber *dest, const decNumber *src,
decContext *set, Int *residue, uInt *status) {
dest->bits=src->bits;
dest->exponent=src->exponent;
decSetCoeff(dest, set, src->lsu, src->digits, residue, status);
} // decCopyFit
/* ------------------------------------------------------------------ */
/* decSetCoeff -- set the coefficient of a number */
/* */
/* dn is the number whose coefficient array is to be set. */
/* It must have space for set->digits digits */
/* set is the context [for size] */
/* lsu -> lsu of the source coefficient [may be dn->lsu] */
/* len is digits in the source coefficient [may be dn->digits] */
/* residue is the residue accumulator. This has values as in */
/* decApplyRound, and will be unchanged unless the */
/* target size is less than len. In this case, the */
/* coefficient is truncated and the residue is updated to */
/* reflect the previous residue and the dropped digits. */
/* status is the status accumulator, as usual */
/* */
/* The coefficient may already be in the number, or it can be an */
/* external intermediate array. If it is in the number, lsu must == */
/* dn->lsu and len must == dn->digits. */
/* */
/* Note that the coefficient length (len) may be < set->digits, and */
/* in this case this merely copies the coefficient (or is a no-op */
/* if dn->lsu==lsu). */
/* */
/* Note also that (only internally, from decQuantizeOp and */
/* decSetSubnormal) the value of set->digits may be less than one, */
/* indicating a round to left. This routine handles that case */
/* correctly; caller ensures space. */
/* */
/* dn->digits, dn->lsu (and as required), and dn->exponent are */
/* updated as necessary. dn->bits (sign) is unchanged. */
/* */
/* DEC_Rounded status is set if any digits are discarded. */
/* DEC_Inexact status is set if any non-zero digits are discarded, or */
/* incoming residue was non-0 (implies rounded) */
/* ------------------------------------------------------------------ */
// mapping array: maps 0-9 to canonical residues, so that a residue
// can be adjusted in the range [-1, +1] and achieve correct rounding
// 0 1 2 3 4 5 6 7 8 9
static const uByte resmap[10]={0, 3, 3, 3, 3, 5, 7, 7, 7, 7};
static void decSetCoeff(decNumber *dn, decContext *set, const Unit *lsu,
Int len, Int *residue, uInt *status) {
Int discard; // number of digits to discard
uInt cut; // cut point in Unit
const Unit *up; // work
Unit *target; // ..
Int count; // ..
#if DECDPUN<=4
uInt temp; // ..
#endif
discard=len-set->digits; // digits to discard
if (discard<=0) { // no digits are being discarded
if (dn->lsu!=lsu) { // copy needed
// copy the coefficient array to the result number; no shift needed
count=len; // avoids D2U
up=lsu;
for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
*target=*up;
dn->digits=len; // set the new length
}
// dn->exponent and residue are unchanged, record any inexactitude
if (*residue!=0) *status|=(DEC_Inexact | DEC_Rounded);
return;
}
// some digits must be discarded ...
dn->exponent+=discard; // maintain numerical value
*status|=DEC_Rounded; // accumulate Rounded status
if (*residue>1) *residue=1; // previous residue now to right, so reduce
if (discard>len) { // everything, +1, is being discarded
// guard digit is 0
// residue is all the number [NB could be all 0s]
if (*residue<=0) { // not already positive
count=len; // avoids D2U
for (up=lsu; count>0; up++, count-=DECDPUN) if (*up!=0) { // found non-0
*residue=1;
break; // no need to check any others
}
}
if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
*dn->lsu=0; // coefficient will now be 0
dn->digits=1; // ..
return;
} // total discard
// partial discard [most common case]
// here, at least the first (most significant) discarded digit exists
// spin up the number, noting residue during the spin, until get to
// the Unit with the first discarded digit. When reach it, extract
// it and remember its position
count=0;
for (up=lsu;; up++) {
count+=DECDPUN;
if (count>=discard) break; // full ones all checked
if (*up!=0) *residue=1;
} // up
// here up -> Unit with first discarded digit
cut=discard-(count-DECDPUN)-1;
if (cut==DECDPUN-1) { // unit-boundary case (fast)
Unit half=(Unit)powers[DECDPUN]>>1;
// set residue directly
if (*up>=half) {
if (*up>half) *residue=7;
else *residue+=5; // add sticky bit
}
else { // <half
if (*up!=0) *residue=3; // [else is 0, leave as sticky bit]
}
if (set->digits<=0) { // special for Quantize/Subnormal :-(
*dn->lsu=0; // .. result is 0
dn->digits=1; // ..
}
else { // shift to least
count=set->digits; // now digits to end up with
dn->digits=count; // set the new length
up++; // move to next
// on unit boundary, so shift-down copy loop is simple
for (target=dn->lsu; count>0; target++, up++, count-=DECDPUN)
*target=*up;
}
} // unit-boundary case
else { // discard digit is in low digit(s), and not top digit
uInt discard1; // first discarded digit
uInt quot, rem; // for divisions
if (cut==0) quot=*up; // is at bottom of unit
else /* cut>0 */ { // it's not at bottom of unit
#if DECDPUN<=4
quot=QUOT10(*up, cut);
rem=*up-quot*powers[cut];
#else
rem=*up%powers[cut];
quot=*up/powers[cut];
#endif
if (rem!=0) *residue=1;
}
// discard digit is now at bottom of quot
#if DECDPUN<=4
temp=(quot*6554)>>16; // fast /10
// Vowels algorithm here not a win (9 instructions)
discard1=quot-X10(temp);
quot=temp;
#else
discard1=quot%10;
quot=quot/10;
#endif
// here, discard1 is the guard digit, and residue is everything
// else [use mapping array to accumulate residue safely]
*residue+=resmap[discard1];
cut++; // update cut
// here: up -> Unit of the array with bottom digit
// cut is the division point for each Unit
// quot holds the uncut high-order digits for the current unit
if (set->digits<=0) { // special for Quantize/Subnormal :-(
*dn->lsu=0; // .. result is 0
dn->digits=1; // ..
