847 lines
32 KiB
C
847 lines
32 KiB
C
/* Decimal 64-bit format module for the decNumber C Library.
|
|
Copyright (C) 2005, 2007, 2009 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 64-bit format module */
|
|
/* ------------------------------------------------------------------ */
|
|
/* This module comprises the routines for decimal64 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 16 /* make decNumbers with space for 16 */
|
|
#include "decNumber.h" /* base number library */
|
|
#include "decNumberLocal.h" /* decNumber local types, etc. */
|
|
#include "decimal64.h" /* our primary include */
|
|
|
|
/* Utility routines and tables [in decimal64.c]; externs for C++ */
|
|
extern const uInt COMBEXP[32], COMBMSD[32];
|
|
extern const uShort DPD2BIN[1024];
|
|
extern const uShort BIN2DPD[1000];
|
|
extern const uByte BIN2CHAR[4001];
|
|
|
|
extern void decDigitsFromDPD(decNumber *, const uInt *, Int);
|
|
extern void decDigitsToDPD(const decNumber *, uInt *, Int);
|
|
|
|
#if DECTRACE || DECCHECK
|
|
void decimal64Show(const decimal64 *); /* 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))
|
|
|
|
/* define and include the tables to use for conversions */
|
|
#define DEC_BIN2CHAR 1
|
|
#define DEC_DPD2BIN 1
|
|
#define DEC_BIN2DPD 1 /* used for all sizes */
|
|
#include "decDPD.h" /* lookup tables */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal64FromNumber -- convert decNumber to decimal64 */
|
|
/* */
|
|
/* ds is the target decimal64 */
|
|
/* 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 DECIMAL64_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. */
|
|
/* ------------------------------------------------------------------ */
|
|
decimal64 * decimal64FromNumber(decimal64 *d64, 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[2]={0, 0}; /* target 64-bit */
|
|
#define targhi targar[1] /* name the word with the sign */
|
|
#define targlo targar[0] /* and the other */
|
|
|
|
/* 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 */
|
|
/* decimal64] */
|
|
ae=dn->exponent+dn->digits-1; /* [0 if special] */
|
|
if (dn->digits>DECIMAL64_Pmax /* too many digits */
|
|
|| ae>DECIMAL64_Emax /* likely overflow */
|
|
|| ae<DECIMAL64_Emin) { /* likely underflow */
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64); /* [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<DECIMAL64_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<-DECIMAL64_Bias) {
|
|
exp=0; /* low clamp */
|
|
status|=DEC_Clamped;
|
|
}
|
|
else {
|
|
exp=dn->exponent+DECIMAL64_Bias; /* bias exponent */
|
|
if (exp>DECIMAL64_Ehigh) { /* top clamp */
|
|
exp=DECIMAL64_Ehigh;
|
|
status|=DEC_Clamped;
|
|
}
|
|
}
|
|
comb=(exp>>5) & 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+DECIMAL64_Bias); /* bias exponent */
|
|
if (exp>DECIMAL64_Ehigh) { /* fold-down case */
|
|
pad=exp-DECIMAL64_Ehigh;
|
|
exp=DECIMAL64_Ehigh; /* [to maximum] */
|
|
status|=DEC_Clamped;
|
|
}
|
|
|
|
/* fastpath common case */
|
|
if (DECDPUN==3 && pad==0) {
|
|
uInt dpd[6]={0,0,0,0,0,0};
|
|
uInt i;
|
|
Int d=dn->digits;
|
|
for (i=0; d>0; i++, d-=3) dpd[i]=BIN2DPD[dn->lsu[i]];
|
|
targlo =dpd[0];
|
|
targlo|=dpd[1]<<10;
|
|
targlo|=dpd[2]<<20;
|
|
