561 lines
22 KiB
C
561 lines
22 KiB
C
/* Decimal 128-bit format module for the decNumber C Library.
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Copyright (C) 2005-2015 Free Software Foundation, Inc.
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Contributed by IBM Corporation. Author Mike Cowlishaw.
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This file is part of GCC.
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GCC is free software; you can redistribute it and/or modify it under
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the terms of the GNU General Public License as published by the Free
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Software Foundation; either version 3, or (at your option) any later
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version.
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GCC is distributed in the hope that it will be useful, but WITHOUT ANY
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WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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Under Section 7 of GPL version 3, you are granted additional
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permissions described in the GCC Runtime Library Exception, version
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3.1, as published by the Free Software Foundation.
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You should have received a copy of the GNU General Public License and
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a copy of the GCC Runtime Library Exception along with this program;
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see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
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<http://www.gnu.org/licenses/>. */
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/* ------------------------------------------------------------------ */
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/* Decimal 128-bit format module */
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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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#include "dconfig.h" /* GCC definitions */
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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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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 '.' */
|
|
/*printf("res %s\n", string); */
|
|
return string;
|
|
} /* decimal128ToString */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* to-number -- conversion from numeric string */
|
|
/* */
|
|
/* decimal128FromString(result, string, set); */
|
|
/* */
|
|
/* result is the decimal128 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 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
|