}
else { // shift to least needed
count=set->digits; // now digits to end up with
dn->digits=count; // set the new length
// shift-copy the coefficient array to the result number
for (target=dn->lsu; ; target++) {
*target=(Unit)quot;
count-=(DECDPUN-cut);
if (count<=0) break;
up++;
quot=*up;
#if DECDPUN<=4
quot=QUOT10(quot, cut);
rem=*up-quot*powers[cut];
#else
rem=quot%powers[cut];
quot=quot/powers[cut];
#endif
*target=(Unit)(*target+rem*powers[DECDPUN-cut]);
count-=cut;
if (count<=0) break;
} // shift-copy loop
} // shift to least
} // not unit boundary
if (*residue!=0) *status|=DEC_Inexact; // record inexactitude
return;
} // decSetCoeff
/* ------------------------------------------------------------------ */
/* decApplyRound -- apply pending rounding to a number */
/* */
/* dn is the number, with space for set->digits digits */
/* set is the context [for size and rounding mode] */
/* residue indicates pending rounding, being any accumulated */
/* guard and sticky information. It may be: */
/* 6-9: rounding digit is >5 */
/* 5: rounding digit is exactly half-way */
/* 1-4: rounding digit is <5 and >0 */
/* 0: the coefficient is exact */
/* -1: as 1, but the hidden digits are subtractive, that */
/* is, of the opposite sign to dn. In this case the */
/* coefficient must be non-0. This case occurs when */
/* subtracting a small number (which can be reduced to */
/* a sticky bit); see decAddOp. */
/* status is the status accumulator, as usual */
/* */
/* This routine applies rounding while keeping the length of the */
/* coefficient constant. The exponent and status are unchanged */
/* except if: */
/* */
/* -- the coefficient was increased and is all nines (in which */
/* case Overflow could occur, and is handled directly here so */
/* the caller does not need to re-test for overflow) */
/* */
/* -- the coefficient was decreased and becomes all nines (in which */
/* case Underflow could occur, and is also handled directly). */
/* */
/* All fields in dn are updated as required. */
/* */
/* ------------------------------------------------------------------ */
static void decApplyRound(decNumber *dn, decContext *set, Int residue,
uInt *status) {
Int bump; // 1 if coefficient needs to be incremented
// -1 if coefficient needs to be decremented
if (residue==0) return; // nothing to apply
bump=0; // assume a smooth ride
// now decide whether, and how, to round, depending on mode
switch (set->round) {
case DEC_ROUND_05UP: { // round zero or five up (for reround)
// This is the same as DEC_ROUND_DOWN unless there is a
// positive residue and the lsd of dn is 0 or 5, in which case
// it is bumped; when residue is <0, the number is therefore
// bumped down unless the final digit was 1 or 6 (in which
// case it is bumped down and then up -- a no-op)
Int lsd5=*dn->lsu%5; // get lsd and quintate
if (residue<0 && lsd5!=1) bump=-1;
else if (residue>0 && lsd5==0) bump=1;
// [bump==1 could be applied directly; use common path for clarity]
break;} // r-05
case DEC_ROUND_DOWN: {
// no change, except if negative residue
if (residue<0) bump=-1;
break;} // r-d
case DEC_ROUND_HALF_DOWN: {
if (residue>5) bump=1;
break;} // r-h-d
case DEC_ROUND_HALF_EVEN: {
if (residue>5) bump=1; // >0.5 goes up
else if (residue==5) { // exactly 0.5000...
// 0.5 goes up iff [new] lsd is odd
if (*dn->lsu & 0x01) bump=1;
}
break;} // r-h-e
case DEC_ROUND_HALF_UP: {
if (residue>=5) bump=1;
break;} // r-h-u
case DEC_ROUND_UP: {
if (residue>0) bump=1;
break;} // r-u
case DEC_ROUND_CEILING: {
// same as _UP for positive numbers, and as _DOWN for negatives
// [negative residue cannot occur on 0]
if (decNumberIsNegative(dn)) {
if (residue<0) bump=-1;
}
else {
if (residue>0) bump=1;
}
break;} // r-c
case DEC_ROUND_FLOOR: {
// same as _UP for negative numbers, and as _DOWN for positive
// [negative residue cannot occur on 0]
if (!decNumberIsNegative(dn)) {
if (residue<0) bump=-1;
}
else {
if (residue>0) bump=1;
}
break;} // r-f
default: { // e.g., DEC_ROUND_MAX
*status|=DEC_Invalid_context;
#if DECTRACE || (DECCHECK && DECVERB)
printf("Unknown rounding mode: %d\n", set->round);
#endif
break;}
} // switch
// now bump the number, up or down, if need be
if (bump==0) return; // no action required
// Simply use decUnitAddSub unless bumping up and the number is
// all nines. In this special case set to 100... explicitly
// and adjust the exponent by one (as otherwise could overflow
// the array)
// Similarly handle all-nines result if bumping down.
if (bump>0) {
Unit *up; // work
uInt count=dn->digits; // digits to be checked
for (up=dn->lsu; ; up++) {
if (count<=DECDPUN) {
// this is the last Unit (the msu)
if (*up!=powers[count]-1) break; // not still 9s
// here if it, too, is all nines
*up=(Unit)powers[count-1]; // here 999 -> 100 etc.
for (up=up-1; up>=dn->lsu; up--) *up=0; // others all to 0
dn->exponent++; // and bump exponent
// [which, very rarely, could cause Overflow...]
if ((dn->exponent+dn->digits)>set->emax+1) {
decSetOverflow(dn, set, status);
}
return; // done
}
// a full unit to check, with more to come
if (*up!=DECDPUNMAX) break; // not still 9s
count-=DECDPUN;
} // up
} // bump>0
else { // -1
// here checking for a pre-bump of 1000... (leading 1, all
// other digits zero)
Unit *up, *sup; // work
uInt count=dn->digits; // digits to be checked
for (up=dn->lsu; ; up++) {
if (count<=DECDPUN) {
// this is the last Unit (the msu)
if (*up!=powers[count-1]) break; // not 100..