if (dn->digits>6) {
|
|
targlo|=dpd[3]<<30;
|
|
targhi =dpd[3]>>2;
|
|
targhi|=dpd[4]<<8;
|
|
}
|
|
msd=dpd[5]; /* [did not really need conversion] */
|
|
}
|
|
else { /* general case */
|
|
decDigitsToDPD(dn, targar, pad);
|
|
/* save and clear the top digit */
|
|
msd=targhi>>18;
|
|
targhi&=0x0003ffff;
|
|
}
|
|
|
|
/* create the combination field */
|
|
if (msd>=8) comb=0x18 | ((exp>>7) & 0x06) | (msd & 0x01);
|
|
else comb=((exp>>5) & 0x18) | msd;
|
|
}
|
|
targhi|=comb<<26; /* add combination field .. */
|
|
targhi|=(exp&0xff)<<18; /* .. and exponent continuation */
|
|
} /* finite */
|
|
|
|
if (dn->bits&DECNEG) targhi|=0x80000000; /* add sign bit */
|
|
|
|
/* now write to storage; this is now always endian */
|
|
if (DECLITEND) {
|
|
/* lo int then hi */
|
|
UBFROMUI(d64->bytes, targar[0]);
|
|
UBFROMUI(d64->bytes+4, targar[1]);
|
|
}
|
|
else {
|
|
/* hi int then lo */
|
|
UBFROMUI(d64->bytes, targar[1]);
|
|
UBFROMUI(d64->bytes+4, targar[0]);
|
|
}
|
|
|
|
if (status!=0) decContextSetStatus(set, status); /* pass on status */
|
|
/* decimal64Show(d64); */
|
|
return d64;
|
|
} /* decimal64FromNumber */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal64ToNumber -- convert decimal64 to decNumber */
|
|
/* d64 is the source decimal64 */
|
|
/* dn is the target number, with appropriate space */
|
|
/* No error is possible. */
|
|
/* ------------------------------------------------------------------ */
|
|
decNumber * decimal64ToNumber(const decimal64 *d64, 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[2]; /* source 64-bit */
|
|
#define sourhi sourar[1] /* name the word with the sign */
|
|
#define sourlo sourar[0] /* and the lower word */
|
|
|
|
/* load source from storage; this is endian */
|
|
if (DECLITEND) {
|
|
sourlo=UBTOUI(d64->bytes ); /* directly load the low int */
|
|
sourhi=UBTOUI(d64->bytes+4); /* then the high int */
|
|
}
|
|
else {
|
|
sourhi=UBTOUI(d64->bytes ); /* directly load the high int */
|
|
sourlo=UBTOUI(d64->bytes+4); /* 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<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias; /* unbiased */
|
|
}
|
|
|
|
/* get the coefficient */
|
|
sourhi&=0x0003ffff; /* clean coefficient continuation */
|
|
if (msd) { /* non-zero msd */
|
|
sourhi|=msd<<18; /* prefix to coefficient */
|
|
need=6; /* process 6 declets */
|
|
}
|
|
else { /* msd=0 */
|
|
if (!sourhi) { /* top word 0 */
|
|
if (!sourlo) return dn; /* easy: coefficient is 0 */
|
|
need=3; /* process at least 3 declets */
|
|
if (sourlo&0xc0000000) need++; /* process 4 declets */
|
|
/* [could reduce some more, here] */
|
|
}
|
|
else { /* some bits in top word, msd=0 */
|
|
need=4; /* process at least 4 declets */
|
|
if (sourhi&0x0003ff00) need++; /* top declet!=0, process 5 */
|
|
}
|
|
} /*msd=0 */
|
|
|
|
decDigitsFromDPD(dn, sourar, need); /* process declets */
|
|
return dn;
|
|
} /* decimal64ToNumber */
|
|
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* to-scientific-string -- conversion to numeric string */
|
|
/* to-engineering-string -- conversion to numeric string */
|
|
/* */
|
|
/* decimal64ToString(d64, string); */
|
|
/* decimal64ToEngString(d64, string); */
|
|
/* */
|
|
