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prodejna/qdecimal/decnumber/decCommon.c

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service plugin and qdecimal library has been added
9 years ago
/* ------------------------------------------------------------------ */
/* decCommon.c -- common code for all three fixed-size types */
/* ------------------------------------------------------------------ */
/* Copyright (c) IBM Corporation, 2000, 2010. 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 included in the package as decNumber.pdf. This */
/* document is also available in HTML, together with 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 code that is shared between all the formats */
/* (decSingle, decDouble, and decQuad); it includes set and extract */
/* of format components, widening, narrowing, and string conversions. */
/* */
/* Unlike decNumber, parameterization takes place at compile time */
/* rather than at runtime. The parameters are set in the decDouble.c */
/* (etc.) files, which then include this one to produce the compiled */
/* code. The functions here, therefore, are code shared between */
/* multiple formats. */
/* ------------------------------------------------------------------ */
// Names here refer to decFloat rather than to decDouble, etc., and
// the functions are in strict alphabetical order.
// Constants, tables, and debug function(s) are included only for QUAD
// (which will always be compiled if DOUBLE or SINGLE are used).
//
// Whenever a decContext is used, only the status may be set (using
// OR) or the rounding mode read; all other fields are ignored and
// untouched.
// names for simpler testing and default context
#if DECPMAX==7
#define SINGLE 1
#define DOUBLE 0
#define QUAD 0
#define DEFCONTEXT DEC_INIT_DECIMAL32
#elif DECPMAX==16
#define SINGLE 0
#define DOUBLE 1
#define QUAD 0
#define DEFCONTEXT DEC_INIT_DECIMAL64
#elif DECPMAX==34
#define SINGLE 0
#define DOUBLE 0
#define QUAD 1
#define DEFCONTEXT DEC_INIT_DECIMAL128
#else
#error Unexpected DECPMAX value
#endif
/* Assertions */
#if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34
#error Unexpected Pmax (DECPMAX) value for this module
#endif
// Assert facts about digit characters, etc.
#if ('9'&0x0f)!=9
#error This module assumes characters are of the form 0b....nnnn
// where .... are don't care 4 bits and nnnn is 0000 through 1001
#endif
#if ('9'&0xf0)==('.'&0xf0)
#error This module assumes '.' has a different mask than a digit
#endif
// Assert ToString lay-out conditions
#if DECSTRING<DECPMAX+9
#error ToString needs at least 8 characters for lead-in and dot
#endif
#if DECPMAX+DECEMAXD+5 > DECSTRING
#error Exponent form can be too long for ToString to lay out safely
#endif
#if DECEMAXD > 4
#error Exponent form is too long for ToString to lay out
// Note: code for up to 9 digits exists in archives [decOct]
#endif
/* Private functions used here and possibly in decBasic.c, etc. */
static decFloat * decFinalize(decFloat *, bcdnum *, decContext *);
static Flag decBiStr(const char *, const char *, const char *);
/* Macros and private tables; those which are not format-dependent */
/* are only included if decQuad is being built. */
/* ------------------------------------------------------------------ */
/* Combination field lookup tables (uInts to save measurable work) */
/* */
/* DECCOMBEXP - 2 most-significant-bits of exponent (00, 01, or */
/* 10), shifted left for format, or DECFLOAT_Inf/NaN */
/* DECCOMBWEXP - The same, for the next-wider format (unless QUAD) */
/* DECCOMBMSD - 4-bit most-significant-digit */
/* [0 if the index is a special (Infinity or NaN)] */
/* DECCOMBFROM - 5-bit combination field from EXP top bits and MSD */
/* (placed in uInt so no shift is needed) */
/* */
/* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign */
/* and 5-bit combination field (0-63, the second half of the table */
/* identical to the first half) */
/* DECCOMBFROM is indexed by expTopTwoBits*16 + msd */
/* */
/* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are */
/* only included once, when QUAD is being built */
/* ------------------------------------------------------------------ */
static const uInt DECCOMBEXP[64]={
0, 0, 0, 0, 0, 0, 0, 0,
1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
0, 0, 1<<DECECONL, 1<<DECECONL,
2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN,
0, 0, 0, 0, 0, 0, 0, 0,
1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
1<<DECECONL, 1<<DECECONL, 1<<DECECONL, 1<<DECECONL,
2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
2<<DECECONL, 2<<DECECONL, 2<<DECECONL, 2<<DECECONL,
0, 0, 1<<DECECONL, 1<<DECECONL,
2<<DECECONL, 2<<DECECONL, DECFLOAT_Inf, DECFLOAT_NaN};
#if !QUAD
static const uInt DECCOMBWEXP[64]={
0, 0, 0, 0, 0, 0, 0, 0,
1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
0, 0, 1<<DECWECONL, 1<<DECWECONL,
2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN,
0, 0, 0, 0, 0, 0, 0, 0,
1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL, 1<<DECWECONL,
2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL, 2<<DECWECONL,
0, 0, 1<<DECWECONL, 1<<DECWECONL,
2<<DECWECONL, 2<<DECWECONL, DECFLOAT_Inf, DECFLOAT_NaN};
#endif
#if QUAD
const uInt DECCOMBMSD[64]={
0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0,
0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7,
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 8, 9, 0, 0};
const uInt DECCOMBFROM[48]={
0x00000000, 0x04000000, 0x08000000, 0x0C000000, 0x10000000, 0x14000000,
0x18000000, 0x1C000000, 0x60000000, 0x64000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000, 0x24000000,
0x28000000, 0x2C000000, 0x30000000, 0x34000000, 0x38000000, 0x3C000000,
0x68000000, 0x6C000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000,
0x00000000, 0x00000000, 0x40000000, 0x44000000, 0x48000000, 0x4C000000,
0x50000000, 0x54000000, 0x58000000, 0x5C000000, 0x70000000, 0x74000000,
0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000};
/* ------------------------------------------------------------------ */
/* Request and include the tables to use for conversions */
/* ------------------------------------------------------------------ */
#define DEC_BCD2DPD 1 // 0-0x999 -> DPD
#define DEC_BIN2DPD 1 // 0-999 -> DPD
#define DEC_BIN2BCD8 1 // 0-999 -> ddd, len
#define DEC_DPD2BCD8 1 // DPD -> ddd, len
#define DEC_DPD2BIN 1 // DPD -> 0-999
#define DEC_DPD2BINK 1 // DPD -> 0-999000
#define DEC_DPD2BINM 1 // DPD -> 0-999000000
#include "decDPD.h" // source of the lookup tables
#endif
/* ----------------------------------------------------------------- */
/* 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, targ is the same */
/* length as str1 and str2, and each character of targ is in one */
/* of 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
/* ------------------------------------------------------------------ */
/* decFinalize -- adjust and store a final result */
/* */
/* df is the decFloat format number which gets the final result */
/* num is the descriptor of the number to be checked and encoded */
/* [its values, including the coefficient, may be modified] */
/* set is the context to use */
/* returns df */
/* */
/* The num descriptor may point to a bcd8 string of any length; this */
/* string may have leading insignificant zeros. If it has more than */
/* DECPMAX digits then the final digit can be a round-for-reround */
/* digit (i.e., it may include a sticky bit residue). */
/* */
/* The exponent (q) may be one of the codes for a special value and */
/* can be up to 999999999 for conversion from string. */
/* */
/* No error is possible, but Inexact, Underflow, and/or Overflow may */
/* be set. */
/* ------------------------------------------------------------------ */
// Constant whose size varies with format; also the check for surprises
static uByte allnines[DECPMAX]=
#if SINGLE
{9, 9, 9, 9, 9, 9, 9};
#elif DOUBLE
{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
#elif QUAD
{9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
#endif
static decFloat * decFinalize(decFloat *df, bcdnum *num,
decContext *set) {
uByte *ub; // work
uInt dpd; // ..
uInt uiwork; // for macros
uByte *umsd=num->msd; // local copy
uByte *ulsd=num->lsd; // ..
