/* ------------------------------------------------------------------ */ /* decCommon.c -- common code for all three fixed-size types */ /* ------------------------------------------------------------------ */ /* Copyright (c) IBM Corporation, 2000, 2010. All rights reserved. */ /* */ /* This software is made available under the terms of the */ /* ICU License -- ICU 1.8.1 and later. */ /* */ /* The description and User's Guide ("The decNumber C Library") for */ /* this software is included in the package as decNumber.pdf. This */ /* document is also available in HTML, together with specifications, */ /* testcases, and Web links, on the General Decimal Arithmetic page. */ /* */ /* Please send comments, suggestions, and corrections to the author: */ /* mfc@uk.ibm.com */ /* Mike Cowlishaw, IBM Fellow */ /* IBM UK, PO Box 31, Birmingham Road, Warwick CV34 5JL, UK */ /* ------------------------------------------------------------------ */ /* This module comprises code that is shared between all the formats */ /* (decSingle, decDouble, and decQuad); it includes set and extract */ /* of format components, widening, narrowing, and string conversions. */ /* */ /* Unlike decNumber, parameterization takes place at compile time */ /* rather than at runtime. The parameters are set in the decDouble.c */ /* (etc.) files, which then include this one to produce the compiled */ /* code. The functions here, therefore, are code shared between */ /* multiple formats. */ /* ------------------------------------------------------------------ */ // Names here refer to decFloat rather than to decDouble, etc., and // the functions are in strict alphabetical order. // Constants, tables, and debug function(s) are included only for QUAD // (which will always be compiled if DOUBLE or SINGLE are used). // // Whenever a decContext is used, only the status may be set (using // OR) or the rounding mode read; all other fields are ignored and // untouched. // names for simpler testing and default context #if DECPMAX==7 #define SINGLE 1 #define DOUBLE 0 #define QUAD 0 #define DEFCONTEXT DEC_INIT_DECIMAL32 #elif DECPMAX==16 #define SINGLE 0 #define DOUBLE 1 #define QUAD 0 #define DEFCONTEXT DEC_INIT_DECIMAL64 #elif DECPMAX==34 #define SINGLE 0 #define DOUBLE 0 #define QUAD 1 #define DEFCONTEXT DEC_INIT_DECIMAL128 #else #error Unexpected DECPMAX value #endif /* Assertions */ #if DECPMAX!=7 && DECPMAX!=16 && DECPMAX!=34 #error Unexpected Pmax (DECPMAX) value for this module #endif // Assert facts about digit characters, etc. #if ('9'&0x0f)!=9 #error This module assumes characters are of the form 0b....nnnn // where .... are don't care 4 bits and nnnn is 0000 through 1001 #endif #if ('9'&0xf0)==('.'&0xf0) #error This module assumes '.' has a different mask than a digit #endif // Assert ToString lay-out conditions #if DECSTRING DECSTRING #error Exponent form can be too long for ToString to lay out safely #endif #if DECEMAXD > 4 #error Exponent form is too long for ToString to lay out // Note: code for up to 9 digits exists in archives [decOct] #endif /* Private functions used here and possibly in decBasic.c, etc. */ static decFloat * decFinalize(decFloat *, bcdnum *, decContext *); static Flag decBiStr(const char *, const char *, const char *); /* Macros and private tables; those which are not format-dependent */ /* are only included if decQuad is being built. */ /* ------------------------------------------------------------------ */ /* Combination field lookup tables (uInts to save measurable work) */ /* */ /* DECCOMBEXP - 2 most-significant-bits of exponent (00, 01, or */ /* 10), shifted left for format, or DECFLOAT_Inf/NaN */ /* DECCOMBWEXP - The same, for the next-wider format (unless QUAD) */ /* DECCOMBMSD - 4-bit most-significant-digit */ /* [0 if the index is a special (Infinity or NaN)] */ /* DECCOMBFROM - 5-bit combination field from EXP top bits and MSD */ /* (placed in uInt so no shift is needed) */ /* */ /* DECCOMBEXP, DECCOMBWEXP, and DECCOMBMSD are indexed by the sign */ /* and 5-bit combination field (0-63, the second half of the table */ /* identical to the first half) */ /* DECCOMBFROM is indexed by expTopTwoBits*16 + msd */ /* */ /* DECCOMBMSD and DECCOMBFROM are not format-dependent and so are */ /* only included once, when QUAD is being built */ /* ------------------------------------------------------------------ */ static const uInt DECCOMBEXP[64]={ 0, 0, 0, 0, 0, 0, 0, 0, 1< DPD #define DEC_BIN2DPD 1 // 0-999 -> DPD #define DEC_BIN2BCD8 1 // 0-999 -> ddd, len #define DEC_DPD2BCD8 1 // DPD -> ddd, len #define DEC_DPD2BIN 1 // DPD -> 0-999 #define DEC_DPD2BINK 1 // DPD -> 0-999000 #define DEC_DPD2BINM 1 // DPD -> 0-999000000 #include "decDPD.h" // source of the lookup tables #endif /* ----------------------------------------------------------------- */ /* decBiStr -- compare string with pairwise options */ /* */ /* targ is the string to compare */ /* str1 is one of the strings to compare against (length may be 0) */ /* str2 is the other; it must be the same length as str1 */ /* */ /* returns 1 if strings compare equal, (that is, targ is the same */ /* length as str1 and str2, and each character of targ is in one */ /* of str1 or str2 in the corresponding position), or 0 otherwise */ /* */ /* This is used for generic caseless compare, including the awkward */ /* case of the Turkish dotted and dotless Is. Use as (for example): */ /* if (decBiStr(test, "mike", "MIKE")) ... */ /* ----------------------------------------------------------------- */ static Flag decBiStr(const char *targ, const char *str1, const char *str2) { for (;;targ++, str1++, str2++) { if (*targ!=*str1 && *targ!=*str2) return 0; // *targ has a match in one (or both, if terminator) if (*targ=='\0') break; } // forever return 1; } // decBiStr /* ------------------------------------------------------------------ */ /* decFinalize -- adjust and store a final result */ /* */ /* df is the decFloat format number which gets the final result */ /* num is the descriptor of the number to be checked and encoded */ /* [its values, including the coefficient, may be modified] */ /* set is the context to use */ /* returns df */ /* */ /* The num descriptor may point to a bcd8 string of any length; this */ /* string may have leading insignificant zeros. If it has more than */ /* DECPMAX digits then the final digit can be a round-for-reround */ /* digit (i.e., it may include a sticky bit residue). */ /* */ /* The exponent (q) may be one of the codes for a special value and */ /* can be up to 999999999 for conversion from string. */ /* */ /* No error is possible, but Inexact, Underflow, and/or Overflow may */ /* be set. */ /* ------------------------------------------------------------------ */ // Constant whose size varies with format; also the check for surprises static uByte allnines[DECPMAX]= #if SINGLE {9, 9, 9, 9, 9, 9, 9}; #elif DOUBLE {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9}; #elif QUAD {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9}; #endif static decFloat * decFinalize(decFloat *df, bcdnum *num, decContext *set) { uByte *ub; // work uInt dpd; // .. uInt uiwork; // for macros uByte *umsd=num->msd; // local copy uByte *ulsd=num->lsd; // .. uInt encode; // encoding accumulator Int length; // coefficient length #if DECCHECK Int clen=ulsd-umsd+1; #if QUAD #define COEXTRA 2 // extra-long coefficent #else #define COEXTRA 0 #endif if (clen<1 || clen>DECPMAX*3+2+COEXTRA) printf("decFinalize: suspect coefficient [length=%ld]\n", (LI)clen); if (num->sign!