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/* Decimal 128-bit format module for the decNumber C Library.
Copyright (C) 2005-2022 Free Software Foundation, Inc.
Contributed by IBM Corporation. Author Mike Cowlishaw.
This file is part of GCC.
GCC is free software; you can redistribute it and/or modify it under
the terms of the GNU General Public License as published by the Free
Software Foundation; either version 3, or (at your option) any later
version.
GCC is distributed in the hope that it will be useful, but WITHOUT ANY
WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
Under Section 7 of GPL version 3, you are granted additional
permissions described in the GCC Runtime Library Exception, version
3.1, as published by the Free Software Foundation.
You should have received a copy of the GNU General Public License and
a copy of the GCC Runtime Library Exception along with this program;
see the files COPYING3 and COPYING.RUNTIME respectively. If not, see
<http://www.gnu.org/licenses/>. */
/* ------------------------------------------------------------------ */
/* Decimal 128-bit format module */
/* ------------------------------------------------------------------ */
/* This module comprises the routines for decimal128 format numbers. */
/* Conversions are supplied to and from decNumber and String. */
/* */
/* This is used when decNumber provides operations, either for all */
/* operations or as a proxy between decNumber and decSingle. */
/* */
/* Error handling is the same as decNumber (qv.). */
/* ------------------------------------------------------------------ */
#include <string.h> /* [for memset/memcpy] */
#include <stdio.h> /* [for printf] */
#include "dconfig.h" /* GCC definitions */
#define DECNUMDIGITS 34 /* make decNumbers with space for 34 */
#include "decNumber.h" /* base number library */
#include "decNumberLocal.h" /* decNumber local types, etc. */
#include "decimal128.h" /* our primary include */
/* Utility routines and tables [in decimal64.c] */
extern const uInt COMBEXP[32], COMBMSD[32];
extern const uShort DPD2BIN[1024];
extern const uShort BIN2DPD[1000]; /* [not used] */
extern const uByte BIN2CHAR[4001];
extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
extern void decDigitsToDPD(const decNumber *, uInt *, Int);
#if DECTRACE || DECCHECK
void decimal128Show(const decimal128 *); /* for debug */
extern void decNumberShow(const decNumber *); /* .. */
#endif
/* Useful macro */
/* Clear a structure (e.g., a decNumber) */
#define DEC_clear(d) memset(d, 0, sizeof(*d))
/* ------------------------------------------------------------------ */
/* decimal128FromNumber -- convert decNumber to decimal128 */
/* */
/* ds is the target decimal128 */
/* dn is the source number (assumed valid) */
/* set is the context, used only for reporting errors */
/* */
/* The set argument is used only for status reporting and for the */
/* rounding mode (used if the coefficient is more than DECIMAL128_Pmax*/
/* digits or an overflow is detected). If the exponent is out of the */
/* valid range then Overflow or Underflow will be raised. */
/* After Underflow a subnormal result is possible. */
/* */
/* DEC_Clamped is set if the number has to be 'folded down' to fit, */
/* by reducing its exponent and multiplying the coefficient by a */
/* power of ten, or if the exponent on a zero had to be clamped. */
/* ------------------------------------------------------------------ */
decimal128 * decimal128FromNumber(decimal128 *d128, const decNumber *dn,
decContext *set) {
uInt status=0; /* status accumulator */
Int ae; /* adjusted exponent */
decNumber dw; /* work */
decContext dc; /* .. */
uInt comb, exp; /* .. */
uInt uiwork; /* for macros */
uInt targar[4]={0,0,0,0}; /* target 128-bit */
#define targhi targar[3] /* name the word with the sign */
