732 lines
15 KiB
C
732 lines
15 KiB
C
/*
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FUNCTION
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<<strtod>>, <<strtodf>>---string to double or float
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INDEX
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strtod
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INDEX
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_strtod_r
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INDEX
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strtodf
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ANSI_SYNOPSIS
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#include <stdlib.h>
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double strtod(const char *<[str]>, char **<[tail]>);
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float strtodf(const char *<[str]>, char **<[tail]>);
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double _strtod_r(void *<[reent]>,
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const char *<[str]>, char **<[tail]>);
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TRAD_SYNOPSIS
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#include <stdlib.h>
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double strtod(<[str]>,<[tail]>)
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char *<[str]>;
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char **<[tail]>;
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float strtodf(<[str]>,<[tail]>)
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char *<[str]>;
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char **<[tail]>;
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double _strtod_r(<[reent]>,<[str]>,<[tail]>)
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char *<[reent]>;
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char *<[str]>;
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char **<[tail]>;
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DESCRIPTION
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The function <<strtod>> parses the character string <[str]>,
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producing a substring which can be converted to a double
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value. The substring converted is the longest initial
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subsequence of <[str]>, beginning with the first
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non-whitespace character, that has the format:
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.[+|-]<[digits]>[.][<[digits]>][(e|E)[+|-]<[digits]>]
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The substring contains no characters if <[str]> is empty, consists
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entirely of whitespace, or if the first non-whitespace
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character is something other than <<+>>, <<->>, <<.>>, or a
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digit. If the substring is empty, no conversion is done, and
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the value of <[str]> is stored in <<*<[tail]>>>. Otherwise,
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the substring is converted, and a pointer to the final string
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(which will contain at least the terminating null character of
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<[str]>) is stored in <<*<[tail]>>>. If you want no
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assignment to <<*<[tail]>>>, pass a null pointer as <[tail]>.
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<<strtodf>> is identical to <<strtod>> except for its return type.
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This implementation returns the nearest machine number to the
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input decimal string. Ties are broken by using the IEEE
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round-even rule.
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The alternate function <<_strtod_r>> is a reentrant version.
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The extra argument <[reent]> is a pointer to a reentrancy structure.
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RETURNS
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<<strtod>> returns the converted substring value, if any. If
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no conversion could be performed, 0 is returned. If the
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correct value is out of the range of representable values,
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plus or minus <<HUGE_VAL>> is returned, and <<ERANGE>> is
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stored in errno. If the correct value would cause underflow, 0
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is returned and <<ERANGE>> is stored in errno.
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Supporting OS subroutines required: <<close>>, <<fstat>>, <<isatty>>,
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<<lseek>>, <<read>>, <<sbrk>>, <<write>>.
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*/
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/****************************************************************
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*
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* The author of this software is David M. Gay.
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*
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* Copyright (c) 1991 by AT&T.
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose without fee is hereby granted, provided that this entire notice
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* is included in all copies of any software which is or includes a copy
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* or modification of this software and in all copies of the supporting
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* documentation for such software.
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*
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* THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED
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* WARRANTY. IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY
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* REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY
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* OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.
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*
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***************************************************************/
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/* Please send bug reports to
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David M. Gay
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AT&T Bell Laboratories, Room 2C-463
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600 Mountain Avenue
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Murray Hill, NJ 07974-2070
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U.S.A.
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dmg@research.att.com or research!dmg
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*/
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#include <_ansi.h>
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#include <reent.h>
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#include <string.h>
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#include "mprec.h"
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double
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_DEFUN (_strtod_r, (ptr, s00, se),
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struct _reent *ptr _AND
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_CONST char *s00 _AND
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char **se)
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{
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int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e1, esign, i, j,
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k, nd, nd0, nf, nz, nz0, sign;
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long e;
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_CONST char *s, *s0, *s1;
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double aadj, aadj1, adj;
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long L;
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unsigned long z;
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__ULong y;
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union double_union rv, rv0;
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_Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
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sign = nz0 = nz = 0;
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rv.d = 0.;
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for (s = s00;; s++)
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switch (*s)
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{
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case '-':
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sign = 1;
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/* no break */
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case '+':
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if (*++s)
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goto break2;
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/* no break */
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case 0:
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s = s00;
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goto ret;
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case '\t':
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case '\n':
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case '\v':
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case '\f':
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case '\r':
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case ' ':
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continue;
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default:
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goto break2;
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}
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break2:
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if (*s == '0')
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{
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nz0 = 1;
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while (*++s == '0');
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if (!*s)
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goto ret;
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}
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s0 = s;
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y = z = 0;
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for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
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if (nd < 9)
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y = 10 * y + c - '0';
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else if (nd < 16)
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z = 10 * z + c - '0';
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nd0 = nd;
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if (c == '.')