=0 && num->sign!=DECFLOAT_Sign) printf("decFinalize: bad sign [%08lx]\n", (LI)num->sign); if (!EXPISSPECIAL(num->exponent) && (num->exponent>1999999999 || num->exponent<-1999999999)) printf("decFinalize: improbable exponent [%ld]\n", (LI)num->exponent); // decShowNum(num, "final"); #endif // A special will have an 'exponent' which is very positive and a // coefficient < DECPMAX length=(uInt)(ulsd-umsd+1); // coefficient length if (!NUMISSPECIAL(num)) { Int drop; // digits to be dropped // skip leading insignificant zeros to calculate an exact length // [this is quite expensive] if (*umsd==0) { for (; umsd+3exponent); // drop can now be > digits for bottom-clamp (subnormal) cases if (drop>0) { // rounding needed // (decFloatQuantize has very similar code to this, so any // changes may need to be made there, too) uByte *roundat; // -> re-round digit uByte reround; // reround value // printf("Rounding; drop=%ld\n", (LI)drop); num->exponent+=drop; // always update exponent // Three cases here: // 1. new LSD is in coefficient (almost always) // 2. new LSD is digit to left of coefficient (so MSD is // round-for-reround digit) // 3. new LSD is to left of case 2 (whole coefficient is sticky) // [duplicate check-stickies code to save a test] // [by-digit check for stickies as runs of zeros are rare] if (dropstatus|=DEC_Inexact; // if adjusted exponent [exp+digits-1] is < EMIN then num is // subnormal -- so raise Underflow if (num->exponentexponent+(ulsd-umsd+1)-1)status|=DEC_Underflow; // next decide whether increment of the coefficient is needed if (set->round==DEC_ROUND_HALF_EVEN) { // fastpath slowest case if (reround>5) bump=1; // >0.5 goes up else if (reround==5) // exactly 0.5000 .. bump=*ulsd & 0x01; // .. up iff [new] lsd is odd } // r-h-e else switch (set->round) { case DEC_ROUND_DOWN: { // no change break;} // r-d case DEC_ROUND_HALF_DOWN: { if (reround>5) bump=1; break;} // r-h-d case DEC_ROUND_HALF_UP: { if (reround>=5) bump=1; break;} // r-h-u case DEC_ROUND_UP: { if (reround>0) bump=1; break;} // r-u case DEC_ROUND_CEILING: { // same as _UP for positive numbers, and as _DOWN for negatives if (!num->sign && reround>0) bump=1; break;} // r-c case DEC_ROUND_FLOOR: { // same as _UP for negative numbers, and as _DOWN for positive // [negative reround cannot occur on 0] if (num->sign && reround>0) bump=1; break;} // r-f case DEC_ROUND_05UP: { if (reround>0) { // anything out there is 'sticky' // bump iff lsd=0 or 5; this cannot carry so it could be // effected immediately with no bump -- but the code // is clearer if this is done the same way as the others if (*ulsd==0 || *ulsd==5) bump=1; } break;} // r-r default: { // e.g., DEC_ROUND_MAX set->status|=DEC_Invalid_context; #if DECCHECK printf("Unknown rounding mode: %ld\n", (LI)set->round); #endif break;} } // switch (not r-h-e) // printf("ReRound: %ld bump: %ld\n", (LI)reround, (LI)bump); if (bump!=0) { // need increment // increment the coefficient; this might end up with 1000... // (after the all nines case) ub=ulsd; for(; ub-3>=umsd && UBTOUI(ub-3)==0x09090909; ub-=4) { UBFROMUI(ub-3, 0); // to 00000000 } // [note ub could now be to left of msd, and it is not safe // to write to the the left of the msd] // now at most 3 digits left to non-9 (usually just the one) for (; ub>=umsd; *ub=0, ub--) { if (*ub==9) continue; // carry *ub+=1; break; } if (ubexponent++; } else { // if coefficient is shorter than Pmax then num is // subnormal, so extend it; this is safe as drop>0 // (or, if the coefficient was supplied above, it could // not be 9); this may make the result normal. ulsd++; *ulsd=0; // [exponent unchanged] #if DECCHECK if (num->exponent!=DECQTINY) // sanity check printf("decFinalize: bad all-nines extend [^%ld, %ld]\n", (LI)num->exponent, (LI)(ulsd-umsd+1)); #endif } // subnormal extend } // had all-nines } // bump needed } // inexact rounding length=ulsd-umsd+1; // recalculate (may be 0) // The coefficient will now fit and has final length unless overflow // decShowNum(num, "rounded"); // if exponent is >=emax may have to clamp, overflow, or fold-down if (num->exponent>DECEMAX-(DECPMAX-1)) { // is edge case // printf("overflow checks...\n"); if (ulsd==umsd && *ulsd==0) { // have zero num->exponent=DECEMAX-(DECPMAX-1); // clamp to max } else if ((num->exponent+length-1)>DECEMAX) { // > Nmax // Overflow -- these could go straight to encoding, here, but // instead num is adjusted to keep the code cleaner Flag needmax=0; // 1 for finite result set->status|=(DEC_Overflow | DEC_Inexact); switch (set->round) { case DEC_ROUND_DOWN: { needmax=1; // never Infinity break;} // r-d case DEC_ROUND_05UP: { needmax=1; // never Infinity break;} // r-05 case DEC_ROUND_CEILING: { if (num->sign) needmax=1; // Infinity iff non-negative break;} // r-c case DEC_ROUND_FLOOR: { if (!num->sign) needmax=1; // Infinity iff negative break;} // r-f default: break; // Infinity in all other cases } if (!needmax) { // easy .. set Infinity num->exponent=DECFLOAT_Inf; *umsd=0; // be clean: coefficient to 0 ulsd=umsd; // .. } else { // return Nmax umsd=allnines; // use constant array ulsd=allnines+DECPMAX-1; num->exponent=DECEMAX-(DECPMAX-1); } } else { // no overflow but non-zero and may have to fold-down Int shift=num->exponent-(DECEMAX-(DECPMAX-1)); if (shift>0) { // fold-down needed // fold down needed; must copy to buffer in order to pad // with zeros safely; fortunately this is not the worst case // path because cannot have had a round uByte buffer[ROUNDUP(DECPMAX+3, 4)]; // [+3 allows uInt padding] uByte *s=umsd; // source uByte *t=buffer; // safe target uByte *tlsd=buffer+(ulsd-umsd)+shift; // target LSD // printf("folddown shift=%ld\n", (LI)shift); for (; s<=ulsd; s+=4, t+=4) UBFROMUI(t, UBTOUI(s)); for (t=tlsd-shift+1; t<=tlsd; t+=4) UBFROMUI(t, 0); // pad 0s num->exponent-=shift; umsd=buffer; ulsd=tlsd; } } // fold-down? length=ulsd-umsd+1; // recalculate length } // high-end edge case } // finite number /*------------------------------------------------------------------*/ /* At this point the result will properly fit the decFloat */ /* encoding, and it can be encoded with no possibility of error */ /*------------------------------------------------------------------*/ // Following code does not alter coefficient (could be allnines array) // fast path possible when DECPMAX digits if (length==DECPMAX) { return decFloatFromBCD(df, num->exponent, umsd, num->sign); } // full-length // slower path when not a full-length number; must care about length // [coefficient length here will be < DECPMAX] if (!NUMISSPECIAL(num)) { // is still finite // encode the combination field and exponent continuation uInt uexp=(uInt)(num->exponent+DECBIAS); // biased exponent uInt code=(uexp>>DECECONL)<<4; // top two bits of exp // [msd==0] // look up the combination field and make high word encode=DECCOMBFROM[code]; // indexed by (0-2)*16+msd encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation } else encode=num->exponent; // special [already in word] encode|=num->sign; // add sign // private macro to extract a declet, n (where 0<=n=umsd) dpd=BCD2DPD[(*ub*256)+(*(ub+1)*16)+*(ub+2)]; \ else {dpd=*(ub+2); if (ub+1==umsd) dpd+=*(ub+1)*16; dpd=BCD2DPD[dpd];} // place the declets in the encoding words and copy to result (df), // according to endianness; in all cases complete the sign word // first #if DECPMAX==7 getDPDt(dpd, 1); encode|=dpd<<10; getDPDt(dpd, 0); encode|=dpd; DFWORD(df, 0)=encode; // just the one word #elif DECPMAX==16 getDPDt(dpd, 4); encode|=dpd<<8; getDPDt(dpd, 3); encode|=dpd>>2; DFWORD(df, 0)=encode; encode=dpd<<30; getDPDt(dpd, 2); encode|=dpd<<20; getDPDt(dpd, 1); encode|=dpd<<10; getDPDt(dpd, 0); encode|=dpd; DFWORD(df, 1)=encode; #elif DECPMAX==34 getDPDt(dpd,10); encode|=dpd<<4; getDPDt(dpd, 9); encode|=dpd>>6; DFWORD(df, 0)=encode; encode=dpd<<26; getDPDt(dpd, 8); encode|=dpd<<16; getDPDt(dpd, 7); encode|=dpd<<6; getDPDt(dpd, 6); encode|=dpd>>4; DFWORD(df, 1)=encode; encode=dpd<<28; getDPDt(dpd, 5); encode|=dpd<<18; getDPDt(dpd, 4); encode|=dpd<<8; getDPDt(dpd, 3); encode|=dpd>>2; DFWORD(df, 2)=encode; encode=dpd<<30; getDPDt(dpd, 2); encode|=dpd<<20; getDPDt(dpd, 1); encode|=dpd<<10; getDPDt(dpd, 0); encode|=dpd; DFWORD(df, 3)=encode; #endif // printf("Status: %08lx\n", (LI)set->status); // decFloatShow(df, "final2"); return df; } // decFinalize /* ------------------------------------------------------------------ */ /* decFloatFromBCD -- set decFloat from exponent, BCD8, and sign */ /* */ /* df is the target decFloat */ /* exp is the in-range unbiased exponent, q, or a special value in */ /* the form returned by decFloatGetExponent */ /* bcdar holds DECPMAX digits to set the coefficient from, one */ /* digit in each byte (BCD8 encoding); the first (MSD) is ignored */ /* if df is a NaN; all are ignored if df is infinite. */ /* All bytes must be in 0-9; results are undefined otherwise. */ /* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */ /* returns df, which will be canonical */ /* */ /* No error is possible, and no status will be set. */ /* ------------------------------------------------------------------ */ decFloat * decFloatFromBCD(decFloat *df, Int exp, const uByte *bcdar, Int sig) { uInt encode, dpd; // work const uByte *ub; // .. if (EXPISSPECIAL(exp)) encode=exp|sig;// specials already encoded else { // is finite // encode the combination field and exponent continuation uInt uexp=(uInt)(exp+DECBIAS); // biased exponent uInt code=(uexp>>DECECONL)<<4; // top two bits of exp code+=bcdar[0]; // add msd // look up the combination field and make high word encode=DECCOMBFROM[code]|sig; // indexed by (0-2)*16+msd encode|=(uexp<<(32-6-DECECONL)) & 0x03ffffff; // exponent continuation } // private macro to extract a declet, n (where 0<=n>2; DFWORD(df, 0)=encode; encode=dpd<<30; getDPDb(dpd, 2); encode|=dpd<<20; getDPDb(dpd, 1); encode|=dpd<<10; getDPDb(dpd, 0); encode|=dpd; DFWORD(df, 1)=encode; #elif DECPMAX==34 getDPDb(dpd,10); encode|=dpd<<4; getDPDb(dpd, 9); encode|=dpd>>6; DFWORD(df, 0)=encode; encode=dpd<<26; getDPDb(dpd, 8); encode|=dpd<<16; getDPDb(dpd, 7); encode|=dpd<<6; getDPDb(dpd, 6); encode|=dpd>>4; DFWORD(df, 1)=encode; encode=dpd<<28; getDPDb(dpd, 5); encode|=dpd<<18; getDPDb(dpd, 4); encode|=dpd<<8; getDPDb(dpd, 3); encode|=dpd>>2; DFWORD(df, 2)=encode; encode=dpd<<30; getDPDb(dpd, 2); encode|=dpd<<20; getDPDb(dpd, 1); encode|=dpd<<10; getDPDb(dpd, 0); encode|=dpd; DFWORD(df, 3)=encode; #endif // decFloatShow(df, "fromB"); return df; } // decFloatFromBCD /* ------------------------------------------------------------------ */ /* decFloatFromPacked -- set decFloat from exponent and packed BCD */ /* */ /* df is the target decFloat */ /* exp is the in-range unbiased exponent, q, or a special value in */ /* the form returned by decFloatGetExponent */ /* packed holds DECPMAX packed decimal digits plus a sign nibble */ /* (all 6 codes are OK); the first (MSD) is ignored if df is a NaN */ /* and all except sign are ignored if df is infinite. For DOUBLE */ /* and QUAD the first (pad) nibble is also ignored in all cases. */ /* All coefficient nibbles must be in 0-9 and sign in A-F; results */ /* are undefined otherwise. */ /* returns df, which will be canonical */ /* */ /* No error is possible, and no status will be set. */ /* ------------------------------------------------------------------ */ decFloat * decFloatFromPacked(decFloat *df, Int exp, const uByte *packed) { uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign] const uByte *ip; // .. uByte *op; // .. Int sig=0; // sign // expand coefficient and sign to BCDAR #if SINGLE op=bcdar+1; // no pad digit #else op=bcdar; // first (pad) digit ignored #endif for (ip=packed; ip>4; *op++=(uByte)(*ip&0x0f); // [final nibble is sign] } op--; // -> sign byte if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign; if (EXPISSPECIAL(exp)) { // Infinity or NaN if (!EXPISINF(exp)) bcdar[1]=0; // a NaN: ignore MSD else memset(bcdar+1, 0, DECPMAX); // Infinite: coefficient to 0 } return decFloatFromBCD(df, exp, bcdar+1, sig); } // decFloatFromPacked /* ------------------------------------------------------------------ */ /* decFloatFromPackedChecked -- set from exponent and packed; checked */ /* */ /* df is the target decFloat */ /* exp is the in-range unbiased exponent, q, or a special value in */ /* the form returned by decFloatGetExponent */ /* packed holds DECPMAX packed decimal digits plus a sign nibble */ /* (all 6 codes are OK); the first (MSD) must be 0 if df is a NaN */ /* and all digits must be 0 if df is infinite. For DOUBLE and */ /* QUAD the first (pad) nibble must be 0. */ /* All coefficient nibbles must be in 0-9 and sign in A-F. */ /* returns df, which will be canonical or NULL if any of the */ /* requirements are not met (if this case df is unchanged); that */ /* is, the input data must be as returned by decFloatToPacked, */ /* except that all six sign codes are acccepted. */ /* */ /* No status will be set. */ /* ------------------------------------------------------------------ */ decFloat * decFloatFromPackedChecked(decFloat *df, Int exp, const uByte *packed) { uByte bcdar[DECPMAX+2]; // work [+1 for pad, +1 for sign] const uByte *ip; // .. uByte *op; // .. Int sig=0; // sign // expand coefficient and sign to BCDAR #if SINGLE op=bcdar+1; // no pad digit #else op=bcdar; // first (pad) digit here #endif for (ip=packed; ip>4; if (*op>9) return NULL; op++; *op=(uByte)(*ip&0x0f); // [final nibble is sign] if (*op>9 && ip sign byte if (*op<=9) return NULL; // bad sign if (*op==DECPMINUS || *op==DECPMINUSALT) sig=DECFLOAT_Sign; #if !SINGLE if (bcdar[0]!