/* d64 is the decimal64 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 * decimal64ToEngString(const decimal64 *d64, char *string){
|
|
decNumber dn; /* work */
|
|
decimal64ToNumber(d64, &dn);
|
|
decNumberToEngString(&dn, string);
|
|
return string;
|
|
} /* decimal64ToEngString */
|
|
|
|
char * decimal64ToString(const decimal64 *d64, 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[2]; /* source 64-bit */
|
|
#define sourhi sourar[1] /* name the word with the sign */
|
|
#define sourlo sourar[0] /* and the lower word */
|
|
|
|
/* load source from storage; this is endian */
|
|
if (DECLITEND) {
|
|
sourlo=UBTOUI(d64->bytes ); /* directly load the low int */
|
|
sourhi=UBTOUI(d64->bytes+4); /* then the high int */
|
|
}
|
|
else {
|
|
sourhi=UBTOUI(d64->bytes ); /* directly load the high int */
|
|
sourlo=UBTOUI(d64->bytes+4); /* 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 && (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<<8)+((sourhi>>18)&0xff)-DECIMAL64_Bias;
|
|
|
|
/* convert 16 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>>8)&0x3ff; /* declet 1 */
|
|
dpd2char;
|
|
dpd=((sourhi&0xff)<<2) | (sourlo>>30); /* declet 2 */
|
|
dpd2char;
|
|
dpd=(sourlo>>20)&0x3ff; /* declet 3 */
|
|
dpd2char;
|
|
dpd=(sourlo>>10)&0x3ff; /* declet 4 */
|
|
dpd2char;
|
|
dpd=(sourlo)&0x3ff; /* declet 5 */
|
|
dpd2char;
|
|
|
|
if (c==cstart) *c++='0'; /* all zeros -- make 0 */
|
|
|
|
if (exp==0) { /* integer or NaN case -- easy */
|
|
*c='\0'; /* terminate */
|
|
return string;
|
|
}
|
|
|
|
/* non-0 exponent */
|
|
e=0; /* assume no E */
|
|
pre=c-cstart+exp;
|
|
/* [here, pre-exp is the digits count (==1 for zero)] */
|
|
if (exp>0 || pre<-5) { /* need exponential form */
|
|
e=pre-1; /* calculate E value */
|
|
pre=1; /* assume one digit before '.' */
|
|
} /* exponential form */
|
|
|
|
/* modify the coefficient, adding 0s, '.', and E+nn as needed */
|
|
s=c-1; /* source (LSD) */
|
|
if (pre>0) { /* ddd.ddd (plain), perhaps with E */
|
|
char *dotat=cstart+pre;
|
|
if (dotat<c) { /* if embedded dot needed... */
|
|
t=c; /* target */
|
|
for (; s>=dotat; s--, t--) *t=*s; /* open the gap; leave t at gap */
|
|
*t='.'; /* insert the dot */
|
|
c++; /* length increased by one */
|
|
}
|
|
|
|
/* finally add the E-part, if needed; it will never be 0, and has */
|
|
/* a maximum length of 3 digits */
|
|
if (e!=0) {
|
|
*c++='E'; /* starts with E */
|
|
*c++='+'; /* assume positive */
|
|
if (e<0) {
|
|
*(c-1)='-'; /* oops, need '-' */
|
|
e=-e; /* uInt, please */
|
|
}
|
|
u=&BIN2CHAR[e*4]; /* -> length byte */
|
|
memcpy(c, u+4-*u, 4); /* copy fixed 4 characters [is safe] */
|
|
c+=*u; /* bump pointer appropriately */
|
|
}
|
|
*c='\0'; /* add terminator */
|
|
/*printf("res %s\n", string); */
|
|
return string;
|
|
} /* pre>0 */
|
|
|
|
/* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (can never have E) */
|
|
t=c+1-pre;
|
|
*(t+1)='\0'; /* can add terminator now */
|
|
for (; s>=cstart; s--, t--) *t=*s; /* shift whole coefficient right */
|
|
c=cstart;
|
|
*c++='0'; /* always starts with 0. */
|
|
*c++='.';
|
|
for (; pre<0; pre++) *c++='0'; /* add any 0's after '.' */
|
|
/*printf("res %s\n", string); */
|
|
return string;
|
|
