diff options
author | Jeff Johnston <jjohnstn@redhat.com> | 2006-06-22 17:59:52 +0000 |
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committer | Jeff Johnston <jjohnstn@redhat.com> | 2006-06-22 17:59:52 +0000 |
commit | f489b5943c8f8655b0a3caddd38114111576ab35 (patch) | |
tree | e5db470212203f6eb28752047e58cb287418bc1b /newlib/libc/stdlib/strtod.c | |
parent | 09fd280ca40c0b1211d3e8b31c3a813150c57c6b (diff) | |
download | newlib-f489b5943c8f8655b0a3caddd38114111576ab35.zip newlib-f489b5943c8f8655b0a3caddd38114111576ab35.tar.gz newlib-f489b5943c8f8655b0a3caddd38114111576ab35.tar.bz2 |
2006-06-22 Jeff Johnston <jjohnstn@redhat.com>
* libc/stdlib/Makefile.am: Add new gdtoa routines.
* libc/stdlib/Makefile.in: Regenerated.
* libc/stdlib/gd_qnan.h: New file.
* libc/stdlib/gdtoa-gethex.c: Ditto.
* libc/stdlib/gdtoa-hexnan.c: Ditto.
* libc/stdlib/gdtoa.h: Ditto.
* libc/stdlib/mprec.c: Add new helper routines needed by
the new gdtoa code.
* libc/stdlib/mprec.h: Integrate some defines and prototypes
used by gdtoa routines here.
* libc/stdlib/strtod.c: Rebased on David M. Gay's gdtoa-strtod.c
which adds C99 support such as nan, inf, and hexadecimal input
format.
Diffstat (limited to 'newlib/libc/stdlib/strtod.c')
-rw-r--r-- | newlib/libc/stdlib/strtod.c | 1597 |
1 files changed, 991 insertions, 606 deletions
diff --git a/newlib/libc/stdlib/strtod.c b/newlib/libc/stdlib/strtod.c index 9b70dfc..57297e0 100644 --- a/newlib/libc/stdlib/strtod.c +++ b/newlib/libc/stdlib/strtod.c @@ -70,37 +70,130 @@ Supporting OS subroutines required: <<close>>, <<fstat>>, <<isatty>>, */ /**************************************************************** - * - * The author of this software is David M. Gay. - * - * Copyright (c) 1991 by AT&T. - * - * 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 AUTHOR NOR AT&T MAKES ANY - * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY - * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE. - * - ***************************************************************/ - -/* Please send bug reports to - David M. Gay - AT&T Bell Laboratories, Room 2C-463 - 600 Mountain Avenue - Murray Hill, NJ 07974-2070 - U.S.A. - dmg@research.att.com or research!dmg - */ + +The author of this software is David M. Gay. + +Copyright (C) 1998-2001 by Lucent Technologies +All Rights Reserved + +Permission to use, copy, modify, and distribute this software and +its documentation for any purpose and without fee is hereby +granted, provided that the above copyright notice appear in all +copies and that both that the copyright notice and this +permission notice and warranty disclaimer appear in supporting +documentation, and that the name of Lucent or any of its entities +not be used in advertising or publicity pertaining to +distribution of the software without specific, written prior +permission. + +LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, +INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. +IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY +SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES +WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER +IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, +ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF +THIS SOFTWARE. + +****************************************************************/ + +/* Please send bug reports to David M. Gay (dmg at acm dot org, + * with " at " changed at "@" and " dot " changed to "."). */ + +/* Original file gdtoa-strtod.c Modified 06-21-2006 by Jeff Johnston to work within newlib. */ #include <_ansi.h> -#include <reent.h> +#include <errno.h> #include <string.h> #include "mprec.h" +#include "gdtoa.h" +#include "gd_qnan.h" + +/* #ifndef NO_FENV_H */ +/* #include <fenv.h> */ +/* #endif */ + +#ifdef USE_LOCALE +#include "locale.h" +#endif + +#ifdef IEEE_Arith +#ifndef NO_IEEE_Scale +#define Avoid_Underflow +#undef tinytens +/* The factor of 2^53 in tinytens[4] helps us avoid setting the underflow */ +/* flag unnecessarily. It leads to a song and dance at the end of strtod. */ +static _CONST double tinytens[] = { 1e-16, 1e-32, 1e-64, 1e-128, + 9007199254740992.e-256 + }; +#endif +#endif + +#ifdef Honor_FLT_ROUNDS +#define Rounding rounding +#undef Check_FLT_ROUNDS +#define Check_FLT_ROUNDS +#else +#define Rounding Flt_Rounds +#endif + +static void +_DEFUN (ULtod, (L, bits, exp, k), + __ULong *L _AND + __ULong *bits _AND + Long exp _AND + int k) +{ + switch(k & STRTOG_Retmask) { + case STRTOG_NoNumber: + case STRTOG_Zero: + L[0] = L[1] = 0; + break; + + case STRTOG_Denormal: + L[_1] = bits[0]; + L[_0] = bits[1]; + break; + + case STRTOG_Normal: + case STRTOG_NaNbits: + L[_1] = bits[0]; + L[_0] = (bits[1] & ~0x100000) | ((exp + 0x3ff + 52) << 20); + break; + + case STRTOG_Infinite: + L[_0] = 0x7ff00000; + L[_1] = 0; + break; + + case STRTOG_NaN: + L[_0] = 0x7fffffff; + L[_1] = (__ULong)-1; + } + if (k & STRTOG_Neg) + L[_0] |= 0x80000000L; +} + +#ifdef INFNAN_CHECK +static int +_DEFUN (match, (sp, t), + _CONST char **sp _AND + char *t) +{ + int c, d; + _CONST char *s = *sp; + + while( (d = *t++) !=0) { + if ((c = *++s) >= 'A' && c <= 'Z') + c += 'a' - 'A'; + if (c != d) + return 0; + } + *sp = s + 1; + return 1; +} +#endif /* INFNAN_CHECK */ + double _DEFUN (_strtod_r, (ptr, s00, se), @@ -108,627 +201,919 @@ _DEFUN (_strtod_r, (ptr, s00, se), _CONST char *s00 _AND char **se) { - int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e1, esign, i, j, - k, nd, nd0, nf, nz, nz0, sign; - long e; - _CONST char *s, *s0, *s1, *s2; - double aadj, aadj1, adj; - long L; - unsigned long z; - __ULong y; - union double_union rv, rv0; - int nanflag; - - _Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; - sign = nz0 = nz = nanflag = 0; - rv.d = 0.; - for (s = s00;; s++) - switch (*s) - { - case '-': - sign = 1; - /* no break */ - case '+': - if (*++s) - goto break2; - /* no break */ - case 0: - s = s00; - goto ret; - case '\t': - case '\n': - case '\v': - case '\f': - case '\r': - case ' ': - continue; - default: - goto break2; - } -break2: - if (*s == 'n' || *s == 'N') - { - ++s; - if (*s == 'a' || *s == 'A') - { - ++s; - if (*s == 'n' || *s == 'N') - { - nanflag = 1; - ++s; - goto ret; - } - } - s = s00; - goto ret; - } - else if (*s == '0') - { - nz0 = 1; - while (*++s == '0'); - if (!*s) - goto ret; - } - s0 = s; - y = z = 0; - for (nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) - if (nd < 9) - y = 10 * y + c - '0'; - else if (nd < 16) - z = 10 * z + c - '0'; - nd0 = nd; - if (c == '.') - { - c = *++s; - if (!nd) - { - for (; c == '0'; c = *++s) - nz++; - if (c > '0' && c <= '9') - { - s0 = s; - nf += nz; - nz = 0; - goto have_dig; - } - goto dig_done; - } - for (; c >= '0' && c <= '9'; c = *++s) - { - have_dig: - nz++; - if (c -= '0') - { - nf += nz; - for (i = 1; i < nz; i++) - if (nd++ < 9) - y *= 10; - else if (nd <= DBL_DIG + 1) - z *= 10; - if (nd++ < 9) - y = 10 * y + c; - else if (nd <= DBL_DIG + 1) - z = 10 * z + c; - nz = 0; - } - } - } -dig_done: - e = 0; - if (c == 'e' || c == 'E') - { - if (!nd && !nz && !nz0) - { - s = s00; - goto ret; - } - s2 = s; - esign = 0; - switch (c = *++s) - { - case '-': - esign = 1; - case '+': - c = *++s; - } - if (c >= '0' && c <= '9') - { - while (c == '0') - c = *++s; - if (c > '0' && c <= '9') - { - e = c - '0'; - s1 = s; - while ((c = *++s) >= '0' && c <= '9') - e = 10 * e + c - '0'; - if (s - s1 > 8) - /* Avoid confusion from exponents - * so large that e might overflow. - */ - e = 9999999L; - if (esign) - e = -e; - } - else - e = 0; - } - else - s = s2; - } - if (!nd) - { - if (!nz && !nz0) - s = s00; - goto ret; - } - e1 = e -= nf; - - /* Now we have nd0 digits, starting at s0, followed by a - * decimal point, followed by nd-nd0 digits. The number we're - * after is the integer represented by those digits times - * 10**e */ - - if (!nd0) - nd0 = nd; - k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; - rv.d = y; - if (k > 9) - rv.d = tens[k - 9] * rv.d + z; - bd0 = 0; - if (nd <= DBL_DIG +#ifdef Avoid_Underflow + int scale; +#endif + int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, decpt, dsign, + e, e1, esign, i, j, k, nd, nd0, nf, nz, nz0, sign; + _CONST char *s, *s0, *s1; + double aadj, aadj1, adj, rv, rv0; + Long L; + __ULong y, z; + _Bigint *bb, *bb1, *bd, *bd0, *bs, *delta; +#ifdef SET_INEXACT + int inexact, oldinexact; +#endif +#ifdef Honor_FLT_ROUNDS + int rounding; +#endif + + delta = bs = bd = NULL; + sign = nz0 = nz = decpt = 0; + dval(rv) = 0.; + for(s = s00;;s++) switch(*s) { + case '-': + sign = 1; + /* no break */ + case '+': + if (*++s) + goto break2; + /* no break */ + case 0: + goto ret0; + case '\t': + case '\n': + case '\v': + case '\f': + case '\r': + case ' ': + continue; + default: + goto break2; + } + break2: + if (*s == '0') { +#ifndef NO_HEX_FP + { + static FPI fpi = { 53, 1-1023-53+1, 2046-1023-53+1, 1, SI }; + Long exp; + __ULong bits[2]; + switch(s[1]) { + case 'x': + case 'X': + { +#if defined(FE_DOWNWARD) && defined(FE_TONEAREST) && defined(FE_TOWARDZERO) && defined(FE_UPWARD) + FPI fpi1 = fpi; + switch(fegetround()) { + case FE_TOWARDZERO: fpi1.rounding = 0; break; + case FE_UPWARD: fpi1.rounding = 2; break; + case FE_DOWNWARD: fpi1.rounding = 3; + } +#else +#define fpi1 fpi +#endif + switch((i = gethex(ptr, &s, &fpi1, &exp, &bb, sign)) & STRTOG_Retmask) { + case STRTOG_NoNumber: + s = s00; + sign = 0; + case STRTOG_Zero: + break; + default: + if (bb) { + copybits(bits, fpi.nbits, bb); + Bfree(ptr,bb); + } + ULtod(((U*)&rv)->L, bits, exp, i); + }} + goto ret; + } + } +#endif + nz0 = 1; + while(*++s == '0') ; + if (!*s) + goto ret; + } + s0 = s; + y = z = 0; + for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++) + if (nd < 9) + y = 10*y + c - '0'; + else if (nd < 16) + z = 10*z + c - '0'; + nd0 = nd; +#ifdef USE_LOCALE + if (c == *localeconv()->decimal_point) +#else + if (c == '.') +#endif + { + decpt = 1; + c = *++s; + if (!nd) { + for(; c == '0'; c = *++s) + nz++; + if (c > '0' && c <= '9') { + s0 = s; + nf += nz; + nz = 0; + goto have_dig; + } + goto dig_done; + } + for(; c >= '0' && c <= '9'; c = *++s) { + have_dig: + nz++; + if (c -= '0') { + nf += nz; + for(i = 1; i < nz; i++) + if (nd++ < 9) + y *= 10; + else if (nd <= DBL_DIG + 1) + z *= 10; + if (nd++ < 9) + y = 10*y + c; + else if (nd <= DBL_DIG + 1) + z = 10*z + c; + nz = 0; + } + } + } + dig_done: + e = 0; + if (c == 'e' || c == 'E') { + if (!nd && !nz && !nz0) { + goto ret0; + } + s00 = s; + esign = 0; + switch(c = *++s) { + case '-': + esign = 1; + case '+': + c = *++s; + } + if (c >= '0' && c <= '9') { + while(c == '0') + c = *++s; + if (c > '0' && c <= '9') { + L = c - '0'; + s1 = s; + while((c = *++s) >= '0' && c <= '9') + L = 10*L + c - '0'; + if (s - s1 > 8 || L > 19999) + /* Avoid confusion from exponents + * so large that e might overflow. + */ + e = 19999; /* safe for 16 bit ints */ + else + e = (int)L; + if (esign) + e = -e; + } + else + e = 0; + } + else + s = s00; + } + if (!nd) { + if (!nz && !nz0) { +#ifdef INFNAN_CHECK + /* Check for Nan and Infinity */ + __ULong bits[2]; + static FPI fpinan = /* only 52 explicit bits */ + { 52, 1-1023-53+1, 2046-1023-53+1, 1, SI }; + if (!decpt) + switch(c) { + case 'i': + case 'I': + if (match(&s,"nf")) { + --s; + if (!match(&s,"inity")) + ++s; + dword0(rv) = 0x7ff00000; + dword1(rv) = 0; + goto ret; + } + break; + case 'n': + case 'N': + if (match(&s, "an")) { +#ifndef No_Hex_NaN + if (*s == '(' /*)*/ + && hexnan(&s, &fpinan, bits) + == STRTOG_NaNbits) { + dword0(rv) = 0x7ff00000 | bits[1]; + dword1(rv) = bits[0]; + } + else { +#endif + dword0(rv) = NAN_WORD0; + dword1(rv) = NAN_WORD1; +#ifndef No_Hex_NaN + } +#endif + goto ret; + } + } +#endif /* INFNAN_CHECK */ + ret0: + s = s00; + sign = 0; + } + goto ret; + } + e1 = e -= nf; + + /* Now we have nd0 digits, starting at s0, followed by a + * decimal point, followed by nd-nd0 digits. The number we're + * after is the integer represented by those digits times + * 10**e */ + + if (!nd0) + nd0 = nd; + k = nd < DBL_DIG + 1 ? nd : DBL_DIG + 1; + dval(rv) = y; + if (k > 9) { +#ifdef SET_INEXACT + if (k > DBL_DIG) + oldinexact = get_inexact(); +#endif + dval(rv) = tens[k - 9] * dval(rv) + z; + } + bd0 = 0; + if (nd <= DBL_DIG #ifndef RND_PRODQUOT - && FLT_ROUNDS == 1 -#endif - ) - { - if (!e) - goto ret; - if (e > 0) - { - if (e <= Ten_pmax) - { +#ifndef Honor_FLT_ROUNDS + && Flt_Rounds == 1 +#endif +#endif + ) { + if (!e) + goto ret; + if (e > 0) { + if (e <= Ten_pmax) { #ifdef VAX - goto vax_ovfl_check; + goto vax_ovfl_check; #else - /* rv.d = */ rounded_product (rv.d, tens[e]); - goto ret; -#endif - } - i = DBL_DIG - nd; - if (e <= Ten_pmax + i) - { - /* A fancier test would sometimes let us do +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv = -rv; + sign = 0; + } +#endif + /* rv = */ rounded_product(dval(rv), tens[e]); + goto ret; +#endif + } + i = DBL_DIG - nd; + if (e <= Ten_pmax + i) { + /* A fancier test would sometimes let us do * this for larger i values. */ - e -= i; - rv.d *= tens[i]; +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv = -rv; + sign = 0; + } +#endif + e -= i; + dval(rv) *= tens[i]; #ifdef VAX - /* VAX exponent range is so narrow we must - * worry about overflow here... - */ - vax_ovfl_check: - word0 (rv) -= P * Exp_msk1; - /* rv.d = */ rounded_product (rv.d, tens[e]); - if ((word0 (rv) & Exp_mask) - > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) - goto ovfl; - word0 (rv) += P * Exp_msk1; + /* VAX exponent range is so narrow we must + * worry about overflow here... + */ + vax_ovfl_check: + dword0(rv) -= P*Exp_msk1; + /* rv = */ rounded_product(dval(rv), tens[e]); + if ((dword0(rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) + goto ovfl; + dword0(rv) += P*Exp_msk1; #else - /* rv.d = */ rounded_product (rv.d, tens[e]); + /* rv = */ rounded_product(dval(rv), tens[e]); #endif - goto ret; - } - } + goto ret; + } + } #ifndef Inaccurate_Divide - else if (e >= -Ten_pmax) - { - /* rv.d = */ rounded_quotient (rv.d, tens[-e]); - goto ret; - } -#endif - } - e1 += nd - k; - - /* Get starting approximation = rv.d * 10**e1 */ - - if (e1 > 0) - { - if ((i = e1 & 15) != 0) - rv.d *= tens[i]; - if (e1 &= ~15) - { - if (e1 > DBL_MAX_10_EXP) - { - ovfl: - ptr->_errno = ERANGE; -#ifdef _HAVE_STDC - rv.d = HUGE_VAL; -#else - /* Can't trust HUGE_VAL */ + else if (e >= -Ten_pmax) { +#ifdef Honor_FLT_ROUNDS + /* round correctly FLT_ROUNDS = 2 or 3 */ + if (sign) { + rv = -rv; + sign = 0; + } +#endif + /* rv = */ rounded_quotient(dval(rv), tens[-e]); + goto ret; + } +#endif + } + e1 += nd - k; + #ifdef IEEE_Arith - word0 (rv) = Exp_mask; -#ifndef _DOUBLE_IS_32BITS - word1 (rv) = 0; +#ifdef SET_INEXACT + inexact = 1; + if (k <= DBL_DIG) + oldinexact = get_inexact(); #endif -#else - word0 (rv) = Big0; -#ifndef _DOUBLE_IS_32BITS - word1 (rv) = Big1; -#endif -#endif -#endif - if (bd0) - goto retfree; - goto ret; - } - if (e1 >>= 4) - { - for (j = 0; e1 > 1; j++, e1 >>= 1) - if (e1 & 1) - rv.d *= bigtens[j]; - /* The last multiplication could overflow. */ - word0 (rv) -= P * Exp_msk1; - rv.d *= bigtens[j]; - if ((z = word0 (rv) & Exp_mask) - > Exp_msk1 * (DBL_MAX_EXP + Bias - P)) - goto ovfl; - if (z > Exp_msk1 * (DBL_MAX_EXP + Bias - 1 - P)) - { - /* set to largest number */ - /* (Can't trust DBL_MAX) */ - word0 (rv) = Big0; -#ifndef _DOUBLE_IS_32BITS - word1 (rv) = Big1; +#ifdef Avoid_Underflow + scale = 0; #endif +#ifdef Honor_FLT_ROUNDS + if ((rounding = Flt_Rounds) >= 2) { + if (sign) + rounding = rounding == 2 ? 