// here if have the 1000... case
sup=up; // save msu pointer
*up=(Unit)powers[count]-1; // here 100 in msu -> 999
// others all to all-nines, too
for (up=up-1; up>=dn->lsu; up--) *up=(Unit)powers[DECDPUN]-1;
dn->exponent--; // and bump exponent
// iff the number was at the subnormal boundary (exponent=etiny)
// then the exponent is now out of range, so it will in fact get
// clamped to etiny and the final 9 dropped.
// printf(">> emin=%d exp=%d sdig=%d\n", set->emin,
// dn->exponent, set->digits);
if (dn->exponent+1==set->emin-set->digits+1) {
if (count==1 && dn->digits==1) *sup=0; // here 9 -> 0[.9]
else {
*sup=(Unit)powers[count-1]-1; // here 999.. in msu -> 99..
dn->digits--;
}
dn->exponent++;
*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
}
return; // done
}
// a full unit to check, with more to come
if (*up!=0) break; // not still 0s
count-=DECDPUN;
} // up
} // bump<0
// Actual bump needed. Do it.
decUnitAddSub(dn->lsu, D2U(dn->digits), uarrone, 1, 0, dn->lsu, bump);
} // decApplyRound
#if DECSUBSET
/* ------------------------------------------------------------------ */
/* decFinish -- finish processing a number */
/* */
/* dn is the number */
/* set is the context */
/* residue is the rounding accumulator (as in decApplyRound) */
/* status is the accumulator */
/* */
/* This finishes off the current number by: */
/* 1. If not extended: */
/* a. Converting a zero result to clean '0' */
/* b. Reducing positive exponents to 0, if would fit in digits */
/* 2. Checking for overflow and subnormals (always) */
/* Note this is just Finalize when no subset arithmetic. */
/* All fields are updated as required. */
/* ------------------------------------------------------------------ */
static void decFinish(decNumber *dn, decContext *set, Int *residue,
uInt *status) {
if (!set->extended) {
if ISZERO(dn) { // value is zero
dn->exponent=0; // clean exponent ..
dn->bits=0; // .. and sign
return; // no error possible
}
if (dn->exponent>=0) { // non-negative exponent
// >0; reduce to integer if possible
if (set->digits >= (dn->exponent+dn->digits)) {
dn->digits=decShiftToMost(dn->lsu, dn->digits, dn->exponent);
dn->exponent=0;
}
}
} // !extended
decFinalize(dn, set, residue, status);
} // decFinish
#endif
/* ------------------------------------------------------------------ */
/* decFinalize -- final check, clamp, and round of a number */
/* */
/* dn is the number */
/* set is the context */
/* residue is the rounding accumulator (as in decApplyRound) */
/* status is the status accumulator */
/* */
/* This finishes off the current number by checking for subnormal */
/* results, applying any pending rounding, checking for overflow, */
/* and applying any clamping. */
/* Underflow and overflow conditions are raised as appropriate. */
/* All fields are updated as required. */
/* ------------------------------------------------------------------ */
static void decFinalize(decNumber *dn, decContext *set, Int *residue,
uInt *status) {
Int shift; // shift needed if clamping
Int tinyexp=set->emin-dn->digits+1; // precalculate subnormal boundary
// Must be careful, here, when checking the exponent as the
// adjusted exponent could overflow 31 bits [because it may already
// be up to twice the expected].
// First test for subnormal. This must be done before any final
// round as the result could be rounded to Nmin or 0.
if (dn->exponent<=tinyexp) { // prefilter
Int comp;
decNumber nmin;
// A very nasty case here is dn == Nmin and residue<0
if (dn->exponent<tinyexp) {
// Go handle subnormals; this will apply round if needed.
decSetSubnormal(dn, set, residue, status);
return;
}
// Equals case: only subnormal if dn=Nmin and negative residue
decNumberZero(&nmin);
nmin.lsu[0]=1;
nmin.exponent=set->emin;
comp=decCompare(dn, &nmin, 1); // (signless compare)
if (comp==BADINT) { // oops
*status|=DEC_Insufficient_storage; // abandon...
return;
}
if (*residue<0 && comp==0) { // neg residue and dn==Nmin
decApplyRound(dn, set, *residue, status); // might force down
decSetSubnormal(dn, set, residue, status);
return;
}
}
// now apply any pending round (this could raise overflow).
