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477 lines
22 KiB
C
477 lines
22 KiB
C
/* ------------------------------------------------------------------ */
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/* Decimal 32-bit format module */
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/* ------------------------------------------------------------------ */
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/* Copyright (c) IBM Corporation, 2000, 2008. 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 decimal32 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 7 // make decNumbers with space for 7
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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 "decimal32.h" // our primary include
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/* Utility tables and routines [in decimal64.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 decDigitsToDPD(const decNumber *, uInt *, Int);
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extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
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#if DECTRACE || DECCHECK
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void decimal32Show(const decimal32 *); // 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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/* ------------------------------------------------------------------ */
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/* decimal32FromNumber -- convert decNumber to decimal32 */
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/* */
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/* ds is the target decimal32 */
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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 DECIMAL32_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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decimal32 * decimal32FromNumber(decimal32 *d32, 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 targ=0; // target 32-bit
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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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// decimal32]
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ae=dn->exponent+dn->digits-1; // [0 if special]
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if (dn->digits>DECIMAL32_Pmax // too many digits
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|| ae>DECIMAL32_Emax // likely overflow
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|| ae<DECIMAL32_Emin) { // likely underflow
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decContextDefault(&dc, DEC_INIT_DECIMAL32); // [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) targ=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<DECIMAL32_Pmax)) { // coefficient fits
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decDigitsToDPD(dn, &targ, 0);
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}
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if (dn->bits&DECNAN) targ|=DECIMAL_NaN<<24;
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else targ|=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<-DECIMAL32_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+DECIMAL32_Bias; // bias exponent
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if (exp>DECIMAL32_Ehigh) { // top clamp
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exp=DECIMAL32_Ehigh;
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status|=DEC_Clamped;
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}
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}
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comb=(exp>>3) & 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+DECIMAL32_Bias); // bias exponent
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if (exp>DECIMAL32_Ehigh) { // fold-down case
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pad=exp-DECIMAL32_Ehigh;
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exp=DECIMAL32_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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targ=BIN2DPD[dn->lsu[0]];
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if (dn->digits>3) targ|=(uInt)(BIN2DPD[dn->lsu[1]])<<10;
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msd=(dn->digits==7 ? dn->lsu[2] : 0);
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}
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else { // general case
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decDigitsToDPD(dn, &targ, pad);
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// save and clear the top digit
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msd=targ>>20;
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targ&=0x000fffff;
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}
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// create the combination field
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if (msd>=8) comb=0x18 | ((exp>>5) & 0x06) | (msd & 0x01);
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else comb=((exp>>3) & 0x18) | msd;
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}
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targ|=comb<<26; // add combination field ..
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targ|=(exp&0x3f)<<20; // .. and exponent continuation
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} // finite
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if (dn->bits&DECNEG) targ|=0x80000000; // add sign bit
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// now write to storage; this is endian
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UBFROMUI(d32->bytes, targ); // directly store the int
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if (status!=0) decContextSetStatus(set, status); // pass on status
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// decimal32Show(d32);
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return d32;
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} // decimal32FromNumber
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/* ------------------------------------------------------------------ */
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/* decimal32ToNumber -- convert decimal32 to decNumber */
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/* d32 is the source decimal32 */
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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 * decimal32ToNumber(const decimal32 *d32, 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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uInt sour; // source 32-bit
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uInt uiwork; // for macros
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// load source from storage; this is endian
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sour=UBTOUI(d32->bytes); // directly load the int
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comb=(sour>>26)&0x1f; // combination field
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decNumberZero(dn); // clean number
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if (sour&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 (sour&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<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased
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}
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// get the coefficient
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sour&=0x000fffff; // clean coefficient continuation
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if (msd) { // non-zero msd
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sour|=msd<<20; // prefix to coefficient
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decDigitsFromDPD(dn, &sour, 3); // process 3 declets
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return dn;
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}
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// msd=0
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if (!sour) return dn; // easy: coefficient is 0
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if (sour&0x000ffc00) // need 2 declets?