#define targmh targar[2] /* name the words */
#define targml targar[1] /* .. */
#define targlo targar[0] /* .. */
/* If the number has too many digits, or the exponent could be */
/* out of range then reduce the number under the appropriate */
/* constraints. This could push the number to Infinity or zero, */
/* so this check and rounding must be done before generating the */
/* decimal128] */
ae=dn->exponent+dn->digits-1; /* [0 if special] */
if (dn->digits>DECIMAL128_Pmax /* too many digits */
|| ae>DECIMAL128_Emax /* likely overflow */
|| ae<DECIMAL128_Emin) { /* likely underflow */
decContextDefault(&dc, DEC_INIT_DECIMAL128); /* [no traps] */
dc.round=set->round; /* use supplied rounding */
decNumberPlus(&dw, dn, &dc); /* (round and check) */
/* [this changes -0 to 0, so enforce the sign...] */
dw.bits|=dn->bits&DECNEG;
status=dc.status; /* save status */
dn=&dw; /* use the work number */
} /* maybe out of range */
if (dn->bits&DECSPECIAL) { /* a special value */
if (dn->bits&DECINF) targhi=DECIMAL_Inf<<24;
else { /* sNaN or qNaN */
if ((*dn->lsu!=0 || dn->digits>1) /* non-zero coefficient */
&& (dn->digits<DECIMAL128_Pmax)) { /* coefficient fits */
decDigitsToDPD(dn, targar, 0);
}
if (dn->bits&DECNAN) targhi|=DECIMAL_NaN<<24;
else targhi|=DECIMAL_sNaN<<24;
} /* a NaN */
} /* special */
else { /* is finite */
if (decNumberIsZero(dn)) { /* is a zero */
/* set and clamp exponent */
if (dn->exponent<-DECIMAL128_Bias) {
exp=0; /* low clamp */
status|=DEC_Clamped;
}
else {
exp=dn->exponent+DECIMAL128_Bias; /* bias exponent */
if (exp>DECIMAL128_Ehigh) { /* top clamp */
exp=DECIMAL128_Ehigh;
status|=DEC_Clamped;
}
}
comb=(exp>>9) & 0x18; /* msd=0, exp top 2 bits .. */
}
else { /* non-zero finite number */
uInt msd; /* work */
Int pad=0; /* coefficient pad digits */
/* the dn is known to fit, but it may need to be padded */
exp=(uInt)(dn->exponent+DECIMAL128_Bias); /* bias exponent */
if (exp>DECIMAL128_Ehigh) { /* fold-down case */
pad=exp-DECIMAL128_Ehigh;
exp=DECIMAL128_Ehigh; /* [to maximum] */
status|=DEC_Clamped;
}
/* [fastpath for common case is not a win, here] */
decDigitsToDPD(dn, targar, pad);
/* save and clear the top digit */
msd=targhi>>14;
targhi&=0x00003fff;
/* create the combination field */
if (msd>=8) comb=0x18 | ((exp>>11) & 0x06) | (msd & 0x01);
else comb=((exp>>9) & 0x18) | msd;
}
targhi|=comb<<26; /* add combination field .. */
targhi|=(exp&0xfff)<<14; /* .. and exponent continuation */
} /* finite */
if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
/* now write to storage; this is endian */
if (DECLITEND) {
/* lo -> hi */
UBFROMUI(d128->bytes, targlo);
UBFROMUI(d128->bytes+4, targml);
UBFROMUI(d128->bytes+8, targmh);
UBFROMUI(d128->bytes+12, targhi);
}
else {
/* hi -> lo */
UBFROMUI(d128->bytes, targhi);
UBFROMUI(d128->bytes+4, targmh);
UBFROMUI(d128->bytes+8, targml);
UBFROMUI(d128->bytes+12, targlo);
}
if (status!=0) decContextSetStatus(set, status); /* pass on status */
/* decimal128Show(d128); */
return d128;
} /* decimal128FromNumber */
/* ------------------------------------------------------------------ */
/* decimal128ToNumber -- convert decimal128 to decNumber */
/* d128 is the source decimal128 */
/* dn is the target number, with appropriate space */
/* No error is possible. */
/* ------------------------------------------------------------------ */
decNumber * decimal128ToNumber(const decimal128 *d128, decNumber *dn) {
uInt msd; /* coefficient MSD */
uInt exp; /* exponent top two bits */
uInt comb; /* combination field */
Int need; /* work */
uInt uiwork; /* for macros */
uInt sourar[4]; /* source 128-bit */
#define sourhi sourar[3] /* name the word with the sign */
#define sourmh sourar[2] /* and the mid-high word */
#define sourml sourar[1] /* and the mod-low word */