if (*residue!=0) decApplyRound(dn, set, *residue, status);
// Check for overflow [redundant in the 'rare' case] or clamp
if (dn->exponent<=set->emax-set->digits+1) return; // neither needed
// here when might have an overflow or clamp to do
if (dn->exponent>set->emax-dn->digits+1) { // too big
decSetOverflow(dn, set, status);
return;
}
// here when the result is normal but in clamp range
if (!set->clamp) return;
// here when need to apply the IEEE exponent clamp (fold-down)
shift=dn->exponent-(set->emax-set->digits+1);
// shift coefficient (if non-zero)
if (!ISZERO(dn)) {
dn->digits=decShiftToMost(dn->lsu, dn->digits, shift);
}
dn->exponent-=shift; // adjust the exponent to match
*status|=DEC_Clamped; // and record the dirty deed
return;
} // decFinalize
/* ------------------------------------------------------------------ */
/* decSetOverflow -- set number to proper overflow value */
/* */
/* dn is the number (used for sign [only] and result) */
/* set is the context [used for the rounding mode, etc.] */
/* status contains the current status to be updated */
/* */
/* This sets the sign of a number and sets its value to either */
/* Infinity or the maximum finite value, depending on the sign of */
/* dn and the rounding mode, following IEEE 754 rules. */
/* ------------------------------------------------------------------ */
static void decSetOverflow(decNumber *dn, decContext *set, uInt *status) {
Flag needmax=0; // result is maximum finite value
uByte sign=dn->bits&DECNEG; // clean and save sign bit
if (ISZERO(dn)) { // zero does not overflow magnitude
Int emax=set->emax; // limit value
if (set->clamp) emax-=set->digits-1; // lower if clamping
if (dn->exponent>emax) { // clamp required
dn->exponent=emax;
*status|=DEC_Clamped;
}
return;
}
decNumberZero(dn);
switch (set->round) {
case DEC_ROUND_DOWN: {
needmax=1; // never Infinity
break;} // r-d
case DEC_ROUND_05UP: {
needmax=1; // never Infinity
break;} // r-05
case DEC_ROUND_CEILING: {
if (sign) needmax=1; // Infinity if non-negative
break;} // r-c
case DEC_ROUND_FLOOR: {
if (!sign) needmax=1; // Infinity if negative
break;} // r-f
default: break; // Infinity in all other cases
}
if (needmax) {
decSetMaxValue(dn, set);
dn->bits=sign; // set sign
}
else dn->bits=sign|DECINF; // Value is +/-Infinity
*status|=DEC_Overflow | DEC_Inexact | DEC_Rounded;
} // decSetOverflow
/* ------------------------------------------------------------------ */
/* decSetMaxValue -- set number to +Nmax (maximum normal value) */
/* */
/* dn is the number to set */
/* set is the context [used for digits and emax] */
/* */
/* This sets the number to the maximum positive value. */
/* ------------------------------------------------------------------ */
static void decSetMaxValue(decNumber *dn, decContext *set) {
Unit *up; // work
Int count=set->digits; // nines to add
dn->digits=count;
// fill in all nines to set maximum value
for (up=dn->lsu; ; up++) {
if (count>DECDPUN) *up=DECDPUNMAX; // unit full o'nines
else { // this is the msu
*up=(Unit)(powers[count]-1);
break;
}
count-=DECDPUN; // filled those digits
} // up
dn->bits=0; // + sign
dn->exponent=set->emax-set->digits+1;
} // decSetMaxValue
/* ------------------------------------------------------------------ */
/* decSetSubnormal -- process value whose exponent is <Emin */
/* */
/* dn is the number (used as input as well as output; it may have */
/* an allowed subnormal value, which may need to be rounded) */
/* set is the context [used for the rounding mode] */
/* residue is any pending residue */
/* status contains the current status to be updated */
/* */
/* If subset mode, set result to zero and set Underflow flags. */
/* */
/* Value may be zero with a low exponent; this does not set Subnormal */
/* but the exponent will be clamped to Etiny. */
/* */
/* Otherwise ensure exponent is not out of range, and round as */
/* necessary. Underflow is set if the result is Inexact. */
/* ------------------------------------------------------------------ */
static void decSetSubnormal(decNumber *dn, decContext *set, Int *residue,
uInt *status) {
decContext workset; // work
Int etiny, adjust; // ..
#if DECSUBSET
// simple set to zero and 'hard underflow' for subset
if (!set->extended) {
decNumberZero(dn);
// always full overflow
*status|=DEC_Underflow | DEC_Subnormal | DEC_Inexact | DEC_Rounded;
return;
}
#endif
// Full arithmetic -- allow subnormals, rounded to minimum exponent
// (Etiny) if needed
etiny=set->emin-(set->digits-1); // smallest allowed exponent
if ISZERO(dn) { // value is zero
// residue can never be non-zero here
#if DECCHECK
if (*residue!=0) {
printf("++ Subnormal 0 residue %ld\n", (LI)*residue);
*status|=DEC_Invalid_operation;
}
#endif
if (dn->exponent<etiny) { // clamp required
dn->exponent=etiny;
*status|=DEC_Clamped;
}
return;
}
*status|=DEC_Subnormal; // have a non-zero subnormal
adjust=etiny-dn->exponent; // calculate digits to remove
if (adjust<=0) { // not out of range; unrounded
// residue can never be non-zero here, except in the Nmin-residue
// case (which is a subnormal result), so can take fast-path here
// it may already be inexact (from setting the coefficient)
if (*status&DEC_Inexact) *status|=DEC_Underflow;
return;
}
// adjust>0, so need to rescale the result so exponent becomes Etiny
// [this code is similar to that in rescale]
workset=*set; // clone rounding, etc.
workset.digits=dn->digits-adjust; // set requested length
workset.emin-=adjust; // and adjust emin to match
// [note that the latter can be <1, here, similar to Rescale case]
decSetCoeff(dn, &workset, dn->lsu, dn->digits, residue, status);
decApplyRound(dn, &workset, *residue, status);
// Use 754 default rule: Underflow is set iff Inexact
// [independent of whether trapped]
if (*status&DEC_Inexact) *status|=DEC_Underflow;
// if rounded up a 999s case, exponent will be off by one; adjust
// back if so [it will fit, because it was shortened earlier]
if (dn->exponent>etiny) {
dn->digits=decShiftToMost(dn->lsu, dn->digits, 1);
dn->exponent--; // (re)adjust the exponent.