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{
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c = *++s;
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if (!nd)
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{
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for (; c == '0'; c = *++s)
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nz++;
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if (c > '0' && c <= '9')
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{
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s0 = s;
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nf += nz;
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nz = 0;
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goto have_dig;
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}
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goto dig_done;
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}
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for (; c >= '0' && c <= '9'; c = *++s)
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{
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have_dig:
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nz++;
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if (c -= '0')
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{
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nf += nz;
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for (i = 1; i < nz; i++)
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if (nd++ < 9)
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y *= 10;
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else if (nd <= DBL_DIG + 1)
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z *= 10;
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if (nd++ < 9)
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y = 10 * y + c;
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else if (nd <= DBL_DIG + 1)
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z = 10 * z + c;
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nz = 0;
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}
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}
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}
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dig_done:
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e = 0;
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if (c == 'e' || c == 'E')
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{
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if (!nd && !nz && !nz0)
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{
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s = s00;
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goto ret;
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}
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s00 = s;
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esign = 0;
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switch (c = *++s)
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{
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case '-':
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esign = 1;
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case '+':
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c = *++s;
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}
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if (c >= '0' && c <= '9')
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{
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while (c == '0')
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c = *++s;
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if (c > '0' && c <= '9')
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{
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e = c - '0';
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s1 = s;
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while ((c = *++s) >= '0' && c <= '9')
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e = 10 * e + c - '0';
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if (s - s1 > 8)
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/* Avoid confusion from exponents
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* so large that e might overflow.
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*/
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e = 9999999L;
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if (esign)
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e = -e;
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}
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else
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e = 0;
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}
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else
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s = s00;
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}
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if (!nd)
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{
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if (!nz && !nz0)
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s = s00;
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goto ret;
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}
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e1 = e -= nf;
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/* Now we have nd0 digits, starting at s0, followed by a
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* decimal point, followed by nd-nd0 digits. The number we're
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* after is the integer represented by those digits times
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* 10**e */
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if (!nd0)
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nd0 = nd;
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k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1;
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rv.d = y;
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if (k > 9)
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rv.d = tens[k - 9] * rv.d + z;
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bd0 = 0;
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if (nd <= DBL_DIG
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#ifndef RND_PRODQUOT
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&& FLT_ROUNDS == 1
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#endif
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)
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{
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if (!e)
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goto ret;
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if (e > 0)
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{
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if (e <= Ten_pmax)
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{
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#ifdef VAX
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goto vax_ovfl_check;
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#else
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/* rv.d = */ rounded_product (rv.d, tens[e]);
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goto ret;
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#endif
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}
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i = DBL_DIG - nd;
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if (e <= Ten_pmax + i)
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{
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/* A fancier test would sometimes let us do
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* this for larger i values.
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*/
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e -= i;
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rv.d *= tens[i];
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#ifdef VAX
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/* VAX exponent range is so narrow we must
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* worry about overflow here...