0 : 2; + else + if (rounding != 2) + rounding = 0; } - else - word0 (rv) += P * Exp_msk1; - } - - } - } - else if (e1 < 0) - { - e1 = -e1; - if ((i = e1 & 15) != 0) - rv.d /= tens[i]; - if (e1 &= ~15) - { - e1 >>= 4; - if (e1 >= 1 << n_bigtens) - goto undfl; - for (j = 0; e1 > 1; j++, e1 >>= 1) - if (e1 & 1) - rv.d *= tinytens[j]; - /* The last multiplication could underflow. */ - rv0.d = rv.d; - rv.d *= tinytens[j]; - if (!rv.d) - { - rv.d = 2. * rv0.d; - rv.d *= tinytens[j]; - if (!rv.d) - { - undfl: - rv.d = 0.; - ptr->_errno = ERANGE; - if (bd0) - goto retfree; - goto ret; +#endif +#endif /*IEEE_Arith*/ + + /* Get starting approximation = rv * 10**e1 */ + + if (e1 > 0) { + if ( (i = e1 & 15) !=0) + dval(rv) *= tens[i]; + if (e1 &= ~15) { + if (e1 > DBL_MAX_10_EXP) { + ovfl: +#ifndef NO_ERRNO + ptr->_errno = ERANGE; +#endif + /* Can't trust HUGE_VAL */ +#ifdef IEEE_Arith +#ifdef Honor_FLT_ROUNDS + switch(rounding) { + case 0: /* toward 0 */ + case 3: /* toward -infinity */ + dword0(rv) = Big0; + dword1(rv) = Big1; + break; + default: + dword0(rv) = Exp_mask; + dword1(rv) = 0; + } +#else /*Honor_FLT_ROUNDS*/ + dword0(rv) = Exp_mask; + dword1(rv) = 0; +#endif /*Honor_FLT_ROUNDS*/ +#ifdef SET_INEXACT + /* set overflow bit */ + dval(rv0) = 1e300; + dval(rv0) *= dval(rv0); +#endif +#else /*IEEE_Arith*/ + dword0(rv) = Big0; + dword1(rv) = Big1; +#endif /*IEEE_Arith*/ + if (bd0) + goto retfree; + goto ret; + } + e1 >>= 4; + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(rv) *= bigtens[j]; + /* The last multiplication could overflow. */ + dword0(rv) -= P*Exp_msk1; + dval(rv) *= bigtens[j]; + if ((z = dword0(rv) & Exp_mask) + > Exp_msk1*(DBL_MAX_EXP+Bias-P)) + goto ovfl; + if (z > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) { + /* set to largest number */ + /* (Can't trust DBL_MAX) */ + dword0(rv) = Big0; + dword1(rv) = Big1; + } + else + dword0(rv) += P*Exp_msk1; + } } -#ifndef _DOUBLE_IS_32BITS - word0 (rv) = Tiny0; - word1 (rv) = Tiny1; -#else - word0 (rv) = Tiny1; -#endif - /* The refinement below will clean - * this approximation up. - */ - } - } - } - - /* Now the hard part -- adjusting rv to the correct value.*/ - - /* Put digits into bd: true value = bd * 10^e */ - - bd0 = s2b (ptr, s0, nd0, nd, y); - - for (;;) - { - bd = Balloc (ptr, bd0->_k); - Bcopy (bd, bd0); - bb = d2b (ptr, rv.d, &bbe, &bbbits); /* rv.d = bb * 2^bbe */ - bs = i2b (ptr, 1); - - if (e >= 0) - { - bb2 = bb5 = 0; - bd2 = bd5 = e; - } - else - { - bb2 = bb5 = -e; - bd2 = bd5 = 0; - } - if (bbe >= 0) - bb2 += bbe; - else - bd2 -= bbe; - bs2 = bb2; -#ifdef Sudden_Underflow -#ifdef IBM - j = 1 + 4 * P - 3 - bbbits + ((bbe + bbbits - 1) & 3); + else if (e1 < 0) { + e1 = -e1; + if ( (i = e1 & 15) !=0) + dval(rv) /= tens[i]; + if (e1 >>= 4) { + if (e1 >= 1 << n_bigtens) + goto undfl; +#ifdef Avoid_Underflow + if (e1 & Scale_Bit) + scale = 2*P; + for(j = 0; e1 > 0; j++, e1 >>= 1) + if (e1 & 1) + dval(rv) *= tinytens[j]; + if (scale && (j = 2*P + 1 - ((dword0(rv) & Exp_mask) + >> Exp_shift)) > 0) { + /* scaled rv is denormal; zap j low bits */ + if (j >= 32) { + dword1(rv) = 0; + if (j >= 53) + dword0(rv) = (P+2)*Exp_msk1; + else + dword0(rv) &= 0xffffffff << (j-32); + } + else + dword1(rv) &= 0xffffffff << j; + } #else - j = P + 1 - bbbits; + for(j = 0; e1 > 1; j++, e1 >>= 1) + if (e1 & 1) + dval(rv) *= tinytens[j]; + /* The last multiplication could underflow. */ + dval(rv0) = dval(rv); + dval(rv) *= tinytens[j]; + if (!dval(rv)) { + dval(rv) = 2.