}
// if rounded to zero, it is by definition clamped...
if (ISZERO(dn)) *status|=DEC_Clamped;
} // decSetSubnormal
/* ------------------------------------------------------------------ */
/* decCheckMath - check entry conditions for a math function */
/* */
/* This checks the context and the operand */
/* */
/* rhs is the operand to check */
/* set is the context to check */
/* status is unchanged if both are good */
/* */
/* returns non-zero if status is changed, 0 otherwise */
/* */
/* Restrictions enforced: */
/* */
/* digits, emax, and -emin in the context must be less than */
/* DEC_MAX_MATH (999999), and A must be within these bounds if */
/* non-zero. Invalid_operation is set in the status if a */
/* restriction is violated. */
/* ------------------------------------------------------------------ */
static uInt decCheckMath(const decNumber *rhs, decContext *set,
uInt *status) {
uInt save=*status; // record
if (set->digits>DEC_MAX_MATH
|| set->emax>DEC_MAX_MATH
|| -set->emin>DEC_MAX_MATH) *status|=DEC_Invalid_context;
else if ((rhs->digits>DEC_MAX_MATH
|| rhs->exponent+rhs->digits>DEC_MAX_MATH+1
|| rhs->exponent+rhs->digits<2*(1-DEC_MAX_MATH))
&& !ISZERO(rhs)) *status|=DEC_Invalid_operation;
return (*status!=save);
} // decCheckMath
/* ------------------------------------------------------------------ */
/* decGetInt -- get integer from a number */
/* */
/* dn is the number [which will not be altered] */
/* */
/* returns one of: */
/* BADINT if there is a non-zero fraction */
/* the converted integer */
/* BIGEVEN if the integer is even and magnitude > 2*10**9 */
/* BIGODD if the integer is odd and magnitude > 2*10**9 */
/* */
/* This checks and gets a whole number from the input decNumber. */
/* The sign can be determined from dn by the caller when BIGEVEN or */
/* BIGODD is returned. */
/* ------------------------------------------------------------------ */
static Int decGetInt(const decNumber *dn) {
Int theInt; // result accumulator
const Unit *up; // work
Int got; // digits (real or not) processed
Int ilength=dn->digits+dn->exponent; // integral length
Flag neg=decNumberIsNegative(dn); // 1 if -ve
// The number must be an integer that fits in 10 digits
// Assert, here, that 10 is enough for any rescale Etiny
#if DEC_MAX_EMAX > 999999999
#error GetInt may need updating [for Emax]
#endif
#if DEC_MIN_EMIN < -999999999
#error GetInt may need updating [for Emin]
#endif
if (ISZERO(dn)) return 0; // zeros are OK, with any exponent
up=dn->lsu; // ready for lsu
theInt=0; // ready to accumulate
if (dn->exponent>=0) { // relatively easy
// no fractional part [usual]; allow for positive exponent
got=dn->exponent;
}
else { // -ve exponent; some fractional part to check and discard
Int count=-dn->exponent; // digits to discard
// spin up whole units until reach the Unit with the unit digit
for (; count>=DECDPUN; up++) {
if (*up!=0) return BADINT; // non-zero Unit to discard
count-=DECDPUN;
}
if (count==0) got=0; // [a multiple of DECDPUN]
else { // [not multiple of DECDPUN]
Int rem; // work
// slice off fraction digits and check for non-zero
#if DECDPUN<=4
theInt=QUOT10(*up, count);
rem=*up-theInt*powers[count];
#else
rem=*up%powers[count]; // slice off discards
theInt=*up/powers[count];
#endif
if (rem!=0) return BADINT; // non-zero fraction
// it looks good
got=DECDPUN-count; // number of digits so far
up++; // ready for next
}
}
// now it's known there's no fractional part
// tricky code now, to accumulate up to 9.3 digits
if (got==0) {theInt=*up; got+=DECDPUN; up++;} // ensure lsu is there
if (ilength<11) {
Int save=theInt;
// collect any remaining unit(s)
for (; got<ilength; up++) {
theInt+=*up*powers[got];
got+=DECDPUN;
}
if (ilength==10) { // need to check for wrap
if (theInt/(Int)powers[got-DECDPUN]!=(Int)*(up-1)) ilength=11;
// [that test also disallows the BADINT result case]
else if (neg && theInt>1999999997) ilength=11;
else if (!neg && theInt>999999999) ilength=11;
if (ilength==11) theInt=save; // restore correct low bit
}
}
if (ilength>10) { // too big
if (theInt&1) return BIGODD; // bottom bit 1
return BIGEVEN; // bottom bit 0
}
if (neg) theInt=-theInt; // apply sign
return theInt;
} // decGetInt
/* ------------------------------------------------------------------ */
/* decDecap -- decapitate the coefficient of a number */
/* */
/* dn is the number to be decapitated */
/* drop is the number of digits to be removed from the left of dn; */
/* this must be <= dn->digits (if equal, the coefficient is */
/* set to 0) */
/* */
/* Returns dn; dn->digits will be <= the initial digits less drop */
/* (after removing drop digits there may be leading zero digits */
/* which will also be removed). Only dn->lsu and dn->digits change. */
/* ------------------------------------------------------------------ */
static decNumber *decDecap(decNumber *dn, Int drop) {
Unit *msu; // -> target cut point
Int cut; // work
if (drop>=dn->digits) { // losing the whole thing
#if DECCHECK
if (drop>dn->digits)
printf("decDecap called with drop>digits [%ld>%ld]\n",
(LI)drop, (LI)dn->digits);
#endif
dn->lsu[0]=0;
dn->digits=1;
return dn;
}
msu=dn->lsu+D2U(dn->digits-drop)-1; // -> likely msu
cut=MSUDIGITS(dn->digits-drop); // digits to be in use in msu
if (cut!=DECDPUN) *msu%=powers[cut]; // clear left digits
// that may have left leading zero digits, so do a proper count...
