ref: 7bab97a7d86415598ae7b18cf693c22f54de7fb6
dir: /jsdtoa.c/
/* The authors of this software are Rob Pike and Ken Thompson.
* Copyright (c) 2002 by Lucent Technologies.
* Permission to use, copy, modify, and distribute this software for any
* purpose without fee is hereby granted, provided that this entire notice
* is included in all copies of any software which is or includes a copy
* or modification of this software and in all copies of the supporting
* documentation for such software.
* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
* WARRANTY. IN PARTICULAR, NEITHER THE AUTHORS NOR LUCENT TECHNOLOGIES MAKE ANY
* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
*/
#include <stdio.h>
#include <math.h>
#include <float.h>
#include <string.h>
#include <stdlib.h>
#include <errno.h>
enum { NSIGNIF = 17 };
/*
* first few powers of 10, enough for about 1/2 of the
* total space for doubles.
*/
static double pows10[] =
{
1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
1e20, 1e21, 1e22, 1e23, 1e24, 1e25, 1e26, 1e27, 1e28, 1e29,
1e30, 1e31, 1e32, 1e33, 1e34, 1e35, 1e36, 1e37, 1e38, 1e39,
1e40, 1e41, 1e42, 1e43, 1e44, 1e45, 1e46, 1e47, 1e48, 1e49,
1e50, 1e51, 1e52, 1e53, 1e54, 1e55, 1e56, 1e57, 1e58, 1e59,
1e60, 1e61, 1e62, 1e63, 1e64, 1e65, 1e66, 1e67, 1e68, 1e69,
1e70, 1e71, 1e72, 1e73, 1e74, 1e75, 1e76, 1e77, 1e78, 1e79,
1e80, 1e81, 1e82, 1e83, 1e84, 1e85, 1e86, 1e87, 1e88, 1e89,
1e90, 1e91, 1e92, 1e93, 1e94, 1e95, 1e96, 1e97, 1e98, 1e99,
1e100, 1e101, 1e102, 1e103, 1e104, 1e105, 1e106, 1e107, 1e108, 1e109,
1e110, 1e111, 1e112, 1e113, 1e114, 1e115, 1e116, 1e117, 1e118, 1e119,
1e120, 1e121, 1e122, 1e123, 1e124, 1e125, 1e126, 1e127, 1e128, 1e129,
1e130, 1e131, 1e132, 1e133, 1e134, 1e135, 1e136, 1e137, 1e138, 1e139,
1e140, 1e141, 1e142, 1e143, 1e144, 1e145, 1e146, 1e147, 1e148, 1e149,
1e150, 1e151, 1e152, 1e153, 1e154, 1e155, 1e156, 1e157, 1e158, 1e159,
};
#define npows10 ((int)(sizeof(pows10)/sizeof(pows10[0])))
#define pow10(x) fmtpow10(x)
static double
pow10(int n)
{
double d;
int neg;
neg = 0;
if(n < 0){
neg = 1;
n = -n;
}
if(n < npows10)
d = pows10[n];
else{
d = pows10[npows10-1];
for(;;){
n -= npows10 - 1;
if(n < npows10){
d *= pows10[n];
break;
}
d *= pows10[npows10 - 1];
}
}
if(neg)
return 1./d;
return d;
}
/*
* add 1 to the decimal integer string a of length n.
* if 99999 overflows into 10000, return 1 to tell caller
* to move the virtual decimal point.
*/
static int
xadd1(char *a, int n)
{
char *b;
int c;
if(n < 0 || n > NSIGNIF)
return 0;
for(b = a+n-1; b >= a; b--) {
c = *b + 1;
if(c <= '9') {
*b = c;
return 0;
}
*b = '0';
}
/*
* need to overflow adding digit.
* shift number down and insert 1 at beginning.
* decimal is known to be 0s or we wouldn't
* have gotten this far. (e.g., 99999+1 => 00000)
*/
a[0] = '1';
return 1;
}
/*
* subtract 1 from the decimal integer string a.
* if 10000 underflows into 09999, make it 99999
* and return 1 to tell caller to move the virtual
* decimal point. this way, xsub1 is inverse of xadd1.