} /* decimal64ToString */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* to-number -- conversion from numeric string */
|
|
/* */
|
|
/* decimal64FromString(result, string, set); */
|
|
/* */
|
|
/* result is the decimal64 format number which gets the result of */
|
|
/* the conversion */
|
|
/* *string is the character string which should contain a valid */
|
|
/* number (which may be a special value) */
|
|
/* set is the context */
|
|
/* */
|
|
/* The context is supplied to this routine is used for error handling */
|
|
/* (setting of status and traps) and for the rounding mode, only. */
|
|
/* If an error occurs, the result will be a valid decimal64 NaN. */
|
|
/* ------------------------------------------------------------------ */
|
|
decimal64 * decimal64FromString(decimal64 *result, const char *string,
|
|
decContext *set) {
|
|
decContext dc; /* work */
|
|
decNumber dn; /* .. */
|
|
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64); /* no traps, please */
|
|
dc.round=set->round; /* use supplied rounding */
|
|
|
|
decNumberFromString(&dn, string, &dc); /* will round if needed */
|
|
|
|
decimal64FromNumber(result, &dn, &dc);
|
|
if (dc.status!=0) { /* something happened */
|
|
decContextSetStatus(set, dc.status); /* .. pass it on */
|
|
}
|
|
return result;
|
|
} /* decimal64FromString */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal64IsCanonical -- test whether encoding is canonical */
|
|
/* d64 is the source decimal64 */
|
|
/* returns 1 if the encoding of d64 is canonical, 0 otherwise */
|
|
/* No error is possible. */
|
|
/* ------------------------------------------------------------------ */
|
|
uInt decimal64IsCanonical(const decimal64 *d64) {
|
|
decNumber dn; /* work */
|
|
decimal64 canon; /* .. */
|
|
decContext dc; /* .. */
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64);
|
|
decimal64ToNumber(d64, &dn);
|
|
decimal64FromNumber(&canon, &dn, &dc);/* canon will now be canonical */
|
|
return memcmp(d64, &canon, DECIMAL64_Bytes)==0;
|
|
} /* decimal64IsCanonical */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal64Canonical -- copy an encoding, ensuring it is canonical */
|
|
/* d64 is the source decimal64 */
|
|
/* result is the target (may be the same decimal64) */
|
|
/* returns result */
|
|
/* No error is possible. */
|
|
/* ------------------------------------------------------------------ */
|
|
decimal64 * decimal64Canonical(decimal64 *result, const decimal64 *d64) {
|
|
decNumber dn; /* work */
|
|
decContext dc; /* .. */
|
|
decContextDefault(&dc, DEC_INIT_DECIMAL64);
|
|
decimal64ToNumber(d64, &dn);
|
|
decimal64FromNumber(result, &dn, &dc);/* result will now be canonical */
|
|
return result;
|
|
} /* decimal64Canonical */
|
|
|
|
#if DECTRACE || DECCHECK
|
|
/* Macros for accessing decimal64 fields. These assume the
|
|
argument is a reference (pointer) to the decimal64 structure,
|
|
and the decimal64 is in network byte order (big-endian) */
|
|
/* Get sign */
|
|
#define decimal64Sign(d) ((unsigned)(d)->bytes[0]>>7)
|
|
|
|
/* Get combination field */
|
|
#define decimal64Comb(d) (((d)->bytes[0] & 0x7c)>>2)
|
|
|
|
/* Get exponent continuation [does not remove bias] */
|
|
