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840 lines
37 KiB
C
840 lines
37 KiB
C
9 years ago
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/* ------------------------------------------------------------------ */
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/* Decimal 64-bit format module */
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/* ------------------------------------------------------------------ */
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/* Copyright (c) IBM Corporation, 2000, 2009. All rights reserved. */
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/* */
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/* This software is made available under the terms of the */
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/* ICU License -- ICU 1.8.1 and later. */
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/* */
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/* The description and User's Guide ("The decNumber C Library") for */
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/* this software is called decNumber.pdf. This document is */
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/* available, together with arithmetic and format specifications, */
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/* testcases, and Web links, on the General Decimal Arithmetic page. */
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/* */
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/* Please send comments, suggestions, and corrections to the author: */
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/* mfc@uk.ibm.com */
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/* Mike Cowlishaw, IBM Fellow */
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/* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */
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/* ------------------------------------------------------------------ */
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/* This module comprises the routines for decimal64 format numbers. */
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/* Conversions are supplied to and from decNumber and String. */
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/* */
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/* This is used when decNumber provides operations, either for all */
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/* operations or as a proxy between decNumber and decSingle. */
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/* */
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/* Error handling is the same as decNumber (qv.). */
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/* ------------------------------------------------------------------ */
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#include <string.h> // [for memset/memcpy]
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#include <stdio.h> // [for printf]
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#define DECNUMDIGITS 16 // make decNumbers with space for 16
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#include "decNumber.h" // base number library
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#include "decNumberLocal.h" // decNumber local types, etc.
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#include "decimal64.h" // our primary include
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/* Utility routines and tables [in decimal64.c]; externs for C++ */
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// DPD2BIN and the reverse are renamed to prevent link-time conflict
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// if decQuad is also built in the same executable
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#define DPD2BIN DPD2BINx
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#define BIN2DPD BIN2DPDx
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extern const uInt COMBEXP[32], COMBMSD[32];
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extern const uShort DPD2BIN[1024];
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extern const uShort BIN2DPD[1000];
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extern const uByte BIN2CHAR[4001];
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extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
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extern void decDigitsToDPD(const decNumber *, uInt *, Int);
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#if DECTRACE || DECCHECK
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void decimal64Show(const decimal64 *); // for debug
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extern void decNumberShow(const decNumber *); // ..
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#endif
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/* Useful macro */
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// Clear a structure (e.g., a decNumber)
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#define DEC_clear(d) memset(d, 0, sizeof(*d))
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/* define and include the tables to use for conversions */
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#define DEC_BIN2CHAR 1
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#define DEC_DPD2BIN 1
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#define DEC_BIN2DPD 1 // used for all sizes
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#include "decDPD.h" // lookup tables
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/* ------------------------------------------------------------------ */
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/* decimal64FromNumber -- convert decNumber to decimal64 */
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/* */
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/* ds is the target decimal64 */
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/* dn is the source number (assumed valid) */
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/* set is the context, used only for reporting errors */
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/* */
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/* The set argument is used only for status reporting and for the */
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/* rounding mode (used if the coefficient is more than DECIMAL64_Pmax */
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/* digits or an overflow is detected). If the exponent is out of the */
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/* valid range then Overflow or Underflow will be raised. */
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/* After Underflow a subnormal result is possible. */
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/* */
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/* DEC_Clamped is set if the number has to be 'folded down' to fit, */
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/* by reducing its exponent and multiplying the coefficient by a */
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/* power of ten, or if the exponent on a zero had to be clamped. */
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/* ------------------------------------------------------------------ */
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decimal64 * decimal64FromNumber(decimal64 *d64, const decNumber *dn,
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decContext *set) {
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uInt status=0; // status accumulator
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Int ae; // adjusted exponent
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decNumber dw; // work
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decContext dc; // ..
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uInt comb, exp; // ..
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uInt uiwork; // for macros
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uInt targar[2]={0, 0}; // target 64-bit
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#define targhi targar[1] // name the word with the sign
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#define targlo targar[0] // and the other
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// If the number has too many digits, or the exponent could be
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// out of range then reduce the number under the appropriate
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// constraints. This could push the number to Infinity or zero,
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// so this check and rounding must be done before generating the
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// decimal64]
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ae=dn->exponent+dn->digits-1; // [0 if special]
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if (dn->digits>DECIMAL64_Pmax // too many digits
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|| ae>DECIMAL64_Emax // likely overflow
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|| ae<DECIMAL64_Emin) { // likely underflow
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decContextDefault(&dc, DEC_INIT_DECIMAL64); // [no traps]
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dc.round=set->round; // use supplied rounding
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decNumberPlus(&dw, dn, &dc); // (round and check)
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// [this changes -0 to 0, so enforce the sign...]