uInt encode; // encoding accumulator
Int length; // coefficient length
#if DECCHECK
Int clen=ulsd-umsd+1;
#if QUAD
#define COEXTRA 2 // extra-long coefficent
#else
#define COEXTRA 0
#endif
if (clen<1 || clen>DECPMAX*3+2+COEXTRA)
printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen);
if (num->sign!=0 && num->sign!=DECFLOAT_Sign)
printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign);
if (!EXPISSPECIAL(num->exponent)
&& (num->exponent>1999999999 || num->exponent<-1999999999))
printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent);
// decShowNum(num, "final");
#endif
// A special will have an 'exponent' which is very positive and a
// coefficient < DECPMAX
length=(uInt)(ulsd-umsd+1); // coefficient length
if (!NUMISSPECIAL(num)) {
Int drop; // digits to be dropped
// skip leading insignificant zeros to calculate an exact length
// [this is quite expensive]
if (*umsd==0) {
for (; umsd+3<ulsd && UBTOUI(umsd)==0;) umsd+=4;
for (; *umsd==0 && umsd<ulsd;) umsd++;
length=ulsd-umsd+1; // recalculate
}
drop=MAXI(length-DECPMAX, DECQTINY-num->exponent);
// drop can now be > digits for bottom-clamp (subnormal) cases
if (drop>0) { // rounding needed
// (decFloatQuantize has very similar code to this, so any
// changes may need to be made there, too)
uByte *roundat; // -> re-round digit
uByte reround; // reround value
// printf("Rounding; drop=%ld\n", (LI)drop);
num->exponent+=drop; // always update exponent
// Three cases here:
// 1. new LSD is in coefficient (almost always)
// 2. new LSD is digit to left of coefficient (so MSD is
// round-for-reround digit)
// 3. new LSD is to left of case 2 (whole coefficient is sticky)
// [duplicate check-stickies code to save a test]
// [by-digit check for stickies as runs of zeros are rare]
if (drop<length) { // NB lengths not addresses
roundat=umsd+length-drop;
reround=*roundat;
for (ub=roundat+1; ub<=ulsd; ub++) {
if (*ub!=0) { // non-zero to be discarded
reround=DECSTICKYTAB[reround]; // apply sticky bit
break; // [remainder don't-care]
}
} // check stickies
ulsd=roundat-1; // new LSD
}
else { // edge case
if (drop==length) {
roundat=umsd;
reround=*roundat;
}
else {
roundat=umsd-1;
reround=0;
}
for (ub=roundat+1; ub<=ulsd; ub++) {
if (*ub!=0) { // non-zero to be discarded
reround=DECSTICKYTAB[reround]; // apply sticky bit
break; // [remainder don't-care]
}
} // check stickies
*umsd=0; // coefficient is a 0
ulsd=umsd; // ..
}
if (reround!=0) { // discarding non-zero
uInt bump=0;
set->status|=DEC_Inexact;
// if adjusted exponent [exp+digits-1] is < EMIN then num is
// subnormal -- so raise Underflow
if (num->exponent<DECEMIN && (num->exponent+(ulsd-umsd+1)-1)<DECEMIN)
set->status|=DEC_Underflow;
// next decide whether increment of the coefficient is needed
if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case
if (reround>5) bump=1; // >0.5 goes up
else if (reround==5) // exactly 0.5000 ..
bump=*ulsd & 0x01; // .. up iff [new] lsd is odd
} // r-h-e
else switch (set->round) {
case DEC_ROUND_DOWN: {
// no change
break;} // r-d
case DEC_ROUND_HALF_DOWN: {
if (reround>5) bump=1;
break;} // r-h-d
case DEC_ROUND_HALF_UP: {
if (reround>=5) bump=1;
break;} // r-h-u
case DEC_ROUND_UP: {
if (reround>0) bump=1;
break;} // r-u
case DEC_ROUND_CEILING: {
// same as _UP for positive numbers, and as _DOWN for negatives
if (!num->sign && reround>0) bump=1;
break;} // r-c
case DEC_ROUND_FLOOR: {
// same as _UP for negative numbers, and as _DOWN for positive
// [negative reround cannot occur on 0]
if (num->sign && reround>0) bump=1;
break;} // r-f
case DEC_ROUND_05UP: {
if (reround>0) { // anything out there is 'sticky'
// bump iff lsd=0 or 5; this cannot carry so it could be
// effected immediately with no bump -- but the code
// is clearer if this is done the same way as the others
if (*ulsd==0 || *ulsd==5) bump=1;
}
break;} // r-r
default: { // e.g., DEC_ROUND_MAX
set->status|=DEC_Invalid_context;
#if DECCHECK
printf("Unknown rounding mode: %ld\n", (LI)set->round);
#endif
break;}
} // switch (not r-h-e)
// printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump);
if (bump!=0) { // need increment
// increment the coefficient; this might end up with 1000...
// (after the all nines case)
ub=ulsd;
for(; ub-3>=umsd && UBTOUI(ub-3)==0x09090909; ub-=4) {
UBFROMUI(ub-3, 0); // to 00000000
}
// [note ub could now be to left of msd, and it is not safe
// to write to the the left of the msd]
// now at most 3 digits left to non-9 (usually just the one)
for (; ub>=umsd; *ub=0, ub--) {
if (*ub==9) continue; // carry
*ub+=1;
break;
}
if (ub<umsd) { // had all-nines
*umsd=1; // coefficient to 1000...
// usually the 1000... coefficient can be used as-is
if ((ulsd-umsd+1)==DECPMAX) {
num->exponent++;
}
else {
// if coefficient is shorter than Pmax then num is
// subnormal, so extend it; this is safe as drop>0
// (or, if the coefficient was supplied above, it could
// not be 9); this may make the result normal.
ulsd++;
*ulsd=0;
// [exponent unchanged]
#if DECCHECK
if (num->exponent!=DECQTINY) // sanity check
printf("decFinalize: bad all-nines extend [^%ld, %ld]\n",
(LI)num->exponent, (LI)(ulsd-umsd+1));
#endif
} // subnormal extend
} // had all-nines
} // bump needed
} // inexact rounding
length=ulsd-umsd+1; // recalculate (may be <DECPMAX)
} // need round (drop>0)
// The coefficient will now fit and has final length unless overflow
// decShowNum(num, "rounded");
// if exponent is >=emax may have to clamp, overflow, or fold-down
if (num->exponent>DECEMAX-(DECPMAX-1)) { // is edge case
// printf("overflow checks...\n");
if (*ulsd==0 && ulsd==umsd) { // have zero
num->exponent=DECEMAX-(DECPMAX-1); // clamp to max
}
else if ((num->exponent+length-1)>DECEMAX) { // > Nmax
// Overflow -- these could go straight to encoding, here, but
// instead num is adjusted to keep the code cleaner
Flag needmax=0; // 1 for finite result
set->status|=(DEC_Overflow | DEC_Inexact);
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 (num->sign) needmax=1; // Infinity iff non-negative
break;} // r-c
case DEC_ROUND_FLOOR: {
if (!num->sign) needmax=1; // Infinity iff negative
break;} // r-f
default: break; // Infinity in all other cases
}
if (!needmax) { // easy .. set Infinity
num->exponent=DECFLOAT_Inf;
*umsd=0; // be clean: coefficient to 0
ulsd=umsd; // ..