=0) return NULL; // bad pad nibble #endif if (EXPISNAN(exp)) { // a NaN if (bcdar[1]!=0) return NULL; // bad msd } // NaN else if (EXPISINF(exp)) { // is infinite Int i; for (i=0; iDECEMAX-DECPMAX+1) return NULL; if (exp first character of decimal part const char *c; // work uByte *ub; // .. uInt uiwork; // for macros bcdnum num; // collects data for finishing uInt error=DEC_Conversion_syntax; // assume the worst uByte buffer[ROUNDUP(DECSTRING+11, 8)]; // room for most coefficents, // some common rounding, +3, & pad #if DECTRACE // printf("FromString %s ...\n", string); #endif for(;;) { // once-only 'loop' num.sign=0; // assume non-negative num.msd=buffer; // MSD is here always // detect and validate the coefficient, including any leading, // trailing, or embedded '.' // [could test four-at-a-time here (saving 10% for decQuads), // but that risks storage violation because the position of the // terminator is unknown] for (c=string;; c++) { // -> input character if (((unsigned)(*c-'0'))<=9) continue; // '0' through '9' is good if (*c=='\0') break; // most common non-digit if (*c=='.') { if (dotchar!=NULL) break; // not first '.' dotchar=c; // record offset into decimal part continue;} if (c==string) { // first in string... if (*c=='-') { // valid - sign cfirst++; num.sign=DECFLOAT_Sign; continue;} if (*c=='+') { // valid + sign cfirst++; continue;} } // *c is not a digit, terminator, or a valid +, -, or '.' break; } // c loop digits=(uInt)(c-cfirst); // digits (+1 if a dot) if (digits>0) { // had digits and/or dot const char *clast=c-1; // note last coefficient char position Int exp=0; // exponent accumulator if (*c!='\0') { // something follows the coefficient uInt edig; // unsigned work // had some digits and more to come; expect E[+|-]nnn now const char *firstexp; // exponent first non-zero if (*c!='E' && *c!='e') break; c++; // to (optional) sign if (*c=='-' || *c=='+') c++; // step over sign (c=clast+2) if (*c=='\0') break; // no digits! (e.g., '1.2E') for (; *c=='0';) c++; // skip leading zeros [even last] firstexp=c; // remember start [maybe '\0'] // gather exponent digits edig=(uInt)*c-(uInt)'0'; if (edig<=9) { // [check not bad or terminator] exp+=edig; // avoid initial X10 c++; for (;; c++) { edig=(uInt)*c-(uInt)'0'; if (edig>9) break; exp=exp*10+edig; } } // if not now on the '\0', *c must not be a digit if (*c!='\0') break; // (this next test must be after the syntax checks) // if definitely more than the possible digits for format then // the exponent may have wrapped, so simply set it to a certain // over/underflow value if (c>firstexp+DECEMAXD) exp=DECEMAX*2; if (*(clast+2)=='-') exp=-exp; // was negative } // exponent part if (dotchar!=NULL) { // had a '.' digits--; // remove from digits count if (digits==0) break; // was dot alone: bad syntax exp-=(Int)(clast-dotchar); // adjust exponent // [the '.' can now be ignored] } num.exponent=exp; // exponent is good; store it // Here when whole string has been inspected and syntax is good // cfirst->first digit or dot, clast->last digit or dot error=0; // no error possible now // if the number of digits in the coefficient will fit in buffer // then it can simply be converted to bcd8 and copied -- decFinalize // will take care of leading zeros and rounding; the buffer is big // enough for all canonical coefficients, including 0.00000nn... ub=buffer; if (digits<=(Int)(sizeof(buffer)-3)) { // [-3 allows by-4s copy] c=cfirst; if (dotchar!=NULL) { // a dot to worry about if (*(c+1)=='.') { // common canonical case *ub++=(uByte)(*c-'0'); // copy leading digit c+=2; // prepare to handle rest } else for (; c<=clast;) { // '.' could be anywhere // as usual, go by fours when safe; NB it has been asserted // that a '.' does not have the same mask as a digit if (c<=clast-3 // safe for four && (UBTOUI(c)&0xf0f0f0f0)==CHARMASK) { // test four UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); // to BCD8 ub+=4; c+=4; continue; } if (*c=='.') { // found the dot c++; // step over it .. break; // .. and handle the rest } *ub++=(uByte)(*c++-'0'); } } // had dot // Now no dot; do this by fours (where safe) for (; c<=clast-3; c+=4, ub+=4) UBFROMUI(ub, UBTOUI(c)&0x0f0f0f0f); for (; c<=clast; c++, ub++) *ub=(uByte)(*c-'0'); num.lsd=buffer+digits-1; // record new LSD } // fits else { // too long for buffer // [This is a rare and unusual case; arbitrary-length input] // strip leading zeros [but leave final 0 if all 0's] if (*cfirst=='.') cfirst++; // step past dot at start if (*cfirst=='0') { // [cfirst always -> digit] for (; cfirst LSD for (; c<=clast; c++) { // inspect remaining chars if (*c!='0') { // sticky bit needed if (*c=='.') continue; // [ignore] *ub=DECSTICKYTAB[*ub]; // update round-for-reround break; // no need to look at more } } num.lsd=ub; // record LSD // adjust exponent for dropped digits num.exponent+=digits-(Int)(ub-buffer+1); } // too long for buffer } // digits and/or dot else { // no digits or dot were found // only Infinities and NaNs are allowed, here if (*c=='\0') break; // nothing there is bad buffer[0]=0; // default a coefficient of 0 num.lsd=buffer; // .. if (decBiStr(c, "infinity", "INFINITY") || decBiStr(c, "inf", "INF")) num.exponent=DECFLOAT_Inf; else { // should be a NaN num.exponent=DECFLOAT_qNaN; // assume quiet NaN if (*c=='s' || *c=='S') { // probably an sNaN num.exponent=DECFLOAT_sNaN; // effect the 's' c++; // and step over it } if (*c!='N' && *c!='n') break; // check caseless "NaN" c++; if (*c!='a' && *c!='A') break; // .. c++; if (*c!='N' && *c!='n') break; // .. c++; // now either nothing, or nnnn payload (no dots), expected // -> start of integer, and skip leading 0s [including plain 0] for (cfirst=c; *cfirst=='0';) cfirst++; if (*cfirst!='\0') { // not empty or all-0, payload // payload found; check all valid digits and copy to buffer as bcd8 ub=buffer; for (c=cfirst;; c++, ub++) { if ((unsigned)(*c-'0')>9) break; // quit if not 0-9 if (c-cfirst==DECPMAX-1) break; // too many digits *ub=(uByte)(*c-'0'); // good bcd8 } if (*c!