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dw.bits|=dn->bits&DECNEG;
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status=dc.status; // save status
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dn=&dw; // use the work number
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} // maybe out of range
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if (dn->bits&DECSPECIAL) { // a special value
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if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
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else { // sNaN or qNaN
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if ((*dn->lsu!=0 || dn->digits>1) // non-zero coefficient
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&& (dn->digits<DECIMAL64_Pmax)) { // coefficient fits
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decDigitsToDPD(dn, targar, 0);
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}
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if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
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else targhi|=DECIMAL_sNaN<<24;
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} // a NaN
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} // special
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else { // is finite
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if (decNumberIsZero(dn)) { // is a zero
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// set and clamp exponent
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if (dn->exponent<-DECIMAL64_Bias) {
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exp=0; // low clamp
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status|=DEC_Clamped;
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}
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else {
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exp=dn->exponent+DECIMAL64_Bias; // bias exponent
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if (exp>DECIMAL64_Ehigh) { // top clamp
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exp=DECIMAL64_Ehigh;
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status|=DEC_Clamped;
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}
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}
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comb=(exp>>5) & 0x18; // msd=0, exp top 2 bits ..
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}
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else { // non-zero finite number
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uInt msd; // work
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Int pad=0; // coefficient pad digits
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// the dn is known to fit, but it may need to be padded
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exp=(uInt)(dn->exponent+DECIMAL64_Bias); // bias exponent
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if (exp>DECIMAL64_Ehigh) { // fold-down case
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pad=exp-DECIMAL64_Ehigh;
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exp=DECIMAL64_Ehigh; // [to maximum]
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status|=DEC_Clamped;
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}
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// fastpath common case
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if (DECDPUN==3 && pad==0) {
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uInt dpd[6]={0,0,0,0,0,0};
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uInt i;
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Int d=dn->digits;
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for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];
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targlo =dpd[0];
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targlo|=dpd[1]<<10;
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targlo|=dpd[2]<<20;
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if (dn->digits>6) {
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targlo|=dpd[3]<<30;
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targhi =dpd[3]>>2;
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targhi|=dpd[4]<<8;
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}
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msd=dpd[5]; // [did not really need conversion]
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}
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else { // general case
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decDigitsToDPD(dn, targar, pad);
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// save and clear the top digit
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msd=targhi>>18;
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targhi&=0x0003ffff;
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}
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// create the combination field
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if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);
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else comb=((exp>>5) & 0x18) | msd;
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}
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targhi|=comb<<26; // add combination field ..
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targhi|=(exp&0xff)<<18; // .. and exponent continuation
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} // finite
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if (dn->bits&DECNEG) targhi|=0x80000000; // add sign bit
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// now write to storage; this is now always endian
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if (DECLITEND) {
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// lo int then hi
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UBFROMUI(d64->bytes, targar[0]);
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UBFROMUI(d64->bytes+4, targar[1]);
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}
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else {
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// hi int then lo
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UBFROMUI(d64->bytes, targar[1]);
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UBFROMUI(d64->bytes+4, targar[0]);
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}
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if (status!=0) decContextSetStatus(set, status); // pass on status
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// decimal64Show(d64);
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return d64;
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} // decimal64FromNumber
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/* ------------------------------------------------------------------ */
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/* decimal64ToNumber -- convert decimal64 to decNumber */
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/* d64 is the source decimal64 */
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/* dn is the target number, with appropriate space */
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/* No error is possible. */
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/* ------------------------------------------------------------------ */
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decNumber * decimal64ToNumber(const decimal64 *d64, decNumber *dn) {
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uInt msd; // coefficient MSD
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uInt exp; // exponent top two bits
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uInt comb; // combination field
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Int need; // work
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uInt uiwork; // for macros
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uInt sourar[2]; // source 64-bit
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#define sourhi sourar[1] // name the word with the sign
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#define sourlo sourar[0] // and the lower word
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// load source from storage; this is endian
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if (DECLITEND) {
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sourlo=UBTOUI(d64->bytes ); // directly load the low int
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sourhi=UBTOUI(d64->bytes+4); // then the high int
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}
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else {
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sourhi=UBTOUI(d64->bytes ); // directly load the high int
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sourlo=UBTOUI(d64->bytes+4); // then the low int
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}
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comb=(sourhi>>26)&0x1f; // combination field
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decNumberZero(dn); // clean number
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if (sourhi&0x80000000) dn->bits=DECNEG; // set sign if negative
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msd=COMBMSD[comb]; // decode the combination field
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exp=COMBEXP[comb]; // ..
