/* ------------------------------------------------------------------ */ /* Decimal 128-bit format module */ /* ------------------------------------------------------------------ */ /* Copyright (c) IBM Corporation, 2000, 2008. 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 called decNumber.pdf. This document is */ /* available, together with arithmetic and format 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 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 // [for memset/memcpy] #include // [for printf] #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] */ // DPD2BIN and the reverse are renamed to prevent link-time conflict // if decQuad is also built in the same executable #define DPD2BIN DPD2BINx #define BIN2DPD BIN2DPDx 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 || aeround; // 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->digitsbits&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=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; ibytes[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; ibytes[i]); } printf(" D128> %s [S:%d Cb:%02x Ec:%02x] BigEndian\n", buf, decimal128Sign(d128), decimal128Comb(d128), decimal128ExpCon(d128)); } } // decimal128Show #endif