/* FUNCTION <>, <>, <>, <>, <>, <>---string to double or float INDEX strtod INDEX strtof INDEX strtold INDEX strtod_l INDEX strtof_l INDEX strtold_l INDEX _strtod_r SYNOPSIS #include double strtod(const char *restrict <[str]>, char **restrict <[tail]>); float strtof(const char *restrict <[str]>, char **restrict <[tail]>); long double strtold(const char *restrict <[str]>, char **restrict <[tail]>); #include double strtod_l(const char *restrict <[str]>, char **restrict <[tail]>, locale_t <[locale]>); float strtof_l(const char *restrict <[str]>, char **restrict <[tail]>, locale_t <[locale]>); long double strtold_l(const char *restrict <[str]>, char **restrict <[tail]>, locale_t <[locale]>); double _strtod_r(void *<[reent]>, const char *restrict <[str]>, char **restrict <[tail]>); DESCRIPTION <>, <>, <> parse the character string <[str]>, producing a substring which can be converted to a double, float, or long double value, respectively. The substring converted is the longest initial subsequence of <[str]>, beginning with the first non-whitespace character, that has one of these formats: .[+|-]<[digits]>[.[<[digits]>]][(e|E)[+|-]<[digits]>] .[+|-].<[digits]>[(e|E)[+|-]<[digits]>] .[+|-](i|I)(n|N)(f|F)[(i|I)(n|N)(i|I)(t|T)(y|Y)] .[+|-](n|N)(a|A)(n|N)[<(>[<[hexdigits]>]<)>] .[+|-]0(x|X)<[hexdigits]>[.[<[hexdigits]>]][(p|P)[+|-]<[digits]>] .[+|-]0(x|X).<[hexdigits]>[(p|P)[+|-]<[digits]>] The substring contains no characters if <[str]> is empty, consists entirely of whitespace, or if the first non-whitespace character is something other than <<+>>, <<->>, <<.>>, or a digit, and cannot be parsed as infinity or NaN. If the platform does not support NaN, then NaN is treated as an empty substring. If the substring is empty, no conversion is done, and the value of <[str]> is stored in <<*<[tail]>>>. Otherwise, the substring is converted, and a pointer to the final string (which will contain at least the terminating null character of <[str]>) is stored in <<*<[tail]>>>. If you want no assignment to <<*<[tail]>>>, pass a null pointer as <[tail]>. This implementation returns the nearest machine number to the input decimal string. Ties are broken by using the IEEE round-even rule. However, <> is currently subject to double rounding errors. <>, <>, <> are like <>, <>, <> but perform the conversion based on the locale specified by the locale object locale. If <[locale]> is LC_GLOBAL_LOCALE or not a valid locale object, the behaviour is undefined. The alternate function <<_strtod_r>> is a reentrant version. The extra argument <[reent]> is a pointer to a reentrancy structure. RETURNS These functions return the converted substring value, if any. If no conversion could be performed, 0 is returned. If the correct value is out of the range of representable values, plus or minus <> (<>, <>) is returned, and <> is stored in errno. If the correct value would cause underflow, 0 is returned and <> is stored in errno. PORTABILITY <> is ANSI. <>, <> are C99. <>, <>, <> are GNU extensions. Supporting OS subroutines required: <>, <>, <>, <>, <>, <>, <>. */ /**************************************************************** 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. */ #define _GNU_SOURCE #include <_ansi.h> #include #include #include #include "mprec.h" #include "gdtoa.h" #include "gd_qnan.h" #include "../locale/setlocale.h" /* #ifndef NO_FENV_H */ /* #include */ /* #endif */ #include "locale.h" #ifdef IEEE_Arith #ifndef NO_IEEE_Scale #define Avoid_Underflow #undef tinytens /* The factor of 2^106 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, #ifdef _DOUBLE_IS_32BITS 0.0, 0.0, 0.0 #else 1e-64, 1e-128, 9007199254740992. * 9007199254740992.e-256 #endif }; #endif #endif #ifdef Honor_FLT_ROUNDS #define Rounding