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if (exp==3) { // is a special
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if (msd==0) {
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dn->bits|=DECINF;
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return dn; // no coefficient needed
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}
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else if (sourhi&0x02000000) dn->bits|=DECSNAN;
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else dn->bits|=DECNAN;
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msd=0; // no top digit
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}
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else { // is a finite number
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dn->exponent=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; // unbiased
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}
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// get the coefficient
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sourhi&=0x0003ffff; // clean coefficient continuation
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if (msd) { // non-zero msd
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sourhi|=msd<<18; // prefix to coefficient
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need=6; // process 6 declets
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}
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else { // msd=0
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if (!sourhi) { // top word 0
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if (!sourlo) return dn; // easy: coefficient is 0
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need=3; // process at least 3 declets
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if (sourlo&0xc0000000) need++; // process 4 declets
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// [could reduce some more, here]
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}
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else { // some bits in top word, msd=0
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need=4; // process at least 4 declets
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if (sourhi&0x0003ff00) need++; // top declet!=0, process 5
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}
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} //msd=0
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decDigitsFromDPD(dn, sourar, need); // process declets
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return dn;
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} // decimal64ToNumber
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/* ------------------------------------------------------------------ */
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/* to-scientific-string -- conversion to numeric string */
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/* to-engineering-string -- conversion to numeric string */
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/* */
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/* decimal64ToString(d64, string); */
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/* decimal64ToEngString(d64, string); */
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/* */
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/* d64 is the decimal64 format number to convert */
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/* string is the string where the result will be laid out */
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/* */
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/* string must be at least 24 characters */
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/* */
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/* No error is possible, and no status can be set. */
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/* ------------------------------------------------------------------ */
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char * decimal64ToEngString(const decimal64 *d64, char *string){
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decNumber dn; // work
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decimal64ToNumber(d64, &dn);
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decNumberToEngString(&dn, string);
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return string;
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} // decimal64ToEngString
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char * decimal64ToString(const decimal64 *d64, char *string){
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uInt msd; // coefficient MSD
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Int exp; // exponent top two bits or full
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uInt comb; // combination field
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char *cstart; // coefficient start
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char *c; // output pointer in string
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const uByte *u; // work
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char *s, *t; // .. (source, target)
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Int dpd; // ..
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Int pre, e; // ..
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uInt uiwork; // for macros
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uInt sourar[2]; // source 64-bit
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#define sourhi sourar[1] // name the word with the sign
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#define sourlo sourar[0] // and the lower word
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// load source from storage; this is endian
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if (DECLITEND) {
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sourlo=UBTOUI(d64->bytes ); // directly load the low int
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sourhi=UBTOUI(d64->bytes+4); // then the high int
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}
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else {
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sourhi=UBTOUI(d64->bytes ); // directly load the high int
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sourlo=UBTOUI(d64->bytes+4); // then the low int
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}
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c=string; // where result will go
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if (((Int)sourhi)<0) *c++='-'; // handle sign
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comb=(sourhi>>26)&0x1f; // combination field
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msd=COMBMSD[comb]; // decode the combination field
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exp=COMBEXP[comb]; // ..
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if (exp==3) {
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if (msd==0) { // infinity
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strcpy(c, "Inf");
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strcpy(c+3, "inity");
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return string; // easy
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}
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if (sourhi&0x02000000) *c++='s'; // sNaN
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strcpy(c, "NaN"); // complete word
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c+=3; // step past
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if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; // zero payload
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// otherwise drop through to add integer; set correct exp
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exp=0; msd=0; // setup for following code
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}
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else exp=(exp<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;
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// convert 16 digits of significand to characters
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cstart=c; // save start of coefficient
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if (msd) *c++='0'+(char)msd; // non-zero most significant digit
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// Now decode the declets. After extracting each one, it is
|
||
|
|
// decoded to binary and then to a 4-char sequence by table lookup;
|
||
|
|
// the 4-chars are a 1-char length (significant digits, except 000
|
||
|
|
// has length 0). This allows us to left-align the first declet
|
||
|
|
// with non-zero content, then remaining ones are full 3-char
|
||
|
|
// length. We use fixed-length memcpys because variable-length
|
||
|
|
// causes a subroutine call in GCC. (These are length 4 for speed
|
||
|
|
// and are safe because the array has an extra terminator byte.)