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*/
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vax_ovfl_check:
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word0 (rv) -= P * Exp_msk1;
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/* rv.d = */ rounded_product (rv.d, tens[e]);
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if ((word0 (rv) & Exp_mask)
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> Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P))
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goto ovfl;
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word0 (rv) += P * Exp_msk1;
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#else
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/* rv.d = */ rounded_product (rv.d, tens[e]);
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#endif
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goto ret;
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}
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}
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#ifndef Inaccurate_Divide
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else if (e >= -Ten_pmax)
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{
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/* rv.d = */ rounded_quotient (rv.d, tens[-e]);
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goto ret;
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}
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#endif
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}
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e1 += nd - k;
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/* Get starting approximation = rv.d * 10**e1 */
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if (e1 > 0)
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{
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if ((i = e1 & 15) != 0)
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rv.d *= tens[i];
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if (e1 &= ~15)
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{
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if (e1 > DBL_MAX_10_EXP)
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{
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ovfl:
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ptr->_errno = ERANGE;
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#ifdef _HAVE_STDC
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rv.d = HUGE_VAL;
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#else
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/* Can't trust HUGE_VAL */
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#ifdef IEEE_Arith
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word0 (rv) = Exp_mask;
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#ifndef _DOUBLE_IS_32BITS
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word1 (rv) = 0;
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#endif
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#else
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word0 (rv) = Big0;
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#ifndef _DOUBLE_IS_32BITS
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word1 (rv) = Big1;
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#endif
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#endif
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#endif
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if (bd0)
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goto retfree;
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goto ret;
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}
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if (e1 >>= 4)
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{
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for (j = 0; e1 > 1; j++, e1 >>= 1)
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if (e1 & 1)
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rv.d *= bigtens[j];
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/* The last multiplication could overflow. */
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word0 (rv) -= P * Exp_msk1;
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rv.d *= bigtens[j];
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if ((z = word0 (rv) & Exp_mask)
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> Exp_msk1 * (DBL_MAX_EXP + Bias - P))
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goto ovfl;
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if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P))
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{
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/* set to largest number */
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/* (Can't trust DBL_MAX) */
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word0 (rv) = Big0;
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#ifndef _DOUBLE_IS_32BITS
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word1 (rv) = Big1;
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#endif
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}
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else
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word0 (rv) += P * Exp_msk1;
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}
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}
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}
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else if (e1 < 0)
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{
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e1 = -e1;
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if ((i = e1 & 15) != 0)
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rv.d /= tens[i];
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if (e1 &= ~15)
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{
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e1 >>= 4;
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if (e1 >= 1 << n_bigtens)
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goto undfl;
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for (j = 0; e1 > 1; j++, e1 >>= 1)
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if (e1 & 1)
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rv.d *= tinytens[j];
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/* The last multiplication could underflow. */
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rv0.d = rv.d;
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rv.d *= tinytens[j];
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if (!rv.d)
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{
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rv.d = 2. * rv0.d;
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rv.d *= tinytens[j];
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if (!rv.d)
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{
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undfl:
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rv.d = 0.;
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ptr->_errno = ERANGE;
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if (bd0)
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goto retfree;
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goto ret;
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}
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#ifndef _DOUBLE_IS_32BITS
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word0 (rv) = Tiny0;
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word1 (rv) = Tiny1;
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#else
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word0 (rv) = Tiny1;
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#endif
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/* The refinement below will clean
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* this approximation up.
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*/
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}
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}
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}
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/* Now the hard part -- adjusting rv to the correct value.*/
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/* Put digits into bd: true value = bd * 10^e */
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bd0 = s2b (ptr, s0, nd0, nd, y);
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for (;;)
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{
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bd = Balloc (ptr, bd0->_k);
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Bcopy (bd, bd0);
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bb = d2b (ptr, rv.d, &bbe, &bbbits); /* rv.d = bb * 2^bbe */
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bs = i2b (ptr, 1);
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if (e >= 0)
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{
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bb2 = bb5 = 0;
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bd2 = bd5 = e;
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}
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else
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{
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bb2 = bb5 = -e;
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bd2 = bd5 = 0;
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}
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if (bbe >= 0)
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bb2 += bbe;
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else
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bd2 -= bbe;
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bs2 = bb2;
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#ifdef Sudden_Underflow
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#ifdef IBM
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j = 1 + 4 * P - 3 - bbbits + ((bbe + bbbits - 1) & 3);
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#else
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j = P + 1 - bbbits;
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#endif
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#else
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i = bbe + bbbits - 1; /* logb(rv.d) */
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if (i < Emin) /* denormal */
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j = bbe + (P - Emin);
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else
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j = P + 1 - bbbits;
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#endif
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bb2 += j;
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bd2 += j;
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i = bb2 < bd2 ? bb2 : bd2;
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if (i > bs2)
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i = bs2;
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if (i > 0)
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{
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bb2 -= i;
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bd2 -= i;
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bs2 -= i;
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}
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if (bb5 > 0)
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{
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bs = pow5mult (ptr, bs, bb5);
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bb1 = mult (ptr, bs, bb);
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Bfree (ptr, bb);
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bb = bb1;
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}
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if (bb2 > 0)
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bb = lshift (ptr, bb, bb2);
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if (bd5 > 0)
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bd = pow5mult (ptr, bd, bd5);
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if (bd2 > 0)
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bd = lshift (ptr, bd, bd2);
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if (bs2 > 0)
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bs = lshift (ptr, bs, bs2);
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delta = diff (ptr, bb, bd);
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dsign = delta->_sign;
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delta->_sign = 0;
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i = cmp (delta, bs);
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if (i < 0)
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{
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/* Error is less than half an ulp -- check for
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* special case of mantissa a power of two.