#define decimal64ExpCon(d) ((((d)->bytes[0] & 0x03)<<6) \
|
|
| ((unsigned)(d)->bytes[1]>>2))
|
|
|
|
/* Set sign [this assumes sign previously 0] */
|
|
#define decimal64SetSign(d, b) { \
|
|
(d)->bytes[0]|=((unsigned)(b)<<7);}
|
|
|
|
/* Set exponent continuation [does not apply bias] */
|
|
/* This assumes range has been checked and exponent previously 0; */
|
|
/* type of exponent must be unsigned */
|
|
#define decimal64SetExpCon(d, e) { \
|
|
(d)->bytes[0]|=(uByte)((e)>>6); \
|
|
(d)->bytes[1]|=(uByte)(((e)&0x3F)<<2);}
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decimal64Show -- display a decimal64 in hexadecimal [debug aid] */
|
|
/* d64 -- the number to show */
|
|
/* ------------------------------------------------------------------ */
|
|
/* Also shows sign/cob/expconfields extracted */
|
|
void decimal64Show(const decimal64 *d64) {
|
|
char buf[DECIMAL64_Bytes*2+1];
|
|
Int i, j=0;
|
|
|
|
if (DECLITEND) {
|
|
for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
|
|
sprintf(&buf[j], "%02x", d64->bytes[7-i]);
|
|
}
|
|
printf(" D64> %s [S:%d Cb:%02x Ec:%02x] LittleEndian\n", buf,
|
|
d64->bytes[7]>>7, (d64->bytes[7]>>2)&0x1f,
|
|
((d64->bytes[7]&0x3)<<6)| (d64->bytes[6]>>2));
|
|
}
|
|
else { /* big-endian */
|
|
for (i=0; i<DECIMAL64_Bytes; i++, j+=2) {
|
|
sprintf(&buf[j], "%02x", d64->bytes[i]);
|
|
}
|
|
printf(" D64> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf,
|
|
decimal64Sign(d64), decimal64Comb(d64), decimal64ExpCon(d64));
|
|
}
|
|
} /* decimal64Show */
|
|
#endif
|
|
|
|
/* ================================================================== */
|
|
/* Shared utility routines and tables */
|
|
/* ================================================================== */
|
|
/* define and include the conversion tables to use for shared code */
|
|
#if DECDPUN==3
|
|
#define DEC_DPD2BIN 1
|
|
#else
|
|
#define DEC_DPD2BCD 1
|
|
#endif
|
|
#include "decDPD.h" /* lookup tables */
|
|
|
|
/* The maximum number of decNumberUnits needed for a working copy of */
|
|
/* the units array is the ceiling of digits/DECDPUN, where digits is */
|
|
/* the maximum number of digits in any of the formats for which this */
|
|
/* is used. decimal128.h must not be included in this module, so, as */
|
|
/* a very special case, that number is defined as a literal here. */
|
|
#define DECMAX754 34
|
|
#define DECMAXUNITS ((DECMAX754+DECDPUN-1)/DECDPUN)
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* Combination field lookup tables (uInts to save measurable work) */
|
|
/* */
|
|
/* COMBEXP - 2-bit most-significant-bits of exponent */
|
|
/* [11 if an Infinity or NaN] */
|
|
/* COMBMSD - 4-bit most-significant-digit */
|
|
/* [0=Infinity, 1=NaN if COMBEXP=11] */
|
|
/* */
|
|
/* Both are indexed by the 5-bit combination field (0-31) */
|
|
/* ------------------------------------------------------------------ */
|
|
const uInt COMBEXP[32]={0, 0, 0, 0, 0, 0, 0, 0,
|
|
1, 1, 1, 1, 1, 1, 1, 1,
|
|
2, 2, 2, 2, 2, 2, 2, 2,
|
|
0, 0, 1, 1, 2, 2, 3, 3};
|
|
const uInt COMBMSD[32]={0, 1, 2, 3, 4, 5, 6, 7,
|
|
0, 1, 2, 3, 4, 5, 6, 7,
|
|
0, 1, 2, 3, 4, 5, 6, 7,
|
|
8, 9, 8, 9, 8, 9, 0, 1};
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decDigitsToDPD -- pack coefficient into DPD form */