|
||
|
|
#define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
|
||
|
|
if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
|
||
|
|
else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
|
||
|
|
|
||
|
|
dpd=(sourhi>>8)&0x3ff; // declet 1
|
||
|
|
dpd2char;
|
||
|
|
dpd=((sourhi&0xff)<<2) | (sourlo>>30); // declet 2
|
||
|
|
dpd2char;
|
||
|
|
dpd=(sourlo>>20)&0x3ff; // declet 3
|
||
|
|
dpd2char;
|
||
|
|
dpd=(sourlo>>10)&0x3ff; // declet 4
|
||
|
|
dpd2char;
|
||
|
|
dpd=(sourlo)&0x3ff; // declet 5
|
||
|
|
dpd2char;
|
||
|
|
|
||
|
|
if (c==cstart) *c++='0'; // all zeros -- make 0
|
||
|
|
|
||
|
|
if (exp==0) { // integer or NaN case -- easy
|
||
|
|
*c='\0'; // terminate
|
||
|
|
return string;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* non-0 exponent */
|
||
|
|
e=0; // assume no E
|
||
|
|
pre=c-cstart+exp;
|
||
|
|
// [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 */
|
||
|
|
s=c-1; // source (LSD)
|
||
|
|
if (pre>0) { // ddd.ddd (plain), perhaps with E
|
||
|
|
char *dotat=cstart+pre;
|
||
|
|
if (dotat<c) { // if embedded dot needed...
|
||
|
|
t=c; // target
|
||
|
|
for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap
|
||
|
|
*t='.'; // insert the dot
|
||
|
|
c++; // length increased by one
|
||
|
|
}
|
||
|
|
|
||
|
|
// finally add the E-part, if needed; it will never be 0, and has
|
||
|
|
// a maximum length of 3 digits
|
||
|
|
if (e!=0) {
|
||
|
|
*c++='E'; // starts with E
|
||
|
|
*c++='+'; // assume positive
|
||
|
|
if (e<0) {
|
||
|
|
*(c-1)='-'; // oops, need '-'
|
||
|
|
e=-e; // uInt, please
|
||
|
|
}
|
||
|
|
u=&BIN2CHAR[e*4]; // -> length byte
|
||
|
|
memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe]
|
||
|
|
c+=*u; // bump pointer appropriately
|
||
|
|
}
|
||
|
|
*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) */
|
||
|
|
t=c+1-pre;
|
||
|
|
*(t+1)='\0'; // can add terminator now
|
||
|
|
for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right
|
||
|
|
c=cstart;
|
||
|
|
*c++='0'; // always starts with 0.
|
||
|
|
*c++='.';
|
||
|
|
for (; pre<0; pre++) *c++='0'; // add any 0's after '.'
|
||
|
|
//printf("res %s\n", string);
|
||
|
|
return string;
|
||
|
|
} // decimal64ToString
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* to-number -- conversion from numeric string */
|
||
|
|
/* */
|
||
|
|
/* decimal64FromString(result, string, set); */
|
||
|
|
/* */
|
||
|
|
/* result is the decimal64 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) */
|
||
|
|
/* set is the context */
|
||
|
|
/* */
|
||
|
|
/* The context is supplied to this routine is used for error handling */
|
||
|
|
/* (setting of status and traps) and for the rounding mode, only. */
|
||
|
|
/* If an error occurs, the result will be a valid decimal64 NaN. */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
decimal64 * decimal64FromString(decimal64 *result, const char *string,
|
||
|
|
decContext *set) {
|
||
|
|
decContext dc; // work
|
||
|
|
decNumber dn; // ..
|
||
|
|
|
||
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64); // no traps, please
|
||
|
|
dc.round=set->round; // use supplied rounding
|
||
|
|
|
||
|
|
decNumberFromString(&dn, string, &dc); // will round if needed
|
||
|
|
|
||
|
|
decimal64FromNumber(result, &dn, &dc);
|
||
|
|
if (dc.status!=0) { // something happened
|
||
|
|
decContextSetStatus(set, dc.status); // .. pass it on
|
||
|
|
}
|
||
|
|
return result;
|
||
|
|
} // decimal64FromString
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* decimal64IsCanonical -- test whether encoding is canonical */
|
||
|
|
/* d64 is the source decimal64 */
|
||
|
|
/* returns 1 if the encoding of d64 is canonical, 0 otherwise */
|
||
|
|
/* No error is possible. */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
uInt decimal64IsCanonical(const decimal64 *d64) {
|
||
|
|
decNumber dn; // work
|
||
|
|
decimal64 canon; // ..