#define sourlo sourar[0] /* and the lowest word */
/* load source from storage; this is endian */
if (DECLITEND) {
sourlo=UBTOUI(d128->bytes ); /* directly load the low int */
sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
sourhi=UBTOUI(d128->bytes+12); /* then the high int */
}
else {
sourhi=UBTOUI(d128->bytes ); /* directly load the high int */
sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
sourlo=UBTOUI(d128->bytes+12); /* then the low int */
}
comb=(sourhi>>26)&0x1f; /* combination field */
decNumberZero(dn); /* clean number */
if (sourhi&0x80000000) dn->bits=DECNEG; /* set sign if negative */
msd=COMBMSD[comb]; /* decode the combination field */
exp=COMBEXP[comb]; /* .. */
if (exp==3) { /* is a special */
if (msd==0) {
dn->bits|=DECINF;
return dn; /* no coefficient needed */
}
else if (sourhi&0x02000000) dn->bits|=DECSNAN;
else dn->bits|=DECNAN;
msd=0; /* no top digit */
}
else { /* is a finite number */
dn->exponent=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
}
/* get the coefficient */
sourhi&=0x00003fff; /* clean coefficient continuation */
if (msd) { /* non-zero msd */
sourhi|=msd<<14; /* prefix to coefficient */
need=12; /* process 12 declets */
}
else { /* msd=0 */
if (sourhi) need=11; /* declets to process */
else if (sourmh) need=10;
else if (sourml) need=7;
else if (sourlo) need=4;
else return dn; /* easy: coefficient is 0 */
} /*msd=0 */
decDigitsFromDPD(dn, sourar, need); /* process declets */
/* decNumberShow(dn); */
return dn;
} /* decimal128ToNumber */
/* ------------------------------------------------------------------ */
/* to-scientific-string -- conversion to numeric string */
/* to-engineering-string -- conversion to numeric string */
/* */
/* decimal128ToString(d128, string); */
/* decimal128ToEngString(d128, string); */
/* */
/* d128 is the decimal128 format number to convert */
/* string is the string where the result will be laid out */
/* */
/* string must be at least 24 characters */
/* */
/* No error is possible, and no status can be set. */
/* ------------------------------------------------------------------ */
char * decimal128ToEngString(const decimal128 *d128, char *string){
decNumber dn; /* work */
decimal128ToNumber(d128, &dn);
decNumberToEngString(&dn, string);
return string;
} /* decimal128ToEngString */
char * decimal128ToString(const decimal128 *d128, char *string){
uInt msd; /* coefficient MSD */
Int exp; /* exponent top two bits or full */
uInt comb; /* combination field */
char *cstart; /* coefficient start */
char *c; /* output pointer in string */
const uByte *u; /* work */
char *s, *t; /* .. (source, target) */
Int dpd; /* .. */
Int pre, e; /* .. */
uInt uiwork; /* for macros */
uInt sourar[4]; /* source 128-bit */
#define sourhi sourar[3] /* name the word with the sign */
#define sourmh sourar[2] /* and the mid-high word */
#define sourml sourar[1] /* and the mod-low word */
#define sourlo sourar[0] /* and the lowest word */
/* load source from storage; this is endian */
if (DECLITEND) {
sourlo=UBTOUI(d128->bytes ); /* directly load the low int */
sourml=UBTOUI(d128->bytes+4 ); /* then the mid-low */
sourmh=UBTOUI(d128->bytes+8 ); /* then the mid-high */
sourhi=UBTOUI(d128->bytes+12); /* then the high int */
}
else {
sourhi=UBTOUI(d128->bytes ); /* directly load the high int */
sourmh=UBTOUI(d128->bytes+4 ); /* then the mid-high */
sourml=UBTOUI(d128->bytes+8 ); /* then the mid-low */
sourlo=UBTOUI(d128->bytes+12); /* then the low int */
}
c=string; /* where result will go */
if (((Int)sourhi)<0) *c++='-'; /* handle sign */
comb=(sourhi>>26)&0x1f; /* combination field */
msd=COMBMSD[comb]; /* decode the combination field */
exp=COMBEXP[comb]; /* .. */
if (exp==3) {
if (msd==0) { /* infinity */
strcpy(c, "Inf");
strcpy(c+3, "inity");
return string; /* easy */
}
