ref: e676a871f07b0d80c6791a2db0b4b361f277d8e8
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>
#include "jsi.h"
typedef unsigned long ulong;
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
js_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
js_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;
js_fmtexp(s+NSIGNIF, e);
/*
* adjust conversion until strtod(s) == f exactly.
*/
for(i=0; i<10; i++) {
g = js_strtod(s, NULL);
if(f > g) {
if(xadd1(s, NSIGNIF)) {
/* gained a digit */
e--;
js_fmtexp(s+NSIGNIF, e);
}
continue;
}
if(f < g) {
if(xsub1(s, NSIGNIF)) {
/* lost a digit */
e++;
js_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 = js_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--;
js_fmtexp(tmp+NSIGNIF, ee);
}
g = js_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 = js_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;
}
static inline ulong
umuldiv(ulong a, ulong b, ulong c)
{
double d;
d = ((double)a * (double)b) / (double)c;
if(d >= 4294967295.)
d = 4294967295.;
return (ulong)d;
}
/*
* This routine will convert to arbitrary precision
* floating point entirely in multi-precision fixed.
* The answer is the closest floating point number to
* the given decimal number. Exactly half way are
* rounded ala ieee rules.
* Method is to scale input decimal between .500 and .999...
* with external power of 2, then binary search for the
* closest mantissa to this decimal number.
* Nmant is is the required precision. (53 for ieee dp)
* Nbits is the max number of bits/word. (must be <= 28)
* Prec is calculated - the number of words of fixed mantissa.
*/
enum
{
Nbits = 28, /* bits safely represented in a ulong */
Nmant = 53, /* bits of precision required */
Prec = (Nmant+Nbits+1)/Nbits, /* words of Nbits each to represent mantissa */
Sigbit = 1<<(Prec*Nbits-Nmant), /* first significant bit of Prec-th word */
Ndig = 1500,
One = (ulong)(1<<Nbits),
Half = (ulong)(One>>1),
Maxe = 310,
Fsign = 1<<0, /* found - */
Fesign = 1<<1, /* found e- */
Fdpoint = 1<<2, /* found . */
S0 = 0, /* _ _S0 +S1 #S2 .S3 */
S1, /* _+ #S2 .S3 */
S2, /* _+# #S2 .S4 eS5 */
S3, /* _+. #S4 */
S4, /* _+#.# #S4 eS5 */
S5, /* _+#.#e +S6 #S7 */
S6, /* _+#.#e+ #S7 */
S7 /* _+#.#e+# #S7 */
};
static int xcmp(char*, char*);
static int fpcmp(char*, ulong*);
static void frnorm(ulong*);
static void divascii(char*, int*, int*, int*);
static void mulascii(char*, int*, int*, int*);
typedef struct Tab Tab;
struct Tab
{
int bp;
int siz;
char* cmp;
};
double
js_strtod(const char *as, char **aas)
{
int na, ex, dp, bp, c, i, flag, state;
ulong low[Prec], hig[Prec], mid[Prec];
double d;
char *s, a[Ndig];
flag = 0; /* Fsign, Fesign, Fdpoint */
na = 0; /* number of digits of a[] */
dp = 0; /* na of decimal point */
ex = 0; /* exonent */
state = S0;
for(s=(char*)as;; s++) {
c = *s;
if(c >= '0' && c <= '9') {
switch(state) {
case S0:
case S1:
case S2:
state = S2;
break;
case S3:
case S4:
state = S4;
break;
case S5:
case S6:
case S7:
state = S7;
ex = ex*10 + (c-'0');
continue;
}
if(na == 0 && c == '0') {
dp--;
continue;
}
if(na < Ndig-50)
a[na++] = c;
continue;
}
switch(c) {
case '\t':
case '\n':
case '\v':
case '\f':
case '\r':
case ' ':
if(state == S0)
continue;
break;
case '-':
if(state == S0)
flag |= Fsign;
else
flag |= Fesign;
/* fall through */
case '+':
if(state == S0)
state = S1;
else
if(state == S5)
state = S6;
else
break; /* syntax */
continue;
case '.':
flag |= Fdpoint;
dp = na;
if(state == S0 || state == S1) {
state = S3;
continue;
}
if(state == S2) {
state = S4;
continue;
}
break;
case 'e':
case 'E':
if(state == S2 || state == S4) {
state = S5;
continue;
}
break;
}
break;
}
/*
* clean up return char-pointer
*/
switch(state) {
case S0:
if(xcmp(s, "nan") == 0) {
if(aas != NULL)
*aas = s+3;
goto retnan;
}
/* fall through */
case S1:
if(xcmp(s, "infinity") == 0) {
if(aas != NULL)
*aas = s+8;
goto retinf;
}
if(xcmp(s, "inf") == 0) {
if(aas != NULL)
*aas = s+3;
goto retinf;
}
/* fall through */
case S3:
if(aas != NULL)
*aas = (char*)as;
goto ret0; /* no digits found */
case S6:
s--; /* back over +- */
/* fall through */
case S5:
s--; /* back over e */
break;
}
if(aas != NULL)
*aas = s;
if(flag & Fdpoint)
while(na > 0 && a[na-1] == '0')
na--;
if(na == 0)
goto ret0; /* zero */
a[na] = 0;
if(!(flag & Fdpoint))
dp = na;
if(flag & Fesign)
ex = -ex;
dp += ex;
if(dp < -Maxe){
errno = ERANGE;
goto ret0; /* underflow by exp */
} else
if(dp > +Maxe)
goto retinf; /* overflow by exp */
/*
* normalize the decimal ascii number
* to range .[5-9][0-9]* e0
*/
bp = 0; /* binary exponent */
while(dp > 0)
divascii(a, &na, &dp, &bp);
while(dp < 0 || a[0] < '5')
mulascii(a, &na, &dp, &bp);
/* close approx by naive conversion */
mid[0] = 0;
mid[1] = 1;
for(i=0; (c=a[i]) != '\0'; i++) {
mid[0] = mid[0]*10 + (c-'0');
mid[1] = mid[1]*10;
if(i >= 8)
break;
}
low[0] = umuldiv(mid[0], One, mid[1]);
hig[0] = umuldiv(mid[0]+1, One, mid[1]);
for(i=1; i<Prec; i++) {
low[i] = 0;
hig[i] = One-1;
}
/* binary search for closest mantissa */
for(;;) {
/* mid = (hig + low) / 2 */
c = 0;
for(i=0; i<Prec; i++) {
mid[i] = hig[i] + low[i];
if(c)
mid[i] += One;
c = mid[i] & 1;
mid[i] >>= 1;
}
frnorm(mid);
/* compare */
c = fpcmp(a, mid);
if(c > 0) {
c = 1;
for(i=0; i<Prec; i++)
if(low[i] != mid[i]) {
c = 0;
low[i] = mid[i];
}
if(c)
break; /* between mid and hig */
continue;
}
if(c < 0) {
for(i=0; i<Prec; i++)
hig[i] = mid[i];
continue;
}
/* only hard part is if even/odd roundings wants to go up */
c = mid[Prec-1] & (Sigbit-1);
if(c == Sigbit/2 && (mid[Prec-1]&Sigbit) == 0)
mid[Prec-1] -= c;
break; /* exactly mid */
}
/* normal rounding applies */
c = mid[Prec-1] & (Sigbit-1);
mid[Prec-1] -= c;
if(c >= Sigbit/2) {
mid[Prec-1] += Sigbit;
frnorm(mid);
}
goto out;
ret0:
if(flag & Fsign)