|
||
|
|
decContext dc; // ..
|
||
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64);
|
||
|
|
decimal64ToNumber(d64, &dn);
|
||
|
|
decimal64FromNumber(&canon, &dn, &dc);// canon will now be canonical
|
||
|
|
return memcmp(d64, &canon, DECIMAL64_Bytes)==0;
|
||
|
|
} // decimal64IsCanonical
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* decimal64Canonical -- copy an encoding, ensuring it is canonical */
|
||
|
|
/* d64 is the source decimal64 */
|
||
|
|
/* result is the target (may be the same decimal64) */
|
||
|
|
/* returns result */
|
||
|
|
/* No error is possible. */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {
|
||
|
|
decNumber dn; // work
|
||
|
|
decContext dc; // ..
|
||
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64);
|
||
|
|
decimal64ToNumber(d64, &dn);
|
||
|
|
decimal64FromNumber(result, &dn, &dc);// result will now be canonical
|
||
|
|
return result;
|
||
|
|
} // decimal64Canonical
|
||
|
|
|
||
|
|
#if DECTRACE || DECCHECK
|
||
|
|
/* Macros for accessing decimal64 fields. These assume the
|
||
|
|
argument is a reference (pointer) to the decimal64 structure,
|
||
|
|
and the decimal64 is in network byte order (big-endian) */
|
||
|
|
// Get sign
|
||
|
|
#define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7)
|
||
|
|
|
||
|
|
// Get combination field
|
||
|
|
#define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2)
|
||
|
|
|
||
|
|
// Get exponent continuation [does not remove bias]
|
||
|
|
#define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \
|
||
|
|
| ((unsigned)(d)->bytes[1]>>2))
|
||
|
|
|
||
|
|
// Set sign [this assumes sign previously 0]
|
||
|
|
#define decimal64SetSign(d, b) { \
|
||
|
|
(d)->bytes[0]|=((unsigned)(b)<<7);}
|
||
|
|
|
||
|
|
// Set exponent continuation [does not apply bias]
|
||
|
|
// This assumes range has been checked and exponent previously 0;
|
||
|
|
// type of exponent must be unsigned
|
||
|
|
#define decimal64SetExpCon(d, e) { \
|
||
|
|
(d)->bytes[0]|=(uByte)((e)>>6); \
|
||
|
|
(d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);}
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */
|
||
|
|
/* d64 -- the number to show */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
// Also shows sign/cob/expconfields extracted
|
||
|
|
void decimal64Show(const decimal64 *d64) {
|
||
|
|
char buf[DECIMAL64_Bytes*2+1];
|
||
|
|
Int i, j=0;
|
||
|
|
|
||
|
|
if (DECLITEND) {
|
||
|
|
for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
|
||
|
|
sprintf(&buf[j], "%02x", d64->bytes[7-i]);
|
||
|
|
}
|
||
|
|
printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
|
||
|
|
d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,
|
||
|
|
((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));
|
||
|
|
}
|
||
|
|
else { // big-endian
|
||
|
|
for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
|
||
|
|
sprintf(&buf[j], "%02x", d64->bytes[i]);
|
||
|
|
}
|
||
|
|
printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
|
||
|
|
decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));
|
||
|
|
}
|
||
|
|
} // decimal64Show
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/* ================================================================== */
|
||
|
|
/* Shared utility routines and tables */
|
||
|
|
/* ================================================================== */
|
||
|
|
// define and include the conversion tables to use for shared code
|
||
|
|
#if DECDPUN==3
|
||
|
|
#define DEC_DPD2BIN 1
|
||
|
|
#else
|
||
|
|
#define DEC_DPD2BCD 1
|
||
|
|
#endif
|
||
|
|
#include "decDPD.h" // lookup tables
|
||
|
|
|
||
|
|
// The maximum number of decNumberUnits needed for a working copy of
|
||
|
|
// the units array is the ceiling of digits/DECDPUN, where digits is
|
||
|
|
// the maximum number of digits in any of the formats for which this
|
||
|
|
// is used. decimal128.h must not be included in this module, so, as
|
||
|
|
// a very special case, that number is defined as a literal here.