}
else { // return Nmax
umsd=allnines; // use constant array
ulsd=allnines+DECPMAX-1;
num->exponent=DECEMAX-(DECPMAX-1);
}
}
else { // no overflow but non-zero and may have to fold-down
Int shift=num->exponent-(DECEMAX-(DECPMAX-1));
if (shift>0) { // fold-down needed
// fold down needed; must copy to buffer in order to pad
// with zeros safely; fortunately this is not the worst case
// path because cannot have had a round
uByte buffer[ROUNDUP(DECPMAX+3, 4)]; // [+3 allows uInt padding]
uByte *s=umsd; // source
uByte *t=buffer; // safe target
uByte *tlsd=buffer+(ulsd-umsd)+shift; // target LSD
// printf("folddown shift=%ld\n", (LI)shift);
for (; s<=ulsd; s+=4, t+=4) UBFROMUI(t, UBTOUI(s));
for (t=tlsd-shift+1; t<=tlsd; t+=4) UBFROMUI(t, 0); // pad 0s
num->exponent-=shift;
umsd=buffer;
ulsd=tlsd;
}
} // fold-down?
length=ulsd-umsd+1; // recalculate length
} // high-end edge case
} // finite number
/*------------------------------------------------------------------*/
/* At this point the result will properly fit the decFloat */
/* encoding, and it can be encoded with no possibility of error */
/*------------------------------------------------------------------*/
// Following code does not alter coefficient (could be allnines array)
// fast path possible when DECPMAX digits
if (length==DECPMAX) {
return decFloatFromBCD(df, num->exponent, umsd, num->sign);
} // full-length
// slower path when not a full-length number; must care about length
// [coefficient length here will be < DECPMAX]
if (!NUMISSPECIAL(num)) { // is still finite
// encode the combination field and exponent continuation
uInt uexp=(uInt)(num->exponent+DECBIAS); // biased exponent
uInt code=(uexp>>DECECONL)<<4; // top two bits of exp
// [msd==0]
// look up the combination field and make high word
encode=DECCOMBFROM[code]; // indexed by (0-2)*16+msd
encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation
}
else encode=num->exponent; // special [already in word]
encode|=num->sign; // add sign
// private macro to extract a declet, n (where 0<=n<DECLETS and 0
// refers to the declet from the least significant three digits)
// and put the corresponding DPD code into dpd. Access to umsd and
// ulsd (pointers to the most and least significant digit of the
// variable-length coefficient) is assumed, along with use of a
// working pointer, uInt *ub.
// As not full-length then chances are there are many leading zeros
// [and there may be a partial triad]
#define getDPDt(dpd, n) ub=ulsd-(3*(n))-2; \
if (ub<umsd-2) dpd=0; \
else if (ub>=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; \
else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];}
// place the declets in the encoding words and copy to result (df),
// according to endianness; in all cases complete the sign word
// first
#if DECPMAX==7
getDPDt(dpd, 1);
encode|=dpd<<10;
getDPDt(dpd, 0);
encode|=dpd;
DFWORD(df, 0)=encode; // just the one word
#elif DECPMAX==16
getDPDt(dpd, 4); encode|=dpd<<8;
getDPDt(dpd, 3); encode|=dpd>>2;
DFWORD(df, 0)=encode;
encode=dpd<<30;
getDPDt(dpd, 2); encode|=dpd<<20;
getDPDt(dpd, 1); encode|=dpd<<10;
getDPDt(dpd, 0); encode|=dpd;
DFWORD(df, 1)=encode;
#elif DECPMAX==34
getDPDt(dpd,10); encode|=dpd<<4;
getDPDt(dpd, 9); encode|=dpd>>6;
DFWORD(df, 0)=encode;
encode=dpd<<26;
getDPDt(dpd, 8); encode|=dpd<<16;
getDPDt(dpd, 7); encode|=dpd<<6;
getDPDt(dpd, 6); encode|=dpd>>4;
DFWORD(df, 1)=encode;
encode=dpd<<28;
getDPDt(dpd, 5); encode|=dpd<<18;
getDPDt(dpd, 4); encode|=dpd<<8;
getDPDt(dpd, 3); encode|=dpd>>2;
DFWORD(df, 2)=encode;
encode=dpd<<30;
getDPDt(dpd, 2); encode|=dpd<<20;
getDPDt(dpd, 1); encode|=dpd<<10;
getDPDt(dpd, 0); encode|=dpd;
DFWORD(df, 3)=encode;
#endif
// printf("Status: %08lx\n", (LI)set->status);
// decFloatShow(df, "final2");
return df;
} // decFinalize
/* ------------------------------------------------------------------ */
/* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign */
/* */
/* df is the target decFloat */
/* exp is the in-range unbiased exponent, q, or a special value in */
/* the form returned by decFloatGetExponent */
/* bcdar holds DECPMAX digits to set the coefficient from, one */
/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */
/* if df is a NaN; all are ignored if df is infinite. */
/* All bytes must be in 0-9; results are undefined otherwise. */
/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */
/* returns df, which will be canonical */
/* */
/* No error is possible, and no status will be set. */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar,
Int sig) {
uInt encode, dpd; // work
const uByte *ub; // ..
if (EXPISSPECIAL(exp)) encode=exp|sig;// specials already encoded
else { // is finite
// encode the combination field and exponent continuation
uInt uexp=(uInt)(exp+DECBIAS); // biased exponent
uInt code=(uexp>>DECECONL)<<4; // top two bits of exp
code+=bcdar[0]; // add msd
// look up the combination field and make high word
encode=DECCOMBFROM[code]|sig; // indexed by (0-2)*16+msd
encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation
}
// private macro to extract a declet, n (where 0<=n<DECLETS and 0
// refers to the declet from the least significant three digits)
// and put the corresponding DPD code into dpd.
// Use of a working pointer, uInt *ub, is assumed.
#define getDPDb(dpd, n) ub=bcdar+DECPMAX-1-(3*(n))-2; \
dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)];
// place the declets in the encoding words and copy to result (df),
// according to endianness; in all cases complete the sign word
// first
#if DECPMAX==7
getDPDb(dpd, 1);
encode|=dpd<<10;
getDPDb(dpd, 0);
encode|=dpd;
DFWORD(df, 0)=encode; // just the one word
#elif DECPMAX==16
getDPDb(dpd, 4); encode|=dpd<<8;
getDPDb(dpd, 3); encode|=dpd>>2;
DFWORD(df, 0)=encode;
encode=dpd<<30;
getDPDb(dpd, 2); encode|=dpd<<20;
getDPDb(dpd, 1); encode|=dpd<<10;
getDPDb(dpd, 0); encode|=dpd;
DFWORD(df, 1)=encode;
#elif DECPMAX==34
getDPDb(dpd,10); encode|=dpd<<4;
getDPDb(dpd, 9); encode|=dpd>>6;
DFWORD(df, 0)=encode;
encode=dpd<<26;
getDPDb(dpd, 8); encode|=dpd<<16;
getDPDb(dpd, 7); encode|=dpd<<6;
getDPDb(dpd, 6); encode|=dpd>>4;
DFWORD(df, 1)=encode;
encode=dpd<<28;
getDPDb(dpd, 5); encode|=dpd<<18;
getDPDb(dpd, 4); encode|=dpd<<8;
getDPDb(dpd, 3); encode|=dpd>>2;
DFWORD(df, 2)=encode;
encode=dpd<<30;
getDPDb(dpd, 2); encode|=dpd<<20;
getDPDb(dpd, 1); encode|=dpd<<10;
getDPDb(dpd, 0); encode|=dpd;
DFWORD(df, 3)=encode;
#endif
// decFloatShow(df, "fromB");
return df;
} // decFloatFromBCD
/* ------------------------------------------------------------------ */
/* decFloatFromPacked -- set decFloat from exponent and packed BCD */
/* */
/* df is the target decFloat */
/* exp is the in-range unbiased exponent, q, or a special value in */
/* the form returned by decFloatGetExponent */
/* packed holds DECPMAX packed decimal digits plus a sign nibble */
/* (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */
/* and all except sign are ignored if df is infinite. For DOUBLE */
/* and QUAD the first (pad) nibble is also ignored in all cases. */
/* All coefficient nibbles must be in 0-9 and sign in A-F; results */
/* are undefined otherwise. */
/* returns df, which will be canonical */
/* */
/* No error is possible, and no status will be set. */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) {
uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign]
const uByte *ip; // ..
uByte *op; // ..