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*/
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if (dsign || word1 (rv) || word0 (rv) & Bndry_mask)
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break;
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delta = lshift (ptr, delta, Log2P);
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if (cmp (delta, bs) > 0)
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goto drop_down;
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break;
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}
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if (i == 0)
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{
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/* exactly half-way between */
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if (dsign)
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{
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if ((word0 (rv) & Bndry_mask1) == Bndry_mask1
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&& word1 (rv) == 0xffffffff)
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{
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/*boundary case -- increment exponent*/
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word0 (rv) = (word0 (rv) & Exp_mask)
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+ Exp_msk1
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#ifdef IBM
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| Exp_msk1 >> 4
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#endif
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;
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#ifndef _DOUBLE_IS_32BITS
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word1 (rv) = 0;
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#endif
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break;
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}
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}
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else if (!(word0 (rv) & Bndry_mask) && !word1 (rv))
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{
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drop_down:
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/* boundary case -- decrement exponent */
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#ifdef Sudden_Underflow
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L = word0 (rv) & Exp_mask;
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#ifdef IBM
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if (L < Exp_msk1)
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#else
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if (L <= Exp_msk1)
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#endif
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goto undfl;
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L -= Exp_msk1;
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#else
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L = (word0 (rv) & Exp_mask) - Exp_msk1;
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#endif
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word0 (rv) = L | Bndry_mask1;
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#ifndef _DOUBLE_IS_32BITS
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word1 (rv) = 0xffffffff;
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#endif
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#ifdef IBM
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goto cont;
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#else
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break;
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#endif
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}
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#ifndef ROUND_BIASED
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if (!(word1 (rv) & LSB))
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break;