|
||
|
|
#define DECMAX754 34
|
||
|
|
#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* Combination field lookup tables (uInts to save measurable work) */
|
||
|
|
/* */
|
||
|
|
/* COMBEXP - 2-bit most-significant-bits of exponent */
|
||
|
|
/* [11 if an Infinity or NaN] */
|
||
|
|
/* COMBMSD - 4-bit most-significant-digit */
|
||
|
|
/* [0=Infinity, 1=NaN if COMBEXP=11] */
|
||
|
|
/* */
|
||
|
|
/* Both are indexed by the 5-bit combination field (0-31) */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,
|
||
|
|
1, 1, 1, 1, 1, 1, 1, 1,
|
||
|
|
2, 2, 2, 2, 2, 2, 2, 2,
|
||
|
|
0, 0, 1, 1, 2, 2, 3, 3};
|
||
|
|
const uInt COMBMSD[32]={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, 1};
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* decDigitsToDPD -- pack coefficient into DPD form */
|
||
|
|
/* */
|
||
|
|
/* dn is the source number (assumed valid, max DECMAX754 digits) */
|
||
|
|
/* targ is 1, 2, or 4-element uInt array, which the caller must */
|
||
|
|
/* have cleared to zeros */
|
||
|
|
/* shift is the number of 0 digits to add on the right (normally 0) */
|
||
|
|
/* */
|
||
|
|
/* The coefficient must be known small enough to fit. The full */
|
||
|
|
/* coefficient is copied, including the leading 'odd' digit. This */
|
||
|
|
/* digit is retrieved and packed into the combination field by the */
|
||
|
|
/* caller. */
|
||
|
|
/* */
|
||
|
|
/* The target uInts are altered only as necessary to receive the */
|
||
|
|
/* digits of the decNumber. When more than one uInt is needed, they */
|
||
|
|
/* are filled from left to right (that is, the uInt at offset 0 will */
|
||
|
|
/* end up with the least-significant digits). */
|
||
|
|
/* */
|
||
|
|
/* shift is used for 'fold-down' padding. */
|
||
|
|
/* */
|
||
|
|
/* No error is possible. */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
#if DECDPUN<=4
|
||
|
|
// 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)
|
||
|
|
#endif
|
||
|
|
void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {
|
||
|
|
Int cut; // work
|
||
|
|
Int n; // output bunch counter
|
||
|
|
Int digits=dn->digits; // digit countdown
|
||
|
|
uInt dpd; // densely packed decimal value
|
||
|
|
uInt bin; // binary value 0-999
|
||
|
|
uInt *uout=targ; // -> current output uInt
|
||
|
|
uInt uoff=0; // -> current output offset [from right]
|
||
|
|
const Unit *inu=dn->lsu; // -> current input unit
|
||
|
|
Unit uar[DECMAXUNITS]; // working copy of units, iff shifted
|
||
|
|
#if DECDPUN!=3 // not fast path
|
||
|
|
Unit in; // current unit
|
||
|
|
#endif
|
||
|
|
|
||
|
|
if (shift!=0) { // shift towards most significant required
|
||
|
|
// shift the units array to the left by pad digits and copy
|
||
|
|
// [this code is a special case of decShiftToMost, which could
|
||
|
|
// be used instead if exposed and the array were copied first]
|
||
|
|
const Unit *source; // ..
|
||
|
|
Unit *target, *first; // ..