Int sig=0; // sign
// expand coefficient and sign to BCDAR
#if SINGLE
op=bcdar+1; // no pad digit
#else
op=bcdar; // first (pad) digit ignored
#endif
for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
*op++=*ip>>4;
*op++=(uByte)(*ip&0x0f); // [final nibble is sign]
}
op--; // -> sign byte
if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;
if (EXPISSPECIAL(exp)) { // Infinity or NaN
if (!EXPISINF(exp)) bcdar[1]=0; // a NaN: ignore MSD
else memset(bcdar+1, 0, DECPMAX); // Infinite: coefficient to 0
}
return decFloatFromBCD(df, exp, bcdar+1, sig);
} // decFloatFromPacked
/* ------------------------------------------------------------------ */
/* decFloatFromPackedChecked -- set from exponent and packed; checked */
/* */
/* df is the target decFloat */
/* exp is the in-range unbiased exponent, q, or a special value in */
/* the form returned by decFloatGetExponent */
/* packed holds DECPMAX packed decimal digits plus a sign nibble */
/* (all 6 codes are OK); the first (MSD) must be 0 if df is a NaN */
/* and all digits must be 0 if df is infinite. For DOUBLE and */
/* QUAD the first (pad) nibble must be 0. */
/* All coefficient nibbles must be in 0-9 and sign in A-F. */
/* returns df, which will be canonical or NULL if any of the */
/* requirements are not met (if this case df is unchanged); that */
/* is, the input data must be as returned by decFloatToPacked, */
/* except that all six sign codes are acccepted. */
/* */
/* No status will be set. */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromPackedChecked(decFloat *df, Int exp,
const uByte *packed) {
uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign]
const uByte *ip; // ..
uByte *op; // ..
Int sig=0; // sign
// expand coefficient and sign to BCDAR
#if SINGLE
op=bcdar+1; // no pad digit
#else
op=bcdar; // first (pad) digit here
#endif
for (ip=packed; ip<packed+((DECPMAX+2)/2); ip++) {
*op=*ip>>4;
if (*op>9) return NULL;
op++;
*op=(uByte)(*ip&0x0f); // [final nibble is sign]
if (*op>9 && ip<packed+((DECPMAX+2)/2)-1) return NULL;
op++;
}
op--; // -> sign byte
if (*op<=9) return NULL; // bad sign
if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign;
#if !SINGLE
if (bcdar[0]!=0) return NULL; // bad pad nibble
#endif
if (EXPISNAN(exp)) { // a NaN
if (bcdar[1]!=0) return NULL; // bad msd
} // NaN
else if (EXPISINF(exp)) { // is infinite
Int i;
for (i=0; i<DECPMAX; i++) {
if (bcdar[i+1]!=0) return NULL; // should be all zeros
}
} // infinity
else { // finite
// check the exponent is in range
if (exp>DECEMAX-DECPMAX+1) return NULL;
if (exp<DECEMIN-DECPMAX+1) return NULL;
}
return decFloatFromBCD(df, exp, bcdar+1, sig);
} // decFloatFromPacked
/* ------------------------------------------------------------------ */
/* decFloatFromString -- conversion from numeric string */
/* */
/* result is the decFloat format number which gets the result of */
/* the conversion */
/* *string is the character string which should contain a valid */
/* number (which may be a special value), \0-terminated */
/* If there are too many significant digits in the */
/* coefficient it will be rounded. */
/* set is the context */
/* returns result */
/* */
/* 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. */
/* */
/* There is no limit to the coefficient length for finite inputs; */
/* NaN payloads must be integers with no more than DECPMAX-1 digits. */
/* Exponents may have up to nine significant digits. */
/* */
/* If bad syntax is detected, the result will be a quiet NaN. */
/* ------------------------------------------------------------------ */
decFloat * decFloatFromString(decFloat *result, const char *string,
decContext *set) {
Int digits; // count of digits in coefficient
const char *dotchar=NULL; // where dot was found [NULL if none]
const char *cfirst=string; // -> first character of decimal part
const char *c; // work
uByte *ub; // ..
uInt uiwork; // for macros
bcdnum num; // collects data for finishing
uInt error=DEC_Conversion_syntax; // assume the worst
uByte buffer[ROUNDUP(DECSTRING+11, 8)]; // room for most coefficents,
// some common rounding, +3, & pad
#if DECTRACE
// printf("FromString %s ...\n", string);
#endif
for(;;) { // once-only 'loop'
num.sign=0; // assume non-negative
num.msd=buffer; // MSD is here always
// detect and validate the coefficient, including any leading,
// trailing, or embedded '.'
// [could test four-at-a-time here (saving 10% for decQuads),
// but that risks storage violation because the position of the
// terminator is unknown]
for (c=string;; c++) { // -> input character
if (((unsigned)(*c-'0'))<=9) continue; // '0' through '9' is good
if (*c=='\0') break; // most common non-digit
if (*c=='.') {
if (dotchar!=NULL) break; // not first '.'
dotchar=c; // record offset into decimal part
continue;}
if (c==string) { // first in string...
if (*c=='-') { // valid - sign
cfirst++;
num.sign=DECFLOAT_Sign;
continue;}
if (*c=='+') { // valid + sign
cfirst++;
continue;}
}
// *c is not a digit, terminator, or a valid +, -, or '.'
break;
} // c loop
digits=(uInt)(c-cfirst); // digits (+1 if a dot)
if (digits>0) { // had digits and/or dot
const char *clast=c-1; // note last coefficient char position
Int exp=0; // exponent accumulator
if (*c!='\0') { // something follows the coefficient
uInt edig; // unsigned work
// had some digits and more to come; expect E[+|-]nnn now
const char *firstexp; // exponent first non-zero
if (*c!='E' && *c!='e') break;
c++; // to (optional) sign
if (*c=='-' || *c=='+') c++; // step over sign (c=clast+2)
if (*c=='\0') break; // no digits! (e.g., '1.2E')
for (; *c=='0';) c++; // skip leading zeros [even last]
firstexp=c; // remember start [maybe '\0']
// gather exponent digits
edig=(uInt)*c-(uInt)'0';
if (edig<=9) { // [check not bad or terminator]
exp+=edig; // avoid initial X10
c++;
for (;; c++) {
edig=(uInt)*c-(uInt)'0';
if (edig>9) break;
exp=exp*10+edig;
}
}
// if not now on the '\0', *c must not be a digit
if (*c!='\0') break;
// (this next test must be after the syntax checks)
// if definitely more than the possible digits for format then
// the exponent may have wrapped, so simply set it to a certain
// over/underflow value
if (c>firstexp+DECEMAXD) exp=DECEMAX*2;
if (*(clast+2)=='-') exp=-exp; // was negative
} // exponent part
if (dotchar!=NULL) { // had a '.'
digits--; // remove from digits count
if (digits==0) break; // was dot alone: bad syntax
exp-=(Int)(clast-dotchar); // adjust exponent
// [the '.' can now be ignored]
}
num.exponent=exp; // exponent is good; store it
// Here when whole string has been inspected and syntax is good
// cfirst->first digit or dot, clast->last digit or dot
error=0; // no error possible now
// if the number of digits in the coefficient will fit in buffer
// then it can simply be converted to bcd8 and copied -- decFinalize
// will take care of leading zeros and rounding; the buffer is big
// enough for all canonical coefficients, including 0.00000nn...
ub=buffer;
if (digits<=(Int)(sizeof(buffer)-3)) { // [-3 allows by-4s copy]
c=cfirst;
if (dotchar!=NULL) { // a dot to worry about
if (*(c+1)=='.') { // common canonical case
*ub++=(uByte)(*c-'0'); // copy leading digit
c+=2; // prepare to handle rest
}
else for (; c<=clast;) { // '.' could be anywhere
// as usual, go by fours when safe; NB it has been asserted
// that a '.' does not have the same mask as a digit
if (c<=clast-3 // safe for four
&& (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // test four
UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8
ub+=4;
c+=4;
continue;
}
if (*c=='.') { // found the dot
c++; // step over it ..
