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-rw-r--r--src/libfmt/strtod.c539
1 files changed, 539 insertions, 0 deletions
diff --git a/src/libfmt/strtod.c b/src/libfmt/strtod.c
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+++ b/src/libfmt/strtod.c
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+/*
+ * 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 <stdlib.h>
+#include <math.h>
+#include <ctype.h>
+#include <stdlib.h>
+#include <string.h>
+#include <errno.h>
+#include "fmt.h"
+#include "nan.h"
+
+#ifndef nelem
+#define nelem(x) (sizeof(x)/sizeof *(x))
+#endif
+#define nil ((void*)0)
+#define ulong _fmtulong
+typedef unsigned long ulong;
+
+static 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
+fmtstrtod(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;
+ 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 != nil)
+ *aas = s+3;
+ goto retnan;
+ }
+ case S1:
+ if(xcmp(s, "infinity") == 0) {
+ if(aas != nil)
+ *aas = s+8;
+ goto retinf;
+ }
+ if(xcmp(s, "inf") == 0) {
+ if(aas != nil)
+ *aas = s+3;
+ goto retinf;
+ }
+ case S3:
+ if(aas != nil)
+ *aas = (char*)as;
+ goto ret0; /* no digits found */
+ case S6:
+ s--; /* back over +- */
+ case S5:
+ s--; /* back over e */
+ break;
+ }
+ if(aas != nil)
+ *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]; 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:
+ 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:;
+ }
+ return 0;
+}
+
+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)--;
+ }
+ 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)++;
+ }
+ *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 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++) {
+ c2 = *a++;
+ if(isupper(c2))
+ c2 = tolower(c2);
+ if(c1 != c2)
+ return 1;
+ }
+ return 0;
+}
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