*dval(rv0); + dval(rv) *= tinytens[j]; #endif -#else - i = bbe + bbbits - 1; /* logb(rv.d) */ - if (i < Emin) /* denormal */ - j = bbe + (P - Emin); - else - j = P + 1 - bbbits; -#endif - bb2 += j; - bd2 += j; - i = bb2 < bd2 ? bb2 : bd2; - if (i > bs2) - i = bs2; - if (i > 0) - { - bb2 -= i; - bd2 -= i; - bs2 -= i; - } - if (bb5 > 0) - { - bs = pow5mult (ptr, bs, bb5); - bb1 = mult (ptr, bs, bb); - Bfree (ptr, bb); - bb = bb1; - } - if (bb2 > 0) - bb = lshift (ptr, bb, bb2); - if (bd5 > 0) - bd = pow5mult (ptr, bd, bd5); - if (bd2 > 0) - bd = lshift (ptr, bd, bd2); - if (bs2 > 0) - bs = lshift (ptr, bs, bs2); - delta = diff (ptr, bb, bd); - dsign = delta->_sign; - delta->_sign = 0; - i = cmp (delta, bs); - if (i < 0) - { - /* Error is less than half an ulp -- check for - * special case of mantissa a power of two. - */ - if (dsign || word1 (rv) || word0 (rv) & Bndry_mask) - break; - delta = lshift (ptr, delta, Log2P); - if (cmp (delta, bs) > 0) - goto drop_down; - break; - } - if (i == 0) - { - /* exactly half-way between */ - if (dsign) - { - if ((word0 (rv) & Bndry_mask1) == Bndry_mask1 - && word1 (rv) == 0xffffffff) - { - /*boundary case -- increment exponent*/ - word0 (rv) = (word0 (rv) & Exp_mask) - + Exp_msk1 -#ifdef IBM - | Exp_msk1 >> 4 + if (!dval(rv)) { + undfl: + dval(rv) = 0.; +#ifndef NO_ERRNO + ptr->_errno = ERANGE; #endif - ; -#ifndef _DOUBLE_IS_32BITS - word1 (rv) = 0; + if (bd0) + goto retfree; + goto ret; + } +#ifndef Avoid_Underflow + dword0(rv) = Tiny0; + dword1(rv) = Tiny1; + /* The refinement below will clean + * this approximation up. + */ + } #endif - break; + } } - } - else if (!(word0 (rv) & Bndry_mask) && !word1 (rv)) - { - drop_down: - /* boundary case -- decrement exponent */ + + /* Now the hard part -- adjusting rv to the correct value.*/ + + /* Put digits into bd: true value = bd * 10^e */ + + bd0 = s2b(ptr, s0, nd0, nd, y); + + for(;;) { + bd = Balloc(ptr,bd0->_k); + Bcopy(bd, bd0); + bb = d2b(ptr,dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ + bs = i2b(ptr,1); + + if (e >= 0) { + bb2 = bb5 = 0; + bd2 = bd5 = e; + } + else { + bb2 = bb5 = -e; + bd2 = bd5 = 0; + } + if (bbe >= 0) + bb2 += bbe; + else + bd2 -= bbe; + bs2 = bb2; +#ifdef Honor_FLT_ROUNDS + if (rounding != 1) + bs2++; +#endif +#ifdef Avoid_Underflow + j = bbe - scale; + i = j + bbbits - 1; /* logb(rv) */ + if (i < Emin) /* denormal */ + j += P - Emin; + else + j = P + 1 - bbbits; +#else /*Avoid_Underflow*/ #ifdef Sudden_Underflow - L = word0 (rv) & Exp_mask; #ifdef IBM - if (L < Exp_msk1) + j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else - if (L <= Exp_msk1) + j = P + 1 - bbbits; +#endif +#else /*Sudden_Underflow*/ + j = bbe; + i = j + bbbits - 1; /* logb(rv) */ + if (i < Emin) /* denormal */ + j += P - Emin; + else + j = P + 1 - bbbits; +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + bb2 += j; + bd2 += j; +#ifdef Avoid_Underflow + bd2 += scale; +#endif + i = bb2 < bd2 ? bb2 : bd2; + if (i > bs2) + i = bs2; + if (i > 0) { + bb2 -= i; + bd2 -= i; + bs2 -= i; + } + if (bb5 > 0) { + bs = pow5mult(ptr, bs, bb5); + bb1 = mult(ptr, bs, bb); + Bfree(ptr, bb); + bb = bb1; + } + if (bb2 > 0) + bb = lshift(ptr, bb, bb2); + if (bd5 > 0) + bd = pow5mult(ptr, bd, bd5); + if (bd2 > 0) + bd = lshift(ptr, bd, bd2); + if (bs2 > 0) + bs = lshift(ptr, bs, bs2); + delta = diff(ptr, bb, bd); + dsign = delta->_sign; + delta->_sign = 0; + i = cmp(delta, bs); +#ifdef Honor_FLT_ROUNDS + if (rounding != 1) { + if (i < 0) { + /* Error is less than an ulp */ + if (!delta->_x[0] && delta->_wds <= 1) { + /* exact */ +#ifdef SET_INEXACT + inexact = 0; #endif - goto undfl; - L -= Exp_msk1; + break; + } + if (rounding) { + if (dsign) { + adj = 1.; + goto apply_adj; + } + } + else if (!dsign) { + adj = -1.; + if (!dword1(rv) + && !