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decDigitsFromDPD(dn, &sour, 2); // process 2 declets
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else
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decDigitsFromDPD(dn, &sour, 1); // process 1 declet
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return dn;
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} // decimal32ToNumber
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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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/* decimal32ToString(d32, string); */
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/* decimal32ToEngString(d32, string); */
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/* */
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/* d32 is the decimal32 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 * decimal32ToEngString(const decimal32 *d32, char *string){
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decNumber dn; // work
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decimal32ToNumber(d32, &dn);
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decNumberToEngString(&dn, string);
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return string;
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} // decimal32ToEngString
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char * decimal32ToString(const decimal32 *d32, 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 sour; // source 32-bit
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// load source from storage; this is endian
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sour=UBTOUI(d32->bytes); // directly load the int
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c=string; // where result will go
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if (((Int)sour)<0) *c++='-'; // handle sign
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comb=(sour>>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 (sour&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 ((sour&0x000fffff)==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<<6)+((sour>>20)&0x3f)-DECIMAL32_Bias; // unbiased
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// convert 7 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
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// decoded to binary and then to a 4-char sequence by table lookup;
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// the 4-chars are a 1-char length (significant digits, except 000
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// has length 0). This allows us to left-align the first declet
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// with non-zero content, then remaining ones are full 3-char
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// length. We use fixed-length memcpys because variable-length
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// causes a subroutine call in GCC. (These are length 4 for speed
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// and are safe because the array has an extra terminator byte.)
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#define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
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if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
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else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
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dpd=(sour>>10)&0x3ff; // declet 1
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dpd2char;
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dpd=(sour)&0x3ff; // declet 2
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dpd2char;
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if (c==cstart) *c++='0'; // all zeros -- make 0
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if (exp==0) { // integer or NaN case -- easy
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*c='\0'; // terminate
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return string;
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}
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/* non-0 exponent */
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e=0; // assume no E
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pre=c-cstart+exp;
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// [here, pre-exp is the digits count (==1 for zero)]
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if (exp>0 || pre<-5) { // need exponential form
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e=pre-1; // calculate E value
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pre=1; // assume one digit before '.'
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} // exponential form
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/* modify the coefficient, adding 0s, '.', and E+nn as needed */
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s=c-1; // source (LSD)
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if (pre>0) { // ddd.ddd (plain), perhaps with E
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char *dotat=cstart+pre;
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if (dotat<c) { // if embedded dot needed...
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t=c; // target
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for (; s>=dotat; s--, t--) *t=*s; // open the gap; leave t at gap
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*t='.'; // insert the dot
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c++; // length increased by one
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}
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// finally add the E-part, if needed; it will never be 0, and has
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// a maximum length of 3 digits (E-101 case)
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if (e!=0) {
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*c++='E'; // starts with E
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*c++='+'; // assume positive
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if (e<0) {
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*(c-1)='-'; // oops, need '-'
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e=-e; // uInt, please
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}
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u=&BIN2CHAR[e*4]; // -> length byte
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memcpy(c, u+4-*u, 4); // copy fixed 4 characters [is safe]
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c+=*u; // bump pointer appropriately
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}
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*c='\0'; // add terminator
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//printf("res %s\n", string);
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return string;
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} // pre>0
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/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
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t=c+1-pre;
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*(t+1)='\0'; // can add terminator now
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for (; s>=cstart; s--, t--) *t=*s; // shift whole coefficient right
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c=cstart;
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*c++='0'; // always starts with 0.
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*c++='.';
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for (; pre<0; pre++) *c++='0'; // add any 0's after '.'
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//printf("res %s\n", string);
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return string;
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} // decimal32ToString
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/* ------------------------------------------------------------------ */
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/* to-number -- conversion from numeric string */
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/* */
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/* decimal32FromString(result, string, set); */
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/* */
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/* result is the decimal32 format number which gets the result of */
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/* the conversion */
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/* *string is the character string which should contain a valid */
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/* number (which may be a special value) */
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/* set is the context */
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/* */
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/* The context is supplied to this routine is used for error handling */
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/* (setting of status and traps) and for the rounding mode, only. */
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/* If an error occurs, the result will be a valid decimal32 NaN. */
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/* ------------------------------------------------------------------ */
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decimal32 * decimal32FromString(decimal32 *result, const char *string,
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decContext *set) {
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decContext dc; // work
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decNumber dn; // ..