|
||
|
|
uInt next=0; // work
|
||
|
|
|
||
|
|
source=dn->lsu+D2U(digits)-1; // where msu comes from
|
||
|
|
target=uar+D2U(digits)-1+D2U(shift);// where upper part of first cut goes
|
||
|
|
cut=DECDPUN-MSUDIGITS(shift); // where to slice
|
||
|
|
if (cut==0) { // unit-boundary case
|
||
|
|
for (; source>=dn->lsu; source--, target--) *target=*source;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
first=uar+D2U(digits+shift)-1; // where msu will end up
|
||
|
|
for (; source>=dn->lsu; source--, target--) {
|
||
|
|
// split the source Unit and accumulate remainder for next
|
||
|
|
#if DECDPUN<=4
|
||
|
|
uInt quot=QUOT10(*source, cut);
|
||
|
|
uInt rem=*source-quot*DECPOWERS[cut];
|
||
|
|
next+=quot;
|
||
|
|
#else
|
||
|
|
uInt rem=*source%DECPOWERS[cut];
|
||
|
|
next+=*source/DECPOWERS[cut];
|
||
|
|
#endif
|
||
|
|
if (target<=first) *target=(Unit)next; // write to target iff valid
|
||
|
|
next=rem*DECPOWERS[DECDPUN-cut]; // save remainder for next Unit
|
||
|
|
}
|
||
|
|
} // shift-move
|
||
|
|
// propagate remainder to one below and clear the rest
|
||
|
|
for (; target>=uar; target--) {
|
||
|
|
*target=(Unit)next;
|
||
|
|
next=0;
|
||
|
|
}
|
||
|
|
digits+=shift; // add count (shift) of zeros added
|
||
|
|
inu=uar; // use units in working array
|
||
|
|
}
|
||
|
|
|
||
|
|
/* now densely pack the coefficient into DPD declets */
|
||
|
|
|
||
|
|
#if DECDPUN!=3 // not fast path
|
||
|
|
in=*inu; // current unit
|
||
|
|
cut=0; // at lowest digit
|
||
|
|
bin=0; // [keep compiler quiet]
|
||
|
|
#endif
|
||
|
|
|
||
|
|
for(n=0; digits>0; n++) { // each output bunch
|
||
|
|
#if DECDPUN==3 // fast path, 3-at-a-time
|
||
|
|
bin=*inu; // 3 digits ready for convert
|
||
|
|
digits-=3; // [may go negative]
|
||
|
|
inu++; // may need another
|
||
|
|
|
||
|
|
#else // must collect digit-by-digit
|
||
|
|
Unit dig; // current digit
|
||
|
|
Int j; // digit-in-declet count
|
||
|
|
for (j=0; j<3; j++) {
|
||
|
|
#if DECDPUN<=4
|
||
|
|
Unit temp=(Unit)((uInt)(in*6554)>>16);
|
||
|
|
dig=(Unit)(in-X10(temp));
|
||
|
|
in=temp;
|
||
|
|
#else
|
||
|
|
dig=in%10;
|
||
|
|
in=in/10;
|
||
|
|
#endif
|
||
|
|
if (j==0) bin=dig;
|
||
|
|
else if (j==1) bin+=X10(dig);
|
||
|
|
else /* j==2 */ bin+=X100(dig);
|
||
|
|
digits--;
|
||
|
|
if (digits==0) break; // [also protects *inu below]
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
// here there are 3 digits in bin, or have used all input digits
|
||
|
|
|
||
|
|
dpd=BIN2DPD[bin];
|
||
|
|
|
||
|
|
// write declet to uInt array
|
||
|
|
*uout|=dpd<<uoff;
|
||
|
|
uoff+=10;
|
||
|
|
if (uoff<32) continue; // no uInt boundary cross
|
||
|
|
uout++;
|
||
|
|
uoff-=32;
|
||
|
|
*uout|=dpd>>(10-uoff); // collect top bits
|
||
|
|
} // n declets
|
||
|
|
return;
|
||
|
|
} // decDigitsToDPD
|
||
|
|
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
/* decDigitsFromDPD -- unpack a format's coefficient */
|
||
|
|
/* */
|
||
|
|
/* dn is the target number, with 7, 16, or 34-digit space. */
|
||
|
|
/* sour is a 1, 2, or 4-element uInt array containing only declets */
|
||
|
|
/* declets is the number of (right-aligned) declets in sour to */
|
||
|
|
/* be processed. This may be 1 more than the obvious number in */
|
||
|
|
/* a format, as any top digit is prefixed to the coefficient */
|
||
|
|
/* continuation field. It also may be as small as 1, as the */
|
||
|
|
/* caller may pre-process leading zero declets. */
|
||
|
|
/* */
|
||
|
|
/* When doing the 'extra declet' case care is taken to avoid writing */
|
||
|
|
/* extra digits when there are leading zeros, as these could overflow */
|
||
|
|
/* the units array when DECDPUN is not 3. */
|
||
|
|
/* */
|
||
|
|
/* The target uInts are used only as necessary to process declets */
|
||
|
|
/* declets into the decNumber. When more than one uInt is needed, */
|
||
|
|