*/
static int
xsub1(char *a, int n)
{
char *b;
int c;
if(n < 0 || n > NSIGNIF)
return 0;
for(b = a+n-1; b >= a; b--) {
c = *b - 1;
if(c >= '0') {
if(c == '0' && b == a) {
/*
* just zeroed the top digit; shift everyone up.
* decimal is known to be 9s or we wouldn't
* have gotten this far. (e.g., 10000-1 => 09999)
*/
*b = '9';
return 1;
}
*b = c;
return 0;
}
*b = '9';
}
/*
* can't get here. the number a is always normalized
* so that it has a nonzero first digit.
*/
return 0;
}
/*
* format exponent like sprintf(p, "e%+d", e)
*/
void
jsV_fmtexp(char *p, int e)
{
char se[9];
int i;
*p++ = 'e';
if(e < 0) {
*p++ = '-';
e = -e;
} else
*p++ = '+';
i = 0;
while(e) {
se[i++] = e % 10 + '0';
e /= 10;
}
while(i < 1)
se[i++] = '0';
while(i > 0)
*p++ = se[--i];
*p++ = '\0';
}
/*
* compute decimal integer m, exp such that:
* f = m*10^exp
* m is as short as possible with losing exactness
* assumes special cases (NaN, +Inf, -Inf) have been handled.
*/
void
jsV_dtoa(double f, char *s, int *exp, int *neg, int *ns)
{
int c, d, e2, e, ee, i, ndigit, oerrno;
char tmp[NSIGNIF+10];
double g;
oerrno = errno; /* in case strtod smashes errno */
/*
* make f non-negative.
*/
*neg = 0;
if(f < 0) {
f = -f;
*neg = 1;
}
/*
* must handle zero specially.
*/
if(f == 0){
*exp = 0;
s[0] = '0';
s[1] = '\0';
*ns = 1;
return;
}
/*
* find g,e such that f = g*10^e.
* guess 10-exponent using 2-exponent, then fine tune.
*/
frexp(f, &e2);
e = (int)(e2 * .301029995664);
g = f * pow10(-e);
while(g < 1) {
e--;
g = f * pow10(-e);
}
while(g >= 10) {
e++;
g = f * pow10(-e);
}
/*
* convert NSIGNIF digits as a first approximation.
*/
for(i=0; i<NSIGNIF; i++) {
d = (int)g;
s[i] = d+'0';
g = (g-d) * 10;
}
s[i] = 0;
/*
* adjust e because s is 314159... not 3.14159...
*/
e -= NSIGNIF-1;
jsV_fmtexp(s+NSIGNIF, e);
/*
* adjust conversion until strtod(s) == f exactly.
*/
for(i=0; i<10; i++) {
g = strtod(s, NULL);
if(f > g) {
if(xadd1(s, NSIGNIF)) {
/* gained a digit */
e--;
jsV_fmtexp(s+NSIGNIF, e);
}
continue;
}
if(f < g) {
if(xsub1(s, NSIGNIF)) {
/* lost a digit */
e++;
jsV_fmtexp(s+NSIGNIF, e);
}
continue;
}
break;
}
/*
* play with the decimal to try to simplify.
*/
/*
* bump last few digits up to 9 if we can
*/
for(i=NSIGNIF-1; i>=NSIGNIF-3; i--) {
c = s[i];
if(c != '9') {
s[i] = '9';
g = strtod(s, NULL);
if(g != f) {
s[i] = c;
break;
}
}
}
/*
* add 1 in hopes of turning 9s to 0s
*/
if(s[NSIGNIF-1] == '9') {
strcpy(tmp, s);
ee = e;
if(xadd1(tmp, NSIGNIF)) {
ee--;
jsV_fmtexp(tmp+NSIGNIF, ee);
}
g = strtod(tmp, NULL);
if(g == f) {
strcpy(s, tmp);
e = ee;
}
}
/*
* bump last few digits down to 0 as we can.
*/
for(i=NSIGNIF-1; i>=NSIGNIF-3; i--) {
c = s[i];
if(c != '0') {
s[i] = '0';
g = strtod(s, NULL);
if(g != f) {
s[i] = c;
break;
}
}
}
/*
* remove trailing zeros.
*/
ndigit = NSIGNIF;
while(ndigit > 1 && s[ndigit-1] == '0'){
e++;
--ndigit;
}
s[ndigit] = 0;
*exp = e;
*ns = ndigit;
errno = oerrno;
}