break; // .. and handle the rest
}
*ub++=(uByte)(*c++-'0');
}
} // had dot
// Now no dot; do this by fours (where safe)
for (; c<=clast-3; c+=4, ub+=4) UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f);
for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0');
num.lsd=buffer+digits-1; // record new LSD
} // fits
else { // too long for buffer
// [This is a rare and unusual case; arbitrary-length input]
// strip leading zeros [but leave final 0 if all 0's]
if (*cfirst=='.') cfirst++; // step past dot at start
if (*cfirst=='0') { // [cfirst always -> digit]
for (; cfirst<clast; cfirst++) {
if (*cfirst!='0') { // non-zero found
if (*cfirst=='.') continue; // [ignore]
break; // done
}
digits--; // 0 stripped
} // cfirst
} // at least one leading 0
// the coefficient is now as short as possible, but may still
// be too long; copy up to Pmax+1 digits to the buffer, then
// just record any non-zeros (set round-for-reround digit)
for (c=cfirst; c<=clast && ub<=buffer+DECPMAX; c++) {
// (see commentary just above)
if (c<=clast-3 // safe for four
&& (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // four digits
UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8
ub+=4;
c+=3; // [will become 4]
continue;
}
if (*c=='.') continue; // [ignore]
*ub++=(uByte)(*c-'0');
}
ub--; // -> LSD
for (; c<=clast; c++) { // inspect remaining chars
if (*c!='0') { // sticky bit needed
if (*c=='.') continue; // [ignore]
*ub=DECSTICKYTAB[*ub]; // update round-for-reround
break; // no need to look at more
}
}
num.lsd=ub; // record LSD
// adjust exponent for dropped digits
num.exponent+=digits-(Int)(ub-buffer+1);
} // too long for buffer
} // digits and/or dot
else { // no digits or dot were found
// only Infinities and NaNs are allowed, here
if (*c=='\0') break; // nothing there is bad
buffer[0]=0; // default a coefficient of 0
num.lsd=buffer; // ..
if (decBiStr(c, "infinity", "INFINITY")
|| decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf;
else { // should be a NaN
num.exponent=DECFLOAT_qNaN; // assume quiet NaN
if (*c=='s' || *c=='S') { // probably an sNaN
num.exponent=DECFLOAT_sNaN; // effect the 's'
c++; // and step over it
}
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 (no dots), expected
// -> start of integer, and skip leading 0s [including plain 0]
for (cfirst=c; *cfirst=='0';) cfirst++;
if (*cfirst!='\0') { // not empty or all-0, payload
// payload found; check all valid digits and copy to buffer as bcd8
ub=buffer;
for (c=cfirst;; c++, ub++) {
if ((unsigned)(*c-'0')>9) break; // quit if not 0-9
if (c-cfirst==DECPMAX-1) break; // too many digits
*ub=(uByte)(*c-'0'); // good bcd8
}
if (*c!='\0') break; // not all digits, or too many
num.lsd=ub-1; // record new LSD
}
} // NaN or sNaN
error=0; // syntax is OK
} // digits=0 (special expected)
break; // drop out
} // [for(;;) once-loop]
// decShowNum(&num, "fromStr");
if (error!=0) {
set->status|=error;
num.exponent=DECFLOAT_qNaN; // set up quiet NaN
num.sign=0; // .. with 0 sign
buffer[0]=0; // .. and coefficient
num.lsd=buffer; // ..
// decShowNum(&num, "oops");
}
// decShowNum(&num, "dffs");
decFinalize(result, &num, set); // round, check, and lay out
// decFloatShow(result, "fromString");
return result;
} // decFloatFromString
/* ------------------------------------------------------------------ */
/* decFloatFromWider -- conversion from next-wider format */
/* */
/* result is the decFloat format number which gets the result of */
/* the conversion */
/* wider is the decFloatWider format number which will be narrowed */
/* set is the context */
/* returns result */
/* */
/* Narrowing can cause rounding, overflow, etc., but not Invalid */
/* operation (sNaNs are copied and do not signal). */
/* ------------------------------------------------------------------ */
// narrow-to is not possible for decQuad format numbers; simply omit
#if !QUAD
decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider,
decContext *set) {
bcdnum num; // collects data for finishing
uByte bcdar[DECWPMAX]; // room for wider coefficient
uInt widerhi=DFWWORD(wider, 0); // top word
Int exp;
GETWCOEFF(wider, bcdar);
num.msd=bcdar; // MSD is here always
num.lsd=bcdar+DECWPMAX-1; // LSD is here always
num.sign=widerhi&0x80000000; // extract sign [DECFLOAT_Sign=Neg]
// decode the wider combination field to exponent
exp=DECCOMBWEXP[widerhi>>26]; // decode from wider combination field
// if it is a special there's nothing to do unless sNaN; if it's
// finite then add the (wider) exponent continuation and unbias
if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; // include sNaN selector
else exp+=GETWECON(wider)-DECWBIAS;
num.exponent=exp;
// decShowNum(&num, "dffw");
return decFinalize(result, &num, set);// round, check, and lay out
} // decFloatFromWider
#endif
/* ------------------------------------------------------------------ */
/* decFloatGetCoefficient -- get coefficient as BCD8 */
/* */
/* df is the decFloat from which to extract the coefficient */
/* bcdar is where DECPMAX bytes will be written, one BCD digit in */
/* each byte (BCD8 encoding); if df is a NaN the first byte will */
/* be zero, and if it is infinite they will all be zero */
/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
/* 0 otherwise) */
/* */
/* No error is possible, and no status will be set. If df is a */
/* special value the array is set to zeros (for Infinity) or to the */
/* payload of a qNaN or sNaN. */
/* ------------------------------------------------------------------ */
Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) {
if (DFISINF(df)) memset(bcdar, 0, DECPMAX);
else {
GETCOEFF(df, bcdar); // use macro
if (DFISNAN(df)) bcdar[0]=0; // MSD needs correcting
}
return GETSIGN(df);
} // decFloatGetCoefficient
/* ------------------------------------------------------------------ */
/* decFloatGetExponent -- get unbiased exponent */
/* */
/* df is the decFloat from which to extract the exponent */
/* returns the exponent, q. */
/* */
/* No error is possible, and no status will be set. If df is a */
/* special value the first seven bits of the decFloat are returned, */
/* left adjusted and with the first (sign) bit set to 0 (followed by */
/* 25 0 bits). e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN). */
/* ------------------------------------------------------------------ */
Int decFloatGetExponent(const decFloat *df) {
if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000;
return GETEXPUN(df);
} // decFloatGetExponent
/* ------------------------------------------------------------------ */
/* decFloatSetCoefficient -- set coefficient from BCD8 */
/* */
/* df is the target decFloat (and source of exponent/special value) */
/* bcdar holds DECPMAX digits to set the coefficient from, one */
/* digit in each byte (BCD8 encoding); the first (MSD) is ignored */
/* if df is a NaN; all are ignored if df is infinite. */
/* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */
/* returns df, which will be canonical */
/* */
/* No error is possible, and no status will be set. */
/* ------------------------------------------------------------------ */
decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar,
Int sig) {
uInt exp; // for exponent
uByte bcdzero[DECPMAX]; // for infinities
// Exponent/special code is extracted from df
if (DFISSPECIAL(df)) {
exp=DFWORD(df, 0)&0x7e000000;
if (DFISINF(df)) {
memset(bcdzero, 0, DECPMAX);
return decFloatFromBCD(df, exp, bcdzero, sig);
}
}
else exp=GETEXPUN(df);
return decFloatFromBCD(df, exp, bcdar, sig);
} // decFloatSetCoefficient
/* ------------------------------------------------------------------ */
/* decFloatSetExponent -- set exponent or special value */
/* */
/* df is the target decFloat (and source of coefficient/payload) */
/* set is the context for reporting status */
/* exp is the unbiased exponent, q, or a special value in the form */
