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554 lines
25 KiB
C
554 lines
25 KiB
C
/* ------------------------------------------------------------------ */
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/* Decimal 128-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 decimal128 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 34 // make decNumbers with space for 34
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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 "decimal128.h" // our primary include
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/* Utility routines and tables [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]; // [not used]
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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 decimal128Show(const decimal128 *); // 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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/* decimal128FromNumber -- convert decNumber to decimal128 */
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/* */
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/* ds is the target decimal128 */
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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 DECIMAL128_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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decimal128 * decimal128FromNumber(decimal128 *d128, 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[4]={0,0,0,0}; // target 128-bit
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#define targhi targar[3] // name the word with the sign
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#define targmh targar[2] // name the words
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#define targml targar[1] // ..
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#define targlo targar[0] // ..
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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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// decimal128]
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ae=dn->exponent+dn->digits-1; // [0 if special]
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if (dn->digits>DECIMAL128_Pmax // too many digits
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|| ae>DECIMAL128_Emax // likely overflow
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|| ae<DECIMAL128_Emin) { // likely underflow
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decContextDefault(&dc, DEC_INIT_DECIMAL128); // [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<DECIMAL128_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<-DECIMAL128_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+DECIMAL128_Bias; // bias exponent
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if (exp>DECIMAL128_Ehigh) { // top clamp
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exp=DECIMAL128_Ehigh;
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status|=DEC_Clamped;
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}
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}
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comb=(exp>>9) & 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+DECIMAL128_Bias); // bias exponent
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if (exp>DECIMAL128_Ehigh) { // fold-down case
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pad=exp-DECIMAL128_Ehigh;
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exp=DECIMAL128_Ehigh; // [to maximum]
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status|=DEC_Clamped;
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}
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// [fastpath for common case is not a win, here]
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decDigitsToDPD(dn, targar, pad);
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// save and clear the top digit
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msd=targhi>>14;
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targhi&=0x00003fff;
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// create the combination field
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if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);
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else comb=((exp>>9) & 0x18) | msd;
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}
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targhi|=comb<<26; // add combination field ..
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targhi|=(exp&0xfff)<<14; // .. 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 endian
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if (DECLITEND) {
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// lo -> hi
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UBFROMUI(d128->bytes, targlo);
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UBFROMUI(d128->bytes+4, targml);
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UBFROMUI(d128->bytes+8, targmh);
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UBFROMUI(d128->bytes+12, targhi);
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}
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else {
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// hi -> lo
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UBFROMUI(d128->bytes, targhi);
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UBFROMUI(d128->bytes+4, targmh);
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UBFROMUI(d128->bytes+8, targml);
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UBFROMUI(d128->bytes+12, targlo);
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}
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if (status!=0) decContextSetStatus(set, status); // pass on status
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// decimal128Show(d128);
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return d128;
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} // decimal128FromNumber
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/* ------------------------------------------------------------------ */
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/* decimal128ToNumber -- convert decimal128 to decNumber */
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/* d128 is the source decimal128 */
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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 * decimal128ToNumber(const decimal128 *d128, 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[4]; // source 128-bit
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#define sourhi sourar[3] // name the word with the sign
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#define sourmh sourar[2] // and the mid-high word
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#define sourml sourar[1] // and the mod-low word
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#define sourlo sourar[0] // and the lowest word
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// load source from storage; this is endian
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if (DECLITEND) {
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sourlo=UBTOUI(d128->bytes ); // directly load the low int
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sourml=UBTOUI(d128->bytes+4 ); // then the mid-low
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sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high
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sourhi=UBTOUI(d128->bytes+12); // then the high int
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}
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else {
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sourhi=UBTOUI(d128->bytes ); // directly load the high int
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sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high
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sourml=UBTOUI(d128->bytes+8 ); // then the mid-low
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sourlo=UBTOUI(d128->bytes+12); // 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<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased
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}
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// get the coefficient
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sourhi&=0x00003fff; // clean coefficient continuation
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if (msd) { // non-zero msd
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sourhi|=msd<<14; // prefix to coefficient
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need=12; // process 12 declets
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}
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else { // msd=0
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if (sourhi) need=11; // declets to process
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else if (sourmh) need=10;
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else if (sourml) need=7;
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else if (sourlo) need=4;
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else return dn; // easy: coefficient is 0
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} //msd=0
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decDigitsFromDPD(dn, sourar, need); // process declets
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// decNumberShow(dn);
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return dn;
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} // decimal128ToNumber
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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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/* decimal128ToString(d128, string); */
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/* decimal128ToEngString(d128, string); */
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/* */
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/* d128 is the decimal128 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 * decimal128ToEngString(const decimal128 *d128, char *string){
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decNumber dn; // work
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decimal128ToNumber(d128, &dn);
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decNumberToEngString(&dn, string);
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return string;
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} // decimal128ToEngString
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char * decimal128ToString(const decimal128 *d128, 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[4]; // source 128-bit
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#define sourhi sourar[3] // name the word with the sign
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#define sourmh sourar[2] // and the mid-high word
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#define sourml sourar[1] // and the mod-low word
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#define sourlo sourar[0] // and the lowest word
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// load source from storage; this is endian
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if (DECLITEND) {
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sourlo=UBTOUI(d128->bytes ); // directly load the low int
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sourml=UBTOUI(d128->bytes+4 ); // then the mid-low
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sourmh=UBTOUI(d128->bytes+8 ); // then the mid-high
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sourhi=UBTOUI(d128->bytes+12); // then the high int
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}
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else {
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sourhi=UBTOUI(d128->bytes ); // directly load the high int
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sourmh=UBTOUI(d128->bytes+4 ); // then the mid-high
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sourml=UBTOUI(d128->bytes+8 ); // then the mid-low
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sourlo=UBTOUI(d128->bytes+12); // 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 && sourml==0 && sourmh==0
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&& (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<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; // unbiased
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// convert 34 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=(sourhi>>4)&0x3ff; // declet 1
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dpd2char;
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dpd=((sourhi&0xf)<<6) | (sourmh>>26); // declet 2
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dpd2char;
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dpd=(sourmh>>16)&0x3ff; // declet 3
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dpd2char;
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dpd=(sourmh>>6)&0x3ff; // declet 4
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dpd2char;
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dpd=((sourmh&0x3f)<<4) | (sourml>>28); // declet 5
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dpd2char;
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dpd=(sourml>>18)&0x3ff; // declet 6
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dpd2char;
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dpd=(sourml>>8)&0x3ff; // declet 7
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dpd2char;
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dpd=((sourml&0xff)<<2) | (sourlo>>30); // declet 8
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dpd2char;
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dpd=(sourlo>>20)&0x3ff; // declet 9
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dpd2char;
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dpd=(sourlo>>10)&0x3ff; // declet 10
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dpd2char;
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dpd=(sourlo)&0x3ff; // declet 11
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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 4 digits
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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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if (e<1000) { // 3 (or fewer) digits case
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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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else { // 4-digits
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Int thou=((e>>3)*1049)>>17; // e/1000
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Int rem=e-(1000*thou); // e%1000
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*c++='0'+(char)thou;
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u=&BIN2CHAR[rem*4]; // -> length byte
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memcpy(c, u+1, 4); // copy fixed 3+1 characters [is safe]
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c+=3; // bump pointer, always 3 digits
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}
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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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} // decimal128ToString
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/* ------------------------------------------------------------------ */
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/* to-number -- conversion from numeric string */
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/* */
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/* decimal128FromString(result, string, set); */
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/* */
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/* result is the decimal128 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 */
|
|
/* (setting of status and traps) and for the rounding mode, only. */
|
|
/* If an error occurs, the result will be a valid decimal128 NaN. */
|
|
/* ------------------------------------------------------------------ */
|
|
decimal128 * decimal128FromString(decimal128 *result, const char *string,
|
|
decContext *set) {
|
|
decContext dc; // work
|
|
decNumber dn; // ..