='\0') break; // not all digits, or too many num.lsd=ub-1; // record new LSD } } // NaN or sNaN error=0; // syntax is OK } // digits=0 (special expected) break; // drop out } // [for(;;) once-loop] // decShowNum(&num, "fromStr"); if (error!=0) { set->status|=error; num.exponent=DECFLOAT_qNaN; // set up quiet NaN num.sign=0; // .. with 0 sign buffer[0]=0; // .. and coefficient num.lsd=buffer; // .. // decShowNum(&num, "oops"); } // decShowNum(&num, "dffs"); decFinalize(result, &num, set); // round, check, and lay out // decFloatShow(result, "fromString"); return result; } // decFloatFromString /* ------------------------------------------------------------------ */ /* decFloatFromWider -- conversion from next-wider format */ /* */ /* result is the decFloat format number which gets the result of */ /* the conversion */ /* wider is the decFloatWider format number which will be narrowed */ /* set is the context */ /* returns result */ /* */ /* Narrowing can cause rounding, overflow, etc., but not Invalid */ /* operation (sNaNs are copied and do not signal). */ /* ------------------------------------------------------------------ */ // narrow-to is not possible for decQuad format numbers; simply omit #if !QUAD decFloat * decFloatFromWider(decFloat *result, const decFloatWider *wider, decContext *set) { bcdnum num; // collects data for finishing uByte bcdar[DECWPMAX]; // room for wider coefficient uInt widerhi=DFWWORD(wider, 0); // top word Int exp; GETWCOEFF(wider, bcdar); num.msd=bcdar; // MSD is here always num.lsd=bcdar+DECWPMAX-1; // LSD is here always num.sign=widerhi&0x80000000; // extract sign [DECFLOAT_Sign=Neg] // decode the wider combination field to exponent exp=DECCOMBWEXP[widerhi>>26]; // decode from wider combination field // if it is a special there's nothing to do unless sNaN; if it's // finite then add the (wider) exponent continuation and unbias if (EXPISSPECIAL(exp)) exp=widerhi&0x7e000000; // include sNaN selector else exp+=GETWECON(wider)-DECWBIAS; num.exponent=exp; // decShowNum(&num, "dffw"); return decFinalize(result, &num, set);// round, check, and lay out } // decFloatFromWider #endif /* ------------------------------------------------------------------ */ /* decFloatGetCoefficient -- get coefficient as BCD8 */ /* */ /* df is the decFloat from which to extract the coefficient */ /* bcdar is where DECPMAX bytes will be written, one BCD digit in */ /* each byte (BCD8 encoding); if df is a NaN the first byte will */ /* be zero, and if it is infinite they will all be zero */ /* returns the sign of the coefficient (DECFLOAT_Sign if negative, */ /* 0 otherwise) */ /* */ /* No error is possible, and no status will be set. If df is a */ /* special value the array is set to zeros (for Infinity) or to the */ /* payload of a qNaN or sNaN. */ /* ------------------------------------------------------------------ */ Int decFloatGetCoefficient(const decFloat *df, uByte *bcdar) { if (DFISINF(df)) memset(bcdar, 0, DECPMAX); else { GETCOEFF(df, bcdar); // use macro if (DFISNAN(df)) bcdar[0]=0; // MSD needs correcting } return GETSIGN(df); } // decFloatGetCoefficient /* ------------------------------------------------------------------ */ /* decFloatGetExponent -- get unbiased exponent */ /* */ /* df is the decFloat from which to extract the exponent */ /* returns the exponent, q. */ /* */ /* No error is possible, and no status will be set. If df is a */ /* special value the first seven bits of the decFloat are returned, */ /* left adjusted and with the first (sign) bit set to 0 (followed by */ /* 25 0 bits). e.g., -sNaN would return 0x7e000000 (DECFLOAT_sNaN). */ /* ------------------------------------------------------------------ */ Int decFloatGetExponent(const decFloat *df) { if (DFISSPECIAL(df)) return DFWORD(df, 0)&0x7e000000; return GETEXPUN(df); } // decFloatGetExponent /* ------------------------------------------------------------------ */ /* decFloatSetCoefficient -- set coefficient from BCD8 */ /* */ /* df is the target decFloat (and source of exponent/special value) */ /* bcdar holds DECPMAX digits to set the coefficient from, one */ /* digit in each byte (BCD8 encoding); the first (MSD) is ignored */ /* if df is a NaN; all are ignored if df is infinite. */ /* sig is DECFLOAT_Sign to set the sign bit, 0 otherwise */ /* returns df, which will be canonical */ /* */ /* No error is possible, and no status will be set. */ /* ------------------------------------------------------------------ */ decFloat * decFloatSetCoefficient(decFloat *df, const uByte *bcdar, Int sig) { uInt exp; // for exponent uByte bcdzero[DECPMAX]; // for infinities // Exponent/special code is extracted from df if (DFISSPECIAL(df)) { exp=DFWORD(df, 0)&0x7e000000; if (DFISINF(df)) { memset(bcdzero, 0, DECPMAX); return decFloatFromBCD(df, exp, bcdzero, sig); } } else exp=GETEXPUN(df); return decFloatFromBCD(df, exp, bcdar, sig); } // decFloatSetCoefficient /* ------------------------------------------------------------------ */ /* decFloatSetExponent -- set exponent or special value */ /* */ /* df is the target decFloat (and source of coefficient/payload) */ /* set is the context for reporting status */ /* exp is the unbiased exponent, q, or a special value in the form */ /* returned by decFloatGetExponent */ /* returns df, which will be canonical */ /* */ /* No error is possible, but Overflow or Underflow might occur. */ /* ------------------------------------------------------------------ */ decFloat * decFloatSetExponent(decFloat *df, decContext *set, Int exp) { uByte bcdcopy[DECPMAX]; // for coefficient bcdnum num; // work num.exponent=exp; num.sign=decFloatGetCoefficient(df, bcdcopy); // extract coefficient if (DFISSPECIAL(df)) { // MSD or more needs correcting if (DFISINF(df)) memset(bcdcopy, 0, DECPMAX); bcdcopy[0]=0; } num.msd=bcdcopy; num.lsd=bcdcopy+DECPMAX-1; return decFinalize(df, &num, set); } // decFloatSetExponent /* ------------------------------------------------------------------ */ /* decFloatRadix -- returns the base (10) */ /* */ /* df is any decFloat of this format */ /* ------------------------------------------------------------------ */ uInt decFloatRadix(const decFloat *df) { if (df) return 10; // to placate compiler return 10; } // decFloatRadix /* The following function is not available if DECPRINT=0 */ #if DECPRINT /* ------------------------------------------------------------------ */ /* decFloatShow -- printf a decFloat in hexadecimal and decimal */ /* df is the decFloat to show */ /* tag is a tag string displayed with the number */ /* */ /* This is a debug aid; the precise format of the string may change. */ /* ------------------------------------------------------------------ */ void decFloatShow(const decFloat *df, const char *tag) { char hexbuf[DECBYTES*2+DECBYTES/4+1]; // NB blank after every fourth char buff[DECSTRING]; // for value in decimal Int i, j=0; for (i=0; ibytes[DECBYTES-1-i]); #else sprintf(&hexbuf[j], "%02x", df->bytes[i]); #endif j+=2; // the next line adds blank (and terminator) after final pair, too if ((i+1)%4==0) {strcpy(&hexbuf[j], " "); j++;} } decFloatToString(df, buff); printf(">%s> %s [big-endian] %s\n", tag, hexbuf, buff); return; } // decFloatShow #endif /* ------------------------------------------------------------------ */ /* decFloatToBCD -- get sign, exponent, and BCD8 from a decFloat */ /* */ /* df is the source decFloat */ /* exp will be set to the unbiased exponent, q, or to a special */ /* value in the form returned by decFloatGetExponent */ /* bcdar is where DECPMAX bytes will be written, one BCD digit in */ /* each byte (BCD8 encoding); if df is a NaN the first byte will */ /* be zero, and if it is infinite they will all be zero */ /* returns the sign of the coefficient (DECFLOAT_Sign if negative, */ /* 0 otherwise) */ /* */ /* No error is possible, and no status will be set. */ /* ------------------------------------------------------------------ */ Int decFloatToBCD(const decFloat *df, Int *exp, uByte *bcdar) { if (DFISINF(df)) { memset(bcdar, 0, DECPMAX); *exp=DFWORD(df, 0)&0x7e000000; } else { GETCOEFF(df, bcdar); // use macro if (DFISNAN(df)) { bcdar[0]=0; // MSD needs correcting *exp=DFWORD(df, 0)&0x7e000000; } else { // finite *exp=GETEXPUN(df); } } return GETSIGN(df); } // decFloatToBCD /* ------------------------------------------------------------------ */ /* decFloatToEngString -- conversion to numeric string, engineering */ /* */ /* df is the decFloat format number to convert */ /* string is the string where the result will be laid out */ /* */ /* string must be at least DECPMAX+9 characters (the worst case is */ /* "-0.00000nnn...nnn\0", which is as long as the exponent form when */ /* DECEMAXD<=4); this condition is asserted above */ /* */ /* No error is possible, and no status will be set */ /* ------------------------------------------------------------------ */ char * decFloatToEngString(const decFloat *df, 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 char *s, *t; // .. (source, target) Int pre, e; // work const uByte *u; // .. uInt uiwork; // for macros [one compiler needs // volatile here to avoid bug, but // that doubles execution time] // Source words; macro handles endianness uInt sourhi=DFWORD(df, 0); // word with sign #if DECPMAX==16 uInt sourlo=DFWORD(df, 1); #elif DECPMAX==34 uInt sourmh=DFWORD(df, 1); uInt sourml=DFWORD(df, 2); uInt sourlo=DFWORD(df, 3); #endif c=string; // where result will go if (((Int)sourhi)<0) *c++='-'; // handle sign comb=sourhi>>26; // sign+combination field msd=DECCOMBMSD[comb]; // decode the combination field exp=DECCOMBEXP[comb]; // .. if (EXPISSPECIAL(exp)) { // special if (exp==DECFLOAT_Inf) { // 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 // quick exit if the payload is zero #if DECPMAX==7 if ((sourhi&0x000fffff)==0) return string; #elif DECPMAX==16 if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; #elif DECPMAX==34 if (sourlo==0 && sourml==0 && sourmh==0 && (sourhi&0x00003fff)==0) return string; #endif // otherwise drop through to add integer; set correct exp etc. exp=0; msd=0; // setup for following code } else { // complete exponent; top two bits are in place exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias } /* convert the digits of the significand to characters */ cstart=c; // save start of coefficient if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit // Decode the declets. After extracting each declet, it is // decoded to a 4-uByte sequence by table lookup; the four uBytes // are the three encoded BCD8 digits followed by a 1-byte length // (significant digits, except that 000 has length 0). This allows // us to left-align the first declet with non-zero content, then // the remaining ones are full 3-char length. Fixed-length copies // are used because variable-length memcpy causes a subroutine call // in at least two compilers. (The copies are length 4 for speed // and are safe because the last item in the array is of length // three and has the length byte following.) #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \ if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \ else if (*(u+3)) { \ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);} #if DECPMAX==7 dpd2char(sourhi>>10); // declet 1 dpd2char(sourhi); // declet 2 #elif DECPMAX==16 dpd2char(sourhi>>8); // declet 1 dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2 dpd2char(sourlo>>20); // declet 3 dpd2char(sourlo>>10); // declet 4 dpd2char(sourlo); // declet 5 #elif DECPMAX==34 dpd2char(sourhi>>4); // declet 1 dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2 dpd2char(sourmh>>16); // declet 3 dpd2char(sourmh>>6); // declet 4 dpd2char((sourmh<<4) | (sourml>>28)); // declet 5 dpd2char(sourml>>18); // declet 6 dpd2char(sourml>>8); // declet 7 dpd2char((sourml<<2) | (sourlo>>30)); // declet 8 dpd2char(sourlo>>20); // declet 9 dpd2char(sourlo>>10); // declet 10 dpd2char(sourlo); // declet 11 #endif if (c==cstart) *c++='0'; // all zeros, empty -- make "0" if (exp==0) { // integer or NaN case -- easy *c='\0'; // terminate return string; } /* non-0 exponent */ e=0; // assume no E pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1] // [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 '.' if (e!=0) { // engineering: may need to adjust Int adj; // adjustment // The C remainder operator is undefined for negative numbers, so // a positive remainder calculation must be used here if (e<0) { adj=(-e)%3; if (adj!=0) adj=3-adj; } else { // e>0 adj=e%3; } e=e-adj; // if dealing with zero still produce an exponent which is a // multiple of three, as expected, but there will only be the // one zero before the E, still. Otherwise note the padding. if (!DFISZERO(df)) pre+=adj; else { // is zero if (adj!