(dword0(rv) & Frac_mask)) { + y = dword0(rv) & Exp_mask; +#ifdef Avoid_Underflow + if (!scale || y > 2*P*Exp_msk1) #else - L = (word0 (rv) & Exp_mask) - Exp_msk1; + if (y) #endif - word0 (rv) = L | Bndry_mask1; -#ifndef _DOUBLE_IS_32BITS - word1 (rv) = 0xffffffff; + { + delta = lshift(ptr, delta,Log2P); + if (cmp(delta, bs) <= 0) + adj = -0.5; + } + } + apply_adj: +#ifdef Avoid_Underflow + if (scale && (y = dword0(rv) & Exp_mask) + <= 2*P*Exp_msk1) + dword0(adj) += (2*P+1)*Exp_msk1 - y; +#else +#ifdef Sudden_Underflow + if ((dword0(rv) & Exp_mask) <= + P*Exp_msk1) { + dword0(rv) += P*Exp_msk1; + dval(rv) += adj*ulp(dval(rv)); + dword0(rv) -= P*Exp_msk1; + } + else +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + dval(rv) += adj*ulp(dval(rv)); + } + break; + } + adj = ratio(delta, bs); + if (adj < 1.) + adj = 1.; + if (adj <= 0x7ffffffe) { + /* adj = rounding ? ceil(adj) : floor(adj); */ + y = adj; + if (y != adj) { + if (!((rounding>>1) ^ dsign)) + y++; + adj = y; + } + } +#ifdef Avoid_Underflow + if (scale && (y = dword0(rv) & Exp_mask) <= 2*P*Exp_msk1) + dword0(adj) += (2*P+1)*Exp_msk1 - y; +#else +#ifdef Sudden_Underflow + if ((dword0(rv) & Exp_mask) <= P*Exp_msk1) { + dword0(rv) += P*Exp_msk1; + adj *= ulp(dval(rv)); + if (dsign) + dval(rv) += adj; + else + dval(rv) -= adj; + dword0(rv) -= P*Exp_msk1; + goto cont; + } +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + adj *= ulp(dval(rv)); + if (dsign) + dval(rv) += adj; + else + dval(rv) -= adj; + goto cont; + } +#endif /*Honor_FLT_ROUNDS*/ + + if (i < 0) { + /* Error is less than half an ulp -- check for + * special case of mantissa a power of two. + */ + if (dsign || dword1(rv) || dword0(rv) & Bndry_mask +#ifdef IEEE_Arith +#ifdef Avoid_Underflow + || (dword0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 +#else + || (dword0(rv) & Exp_mask) <= Exp_msk1 +#endif +#endif + ) { +#ifdef SET_INEXACT + if (!delta->x[0] && delta->wds <= 1) + inexact = 0; +#endif + break; + } + if (!delta->_x[0] && delta->_wds <= 1) { + /* exact result */ +#ifdef SET_INEXACT + inexact = 0; +#endif + break; + } + delta = lshift(ptr,delta,Log2P); + if (cmp(delta, bs) > 0) + goto drop_down; + break; + } + if (i == 0) { + /* exactly half-way between */ + if (dsign) { + if ((dword0(rv) & Bndry_mask1) == Bndry_mask1 + && dword1(rv) == ( +#ifdef Avoid_Underflow + (scale && (y = dword0(rv) & Exp_mask) <= 2*P*Exp_msk1) + ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : +#endif + 0xffffffff)) { + /*boundary case -- increment exponent*/ + dword0(rv) = (dword0(rv) & Exp_mask) + + Exp_msk1 +#ifdef IBM + | Exp_msk1 >> 4 +#endif + ; + dword1(rv) = 0; +#ifdef Avoid_Underflow + dsign = 0; #endif + break; + } + } + else if (!(dword0(rv) & Bndry_mask) && !dword1(rv)) { + drop_down: + /* boundary case -- decrement exponent */ +#ifdef Sudden_Underflow /*{{*/ + L = dword0(rv) & Exp_mask; +#ifdef IBM + if (L < Exp_msk1) +#else +#ifdef Avoid_Underflow + if (L <= (scale ? (2*P+1)*Exp_msk1 : Exp_msk1)) +#else + if (L <= Exp_msk1) +#endif /*Avoid_Underflow*/ +#endif /*IBM*/ + goto undfl; + L -= Exp_msk1; +#else /*Sudden_Underflow}{*/ +#ifdef Avoid_Underflow + if (scale) { + L = dword0(rv) & Exp_mask; + if (L <= (2*P+1)*Exp_msk1) { + if (L > (P+2)*Exp_msk1) + /* round even ==> */ + /* accept rv */ + break; + /* rv = smallest denormal */ + goto undfl; + } + } +#endif /*Avoid_Underflow*/ + L = (dword0(rv) & Exp_mask) - Exp_msk1; +#endif /*Sudden_Underflow}*/ + dword0(rv) = L | Bndry_mask1; + dword1(rv) = 0xffffffff; #ifdef IBM - goto cont; + goto cont; #else - break; + break; #endif - } + } #ifndef ROUND_BIASED - if (!(word1 (rv) & LSB)) - break; + if (!