|
|
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL128); // no traps, please
|
|
dc.round=set->round; // use supplied rounding
|
|
|
|
decNumberFromString(&dn, string, &dc); // will round if needed
|
|
decimal128FromNumber(result, &dn, &dc);
|
|
if (dc.status!=0) { // something happened
|
|
decContextSetStatus(set, dc.status); // .. pass it on
|
|
}
|
|
return result;
|
|
} // decimal128FromString
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal128IsCanonical -- test whether encoding is canonical */
|
|
/* d128 is the source decimal128 */
|
|
/* returns 1 if the encoding of d128 is canonical, 0 otherwise */
|
|
/* No error is possible. */
|
|
/* ------------------------------------------------------------------ */
|
|
uInt decimal128IsCanonical(const decimal128 *d128) {
|
|
decNumber dn; // work
|
|
decimal128 canon; // ..
|
|
decContext dc; // ..
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL128);
|
|
decimal128ToNumber(d128, &dn);
|
|
decimal128FromNumber(&canon, &dn, &dc);// canon will now be canonical
|
|
return memcmp(d128, &canon, DECIMAL128_Bytes)==0;
|
|
} // decimal128IsCanonical
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal128Canonical -- copy an encoding, ensuring it is canonical */
|
|
/* d128 is the source decimal128 */
|
|
/* result is the target (may be the same decimal128) */
|
|
/* returns result */
|
|
/* No error is possible. */
|
|
/* ------------------------------------------------------------------ */
|
|
decimal128 * decimal128Canonical(decimal128 *result, const decimal128 *d128) {
|
|
decNumber dn; // work
|
|
decContext dc; // ..
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL128);
|
|
decimal128ToNumber(d128, &dn);
|
|
decimal128FromNumber(result, &dn, &dc);// result will now be canonical
|
|
return result;
|
|
} // decimal128Canonical
|
|
|
|
#if DECTRACE || DECCHECK
|
|
/* Macros for accessing decimal128 fields. These assume the argument
|
|
is a reference (pointer) to the decimal128 structure, and the
|
|
decimal128 is in network byte order (big-endian) */
|
|
// Get sign
|
|
#define decimal128Sign(d) ((unsigned)(d)->bytes[0]>>7)
|
|
|
|
// Get combination field
|
|
#define decimal128Comb(d) (((d)->bytes[0] & 0x7c)>>2)
|
|
|
|
// Get exponent continuation [does not remove bias]
|
|
#define decimal128ExpCon(d) ((((d)->bytes[0] & 0x03)<<10) \
|
|
| ((unsigned)(d)->bytes[1]<<2) \
|
|
| ((unsigned)(d)->bytes[2]>>6))
|
|
|
|
// Set sign [this assumes sign previously 0]
|
|
#define decimal128SetSign(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 decimal128SetExpCon(d, e) { \
|
|
(d)->bytes[0]|=(uByte)((e)>>10); \
|
|
(d)->bytes[1] =(uByte)(((e)&0x3fc)>>2); \
|
|
(d)->bytes[2]|=(uByte)(((e)&0x03)<<6);}
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal128Show -- display a decimal128 in hexadecimal [debug aid] */
|
|
/* d128 -- the number to show */
|
|
/* ------------------------------------------------------------------ */
|
|
// Also shows sign/cob/expconfields extracted
|
|
void decimal128Show(const decimal128 *d128) {
|
|
char buf[DECIMAL128_Bytes*2+1];
|
|
Int i, j=0;
|
|
|
|
if (DECLITEND) {
|
|
for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
|
|
sprintf(&buf[j], "%02x", d128->bytes[15-i]);
|
|
}
|
|
printf(" D128> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
|
|
d128->bytes[15]>>7, (d128->bytes[15]>>2)&0x1f,
|
|
((d128->bytes[15]&0x3)<<10)|(d128->bytes[14]<<2)|
|
|
(d128->bytes[13]>>6));
|
|
}
|
|
else {
|
|
for (i=0; i<DECIMAL128_Bytes; i++, j+=2) {
|
|
sprintf(&buf[j], "%02x", d128->bytes[i]);
|
|
}
|
|
printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
|
|
decimal128Sign(d128), decimal128Comb(d128),
|
|
decimal128ExpCon(d128));
|
|
}
|
|
} // decimal128Show
|
|
#endif
|