|
|
/* */
|
|
/* dn is the source number (assumed valid, max DECMAX754 digits) */
|
|
/* targ is 1, 2, or 4-element uInt array, which the caller must */
|
|
/* have cleared to zeros */
|
|
/* shift is the number of 0 digits to add on the right (normally 0) */
|
|
/* */
|
|
/* The coefficient must be known small enough to fit. The full */
|
|
/* coefficient is copied, including the leading 'odd' digit. This */
|
|
/* digit is retrieved and packed into the combination field by the */
|
|
/* caller. */
|
|
/* */
|
|
/* The target uInts are altered only as necessary to receive the */
|
|
/* digits of the decNumber. When more than one uInt is needed, they */
|
|
/* are filled from left to right (that is, the uInt at offset 0 will */
|
|
/* end up with the least-significant digits). */
|
|
/* */
|
|
/* shift is used for 'fold-down' padding. */
|
|
/* */
|
|
/* No error is possible. */
|
|
/* ------------------------------------------------------------------ */
|
|
#if DECDPUN<=4
|
|
/* Constant multipliers for divide-by-power-of five using reciprocal */
|
|
/* multiply, after removing powers of 2 by shifting, and final shift */
|
|
/* of 17 [we only need up to **4] */
|
|
static const uInt multies[]={131073, 26215, 5243, 1049, 210};
|
|
/* QUOT10 -- macro to return the quotient of unit u divided by 10**n */
|
|
#define QUOT10(u, n) ((((uInt)(u)>>(n))*multies[n])>>17)
|
|
#endif
|
|
void decDigitsToDPD(const decNumber *dn, uInt *targ, Int shift) {
|
|
Int cut; /* work */
|
|
Int n; /* output bunch counter */
|
|
Int digits=dn->digits; /* digit countdown */
|
|
uInt dpd; /* densely packed decimal value */
|
|
uInt bin; /* binary value 0-999 */
|
|
uInt *uout=targ; /* -> current output uInt */
|
|
uInt uoff=0; /* -> current output offset [from right] */
|
|
const Unit *inu=dn->lsu; /* -> current input unit */
|
|
Unit uar[DECMAXUNITS]; /* working copy of units, iff shifted */
|
|
#if DECDPUN!=3 /* not fast path */
|
|
Unit in; /* current unit */
|
|
#endif
|
|
|
|
if (shift!=0) { /* shift towards most significant required */
|
|
/* shift the units array to the left by pad digits and copy */
|
|
/* [this code is a special case of decShiftToMost, which could */
|
|
/* be used instead if exposed and the array were copied first] */
|
|
const Unit *source; /* .. */
|
|
Unit *target, *first; /* .. */
|
|
uInt next=0; /* work */
|
|
|
|
source=dn->lsu+D2U(digits)-1; /* where msu comes from */
|
|
target=uar+D2U(digits)-1+D2U(shift);/* where upper part of first cut goes */
|
|
cut=DECDPUN-MSUDIGITS(shift); /* where to slice */
|
|
if (cut==0) { /* unit-boundary case */
|
|
for (; source>=dn->lsu; source--, target--) *target=*source;
|
|
}
|
|
else {
|
|
first=uar+D2U(digits+shift)-1; /* where msu will end up */
|
|
for (; source>=dn->lsu; source--, target--) {
|
|
/* split the source Unit and accumulate remainder for next */
|
|
#if DECDPUN<=4
|
|
uInt quot=QUOT10(*source, cut);
|
|
uInt rem=*source-quot*DECPOWERS[cut];
|
|
next+=quot;
|
|
#else
|
|
uInt rem=*source%DECPOWERS[cut];
|
|
next+=*source/DECPOWERS[cut];
|
|
#endif
|
|
if (target<=first) *target=(Unit)next; /* write to target iff valid */
|
|
