/* ------------------------------------------------------------------ */
/* 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 <string.h> // [for memset/memcpy]
#include <stdio.h> // [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
|| 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