mirror of https://gitea.it/1414codeforge/ubgpsuite
You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
562 lines
9.4 KiB
C
562 lines
9.4 KiB
C
3 years ago
|
// SPDX-License-Identifier: LGPL-3.0-or-later
|
||
|
|
||
|
/**
|
||
|
* \file numlib_atof.c
|
||
|
*
|
||
|
* Implements ASCII to float conversion.
|
||
|
*
|
||
|
* \copyright The Plan9 Authors
|
||
|
* \copyright The DoubleFourteen Code Forge (C) All Rights Reserved
|
||
|
* \author Lorenzo Cogotti
|
||
|
*
|
||
|
* Algorithm based on Plan9 strtod(), licensed under LUCENT PUBLIC LICENSE:
|
||
|
* Copyright (C) 2003, Lucent Technologies Inc. and others. All Rights Reserved.
|
||
|
*
|
||
|
* Original source code available at: https://9p.io/sources/plan9/
|
||
|
*/
|
||
|
|
||
|
#include "numlib.h"
|
||
|
|
||
|
#include <math.h>
|
||
|
#include <string.h>
|
||
|
|
||
|
/*
|
||
|
* 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.
|
||
|
*/
|
||
|
|
||
|
#define Nbits 28 // bits safely represented in an unsigned long
|
||
|
#define Nmant 53 // bits of precision required
|
||
|
#define Bias 1022
|
||
|
#define Prec ((Nmant+Nbits+1) / Nbits) // words of Nbits each to represent mantissa
|
||
|
#define Sigbit (1uLL << (Prec*Nbits-Nmant)) // first significant bit of Prec-th word
|
||
|
#define Ndig 1500
|
||
|
#define One (1uL << Nbits)
|
||
|
#define Half (One >> 1)
|
||
|
#define Maxe 310
|
||
|
|
||
|
#define Fsign BIT(0) // found -
|
||
|
#define Fesign BIT(1) // found e-
|
||
|
#define Fdpoint BIT(2) // found .
|
||
|
|
||
|
enum {
|
||
|
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
|
||
|
};
|
||
|
|
||
|
typedef struct {
|
||
|
int bp;
|
||
|
int siz;
|
||
|
const char *cmp;
|
||
|
} Tab;
|
||
|
|
||
|
static unsigned long umuldiv(unsigned long a, unsigned long b, unsigned long c)
|
||
|
{
|
||
|
return ((unsigned long long) a * (unsigned long long) b) / c;
|
||
|
}
|
||
|
|
||
|
static void frnorm(unsigned long *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, unsigned long *f)
|
||
|
{
|
||
|
unsigned long tf[Prec];
|
||
|
int i, d, c;
|
||
|
|
||
|
for (i = 0; i < Prec; i++)
|
||
|
tf[i] = f[i];
|
||
|
|
||
|
while (TRUE) {
|
||
|
// 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 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)--;
|
||
|
}
|
||
|
while (TRUE) {
|
||
|
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)++;
|
||
|
}
|
||
|
*p = '\0';
|
||
|
}
|
||
|
|
||
|
static void divby(char *a, int *na, int b)
|
||
|
{
|
||
|
while (b > 9) {
|
||
|
_divby(a, na, 9);
|
||
|
a[*na] = 0;
|
||
|
b -= 9;
|
||
|
}
|
||
|
if (b > 0)
|
||
|
_divby(a, na, b);
|
||
|
}
|
||
|
|
||
|
static const 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;
|
||
|
const Tab *t;
|
||
|
|
||
|
d = *dp;
|
||
|
if (d >= (int) ARRAY_SIZE(tab1))
|
||
|
d = ARRAY_SIZE(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 void mulby(char *a, char *p, char *q, int b)
|
||
|
{
|
||
|
int n, c;
|
||
|
|
||
|
n = 0;
|
||
|
*p = 0;
|
||
|
while (TRUE) {
|
||
|
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 const 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;
|
||
|
const Tab *t;
|
||
|
|
||
|
d = -*dp;
|
||
|
if (d >= (int) ARRAY_SIZE(tab2))
|
||
|
d = ARRAY_SIZE(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 Boolean xcmp(const char *a, const char *b)
|
||
|
{
|
||
|
int c1, c2;
|
||
|
|
||
|
while ((c1 = *b++) != '\0') {
|
||
|
c2 = *a++;
|
||
|
|
||
|
// Make c2 lowercase
|
||
|
c2 |= ((c2 >= 'A' && c2 <= 'Z') << 5);
|
||
|
if (c1 != c2)
|
||
|