if (sourhi&0x02000000) *c++='s'; /* sNaN */
strcpy(c, "NaN"); /* complete word */
c+=3; /* step past */
if (sourlo==0 && sourml==0 && sourmh==0
&& (sourhi&0x0003ffff)==0) return string; /* zero payload */
/* otherwise drop through to add integer; set correct exp */
exp=0; msd=0; /* setup for following code */
}
else exp=(exp<<12)+((sourhi>>14)&0xfff)-DECIMAL128_Bias; /* unbiased */
/* convert 34 digits of significand to characters */
cstart=c; /* save start of coefficient */
if (msd) *c++='0'+(char)msd; /* non-zero most significant digit */
/* Now decode the declets. After extracting each one, it is */
/* decoded to binary and then to a 4-char sequence by table lookup; */
/* the 4-chars are a 1-char length (significant digits, except 000 */
/* has length 0). This allows us to left-align the first declet */
/* with non-zero content, then remaining ones are full 3-char */
/* length. We use fixed-length memcpys because variable-length */
/* causes a subroutine call in GCC. (These are length 4 for speed */
/* and are safe because the array has an extra terminator byte.) */
#define dpd2char u=&BIN2CHAR[DPD2BIN[dpd]*4]; \
if (c!=cstart) {memcpy(c, u+1, 4); c+=3;} \
else if (*u) {memcpy(c, u+4-*u, 4); c+=*u;}
dpd=(sourhi>>4)&0x3ff; /* declet 1 */
dpd2char;
dpd=((sourhi&0xf)<<6) | (sourmh>>26); /* declet 2 */
dpd2char;
dpd=(sourmh>>16)&0x3ff; /* declet 3 */
dpd2char;
dpd=(sourmh>>6)&0x3ff; /* declet 4 */
dpd2char;
dpd=((sourmh&0x3f)<<4) | (sourml>>28); /* declet 5 */
dpd2char;
dpd=(sourml>>18)&0x3ff; /* declet 6 */
dpd2char;
dpd=(sourml>>8)&0x3ff; /* declet 7 */
dpd2char;
dpd=((sourml&0xff)<<2) | (sourlo>>30); /* declet 8 */
dpd2char;
dpd=(sourlo>>20)&0x3ff; /* declet 9 */
dpd2char;
dpd=(sourlo>>10)&0x3ff; /* declet 10 */
dpd2char;
dpd=(sourlo)&0x3ff; /* declet 11 */
dpd2char;
if (c==cstart) *c++='0'; /* all zeros -- make 0 */
if (exp==0) { /* integer or NaN case -- easy */
*c='\0'; /* terminate */
return string;
}
/* non-0 exponent */
e=0; /* assume no E */
pre=c-cstart+exp;
/* [here, pre-exp is the digits count (==1 for zero)] */
if (exp>0 || pre<-5) { /* need exponential form */
e=pre-1; /* calculate E value */
pre=1; /* assume one digit before '.' */
} /* exponential form */
/* modify the coefficient, adding 0s, '.', and E+nn as needed */
s=c-1; /* source (LSD) */
if (pre>0) { /* ddd.ddd (plain), perhaps with E */
char *dotat=cstart+pre;
if (dotat<c) { /* if embedded dot needed... */
t=c; /* target */
for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
*t='.'; /* insert the dot */
c++; /* length increased by one */
}
/* finally add the E-part, if needed; it will never be 0, and has */
/* a maximum length of 4 digits */
if (e!=0) {
*c++='E'; /* starts with E */
*c++='+'; /* assume positive */
if (e<0) {
*(c-1)='-'; /* oops, need '-' */
e=-e; /* uInt, please */
}
if (e<1000) { /* 3 (or fewer) digits case */
u=&BIN2CHAR[e*4]; /* -> length byte */
memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */
c+=*u; /* bump pointer appropriately */
}
else { /* 4-digits */
Int thou=((e>>3)*1049)>>17; /* e/1000 */
Int rem=e-(1000*thou); /* e%1000 */
*c++='0'+(char)thou;
u=&BIN2CHAR[rem*4]; /* -> length byte */
memcpy(c, u+1, 4); /* copy fixed 3+1 characters [is safe] */
c+=3; /* bump pointer, always 3 digits */
}
}
*c='\0'; /* add terminator */
/*printf("res %s\n", string); */
return string;
} /* pre>0 */
/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
t=c+1-pre;
*(t+1)='\0'; /* can add terminator now */
for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */
c=cstart;
*c++='0'; /* always starts with 0. */
*c++='.';
for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */
/*printf("res %s\n", string); */
return string;
} /* 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
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