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#endif
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if (dsign)
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rv.d += ulp (rv.d);
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#ifndef ROUND_BIASED
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else
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|
{
|
|
rv.d -= ulp (rv.d);
|
|
#ifndef Sudden_Underflow
|
|
if (!rv.d)
|
|
goto undfl;
|
|
#endif
|
|
}
|
|
#endif
|
|
break;
|
|
}
|
|
if ((aadj = ratio (delta, bs)) <= 2.)
|
|
{
|
|
if (dsign)
|
|
aadj = aadj1 = 1.;
|
|
else if (word1 (rv) || word0 (rv) & Bndry_mask)
|
|
{
|
|
#ifndef Sudden_Underflow
|
|
if (word1 (rv) == Tiny1 && !word0 (rv))
|
|
goto undfl;
|
|
#endif
|
|
aadj = 1.;
|
|
aadj1 = -1.;
|
|
}
|
|
else
|
|
{
|
|
/* special case -- power of FLT_RADIX to be */
|
|
/* rounded down... */
|
|
|
|
if (aadj < 2. / FLT_RADIX)
|
|
aadj = 1. / FLT_RADIX;
|
|
else
|
|
aadj *= 0.5;
|
|
aadj1 = -aadj;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
aadj *= 0.5;
|
|
aadj1 = dsign ? aadj : -aadj;
|
|
#ifdef Check_FLT_ROUNDS
|
|
switch (FLT_ROUNDS)
|
|
{
|
|
case 2: /* towards +infinity */
|
|
aadj1 -= 0.5;
|
|
break;
|
|
case 0: /* towards 0 */
|
|
case 3: /* towards -infinity */
|
|
aadj1 += 0.5;
|
|
}
|
|
#else
|
|
if (FLT_ROUNDS == 0)
|
|
aadj1 += 0.5;
|
|
#endif
|
|
}
|
|
y = word0 (rv) & Exp_mask;
|
|
|
|
/* Check for overflow */
|
|
|
|
if (y == Exp_msk1 * (DBL_MAX_EXP + Bias - 1))
|
|
{
|
|
rv0.d = rv.d;
|
|
word0 (rv) -= P * Exp_msk1;
|
|
adj = aadj1 * ulp (rv.d);
|
|
rv.d += adj;
|
|
if ((word0 (rv) & Exp_mask) >=
|
|
Exp_msk1 * (DBL_MAX_EXP + Bias - P))
|
|
{
|
|
if (word0 (rv0) == Big0 && word1 (rv0) == Big1)
|
|
goto ovfl;
|
|
#ifdef _DOUBLE_IS_32BITS
|
|
word0 (rv) = Big1;
|
|
#else
|
|
word0 (rv) = Big0;
|
|
word1 (rv) = Big1;
|
|
#endif
|
|
goto cont;
|
|
}
|
|
else
|
|
word0 (rv) += P * Exp_msk1;
|
|
}
|
|
else
|
|
{
|
|
#ifdef Sudden_Underflow
|
|
if ((word0 (rv) & Exp_mask) <= P * Exp_msk1)
|
|
{
|
|
rv0.d = rv.d;
|
|
word0 (rv) += P * Exp_msk1;
|
|
adj = aadj1 * ulp (rv.d);
|
|
rv.d += adj;
|
|
#ifdef IBM
|
|
if ((word0 (rv) & Exp_mask) < P * Exp_msk1)
|
|
#else
|
|
if ((word0 (rv) & Exp_mask) <= P * Exp_msk1)
|
|
#endif
|
|
{
|
|
if (word0 (rv0) == Tiny0
|
|
&& word1 (rv0) == Tiny1)
|
|
goto undfl;
|
|
word0 (rv) = Tiny0;
|
|
word1 (rv) = Tiny1;
|
|
goto cont;
|
|
}
|
|
else
|
|
word0 (rv) -= P * Exp_msk1;
|
|
}
|
|
else
|
|
{
|
|
adj = aadj1 * ulp (rv.d);
|
|
rv.d += adj;
|
|
}
|
|
#else
|
|
/* Compute adj so that the IEEE rounding rules will
|
|
* correctly round rv.d + adj in some half-way cases.
|
|
* If rv.d * ulp(rv.d) is denormalized (i.e.,
|
|
* y <= (P-1)*Exp_msk1), we must adjust aadj to avoid
|
|
* trouble from bits lost to denormalization;
|
|
* example: 1.2e-307 .
|
|
*/
|
|
if (y <= (P - 1) * Exp_msk1 && aadj >= 1.)
|
|
{
|
|
aadj1 = (double) (int) (aadj + 0.5);
|
|
if (!dsign)
|
|
aadj1 = -aadj1;
|
|
}
|
|
adj = aadj1 * ulp (rv.d);
|
|
rv.d += adj;
|
|
#endif
|
|
}
|
|
z = word0 (rv) & Exp_mask;
|
|
if (y == z)
|
|
{
|
|
/* Can we stop now? */
|
|
L = aadj;
|
|
aadj -= L;
|
|
/* The tolerances below are conservative. */
|
|
if (dsign || word1 (rv) || word0 (rv) & Bndry_mask)
|
|
{
|
|
if (aadj < .4999999 || aadj > .5000001)
|
|
break;
|
|
}
|
|
else if (aadj < .4999999 / FLT_RADIX)
|
|
break;
|
|
}
|
|
cont:
|
|
Bfree (ptr, bb);
|
|
Bfree (ptr, bd);
|
|
Bfree (ptr, bs);
|
|
Bfree (ptr, delta);
|
|
}
|
|
retfree:
|
|
Bfree (ptr, bb);
|
|
Bfree (ptr, bd);
|
|
Bfree (ptr, bs);
|
|
Bfree (ptr, bd0);
|
|
Bfree (ptr, delta);
|
|
ret:
|
|
if (se)
|
|
*se = (char *) s;
|
|
return sign ? -rv.d : rv.d;
|
|
}
|
|
|
|
#ifndef NO_REENT
|
|
|
|
double
|
|
_DEFUN (strtod, (s00, se),
|
|
_CONST char *s00 _AND char **se)
|
|
{
|
|
return _strtod_r (_REENT, s00, se);
|
|
}
|
|
|
|
float
|
|
_DEFUN (strtodf, (s00, se),
|
|
_CONST char *s00 _AND
|
|
char **se)
|
|
{
|
|
return _strtod_r (_REENT, s00, se);
|
|
}
|
|
|
|
#endif
|