next=rem*DECPOWERS[DECDPUN-cut]; /* save remainder for next Unit */
|
|
}
|
|
} /* shift-move */
|
|
/* propagate remainder to one below and clear the rest */
|
|
for (; target>=uar; target--) {
|
|
*target=(Unit)next;
|
|
next=0;
|
|
}
|
|
digits+=shift; /* add count (shift) of zeros added */
|
|
inu=uar; /* use units in working array */
|
|
}
|
|
|
|
/* now densely pack the coefficient into DPD declets */
|
|
|
|
#if DECDPUN!=3 /* not fast path */
|
|
in=*inu; /* current unit */
|
|
cut=0; /* at lowest digit */
|
|
bin=0; /* [keep compiler quiet] */
|
|
#endif
|
|
|
|
for(n=0; digits>0; n++) { /* each output bunch */
|
|
#if DECDPUN==3 /* fast path, 3-at-a-time */
|
|
bin=*inu; /* 3 digits ready for convert */
|
|
digits-=3; /* [may go negative] */
|
|
inu++; /* may need another */
|
|
|
|
#else /* must collect digit-by-digit */
|
|
Unit dig; /* current digit */
|
|
Int j; /* digit-in-declet count */
|
|
for (j=0; j<3; j++) {
|
|
#if DECDPUN<=4
|
|
Unit temp=(Unit)((uInt)(in*6554)>>16);
|
|
dig=(Unit)(in-X10(temp));
|
|
in=temp;
|
|
#else
|
|
dig=in%10;
|
|
in=in/10;
|
|
#endif
|
|
if (j==0) bin=dig;
|
|
else if (j==1) bin+=X10(dig);
|
|
else /* j==2 */ bin+=X100(dig);
|
|
digits--;
|
|
if (digits==0) break; /* [also protects *inu below] */
|
|
cut++;
|
|
if (cut==DECDPUN) {inu++; in=*inu; cut=0;}
|
|
}
|
|
#endif
|
|
/* here there are 3 digits in bin, or have used all input digits */
|
|
|
|
dpd=BIN2DPD[bin];
|
|
|
|
/* write declet to uInt array */
|
|
*uout|=dpd<<uoff;
|
|
uoff+=10;
|
|
if (uoff<32) continue; /* no uInt boundary cross */
|
|
uout++;
|
|
uoff-=32;
|
|
*uout|=dpd>>(10-uoff); /* collect top bits */
|
|
} /* n declets */
|
|
return;
|
|
} /* decDigitsToDPD */
|
|
|
|
/* ------------------------------------------------------------------ */
|
|
/* decDigitsFromDPD -- unpack a format's coefficient */
|
|
/* */
|
|
/* dn is the target number, with 7, 16, or 34-digit space. */
|
|
/* sour is a 1, 2, or 4-element uInt array containing only declets */
|
|
/* declets is the number of (right-aligned) declets in sour to */
|
|
/* be processed. This may be 1 more than the obvious number in */
|
|
/* a format, as any top digit is prefixed to the coefficient */
|
|
/* continuation field. It also may be as small as 1, as the */
|
|
/* caller may pre-process leading zero declets. */
|
|
/* */
|
|
/* When doing the 'extra declet' case care is taken to avoid writing */
|
|
/* extra digits when there are leading zeros, as these could overflow */
|
|
/* the units array when DECDPUN is not 3. */
|
|
/* */
|
|
/* The target uInts are used only as necessary to process declets */
|
|
/* declets into the decNumber. When more than one uInt is needed, */
|
|
/* they are used from left to right (that is, the uInt at offset 0 */
|
|
/* provides the least-significant digits). */
|
|
/* */
|
|
/* dn->digits is set, but not the sign or exponent. */
|
|
/* No error is possible [the redundant 888 codes are allowed]. */
|
|
/* ------------------------------------------------------------------ */
|
|
void decDigitsFromDPD(decNumber *dn, const uInt *sour, Int declets) {
|
|
|
|
uInt dpd; /* collector for 10 bits */
|
|
Int n; /* counter */
|
|
Unit *uout=dn->lsu; /* -> current output unit */
|