/* returned by decFloatGetExponent */
/* returns df, which will be canonical */
/* */
/* No error is possible, but Overflow or Underflow might occur. */
/* ------------------------------------------------------------------ */
decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) {
uByte bcdcopy[DECPMAX]; // for coefficient
bcdnum num; // work
num.exponent=exp;
num.sign=decFloatGetCoefficient(df, bcdcopy); // extract coefficient
if (DFISSPECIAL(df)) { // MSD or more needs correcting
if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX);
bcdcopy[0]=0;
}
num.msd=bcdcopy;
num.lsd=bcdcopy+DECPMAX-1;
return decFinalize(df, &num, set);
} // decFloatSetExponent
/* ------------------------------------------------------------------ */
/* decFloatRadix -- returns the base (10) */
/* */
/* df is any decFloat of this format */
/* ------------------------------------------------------------------ */
uInt decFloatRadix(const decFloat *df) {
if (df) return 10; // to placate compiler
return 10;
} // decFloatRadix
/* The following function is not available if DECPRINT=0 */
#if DECPRINT
/* ------------------------------------------------------------------ */
/* decFloatShow -- printf a decFloat in hexadecimal and decimal */
/* df is the decFloat to show */
/* tag is a tag string displayed with the number */
/* */
/* This is a debug aid; the precise format of the string may change. */
/* ------------------------------------------------------------------ */
void decFloatShow(const decFloat *df, const char *tag) {
char hexbuf[DECBYTES*2+DECBYTES/4+1]; // NB blank after every fourth
char buff[DECSTRING]; // for value in decimal
Int i, j=0;
for (i=0; i<DECBYTES; i++) {
#if DECLITEND
sprintf(&hexbuf[j], "%02x", df->bytes[DECBYTES-1-i]);
#else
sprintf(&hexbuf[j], "%02x", df->bytes[i]);
#endif
j+=2;
// the next line adds blank (and terminator) after final pair, too
if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;}
}
decFloatToString(df, buff);
printf(">%s> %s [big-endian] %s\n", tag, hexbuf, buff);
return;
} // decFloatShow
#endif
/* ------------------------------------------------------------------ */
/* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat */
/* */
/* df is the source decFloat */
/* exp will be set to the unbiased exponent, q, or to a special */
/* value in the form returned by decFloatGetExponent */
/* bcdar is where DECPMAX bytes will be written, one BCD digit in */
/* each byte (BCD8 encoding); if df is a NaN the first byte will */
/* be zero, and if it is infinite they will all be zero */
/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
/* 0 otherwise) */
/* */
/* No error is possible, and no status will be set. */
/* ------------------------------------------------------------------ */
Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) {
if (DFISINF(df)) {
memset(bcdar, 0, DECPMAX);
*exp=DFWORD(df, 0)&0x7e000000;
}
else {
GETCOEFF(df, bcdar); // use macro
if (DFISNAN(df)) {
bcdar[0]=0; // MSD needs correcting
*exp=DFWORD(df, 0)&0x7e000000;
}
else { // finite
*exp=GETEXPUN(df);
}
}
return GETSIGN(df);
} // decFloatToBCD
/* ------------------------------------------------------------------ */
/* decFloatToEngString -- conversion to numeric string, engineering */
/* */
/* df is the decFloat format number to convert */
/* string is the string where the result will be laid out */
/* */
/* string must be at least DECPMAX+9 characters (the worst case is */
/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */
/* DECEMAXD<=4); this condition is asserted above */
/* */
/* No error is possible, and no status will be set */
/* ------------------------------------------------------------------ */
char * decFloatToEngString(const decFloat *df, char *string){
uInt msd; // coefficient MSD
Int exp; // exponent top two bits or full
uInt comb; // combination field
char *cstart; // coefficient start
char *c; // output pointer in string
char *s, *t; // .. (source, target)
Int pre, e; // work
const uByte *u; // ..
uInt uiwork; // for macros [one compiler needs
// volatile here to avoid bug, but
// that doubles execution time]
// Source words; macro handles endianness
uInt sourhi=DFWORD(df, 0); // word with sign
#if DECPMAX==16
uInt sourlo=DFWORD(df, 1);
#elif DECPMAX==34
uInt sourmh=DFWORD(df, 1);
uInt sourml=DFWORD(df, 2);
uInt sourlo=DFWORD(df, 3);
#endif
c=string; // where result will go
if (((Int)sourhi)<0) *c++='-'; // handle sign
comb=sourhi>>26; // sign+combination field
msd=DECCOMBMSD[comb]; // decode the combination field
exp=DECCOMBEXP[comb]; // ..
if (EXPISSPECIAL(exp)) { // special
if (exp==DECFLOAT_Inf) { // infinity
strcpy(c, "Inf");
strcpy(c+3, "inity");
return string; // easy
}
if (sourhi&0x02000000) *c++='s'; // sNaN
strcpy(c, "NaN"); // complete word
c+=3; // step past
// quick exit if the payload is zero
#if DECPMAX==7
if ((sourhi&0x000fffff)==0) return string;
#elif DECPMAX==16
if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
#elif DECPMAX==34
if (sourlo==0 && sourml==0 && sourmh==0
&& (sourhi&0x00003fff)==0) return string;
#endif
// otherwise drop through to add integer; set correct exp etc.
exp=0; msd=0; // setup for following code
}
else { // complete exponent; top two bits are in place
exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias
}
/* convert the digits of the significand to characters */
cstart=c; // save start of coefficient
if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit
// Decode the declets. After extracting each declet, it is
// decoded to a 4-uByte sequence by table lookup; the four uBytes
// are the three encoded BCD8 digits followed by a 1-byte length
// (significant digits, except that 000 has length 0). This allows
// us to left-align the first declet with non-zero content, then
// the remaining ones are full 3-char length. Fixed-length copies
// are used because variable-length memcpy causes a subroutine call
// in at least two compilers. (The copies are length 4 for speed
// and are safe because the last item in the array is of length
// three and has the length byte following.)
#define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \
if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \
else if (*(u+3)) { \
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}
#if DECPMAX==7
dpd2char(sourhi>>10); // declet 1
dpd2char(sourhi); // declet 2
#elif DECPMAX==16
dpd2char(sourhi>>8); // declet 1
dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2
dpd2char(sourlo>>20); // declet 3
dpd2char(sourlo>>10); // declet 4
dpd2char(sourlo); // declet 5
#elif DECPMAX==34
dpd2char(sourhi>>4); // declet 1
dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2
dpd2char(sourmh>>16); // declet 3
dpd2char(sourmh>>6); // declet 4
dpd2char((sourmh<<4) | (sourml>>28)); // declet 5
dpd2char(sourml>>18); // declet 6
dpd2char(sourml>>8); // declet 7
dpd2char((sourml<<2) | (sourlo>>30)); // declet 8
dpd2char(sourlo>>20); // declet 9
dpd2char(sourlo>>10); // declet 10
dpd2char(sourlo); // declet 11
#endif
if (c==cstart) *c++='0'; // all zeros, empty -- make "0"
if (exp==0) { // integer or NaN case -- easy
*c='\0'; // terminate
return string;
}
/* non-0 exponent */
e=0; // assume no E
pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1]
// [here, pre-exp is the digits count (==1 for zero)]
if (exp>0 || pre<-5) { // need exponential form
e=pre-1; // calculate E value
pre=1; // assume one digit before '.'
if (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 (!DFISZERO(df)) pre+=adj;
else { // is zero
if (adj!=0) { // 0.00Esnn needed
e=e+3;
pre=-(2-adj);
}
} // zero
} // engineering adjustment
} // exponential form
// printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp);
/* modify the coefficient, adding 0s, '.', and E+nn as needed */
if (pre>0) { // ddd.ddd (plain), perhaps with E
// or dd00 padding for engineering
char *dotat=cstart+pre;
if (dotat<c) { // if embedded dot needed...