return -0.0;
return 0;
retnan:
return NAN;
retinf:
/*
* Unix strtod requires these. Plan 9 would return Inf(0) or Inf(-1). */
errno = ERANGE;
if(flag & Fsign)
return -HUGE_VAL;
return HUGE_VAL;
out:
d = 0;
for(i=0; i<Prec; i++)
d = d*One + mid[i];
if(flag & Fsign)
d = -d;
d = ldexp(d, bp - Prec*Nbits);
if(d == 0){ /* underflow */
errno = ERANGE;
}
return d;
}
static void
frnorm(ulong *f)
{
int i, c;
c = 0;
for(i=Prec-1; i>0; i--) {
f[i] += c;
c = f[i] >> Nbits;
f[i] &= One-1;
}
f[0] += c;
}
static int
fpcmp(char *a, ulong* f)
{
ulong tf[Prec];
int i, d, c;
for(i=0; i<Prec; i++)
tf[i] = f[i];
for(;;) {
/* tf *= 10 */
for(i=0; i<Prec; i++)
tf[i] = tf[i]*10;
frnorm(tf);
d = (tf[0] >> Nbits) + '0';
tf[0] &= One-1;
/* compare next digit */
c = *a;
if(c == 0) {
if('0' < d)
return -1;
if(tf[0] != 0)
goto cont;
for(i=1; i<Prec; i++)
if(tf[i] != 0)
goto cont;
return 0;
}
if(c > d)
return +1;
if(c < d)
return -1;
a++;
cont:;
}
}
static inline void
divby(char *a, int *na, int b)
{
int n, c;
char *p;
p = a;
n = 0;
while(n>>b == 0) {
c = *a++;
if(c == 0) {
while(n) {
c = n*10;
if(c>>b)
break;
n = c;
}
goto xx;
}
n = n*10 + c-'0';
(*na)--;
}
for(;;) {
c = n>>b;
n -= c<<b;
*p++ = c + '0';
c = *a++;
if(c == 0)
break;
n = n*10 + c-'0';
}
(*na)++;
xx:
while(n) {
n = n*10;
c = n>>b;
n -= c<<b;
*p++ = c + '0';
(*na)++;
if (*na >= Ndig) break; /* abort if overflowing */
}
*p = 0;
}
static Tab tab1[] =
{
{ 1, 0, "" },
{ 3, 1, "7" },
{ 6, 2, "63" },
{ 9, 3, "511" },
{ 13, 4, "8191" },
{ 16, 5, "65535" },
{ 19, 6, "524287" },
{ 23, 7, "8388607" },
{ 26, 8, "67108863" },
{ 27, 9, "134217727" },
};
static void
divascii(char *a, int *na, int *dp, int *bp)
{
int b, d;
Tab *t;
d = *dp;
if(d >= (int)(nelem(tab1)))
d = (int)(nelem(tab1))-1;
t = tab1 + d;
b = t->bp;
if(memcmp(a, t->cmp, t->siz) > 0)
d--;
*dp -= d;
*bp += b;
divby(a, na, b);
}
static inline void
mulby(char *a, char *p, char *q, int b)
{
int n, c;
n = 0;
*p = 0;
for(;;) {
q--;
if(q < a)
break;
c = *q - '0';
c = (c<<b) + n;
n = c/10;
c -= n*10;
p--;
*p = c + '0';
}
while(n) {
c = n;
n = c/10;
c -= n*10;
p--;
*p = c + '0';
}
}
static Tab tab2[] =
{
{ 1, 1, "" }, /* dp = 0-0 */
{ 3, 3, "125" },
{ 6, 5, "15625" },
{ 9, 7, "1953125" },
{ 13, 10, "1220703125" },
{ 16, 12, "152587890625" },
{ 19, 14, "19073486328125" },
{ 23, 17, "11920928955078125" },
{ 26, 19, "1490116119384765625" },
{ 27, 19, "7450580596923828125" }, /* dp 8-9 */
};
static void
mulascii(char *a, int *na, int *dp, int *bp)
{
char *p;
int d, b;
Tab *t;
d = -*dp;
if(d >= (int)(nelem(tab2)))
d = (int)(nelem(tab2))-1;
t = tab2 + d;
b = t->bp;
if(memcmp(a, t->cmp, t->siz) < 0)
d--;
p = a + *na;
*bp -= b;
*dp += d;
*na += d;
mulby(a, p+d, p, b);
}
static int
xcmp(char *a, char *b)
{
int c1, c2;
while((c1 = *b++) != '\0') {
c2 = *a++;
if(c2 >= 'A' && c2 <= 'Z')
c2 = c2 - 'A' + 'a';
if(c1 != c2)
return 1;
}
return 0;
}