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/* Decimal 128-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 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