dn->digits=decGetDigits(dn->lsu, msu-dn->lsu+1);
return dn;
} // decDecap
/* ------------------------------------------------------------------ */
/* decBiStr -- compare string with pairwise options */
/* */
/* targ is the string to compare */
/* str1 is one of the strings to compare against (length may be 0) */
/* str2 is the other; it must be the same length as str1 */
/* */
/* returns 1 if strings compare equal, (that is, it is the same */
/* length as str1 and str2, and each character of targ is in either */
/* str1 or str2 in the corresponding position), or 0 otherwise */
/* */
/* This is used for generic caseless compare, including the awkward */
/* case of the Turkish dotted and dotless Is. Use as (for example): */
/* if (decBiStr(test, "mike", "MIKE")) ... */
/* ------------------------------------------------------------------ */
static Flag decBiStr(const char *targ, const char *str1, const char *str2) {
for (;;targ++, str1++, str2++) {
if (*targ!=*str1 && *targ!=*str2) return 0;
// *targ has a match in one (or both, if terminator)
if (*targ=='\0') break;
} // forever
return 1;
} // decBiStr
/* ------------------------------------------------------------------ */
/* decNaNs -- handle NaN operand or operands */
/* */
/* res is the result number */
/* lhs is the first operand */
/* rhs is the second operand, or NULL if none */
/* context is used to limit payload length */
/* status contains the current status */
/* returns res in case convenient */
/* */
/* Called when one or both operands is a NaN, and propagates the */
/* appropriate result to res. When an sNaN is found, it is changed */
/* to a qNaN and Invalid operation is set. */
/* ------------------------------------------------------------------ */
static decNumber * decNaNs(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set,
uInt *status) {
// This decision tree ends up with LHS being the source pointer,
// and status updated if need be
if (lhs->bits & DECSNAN)
*status|=DEC_Invalid_operation | DEC_sNaN;
else if (rhs==NULL);
else if (rhs->bits & DECSNAN) {
lhs=rhs;
*status|=DEC_Invalid_operation | DEC_sNaN;
}
else if (lhs->bits & DECNAN);
else lhs=rhs;
// propagate the payload
if (lhs->digits<=set->digits) decNumberCopy(res, lhs); // easy
else { // too long
const Unit *ul;
Unit *ur, *uresp1;
// copy safe number of units, then decapitate
res->bits=lhs->bits; // need sign etc.
uresp1=res->lsu+D2U(set->digits);
for (ur=res->lsu, ul=lhs->lsu; ur<uresp1; ur++, ul++) *ur=*ul;
res->digits=D2U(set->digits)*DECDPUN;
// maybe still too long
if (res->digits>set->digits) decDecap(res, res->digits-set->digits);
}
res->bits&=~DECSNAN; // convert any sNaN to NaN, while
res->bits|=DECNAN; // .. preserving sign
res->exponent=0; // clean exponent
// [coefficient was copied/decapitated]
return res;
} // decNaNs
/* ------------------------------------------------------------------ */
/* decStatus -- apply non-zero status */
/* */
/* dn is the number to set if error */
/* status contains the current status (not yet in context) */
/* set is the context */
/* */
/* If the status is an error status, the number is set to a NaN, */
/* unless the error was an overflow, divide-by-zero, or underflow, */
/* in which case the number will have already been set. */
/* */
/* The context status is then updated with the new status. Note that */
/* this may raise a signal, so control may never return from this */
/* routine (hence resources must be recovered before it is called). */
/* ------------------------------------------------------------------ */
static void decStatus(decNumber *dn, uInt status, decContext *set) {
if (status & DEC_NaNs) { // error status -> NaN
// if cause was an sNaN, clear and propagate [NaN is already set up]
if (status & DEC_sNaN) status&=~DEC_sNaN;
else {
decNumberZero(dn); // other error: clean throughout
dn->bits=DECNAN; // and make a quiet NaN
}
}
decContextSetStatus(set, status); // [may not return]
return;
} // decStatus
/* ------------------------------------------------------------------ */
/* decGetDigits -- count digits in a Units array */
/* */
/* uar is the Unit array holding the number (this is often an */
/* accumulator of some sort) */
/* len is the length of the array in units [>=1] */
/* */
/* returns the number of (significant) digits in the array */
/* */
/* All leading zeros are excluded, except the last if the array has */
/* only zero Units. */
/* ------------------------------------------------------------------ */
// This may be called twice during some operations.
static Int decGetDigits(Unit *uar, Int len) {
Unit *up=uar+(len-1); // -> msu
Int digits=(len-1)*DECDPUN+1; // possible digits excluding msu
#if DECDPUN>4
uInt const *pow; // work
#endif
// (at least 1 in final msu)
#if DECCHECK
if (len<1) printf("decGetDigits called with len<1 [%ld]\n", (LI)len);
#endif
for (; up>=uar; up--) {
if (*up==0) { // unit is all 0s
if (digits==1) break; // a zero has one digit
digits-=DECDPUN; // adjust for 0 unit
continue;}
// found the first (most significant) non-zero Unit
#if DECDPUN>1 // not done yet
if (*up<10) break; // is 1-9
digits++;
#if DECDPUN>2 // not done yet
if (*up<100) break; // is 10-99
digits++;
#if DECDPUN>3 // not done yet
if (*up<1000) break; // is 100-999
digits++;
#if DECDPUN>4 // count the rest ...
for (pow=&powers[4]; *up>=*pow; pow++) digits++;
#endif
#endif
#endif
#endif
break;
} // up
return digits;
} // decGetDigits
#if DECTRACE | DECCHECK
/* ------------------------------------------------------------------ */
/* decNumberShow -- display a number [debug aid] */
/* dn is the number to show */
/* */
/* Shows: sign, exponent, coefficient (msu first), digits */
/* or: sign, special-value */
/* ------------------------------------------------------------------ */
// this is public so other modules can use it
void decNumberShow(const decNumber *dn) {
const Unit *up; // work
uInt u, d; // ..