|
Unit *last=uout; /* will be unit containing msd */
|
|
const uInt *uin=sour; /* -> current input uInt */
|
|
uInt uoff=0; /* -> current input offset [from right] */
|
|
|
|
#if DECDPUN!=3
|
|
uInt bcd; /* BCD result */
|
|
uInt nibble; /* work */
|
|
Unit out=0; /* accumulator */
|
|
Int cut=0; /* power of ten in current unit */
|
|
#endif
|
|
#if DECDPUN>4
|
|
uInt const *pow; /* work */
|
|
#endif
|
|
|
|
/* Expand the densely-packed integer, right to left */
|
|
for (n=declets-1; n>=0; n--) { /* count down declets of 10 bits */
|
|
dpd=*uin>>uoff;
|
|
uoff+=10;
|
|
if (uoff>32) { /* crossed uInt boundary */
|
|
uin++;
|
|
uoff-=32;
|
|
dpd|=*uin<<(10-uoff); /* get waiting bits */
|
|
}
|
|
dpd&=0x3ff; /* clear uninteresting bits */
|
|
|
|
#if DECDPUN==3
|
|
if (dpd==0) *uout=0;
|
|
else {
|
|
*uout=DPD2BIN[dpd]; /* convert 10 bits to binary 0-999 */
|
|
last=uout; /* record most significant unit */
|
|
}
|
|
uout++;
|
|
} /* n */
|
|
|
|
#else /* DECDPUN!=3 */
|
|
if (dpd==0) { /* fastpath [e.g., leading zeros] */
|
|
/* write out three 0 digits (nibbles); out may have digit(s) */
|
|
cut++;
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
if (n==0) break; /* [as below, works even if MSD=0] */
|
|
cut++;
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
cut++;
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
continue;
|
|
}
|
|
|
|
bcd=DPD2BCD[dpd]; /* convert 10 bits to 12 bits BCD */
|
|
|
|
/* now accumulate the 3 BCD nibbles into units */
|
|
nibble=bcd & 0x00f;
|
|
if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
|
cut++;
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
bcd>>=4;
|
|
|
|
/* if this is the last declet and the remaining nibbles in bcd */
|
|
/* are 00 then process no more nibbles, because this could be */
|
|
/* the 'odd' MSD declet and writing any more Units would then */
|
|
/* overflow the unit array */
|
|
if (n==0 && !bcd) break;
|
|
|
|
nibble=bcd & 0x00f;
|
|
if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
|
cut++;
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
bcd>>=4;
|
|
|
|
nibble=bcd & 0x00f;
|
|
if (nibble) out=(Unit)(out+nibble*DECPOWERS[cut]);
|
|
cut++;
|
|
if (cut==DECDPUN) {*uout=out; if (out) {last=uout; out=0;} uout++; cut=0;}
|
|
} /* n */
|
|
if (cut!=0) { /* some more left over */
|
|
*uout=out; /* write out final unit */
|
|
if (out) last=uout; /* and note if non-zero */
|
|
}
|
|
#endif
|
|
|
|
/* here, last points to the most significant unit with digits; */
|
|
/* inspect it to get the final digits count -- this is essentially */
|
|
/* the same code as decGetDigits in decNumber.c */
|
|
dn->digits=(last-dn->lsu)*DECDPUN+1; /* floor of digits, plus */
|
|
/* must be at least 1 digit */
|
|
#if DECDPUN>1
|
|
if (*last<10) return; /* common odd digit or 0 */
|
|
dn->digits++; /* must be 2 at least */
|
|
#if DECDPUN>2
|
|
if (*last<100) return; /* 10-99 */
|
|
dn->digits++; /* must be 3 at least */
|
|
#if DECDPUN>3
|
|
if (*last<1000) return; /* 100-999 */
|
|
dn->digits++; /* must be 4 at least */
|
|
#if DECDPUN>4
|
|
for (pow=&DECPOWERS[4]; *last>=*pow; pow++) dn->digits++;
|
|
#endif
|
|
#endif
|
|
#endif
|
|
#endif
|
|
return;
|
|
} /*decDigitsFromDPD */
|