// move by fours; there must be space for junk at the end
// because there is still space for exponent
s=dotat+ROUNDDOWN4(c-dotat); // source
t=s+1; // target
// open the gap [cannot use memcpy]
for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
*dotat='.';
c++; // length increased by one
} // need dot?
else for (; c<dotat; c++) *c='0'; // pad for engineering
} // pre>0
else {
/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have
E, but only for 0.00E+3 kind of case -- with plenty of spare
space in this case */
pre=-pre+2; // gap width, including "0."
t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point
// backoff if too far to the right
if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit
// now shift the entire coefficient to the right, being careful not
// to access to the left of string [cannot use memcpy]
for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
// for Quads and Singles there may be a character or two left...
s+=3; // where next would come from
for(; s>=cstart; s--, t--) *(t+3)=*(s);
// now have fill 0. through 0.00000; use overlaps to avoid tests
if (pre>=4) {
memcpy(cstart+pre-4, "0000", 4);
memcpy(cstart, "0.00", 4);
}
else { // 2 or 3
*(cstart+pre-1)='0';
memcpy(cstart, "0.", 2);
}
c+=pre; // to end
}
// finally add the E-part, if needed; it will never be 0, and has
// a maximum length of 3 or 4 digits (asserted above)
if (e!=0) {
memcpy(c, "E+", 2); // starts with E, assume +
c++;
if (e<0) {
*c='-'; // oops, need '-'
e=-e; // uInt, please
}
c++;
// Three-character exponents are easy; 4-character a little trickier
#if DECEMAXD<=3
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
// copy fixed 4 characters [is safe], starting at non-zero
// and with character mask to convert BCD to char
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);
c+=*(u+3); // bump pointer appropriately
#elif DECEMAXD==4
if (e<1000) { // 3 (or fewer) digits case
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]
c+=*(u+3); // bump pointer appropriately
}
else { // 4-digits
Int thou=((e>>3)*1049)>>17; // e/1000
Int rem=e-(1000*thou); // e%1000
*c++=(char)('0'+(char)thou); // the thousands digit
u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte
UBFROMUI(c, UBTOUI(u)|CHARMASK);// copy fixed 3+1 characters [is safe]
c+=3; // bump pointer, always 3 digits
}
#endif
}
*c='\0'; // terminate
//printf("res %s\n", string);
return string;
} // decFloatToEngString
/* ------------------------------------------------------------------ */
/* decFloatToPacked -- convert decFloat to Packed decimal + exponent */
/* */
/* df is the source decFloat */
/* exp will be set to the unbiased exponent, q, or to a special */
/* value in the form returned by decFloatGetExponent */
/* packed is where DECPMAX nibbles will be written with the sign as */
/* final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */
/* of zero, and an infinity is all zeros. decDouble and decQuad */
/* have a additional leading zero nibble, leading to result */
/* lengths of 4, 9, and 18 bytes. */
/* returns the sign of the coefficient (DECFLOAT_Sign if negative, */
/* 0 otherwise) */
/* */
/* No error is possible, and no status will be set. */
/* ------------------------------------------------------------------ */
Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) {
uByte bcdar[DECPMAX+2]; // work buffer
uByte *ip=bcdar, *op=packed; // work pointers
if (DFISINF(df)) {
memset(bcdar, 0, DECPMAX+2);
*exp=DECFLOAT_Inf;
}
else {
GETCOEFF(df, bcdar+1); // use macro
if (DFISNAN(df)) {
bcdar[1]=0; // MSD needs clearing
*exp=DFWORD(df, 0)&0x7e000000;
}
else { // finite
*exp=GETEXPUN(df);
}
}
// now pack; coefficient currently at bcdar+1
#if SINGLE
ip++; // ignore first byte
#else
*ip=0; // need leading zero
#endif
// set final byte to Packed BCD sign value
bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS);
// pack an even number of bytes...
for (; op<packed+((DECPMAX+2)/2); op++, ip+=2) {
*op=(uByte)((*ip<<4)+*(ip+1));
}
return (bcdar[DECPMAX+1]==DECPMINUS ? DECFLOAT_Sign : 0);
} // decFloatToPacked
/* ------------------------------------------------------------------ */
/* decFloatToString -- conversion to numeric string */
/* */
/* df is the decFloat format number to convert */
/* string is the string where the result will be laid out */
/* */
/* string must be at least DECPMAX+9 characters (the worst case is */
/* "-0.00000nnn...nnn\0", which is as long as the exponent form when */
/* DECEMAXD<=4); this condition is asserted above */
/* */
/* No error is possible, and no status will be set */
/* ------------------------------------------------------------------ */
char * decFloatToString(const decFloat *df, char *string){
uInt msd; // coefficient MSD
Int exp; // exponent top two bits or full
uInt comb; // combination field
char *cstart; // coefficient start
char *c; // output pointer in string
char *s, *t; // .. (source, target)
Int pre, e; // work
const uByte *u; // ..
uInt uiwork; // for macros [one compiler needs
// volatile here to avoid bug, but
// that doubles execution time]
// Source words; macro handles endianness
uInt sourhi=DFWORD(df, 0); // word with sign
#if DECPMAX==16
uInt sourlo=DFWORD(df, 1);
#elif DECPMAX==34
uInt sourmh=DFWORD(df, 1);
uInt sourml=DFWORD(df, 2);
uInt sourlo=DFWORD(df, 3);
#endif
c=string; // where result will go
if (((Int)sourhi)<0) *c++='-'; // handle sign
comb=sourhi>>26; // sign+combination field
msd=DECCOMBMSD[comb]; // decode the combination field
exp=DECCOMBEXP[comb]; // ..
if (!EXPISSPECIAL(exp)) { // finite
// complete exponent; top two bits are in place
exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias
}
else { // IS special
if (exp==DECFLOAT_Inf) { // infinity
strcpy(c, "Infinity");
return string; // easy
}
if (sourhi&0x02000000) *c++='s'; // sNaN
strcpy(c, "NaN"); // complete word
c+=3; // step past
// quick exit if the payload is zero
#if DECPMAX==7
if ((sourhi&0x000fffff)==0) return string;
#elif DECPMAX==16
if (sourlo==0 && (sourhi&0x0003ffff)==0) return string;
#elif DECPMAX==34
if (sourlo==0 && sourml==0 && sourmh==0
&& (sourhi&0x00003fff)==0) return string;
#endif
// otherwise drop through to add integer; set correct exp etc.
exp=0; msd=0; // setup for following code
}
/* convert the digits of the significand to characters */
cstart=c; // save start of coefficient
if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit
// Decode the declets. After extracting each declet, it is
// decoded to a 4-uByte sequence by table lookup; the four uBytes
// are the three encoded BCD8 digits followed by a 1-byte length
// (significant digits, except that 000 has length 0). This allows
// us to left-align the first declet with non-zero content, then
// the remaining ones are full 3-char length. Fixed-length copies
// are used because variable-length memcpy causes a subroutine call
// in at least two compilers. (The copies are length 4 for speed
// and are safe because the last item in the array is of length
// three and has the length byte following.)