Int cut; // ..
char isign='+'; // main sign
if (dn==NULL) {
printf("NULL\n");
return;}
if (decNumberIsNegative(dn)) isign='-';
printf(" >> %c ", isign);
if (dn->bits&DECSPECIAL) { // Is a special value
if (decNumberIsInfinite(dn)) printf("Infinity");
else { // a NaN
if (dn->bits&DECSNAN) printf("sNaN"); // signalling NaN
else printf("NaN");
}
// if coefficient and exponent are 0, no more to do
if (dn->exponent==0 && dn->digits==1 && *dn->lsu==0) {
printf("\n");
return;}
// drop through to report other information
printf(" ");
}
// now carefully display the coefficient
up=dn->lsu+D2U(dn->digits)-1; // msu
printf("%ld", (LI)*up);
for (up=up-1; up>=dn->lsu; up--) {
u=*up;
printf(":");
for (cut=DECDPUN-1; cut>=0; cut--) {
d=u/powers[cut];
u-=d*powers[cut];
printf("%ld", (LI)d);
} // cut
} // up
if (dn->exponent!=0) {
char esign='+';
if (dn->exponent<0) esign='-';
printf(" E%c%ld", esign, (LI)abs(dn->exponent));
}
printf(" [%ld]\n", (LI)dn->digits);
} // decNumberShow
#endif
#if DECTRACE || DECCHECK
/* ------------------------------------------------------------------ */
/* decDumpAr -- display a unit array [debug/check aid] */
/* name is a single-character tag name */
/* ar is the array to display */
/* len is the length of the array in Units */
/* ------------------------------------------------------------------ */
static void decDumpAr(char name, const Unit *ar, Int len) {
Int i;
const char *spec;
#if DECDPUN==9
spec="%09d ";
#elif DECDPUN==8
spec="%08d ";
#elif DECDPUN==7
spec="%07d ";
#elif DECDPUN==6
spec="%06d ";
#elif DECDPUN==5
spec="%05d ";
#elif DECDPUN==4
spec="%04d ";
#elif DECDPUN==3
spec="%03d ";
#elif DECDPUN==2
spec="%02d ";
#else
spec="%d ";
#endif
printf(" :%c: ", name);
for (i=len-1; i>=0; i--) {
if (i==len-1) printf("%ld ", (LI)ar[i]);
else printf(spec, ar[i]);
}
printf("\n");
return;}
#endif
#if DECCHECK
/* ------------------------------------------------------------------ */
/* decCheckOperands -- check operand(s) to a routine */
/* res is the result structure (not checked; it will be set to */
/* quiet NaN if error found (and it is not NULL)) */
/* lhs is the first operand (may be DECUNRESU) */
/* rhs is the second (may be DECUNUSED) */
/* set is the context (may be DECUNCONT) */
/* returns 0 if both operands, and the context are clean, or 1 */
/* otherwise (in which case the context will show an error, */
/* unless NULL). Note that res is not cleaned; caller should */
/* handle this so res=NULL case is safe. */
/* The caller is expected to abandon immediately if 1 is returned. */
/* ------------------------------------------------------------------ */
static Flag decCheckOperands(decNumber *res, const decNumber *lhs,
const decNumber *rhs, decContext *set) {
Flag bad=0;
if (set==NULL) { // oops; hopeless
#if DECTRACE || DECVERB
printf("Reference to context is NULL.\n");
#endif
bad=1;
return 1;}
else if (set!=DECUNCONT
&& (set->digits<1 || set->round>=DEC_ROUND_MAX)) {
bad=1;
#if DECTRACE || DECVERB
printf("Bad context [digits=%ld round=%ld].\n",
(LI)set->digits, (LI)set->round);
#endif
}
else {
if (res==NULL) {
bad=1;
#if DECTRACE
// this one not DECVERB as standard tests include NULL
printf("Reference to result is NULL.\n");
#endif
}
if (!bad && lhs!=DECUNUSED) bad=(decCheckNumber(lhs));
if (!bad && rhs!=DECUNUSED) bad=(decCheckNumber(rhs));
}
if (bad) {
if (set!=DECUNCONT) decContextSetStatus(set, DEC_Invalid_operation);
if (res!=DECUNRESU && res!=NULL) {
decNumberZero(res);
res->bits=DECNAN; // qNaN
}
}
return bad;
} // decCheckOperands
/* ------------------------------------------------------------------ */
/* decCheckNumber -- check a number */
/* dn is the number to check */
/* returns 0 if the number is clean, or 1 otherwise */
/* */
/* The number is considered valid if it could be a result from some */
/* operation in some valid context. */
/* ------------------------------------------------------------------ */
static Flag decCheckNumber(const decNumber *dn) {
const Unit *up; // work
uInt maxuint; // ..
Int ae, d, digits; // ..
Int emin, emax; // ..
if (dn==NULL) { // hopeless
#if DECTRACE
// this one not DECVERB as standard tests include NULL
printf("Reference to decNumber is NULL.\n");
#endif
return 1;}
// check special values
if (dn->bits & DECSPECIAL) {
if (dn->exponent!=0) {
#if DECTRACE || DECVERB
printf("Exponent %ld (not 0) for a special value [%02x].\n",
(LI)dn->exponent, dn->bits);
#endif
return 1;}
// 2003.09.08: NaNs may now have coefficients, so next tests Inf only
if (decNumberIsInfinite(dn)) {
if (dn->digits!=1) {
#if DECTRACE || DECVERB
printf("Digits %ld (not 1) for an infinity.\n", (LI)dn->digits);
#endif
return 1;}
if (*dn->lsu!=0) {
#if DECTRACE || DECVERB
printf("LSU %ld (not 0) for an infinity.\n", (LI)*dn->lsu);
#endif
decDumpAr('I', dn->lsu, D2U(dn->digits));
return 1;}
} // Inf
// 2002.12.26: negative NaNs can now appear through proposed IEEE
// concrete formats (decimal64, etc.).