=0) { // 0.00Esnn needed e=e+3; pre=-(2-adj); } } // zero } // engineering adjustment } // exponential form // printf("e=%ld pre=%ld exp=%ld\n", (LI)e, (LI)pre, (LI)exp); /* modify the coefficient, adding 0s, '.', and E+nn as needed */ if (pre>0) { // ddd.ddd (plain), perhaps with E // or dd00 padding for engineering char *dotat=cstart+pre; if (dotat=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); *dotat='.'; c++; // length increased by one } // need dot? else for (; c0 else { /* -5<=pre<=0: here for plain 0.ddd or 0.000ddd forms (may have E, but only for 0.00E+3 kind of case -- with plenty of spare space in this case */ pre=-pre+2; // gap width, including "0." t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point // backoff if too far to the right if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit // now shift the entire coefficient to the right, being careful not // to access to the left of string [cannot use memcpy] for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); // for Quads and Singles there may be a character or two left... s+=3; // where next would come from for(; s>=cstart; s--, t--) *(t+3)=*(s); // now have fill 0. through 0.00000; use overlaps to avoid tests if (pre>=4) { memcpy(cstart+pre-4, "0000", 4); memcpy(cstart, "0.00", 4); } else { // 2 or 3 *(cstart+pre-1)='0'; memcpy(cstart, "0.", 2); } c+=pre; // to end } // finally add the E-part, if needed; it will never be 0, and has // a maximum length of 3 or 4 digits (asserted above) if (e!=0) { memcpy(c, "E+", 2); // starts with E, assume + c++; if (e<0) { *c='-'; // oops, need '-' e=-e; // uInt, please } c++; // Three-character exponents are easy; 4-character a little trickier #if DECEMAXD<=3 u=&BIN2BCD8[e*4]; // -> 3 digits + length byte // copy fixed 4 characters [is safe], starting at non-zero // and with character mask to convert BCD to char UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3); // bump pointer appropriately #elif DECEMAXD==4 if (e<1000) { // 3 (or fewer) digits case u=&BIN2BCD8[e*4]; // -> 3 digits + length byte UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above] c+=*(u+3); // bump pointer appropriately } else { // 4-digits Int thou=((e>>3)*1049)>>17; // e/1000 Int rem=e-(1000*thou); // e%1000 *c++=(char)('0'+(char)thou); // the thousands digit u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte UBFROMUI(c, UBTOUI(u)|CHARMASK);// copy fixed 3+1 characters [is safe] c+=3; // bump pointer, always 3 digits } #endif } *c='\0'; // terminate //printf("res %s\n", string); return string; } // decFloatToEngString /* ------------------------------------------------------------------ */ /* decFloatToPacked -- convert decFloat to Packed decimal + exponent */ /* */ /* df is the source decFloat */ /* exp will be set to the unbiased exponent, q, or to a special */ /* value in the form returned by decFloatGetExponent */ /* packed is where DECPMAX nibbles will be written with the sign as */ /* final nibble (0x0c for +, 0x0d for -); a NaN has a first nibble */ /* of zero, and an infinity is all zeros. decDouble and decQuad */ /* have a additional leading zero nibble, leading to result */ /* lengths of 4, 9, and 18 bytes. */ /* returns the sign of the coefficient (DECFLOAT_Sign if negative, */ /* 0 otherwise) */ /* */ /* No error is possible, and no status will be set. */ /* ------------------------------------------------------------------ */ Int decFloatToPacked(const decFloat *df, Int *exp, uByte *packed) { uByte bcdar[DECPMAX+2]; // work buffer uByte *ip=bcdar, *op=packed; // work pointers if (DFISINF(df)) { memset(bcdar, 0, DECPMAX+2); *exp=DECFLOAT_Inf; } else { GETCOEFF(df, bcdar+1); // use macro if (DFISNAN(df)) { bcdar[1]=0; // MSD needs clearing *exp=DFWORD(df, 0)&0x7e000000; } else { // finite *exp=GETEXPUN(df); } } // now pack; coefficient currently at bcdar+1 #if SINGLE ip++; // ignore first byte #else *ip=0; // need leading zero #endif // set final byte to Packed BCD sign value bcdar[DECPMAX+1]=(DFISSIGNED(df) ? DECPMINUS : DECPPLUS); // pack an even number of bytes... for (; op>26; // sign+combination field msd=DECCOMBMSD[comb]; // decode the combination field exp=DECCOMBEXP[comb]; // .. if (!EXPISSPECIAL(exp)) { // finite // complete exponent; top two bits are in place exp+=GETECON(df)-DECBIAS; // .. + continuation and unbias } else { // IS special if (exp==DECFLOAT_Inf) { // infinity strcpy(c, "Infinity"); return string; // easy } if (sourhi&0x02000000) *c++='s'; // sNaN strcpy(c, "NaN"); // complete word c+=3; // step past // quick exit if the payload is zero #if DECPMAX==7 if ((sourhi&0x000fffff)==0) return string; #elif DECPMAX==16 if (sourlo==0 && (sourhi&0x0003ffff)==0) return string; #elif DECPMAX==34 if (sourlo==0 && sourml==0 && sourmh==0 && (sourhi&0x00003fff)==0) return string; #endif // otherwise drop through to add integer; set correct exp etc. exp=0; msd=0; // setup for following code } /* convert the digits of the significand to characters */ cstart=c; // save start of coefficient if (msd) *c++=(char)('0'+(char)msd); // non-zero most significant digit // Decode the declets. After extracting each declet, it is // decoded to a 4-uByte sequence by table lookup; the four uBytes // are the three encoded BCD8 digits followed by a 1-byte length // (significant digits, except that 000 has length 0). This allows // us to left-align the first declet with non-zero content, then // the remaining ones are full 3-char length. Fixed-length copies // are used because variable-length memcpy causes a subroutine call // in at least two compilers. (The copies are length 4 for speed // and are safe because the last item in the array is of length // three and has the length byte following.) #define dpd2char(dpdin) u=&DPD2BCD8[((dpdin)&0x3ff)*4]; \ if (c!=cstart) {UBFROMUI(c, UBTOUI(u)|CHARMASK); c+=3;} \ else if (*(u+3)) { \ UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3);} #if DECPMAX==7 dpd2char(sourhi>>10); // declet 1 dpd2char(sourhi); // declet 2 #elif DECPMAX==16 dpd2char(sourhi>>8); // declet 1 dpd2char((sourhi<<2) | (sourlo>>30)); // declet 2 dpd2char(sourlo>>20); // declet 3 dpd2char(sourlo>>10); // declet 4 dpd2char(sourlo); // declet 5 #elif DECPMAX==34 dpd2char(sourhi>>4); // declet 1 dpd2char((sourhi<<6) | (sourmh>>26)); // declet 2 dpd2char(sourmh>>16); // declet 3 dpd2char(sourmh>>6); // declet 4 dpd2char((sourmh<<4) | (sourml>>28)); // declet 5 dpd2char(sourml>>18); // declet 6 dpd2char(sourml>>8); // declet 7 dpd2char((sourml<<2) | (sourlo>>30)); // declet 8 dpd2char(sourlo>>20); // declet 9 dpd2char(sourlo>>10); // declet 10 dpd2char(sourlo); // declet 11 #endif if (c==cstart) *c++='0'; // all zeros, empty -- make "0" //[This fast path is valid but adds 3-5 cycles to worst case length] //if (exp==0) { // integer or NaN case -- easy // *c='\0'; // terminate // return string; // } e=0; // assume no E pre=(Int)(c-cstart)+exp; // length+exp [c->LSD+1] // [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 */ if (pre>0) { // ddd.ddd (plain), perhaps with E char *dotat=cstart+pre; if (dotat=dotat; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); *dotat='.'; c++; // length increased by one } // need dot? // finally add the E-part, if needed; it will never be 0, and has // a maximum length of 3 or 4 digits (asserted above) if (e!