#define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \
if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \
else if (*(u+3)) { \
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);}
#if DECPMAX==7
dpd2char(sourhi>>10); // declet 1
dpd2char(sourhi); // declet 2
#elif DECPMAX==16
dpd2char(sourhi>>8); // declet 1
dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2
dpd2char(sourlo>>20); // declet 3
dpd2char(sourlo>>10); // declet 4
dpd2char(sourlo); // declet 5
#elif DECPMAX==34
dpd2char(sourhi>>4); // declet 1
dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2
dpd2char(sourmh>>16); // declet 3
dpd2char(sourmh>>6); // declet 4
dpd2char((sourmh<<4) | (sourml>>28)); // declet 5
dpd2char(sourml>>18); // declet 6
dpd2char(sourml>>8); // declet 7
dpd2char((sourml<<2) | (sourlo>>30)); // declet 8
dpd2char(sourlo>>20); // declet 9
dpd2char(sourlo>>10); // declet 10
dpd2char(sourlo); // declet 11
#endif
if (c==cstart) *c++='0'; // all zeros, empty -- make "0"
//[This fast path is valid but adds 3-5 cycles to worst case length]
//if (exp==0) { // integer or NaN case -- easy
// *c='\0'; // terminate
// return string;
// }
e=0; // assume no E
pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1]
// [here, pre-exp is the digits count (==1 for zero)]
if (exp>0 || pre<-5) { // need exponential form
e=pre-1; // calculate E value
pre=1; // assume one digit before '.'
} // exponential form
/* modify the coefficient, adding 0s, '.', and E+nn as needed */
if (pre>0) { // ddd.ddd (plain), perhaps with E
char *dotat=cstart+pre;
if (dotat<c) { // if embedded dot needed...
// [memmove is a disaster, here]
// move by fours; there must be space for junk at the end
// because exponent is still possible
s=dotat+ROUNDDOWN4(c-dotat); // source
t=s+1; // target
// open the gap [cannot use memcpy]
for (; s>=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
*dotat='.';
c++; // length increased by one
} // need dot?
// finally add the E-part, if needed; it will never be 0, and has
// a maximum length of 3 or 4 digits (asserted above)
if (e!=0) {
memcpy(c, "E+", 2); // starts with E, assume +
c++;
if (e<0) {
*c='-'; // oops, need '-'
e=-e; // uInt, please
}
c++;
// Three-character exponents are easy; 4-character a little trickier
#if DECEMAXD<=3
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
// copy fixed 4 characters [is safe], starting at non-zero
// and with character mask to convert BCD to char
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK);
c+=*(u+3); // bump pointer appropriately
#elif DECEMAXD==4
if (e<1000) { // 3 (or fewer) digits case
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]
c+=*(u+3); // bump pointer appropriately
}
else { // 4-digits
Int thou=((e>>3)*1049)>>17; // e/1000
Int rem=e-(1000*thou); // e%1000
*c++=(char)('0'+(char)thou); // the thousands digit
u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte
UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe]
c+=3; // bump pointer, always 3 digits
}
#endif
}
*c='\0'; // add terminator
//printf("res %s\n", string);
return string;
} // pre>0
/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
// Surprisingly, this is close to being the worst-case path, so the
// shift is done by fours; this is a little tricky because the
// rightmost character to be written must not be beyond where the
// rightmost terminator could be -- so backoff to not touch
// terminator position if need be (this can make exact alignments
// for full Doubles, but in some cases needs care not to access too
// far to the left)
pre=-pre+2; // gap width, including "0."
t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point
// backoff if too far to the right
if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit
// now shift the entire coefficient to the right, being careful not
// to access to the left of string [cannot use memcpy]
for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s));
// for Quads and Singles there may be a character or two left...
s+=3; // where next would come from
for(; s>=cstart; s--, t--) *(t+3)=*(s);
// now have fill 0. through 0.00000; use overlaps to avoid tests
if (pre>=4) {
memcpy(cstart+pre-4, "0000", 4);
memcpy(cstart, "0.00", 4);
}
else { // 2 or 3
*(cstart+pre-1)='0';
memcpy(cstart, "0.", 2);
}
*(c+pre)='\0'; // terminate
return string;
} // decFloatToString
/* ------------------------------------------------------------------ */
/* decFloatToWider -- conversion to next-wider format */
/* */
/* source is the decFloat format number which gets the result of */
/* the conversion */
/* wider is the decFloatWider format number which will be narrowed */
/* returns wider */
/* */
/* Widening is always exact; no status is set (sNaNs are copied and */
/* do not signal). The result will be canonical if the source is, */
/* and may or may not be if the source is not. */
/* ------------------------------------------------------------------ */
// widening is not possible for decQuad format numbers; simply omit
#if !QUAD
decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) {
uInt msd;
/* Construct and copy the sign word */
if (DFISSPECIAL(source)) {
// copy sign, combination, and first bit of exponent (sNaN selector)
DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000;
msd=0;
}
else { // is finite number
uInt exp=GETEXPUN(source)+DECWBIAS; // get unbiased exponent and rebias
uInt code=(exp>>DECWECONL)<<29; // set two bits of exp [msd=0]
code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; // add exponent continuation
code|=DFWORD(source, 0)&0x80000000; // add sign
DFWWORD(wider, 0)=code; // .. and place top word in wider
msd=GETMSD(source); // get source coefficient MSD [0-9]
}
/* Copy the coefficient and clear any 'unused' words to left */
#if SINGLE
DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20);
#elif DOUBLE
DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18);
DFWWORD(wider, 3)=DFWORD(source, 1);
DFWWORD(wider, 1)=0;
#endif
return wider;
} // decFloatToWider
#endif
/* ------------------------------------------------------------------ */
/* decFloatVersion -- return package version string */
/* */
/* returns a constant string describing this package */
/* ------------------------------------------------------------------ */
const char *decFloatVersion(void) {
return DECVERSION;
} // decFloatVersion
/* ------------------------------------------------------------------ */
/* decFloatZero -- set to canonical (integer) zero */
/* */
/* df is the decFloat format number to integer +0 (q=0, c=+0) */
/* returns df */
/* */
/* No error is possible, and no status can be set. */
/* ------------------------------------------------------------------ */
decFloat * decFloatZero(decFloat *df){
DFWORD(df, 0)=ZEROWORD; // set appropriate top word
#if DOUBLE || QUAD
DFWORD(df, 1)=0;
#if QUAD
DFWORD(df, 2)=0;
DFWORD(df, 3)=0;
#endif
#endif
// decFloatShow(df, "zero");
return df;
} // decFloatZero
/* ------------------------------------------------------------------ */
/* Private generic function (not format-specific) for development use */
/* ------------------------------------------------------------------ */
// This is included once only, for all to use
#if QUAD && (DECCHECK || DECTRACE)
/* ---------------------------------------------------------------- */
/* decShowNum -- display bcd8 number in debug form */
/* */
/* num is the bcdnum to display */
/* tag is a string to label the display */
/* ---------------------------------------------------------------- */
void decShowNum(const bcdnum *num, const char *tag) {
const char *csign="+"; // sign character
uByte *ub; // work
uInt uiwork; // for macros
if (num->sign==DECFLOAT_Sign) csign="-";
printf(">%s> ", tag);
if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign);
else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign);
else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign);
else { // finite
char qbuf[10]; // for right-aligned q
char *c; // work
const uByte *u; // ..
Int e=num->exponent; // .. exponent
strcpy(qbuf, "q=");
c=&qbuf[2]; // where exponent will go
// lay out the exponent
if (e<0) {
*c++='-'; // add '-'
e=-e; // uInt, please
}
#if DECEMAXD>4
#error Exponent form is too long for ShowNum to lay out
#endif
if (e==0) *c++='0'; // 0-length case
else if (e<1000) { // 3 (or fewer) digits case
u=&BIN2BCD8[e*4]; // -> 3 digits + length byte
UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above]
c+=*(u+3); // bump pointer appropriately
}
else { // 4-digits
Int thou=((e>>3)*1049)>>17; // e/1000
Int rem=e-(1000*thou); // e%1000
*c++=(char)('0'+(char)thou); // the thousands digit
u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte
UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe]
c+=3; // bump pointer, always 3 digits
}
*c='\0'; // add terminator
printf("%7s c=%s", qbuf, csign);
}
if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) {
for (ub=num->msd; ub<=num->lsd; ub++) { // coefficient...
printf("%1x", *ub);
if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); // 4-space
}
}
printf("\n");
} // decShowNum
#endif