return 0;
}
// check the coefficient
if (dn->digits<1 || dn->digits>DECNUMMAXP) {
#if DECTRACE || DECVERB
printf("Digits %ld in number.\n", (LI)dn->digits);
#endif
return 1;}
d=dn->digits;
for (up=dn->lsu; d>0; up++) {
if (d>DECDPUN) maxuint=DECDPUNMAX;
else { // reached the msu
maxuint=powers[d]-1;
if (dn->digits>1 && *up<powers[d-1]) {
#if DECTRACE || DECVERB
printf("Leading 0 in number.\n");
decNumberShow(dn);
#endif
return 1;}
}
if (*up>maxuint) {
#if DECTRACE || DECVERB
printf("Bad Unit [%08lx] in %ld-digit number at offset %ld [maxuint %ld].\n",
(LI)*up, (LI)dn->digits, (LI)(up-dn->lsu), (LI)maxuint);
#endif
return 1;}
d-=DECDPUN;
}
// check the exponent. Note that input operands can have exponents
// which are out of the set->emin/set->emax and set->digits range
// (just as they can have more digits than set->digits).
ae=dn->exponent+dn->digits-1; // adjusted exponent
emax=DECNUMMAXE;
emin=DECNUMMINE;
digits=DECNUMMAXP;
if (ae<emin-(digits-1)) {
#if DECTRACE || DECVERB
printf("Adjusted exponent underflow [%ld].\n", (LI)ae);
decNumberShow(dn);
#endif
return 1;}
if (ae>+emax) {
#if DECTRACE || DECVERB
printf("Adjusted exponent overflow [%ld].\n", (LI)ae);
decNumberShow(dn);
#endif
return 1;}
return 0; // it's OK
} // decCheckNumber
/* ------------------------------------------------------------------ */
/* decCheckInexact -- check a normal finite inexact result has digits */
/* dn is the number to check */
/* set is the context (for status and precision) */
/* sets Invalid operation, etc., if some digits are missing */
/* [this check is not made for DECSUBSET compilation or when */
/* subnormal is not set] */
/* ------------------------------------------------------------------ */
static void decCheckInexact(const decNumber *dn, decContext *set) {
#if !DECSUBSET && DECEXTFLAG
if ((set->status & (DEC_Inexact|DEC_Subnormal))==DEC_Inexact
&& (set->digits!=dn->digits) && !(dn->bits & DECSPECIAL)) {
#if DECTRACE || DECVERB
printf("Insufficient digits [%ld] on normal Inexact result.\n",
(LI)dn->digits);
decNumberShow(dn);
#endif
decContextSetStatus(set, DEC_Invalid_operation);
}
#else
// next is a noop for quiet compiler
if (dn!=NULL && dn->digits==0) set->status|=DEC_Invalid_operation;
#endif
return;
} // decCheckInexact
#endif
#if DECALLOC
#undef malloc
#undef free
/* ------------------------------------------------------------------ */
/* decMalloc -- accountable allocation routine */
/* n is the number of bytes to allocate */
/* */
/* Semantics is the same as the stdlib malloc routine, but bytes */
/* allocated are accounted for globally, and corruption fences are */
/* added before and after the 'actual' storage. */
/* ------------------------------------------------------------------ */
/* This routine allocates storage with an extra twelve bytes; 8 are */
/* at the start and hold: */
/* 0-3 the original length requested */
/* 4-7 buffer corruption detection fence (DECFENCE, x4) */
/* The 4 bytes at the end also hold a corruption fence (DECFENCE, x4) */
/* ------------------------------------------------------------------ */
static void *decMalloc(size_t n) {
uInt size=n+12; // true size
void *alloc; // -> allocated storage
uByte *b, *b0; // work
uInt uiwork; // for macros
alloc=malloc(size); // -> allocated storage
if (alloc==NULL) return NULL; // out of strorage
b0=(uByte *)alloc; // as bytes
decAllocBytes+=n; // account for storage
UBFROMUI(alloc, n); // save n
// printf(" alloc ++ dAB: %ld (%ld)\n", (LI)decAllocBytes, (LI)n);
for (b=b0+4; b<b0+8; b++) *b=DECFENCE;
for (b=b0+n+8; b<b0+n+12; b++) *b=DECFENCE;
return b0+8; // -> play area
} // decMalloc
/* ------------------------------------------------------------------ */
/* decFree -- accountable free routine */
/* alloc is the storage to free */
/* */
/* Semantics is the same as the stdlib malloc routine, except that */
/* the global storage accounting is updated and the fences are */
/* checked to ensure that no routine has written 'out of bounds'. */
/* ------------------------------------------------------------------ */
/* This routine first checks that the fences have not been corrupted. */
/* It then frees the storage using the 'truw' storage address (that */
/* is, offset by 8). */
/* ------------------------------------------------------------------ */
static void decFree(void *alloc) {
uInt n; // original length
uByte *b, *b0; // work
uInt uiwork; // for macros
if (alloc==NULL) return; // allowed; it's a nop
b0=(uByte *)alloc; // as bytes
b0-=8; // -> true start of storage
n=UBTOUI(b0); // lift length
for (b=b0+4; b<b0+8; b++) if (*b!=DECFENCE)
printf("=== Corrupt byte [%02x] at offset %d from %ld ===\n", *b,
b-b0-8, (LI)b0);
for (b=b0+n+8; b<b0+n+12; b++) if (*b!=DECFENCE)
printf("=== Corrupt byte [%02x] at offset +%d from %ld, n=%ld ===\n", *b,
b-b0-8, (LI)b0, (LI)n);
free(b0); // drop the storage
decAllocBytes-=n; // account for storage
// printf(" free -- dAB: %d (%d)\n", decAllocBytes, -n);
} // decFree
#define malloc(a) decMalloc(a)
#define free(a) decFree(a)
#endif
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