return FALSE;
|
||
|
}
|
||
|
return TRUE;
|
||
|
}
|
||
|
|
||
|
double Atof(const char *s, char **endp, NumConvRet *outcome)
|
||
|
{
|
||
|
NumConvRet result;
|
||
|
unsigned long low[Prec], hig[Prec], mid[Prec];
|
||
|
unsigned long num, den;
|
||
|
const char *sp;
|
||
|
double d;
|
||
|
int ona, bp, c, i;
|
||
|
char a[Ndig];
|
||
|
|
||
|
unsigned flag = 0; // Fsign, Fesign, Fdpoint
|
||
|
int na = 0; // number of digits of a[]
|
||
|
int dp = 0; // na of decimal point
|
||
|
int ex = 0; // exponent
|
||
|
|
||
|
int state = S0;
|
||
|
|
||
|
if (!outcome)
|
||
|
outcome = &result;
|
||
|
|
||
|
*outcome = NCVENOERR; // assume conversion is successful
|
||
|
|
||
|
for (sp = s;; sp++) {
|
||
|
c = *sp;
|
||
|
if (c >= '0' && c <= '9') {
|
||
|
switch (state) {
|
||
|
default:
|
||
|
UNREACHABLE;
|
||
|
break;
|
||
|
|
||
|
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 '-':
|
||
|
if (state == S0)
|
||
|
flag |= Fsign;
|
||
|
else
|
||
|
flag |= Fesign;
|
||
|
|
||
|
// FALLTHROUGH
|
||
|
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;
|
||
|
|
||
|
default:
|
||
|
break;
|
||
|
}
|
||
|
|
||
|
break;
|
||
|
}
|
||
|
|
||
|
// Clean up return char-pointer
|
||
|
switch (state) {
|
||
|
case S0:
|
||
|
if (xcmp(sp, "nan")) {
|
||
|
if (endp)
|
||
|
*endp = (char *) sp + 3;
|
||
|
|
||
|
goto retnan;
|
||
|
}
|
||
|
|
||
|
// FALLTHROUGH
|
||
|
case S1:
|
||
|
if (xcmp(sp, "infinity")) {
|
||
|
if (endp)
|
||
|
*endp = (char *) sp + 8;
|
||
|
|
||
|
goto retinf;
|
||
|
}
|
||
|
if (xcmp(sp, "inf")) {
|
||
|
if (endp)
|
||
|
*endp = (char *) sp + 3;
|
||
|
|
||
|
goto retinf;
|
||
|
}
|
||
|
|
||
|
// FALLTHROUGH
|
||
|
case S3:
|
||
|
if (endp)
|
||
|
*endp = (char *) sp;
|
||
|
|
||
|
*outcome = NCVENOTHING;
|
||
|
goto ret0; // no digits found
|
||
|
|
||
|
case S6:
|
||
|
sp--; // back over +-
|
||
|
|
||
|
// FALLTHROUGH
|
||
|
case S5:
|
||
|
sp--; // back over e
|
||
|
break;
|
||
|
}
|
||
|
if (endp)
|
||
|
*endp = (char *) sp;
|
||
|
|
||
|
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-Nmant/3) // actually -Nmant*log(2)/log(10), but Nmant/3 close enough
|
||
|
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);
|
||
|
|
||
|
a[na] = '\0';
|
||
|
|
||
|
// Very small numbers are represented using
|
||
|
// bp = -Bias+1. adjust accordingly.
|
||
|
if (bp < -Bias+1) {
|
||
|
ona = na;
|
||
|
divby(a, &na, -bp-Bias+1);
|
||
|
if (na < ona) {
|
||
|
memmove(a+ona-na, a, na);
|
||
|
memset(a, '0', ona-na);
|
||
|
na = ona;
|
||
|
}
|
||
|
a[na] = '\0';
|
||
|
bp = -Bias+1;
|
||
|
}
|
||
|
|
||
|
// Close approx by naive conversion
|
||
|
num = 0;
|
||
|
den = 1;
|
||
|
for (i = 0; i < 9 && (c = a[i]) != '\0'; i++) {
|
||
|
num = num*10 + (c - '0');
|
||
|
den *= 10;
|
||
|
}
|
||
|
|
||
|
low[0] = umuldiv(num, One, den);
|
||
|
hig[0] = umuldiv(num+1, One, den);
|
||
|
for (i = 1; i < Prec; i++) {
|
||
|
low[i] = 0;
|
||
|
hig[i] = One-1;
|
||
|
}
|
||
|
|
||
|
// Binary search for closest mantissa
|
||
|
while (TRUE) {
|
||
|
// 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 >= (int) Sigbit/2) {
|
||
|
mid[Prec-1] += Sigbit;
|
||
|
frnorm(mid);
|
||
|
}
|
||
|
|
||
|
d = 0;
|
||
|
for (i = 0; i < Prec; i++)
|
||
|
d = d*One + mid[i];
|
||
|
if (flag & Fsign)
|
||
|
d = -d;
|
||
|
|
||
|
d = ldexp(d, bp - Prec*Nbits);
|
||
|
return d;
|
||
|
|
||
|
ret0:
|
||
|
return 0;
|
||
|
|
||
|
retnan:
|
||
|
return NAN;
|
||
|
|
||
|
retinf:
|
||
|
return (flag & Fsign) ? -INFINITY : INFINITY;
|
||
|
}
|
||
|
|