=0) { memcpy(c, "E+", 2); // starts with E, assume + c++; if (e<0) { *c='-'; // oops, need '-' e=-e; // uInt, please } c++; // Three-character exponents are easy; 4-character a little trickier #if DECEMAXD<=3 u=&BIN2BCD8[e*4]; // -> 3 digits + length byte // copy fixed 4 characters [is safe], starting at non-zero // and with character mask to convert BCD to char UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); c+=*(u+3); // bump pointer appropriately #elif DECEMAXD==4 if (e<1000) { // 3 (or fewer) digits case u=&BIN2BCD8[e*4]; // -> 3 digits + length byte UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above] c+=*(u+3); // bump pointer appropriately } else { // 4-digits Int thou=((e>>3)*1049)>>17; // e/1000 Int rem=e-(1000*thou); // e%1000 *c++=(char)('0'+(char)thou); // the thousands digit u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe] c+=3; // bump pointer, always 3 digits } #endif } *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) */ // Surprisingly, this is close to being the worst-case path, so the // shift is done by fours; this is a little tricky because the // rightmost character to be written must not be beyond where the // rightmost terminator could be -- so backoff to not touch // terminator position if need be (this can make exact alignments // for full Doubles, but in some cases needs care not to access too // far to the left) pre=-pre+2; // gap width, including "0." t=cstart+ROUNDDOWN4(c-cstart)+pre; // preferred first target point // backoff if too far to the right if (t>string+DECSTRING-5) t=string+DECSTRING-5; // adjust to fit // now shift the entire coefficient to the right, being careful not // to access to the left of string [cannot use memcpy] for (s=t-pre; s>=string; s-=4, t-=4) UBFROMUI(t, UBTOUI(s)); // for Quads and Singles there may be a character or two left... s+=3; // where next would come from for(; s>=cstart; s--, t--) *(t+3)=*(s); // now have fill 0. through 0.00000; use overlaps to avoid tests if (pre>=4) { memcpy(cstart+pre-4, "0000", 4); memcpy(cstart, "0.00", 4); } else { // 2 or 3 *(cstart+pre-1)='0'; memcpy(cstart, "0.", 2); } *(c+pre)='\0'; // terminate return string; } // decFloatToString /* ------------------------------------------------------------------ */ /* decFloatToWider -- conversion to next-wider format */ /* */ /* source is the decFloat format number which gets the result of */ /* the conversion */ /* wider is the decFloatWider format number which will be narrowed */ /* returns wider */ /* */ /* Widening is always exact; no status is set (sNaNs are copied and */ /* do not signal). The result will be canonical if the source is, */ /* and may or may not be if the source is not. */ /* ------------------------------------------------------------------ */ // widening is not possible for decQuad format numbers; simply omit #if !QUAD decFloatWider * decFloatToWider(const decFloat *source, decFloatWider *wider) { uInt msd; /* Construct and copy the sign word */ if (DFISSPECIAL(source)) { // copy sign, combination, and first bit of exponent (sNaN selector) DFWWORD(wider, 0)=DFWORD(source, 0)&0xfe000000; msd=0; } else { // is finite number uInt exp=GETEXPUN(source)+DECWBIAS; // get unbiased exponent and rebias uInt code=(exp>>DECWECONL)<<29; // set two bits of exp [msd=0] code|=(exp<<(32-6-DECWECONL)) & 0x03ffffff; // add exponent continuation code|=DFWORD(source, 0)&0x80000000; // add sign DFWWORD(wider, 0)=code; // .. and place top word in wider msd=GETMSD(source); // get source coefficient MSD [0-9] } /* Copy the coefficient and clear any 'unused' words to left */ #if SINGLE DFWWORD(wider, 1)=(DFWORD(source, 0)&0x000fffff)|(msd<<20); #elif DOUBLE DFWWORD(wider, 2)=(DFWORD(source, 0)&0x0003ffff)|(msd<<18); DFWWORD(wider, 3)=DFWORD(source, 1); DFWWORD(wider, 1)=0; #endif return wider; } // decFloatToWider #endif /* ------------------------------------------------------------------ */ /* decFloatVersion -- return package version string */ /* */ /* returns a constant string describing this package */ /* ------------------------------------------------------------------ */ const char *decFloatVersion(void) { return DECVERSION; } // decFloatVersion /* ------------------------------------------------------------------ */ /* decFloatZero -- set to canonical (integer) zero */ /* */ /* df is the decFloat format number to integer +0 (q=0, c=+0) */ /* returns df */ /* */ /* No error is possible, and no status can be set. */ /* ------------------------------------------------------------------ */ decFloat * decFloatZero(decFloat *df){ DFWORD(df, 0)=ZEROWORD; // set appropriate top word #if DOUBLE || QUAD DFWORD(df, 1)=0; #if QUAD DFWORD(df, 2)=0; DFWORD(df, 3)=0; #endif #endif // decFloatShow(df, "zero"); return df; } // decFloatZero /* ------------------------------------------------------------------ */ /* Private generic function (not format-specific) for development use */ /* ------------------------------------------------------------------ */ // This is included once only, for all to use #if QUAD && (DECCHECK || DECTRACE) /* ---------------------------------------------------------------- */ /* decShowNum -- display bcd8 number in debug form */ /* */ /* num is the bcdnum to display */ /* tag is a string to label the display */ /* ---------------------------------------------------------------- */ void decShowNum(const bcdnum *num, const char *tag) { const char *csign="+"; // sign character uByte *ub; // work uInt uiwork; // for macros if (num->sign==DECFLOAT_Sign) csign="-"; printf(">%s> ", tag); if (num->exponent==DECFLOAT_Inf) printf("%sInfinity", csign); else if (num->exponent==DECFLOAT_qNaN) printf("%sqNaN", csign); else if (num->exponent==DECFLOAT_sNaN) printf("%ssNaN", csign); else { // finite char qbuf[10]; // for right-aligned q char *c; // work const uByte *u; // .. Int e=num->exponent; // .. exponent strcpy(qbuf, "q="); c=&qbuf[2]; // where exponent will go // lay out the exponent if (e<0) { *c++='-'; // add '-' e=-e; // uInt, please } #if DECEMAXD>4 #error Exponent form is too long for ShowNum to lay out #endif if (e==0) *c++='0'; // 0-length case else if (e<1000) { // 3 (or fewer) digits case u=&BIN2BCD8[e*4]; // -> 3 digits + length byte UBFROMUI(c, UBTOUI(u+3-*(u+3))|CHARMASK); // [as above] c+=*(u+3); // bump pointer appropriately } else { // 4-digits Int thou=((e>>3)*1049)>>17; // e/1000 Int rem=e-(1000*thou); // e%1000 *c++=(char)('0'+(char)thou); // the thousands digit u=&BIN2BCD8[rem*4]; // -> 3 digits + length byte UBFROMUI(c, UBTOUI(u)|CHARMASK); // copy fixed 3+1 characters [is safe] c+=3; // bump pointer, always 3 digits } *c='\0'; // add terminator printf("%7s c=%s", qbuf, csign); } if (!EXPISSPECIAL(num->exponent) || num->msd!=num->lsd || *num->lsd!=0) { for (ub=num->msd; ub<=num->lsd; ub++) { // coefficient... printf("%1x", *ub); if ((num->lsd-ub)%3==0 && ub!=num->lsd) printf(" "); // 4-space } } printf("\n"); } // decShowNum #endif