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decContextDefault(&dc, DEC_INIT_DECIMAL32); // no traps, please
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dc.round=set->round; // use supplied rounding
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decNumberFromString(&dn, string, &dc); // will round if needed
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decimal32FromNumber(result, &dn, &dc);
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if (dc.status!=0) { // something happened
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decContextSetStatus(set, dc.status); // .. pass it on
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}
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return result;
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} // decimal32FromString
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/* ------------------------------------------------------------------ */
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/* decimal32IsCanonical -- test whether encoding is canonical */
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/* d32 is the source decimal32 */
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/* returns 1 if the encoding of d32 is canonical, 0 otherwise */
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/* No error is possible. */
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/* ------------------------------------------------------------------ */
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uInt decimal32IsCanonical(const decimal32 *d32) {
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decNumber dn; // work
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decimal32 canon; // ..
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decContext dc; // ..
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decContextDefault(&dc, DEC_INIT_DECIMAL32);
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decimal32ToNumber(d32, &dn);
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decimal32FromNumber(&canon, &dn, &dc);// canon will now be canonical
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return memcmp(d32, &canon, DECIMAL32_Bytes)==0;
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} // decimal32IsCanonical
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/* ------------------------------------------------------------------ */
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/* decimal32Canonical -- copy an encoding, ensuring it is canonical */
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/* d32 is the source decimal32 */
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/* result is the target (may be the same decimal32) */
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/* returns result */
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/* No error is possible. */
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/* ------------------------------------------------------------------ */
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decimal32 * decimal32Canonical(decimal32 *result, const decimal32 *d32) {
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decNumber dn; // work
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decContext dc; // ..
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decContextDefault(&dc, DEC_INIT_DECIMAL32);
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decimal32ToNumber(d32, &dn);
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decimal32FromNumber(result, &dn, &dc);// result will now be canonical
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return result;
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} // decimal32Canonical
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#if DECTRACE || DECCHECK
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/* Macros for accessing decimal32 fields. These assume the argument
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is a reference (pointer) to the decimal32 structure, and the
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decimal32 is in network byte order (big-endian) */
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// Get sign
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#define decimal32Sign(d) ((unsigned)(d)->bytes[0]>>7)
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// Get combination field
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#define decimal32Comb(d) (((d)->bytes[0] & 0x7c)>>2)
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// Get exponent continuation [does not remove bias]
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#define decimal32ExpCon(d) ((((d)->bytes[0] & 0x03)<<4) \
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| ((unsigned)(d)->bytes[1]>>4))
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// Set sign [this assumes sign previously 0]
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#define decimal32SetSign(d, b) { \
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(d)->bytes[0]|=((unsigned)(b)<<7);}
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// Set exponent continuation [does not apply bias]
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// This assumes range has been checked and exponent previously 0;
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// type of exponent must be unsigned
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#define decimal32SetExpCon(d, e) { \
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(d)->bytes[0]|=(uByte)((e)>>4); \
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(d)->bytes[1]|=(uByte)(((e)&0x0F)<<4);}
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/* ------------------------------------------------------------------ */
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/* decimal32Show -- display a decimal32 in hexadecimal [debug aid] */
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/* d32 -- the number to show */
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/* ------------------------------------------------------------------ */
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// Also shows sign/cob/expconfields extracted - valid bigendian only
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void decimal32Show(const decimal32 *d32) {
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char buf[DECIMAL32_Bytes*2+1];
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Int i, j=0;
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if (DECLITEND) {
|
|
for (i=0; i<DECIMAL32_Bytes; i++, j+=2) {
|
|
sprintf(&buf[j], "%02x", d32->bytes[3-i]);
|
|
}
|
|
printf(" D32> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
|
|
d32->bytes[3]>>7, (d32->bytes[3]>>2)&0x1f,
|
|
((d32->bytes[3]&0x3)<<4)| (d32->bytes[2]>>4));
|
|
}
|
|
else {
|
|
for (i=0; i<DECIMAL32_Bytes; i++, j+=2) {
|
|
sprintf(&buf[j], "%02x", d32->bytes[i]);
|
|
}
|
|
printf(" D32> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
|
|
decimal32Sign(d32), decimal32Comb(d32), decimal32ExpCon(d32));
|
|
}
|
|
} // decimal32Show
|
|
#endif
|