(dword1(rv) & LSB)) + break; #endif - if (dsign) - rv.d += ulp (rv.d); + if (dsign) + dval(rv) += ulp(dval(rv)); #ifndef ROUND_BIASED - else - { - rv.d -= ulp (rv.d); + else { + dval(rv) -= ulp(dval(rv)); #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) - { + if (!dval(rv)) + goto undfl; +#endif + } +#ifdef Avoid_Underflow + dsign = 1 - dsign; +#endif +#endif + break; + } + if ((aadj = ratio(delta, bs)) <= 2.) { + if (dsign) + aadj = aadj1 = 1.; + else if (dword1(rv) || dword0(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; + if (dword1(rv) == Tiny1 && !dword0(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; - } + switch(Rounding) { + 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; + if (Flt_Rounds == 0) + aadj1 += 0.5; +#endif /*Check_FLT_ROUNDS*/ + } + y = dword0(rv) & Exp_mask; + + /* Check for overflow */ + + if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { + dval(rv0) = dval(rv); + dword0(rv) -= P*Exp_msk1; + adj = aadj1 * ulp(dval(rv)); + dval(rv) += adj; + if ((dword0(rv) & Exp_mask) >= + Exp_msk1*(DBL_MAX_EXP+Bias-P)) { + if (dword0(rv0) == Big0 && dword1(rv0) == Big1) + goto ovfl; + dword0(rv) = Big0; + dword1(rv) = Big1; + goto cont; + } + else + dword0(rv) += P*Exp_msk1; + } + else { +#ifdef Avoid_Underflow + if (scale && y <= 2*P*Exp_msk1) { + if (aadj <= 0x7fffffff) { + if ((z = aadj) <= 0) + z = 1; + aadj = z; + aadj1 = dsign ? aadj : -aadj; + } + dword0(aadj1) += (2*P+1)*Exp_msk1 - y; + } + adj = aadj1 * ulp(dval(rv)); + dval(rv) += adj; #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; + if ((dword0(rv) & Exp_mask) <= P*Exp_msk1) { + dval(rv0) = dval(rv); + dword0(rv) += P*Exp_msk1; + adj = aadj1 * ulp(dval(rv)); + dval(rv) += adj; #ifdef IBM - if ((word0 (rv) & Exp_mask) < P * Exp_msk1) + if ((dword0(rv) & Exp_mask) < P*Exp_msk1) #else - if ((word0 (rv) & Exp_mask) <= P * Exp_msk1) + if ((dword0(rv) & Exp_mask) <= P*Exp_msk1) #endif - { - if (word0 (rv0) == Tiny0 - && word1 (rv0) == Tiny1) - goto undfl; - word0 (rv) = Tiny0; - word1 (rv) = Tiny1; - goto cont; + { + if (dword0(rv0) == Tiny0 + && dword1(rv0) == Tiny1) + goto undfl; + dword0(rv) = Tiny0; + dword1(rv) = Tiny1; + goto cont; + } + else + dword0(rv) -= P*Exp_msk1; + } + else { + adj = aadj1 * ulp(dval(rv)); + dval(rv) += adj; + } +#else /*Sudden_Underflow*/ + /* Compute adj so that the IEEE rounding rules will + * correctly round rv + adj in some half-way cases. + * If rv * ulp(rv) 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(dval(rv)); + dval(rv) += adj; +#endif /*Sudden_Underflow*/ +#endif /*Avoid_Underflow*/ + } + z = dword0(rv) & Exp_mask; +#ifndef SET_INEXACT +#ifdef Avoid_Underflow + if (!scale) +#endif + if (y == z) { + /* Can we stop now? */ + L = (Long)aadj; + aadj -= L; + /* The tolerances below are conservative. */ + if (dsign || dword1(rv) || dword0(rv) & Bndry_mask) { + if (aadj < .4999999 || aadj > .5000001) + break; + } + else if (aadj < .4999999/FLT_RADIX) + break; + } +#endif + cont: + Bfree(ptr,bb); + Bfree(ptr,bd); + Bfree(ptr,bs); + Bfree(ptr,delta); } - 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; - - if (nanflag) - return nan (NULL); - return (sign && (s != s00)) ? -rv.d : rv.d; +#ifdef SET_INEXACT + if (inexact) { + if (!oldinexact) { + dword0(rv0) = Exp_1 + (70 << Exp_shift); + dword1(rv0) = 0; + dval(rv0) += 1.; + } + } + else if (!oldinexact) + clear_inexact(); +#endif +#ifdef Avoid_Underflow + if (scale) { + dword0(rv0) = Exp_1 - 2*P*Exp_msk1; + dword1(rv0) = 0; + dval(rv) *= dval(rv0); +#ifndef NO_ERRNO + /* try to avoid the bug of testing an 8087 register value */ + if (dword0(rv) == 0 && dword1(rv) == 0) + ptr->_errno = ERANGE; +#endif + } +#endif /* Avoid_Underflow */ +#ifdef SET_INEXACT + if (inexact && !(dword0(rv) & Exp_mask)) { + /* set underflow bit */ + dval(rv0) = 1e-300; + dval(rv0) *= dval(rv0); + } +#endif + retfree: + Bfree(ptr,bb); + Bfree(ptr,bd); + Bfree(ptr,bs); + Bfree(ptr,bd0); + Bfree(ptr,delta); + ret: + if (se) + *se = (char *)s; + return sign ? -dval(rv) : dval(rv); } #ifndef NO_REENT |