/* they are used from left to right (that is, the uInt at offset 0 */
|
||
|
|
/* provides the least-significant digits). */
|
||
|
|
/* */
|
||
|
|
/* dn->digits is set, but not the sign or exponent. */
|
||
|
|
/* No error is possible [the redundant 888 codes are allowed]. */
|
||
|
|
/* ------------------------------------------------------------------ */
|
||
|
|
void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {
|
||
|
|
|
||
|
|
uInt dpd; // collector for 10 bits
|
||
|
|
Int n; // counter
|
||
|
|
Unit *uout=dn->lsu; // -> current output unit
|
||
|
|
Unit *last=uout; // will be unit containing msd
|
||
|
|
const uInt *uin=sour; // -> current input uInt
|
||
|
|
uInt uoff=0; // -> current input offset [from right]
|
||
|
|
|
||
|
|
#if DECDPUN!=3
|
||
|
|
uInt bcd; // BCD result
|
||
|
|
uInt nibble; // work
|
||
|
|
Unit out=0; // accumulator
|
||
|
|
Int cut=0; // power of ten in current unit
|
||
|
|
#endif
|
||
|
|
#if DECDPUN>4
|
||
|
|
uInt const *pow; // work
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// Expand the densely-packed integer, right to left
|
||
|
|
for (n=declets-1; n>=0; n--) { // count down declets of 10 bits
|
||
|
|
dpd=*uin>>uoff;
|
||
|
|
uoff+=10;
|
||
|
|
if (uoff>32) { // crossed uInt boundary
|
||
|
|
uin++;
|
||
|
|
uoff-=32; // [if using this code for wider, check this]
|
||
|
|
dpd|=*uin<<(10-uoff); // get waiting bits
|
||
|
|
}
|
||
|
|
dpd&=0x3ff; // clear uninteresting bits
|
||
|
|
|
||
|
|
#if DECDPUN==3
|
||
|
|
if (dpd==0) *uout=0;
|
||
|
|
else {
|
||
|
|
*uout=DPD2BIN[dpd]; // convert 10 bits to binary 0-999
|
||
|
|
last=uout; // record most significant unit
|
||
|
|
}
|
||
|
|
uout++;
|
||
|
|
} // n
|
||
|
|
|
||
|
|
#else // DECDPUN!=3
|
||
|
|
if (dpd==0) { // fastpath [e.g., leading zeros]
|
||
|
|
// write out three 0 digits (nibbles); out may have digit(s)
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
||
|
|
if (n==0) break; // [as below, works even if MSD=0]
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
|
||
|
|
bcd=DPD2BCD[dpd]; // convert 10 bits to 12 bits BCD
|
||
|
|
|
||
|
|
// now accumulate the 3 BCD nibbles into units
|
||
|
|
nibble=bcd & 0x00f;
|
||
|
|
if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
||
|
|
bcd>>=4;
|
||
|
|
|
||
|
|
// if this is the last declet and the remaining nibbles in bcd
|
||
|
|
// are 00 then process no more nibbles, because this could be
|
||
|
|
// the 'odd' MSD declet and writing any more Units would then
|
||
|
|
// overflow the unit array
|
||
|
|
if (n==0 && !bcd) break;
|
||
|
|
|
||
|
|
nibble=bcd & 0x00f;
|
||
|
|
if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
||
|
|
bcd>>=4;
|
||
|
|
|
||
|
|
nibble=bcd & 0x00f;
|
||
|
|
if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
||
|
|
cut++;
|
||
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
||
|
|
} // n
|
||
|
|
if (cut!=0) { // some more left over
|
||
|
|
*uout=out; // write out final unit
|
||
|
|
if (out) last=uout; // and note if non-zero
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
// here, last points to the most significant unit with digits;
|
||
|
|
// inspect it to get the final digits count -- this is essentially
|
||
|
|
// the same code as decGetDigits in decNumber.c
|
||
|
|
dn->digits=(last-dn->lsu)*DECDPUN+1; // floor of digits, plus
|
||
|
|
// must be at least 1 digit
|
||
|
|
#if DECDPUN>1
|
||
|
|
if (*last<10) return; // common odd digit or 0
|
||
|
|
dn->digits++; // must be 2 at least
|
||
|
|
#if DECDPUN>2
|
||
|
|
if (*last<100) return; // 10-99
|
||
|
|
dn->digits++; // must be 3 at least
|
||
|
|
#if DECDPUN>3
|
||
|
|
if (*last<1000) return; // 100-999
|
||
|
|
dn->digits++; // must be 4 at least
|
||
|
|
#if DECDPUN>4
|
||
|
|
for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
#endif
|
||
|
|
return;
|
||
|
|
} //decDigitsFromDPD
|