rounding #undef Check_FLT_ROUNDS #define Check_FLT_ROUNDS #else #define Rounding Flt_Rounds #endif #ifdef Avoid_Underflow /*{*/ static double sulp (U x, int scale) { U u; double rv; int i; rv = ulp(dval(x)); if (!scale || (i = 2*P + 1 - ((dword0(x) & Exp_mask) >> Exp_shift)) <= 0) return rv; /* Is there an example where i <= 0 ? */ dword0(u) = Exp_1 + ((__int32_t)i << Exp_shift); #ifndef _DOUBLE_IS_32BITS dword1(u) = 0; #endif return rv * u.d; } #endif /*}*/ #ifndef NO_HEX_FP static void ULtod (__ULong *L, __ULong *bits, Long exp, 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; } #endif /* !NO_HEX_FP */ double _strtod_l (struct _reent *ptr, const char *__restrict s00, char **__restrict se, locale_t loc) { #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, adj; U aadj1, rv, rv0; Long L; __ULong y, z; _Bigint *bb = NULL, *bb1, *bd = NULL, *bd0, *bs = NULL, *delta = NULL; #ifdef Avoid_Underflow __ULong Lsb, Lsb1; #endif #ifdef SET_INEXACT int inexact, oldinexact; #endif #ifdef Honor_FLT_ROUNDS int rounding; #endif struct lconv *lconv = __localeconv_l (loc); int dec_len = strlen (lconv->decimal_point); 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 const 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 the number is not hex, then the parse of 0 is still valid. */ s00 = s + 1; { #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, loc)) & STRTOG_Retmask) { case STRTOG_NoNumber: s = s00; sign = 0; /* FALLTHROUGH */ case STRTOG_Zero: break; default: if (bb) { copybits(bits, fpi.nbits, bb); Bfree(ptr,bb); } ULtod(rv.i, 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 z = 10*z + c - '0'; nd0 = nd; if (strncmp (s, lconv->decimal_point, dec_len) == 0) { decpt = 1; c = *(s += dec_len); 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 const 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; #ifndef _DOUBLE_IS_32BITS dword1(rv) = 0; #endif /*!_DOUBLE_IS_32BITS*/ 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]; #ifndef _DOUBLE_IS_32BITS dword1(rv) = bits[0]; #endif /*!_DOUBLE_IS_32BITS*/ } else { #endif dword0(rv) = NAN_WORD0; #ifndef _DOUBLE_IS_32BITS dword1(rv) = NAN_WORD1; #endif /*!_DOUBLE_IS_32BITS*/ #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 #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; #else #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(rv) = -dval(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. */ #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(rv) = -dval(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: 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 = */ rounded_product(dval(rv), tens[e]); #endif goto ret; } } #ifndef Inaccurate_Divide else if (e >= -Ten_pmax) { #ifdef Honor_FLT_ROUNDS /* round correctly FLT_ROUNDS = 2 or 3 */ if (sign) { dval(rv) = -dval(rv); sign = 0; } #endif /* rv = */ rounded_quotient(dval(rv), tens[-e]); goto ret; } #endif } e1 += nd - k; #ifdef IEEE_Arith #ifdef SET_INEXACT inexact = 1; if (k <= DBL_DIG) oldinexact = get_inexact(); #endif #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; } #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; #ifndef _DOUBLE_IS_32BITS dword1(rv) = Big1; #endif /*!_DOUBLE_IS_32BITS*/ break; default: dword0(rv) = Exp_mask; #ifndef _DOUBLE_IS_32BITS dword1(rv) = 0; #endif /*!_DOUBLE_IS_32BITS*/ } #else /*Honor_FLT_ROUNDS*/ dword0(rv) = Exp_mask; #ifndef _DOUBLE_IS_32BITS dword1(rv) = 0; #endif /*!_DOUBLE_IS_32BITS*/ #endif /*Honor_FLT_ROUNDS*/ #ifdef SET_INEXACT /* set overflow bit */ dval(rv0) = 1e300; dval(rv0) *= dval(rv0); #endif #else /*IEEE_Arith*/ dword0(rv) = Big0; #ifndef _DOUBLE_IS_32BITS dword1(rv) = Big1; #endif /*!_DOUBLE_IS_32BITS*/ #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; #ifndef _DOUBLE_IS_32BITS dword1(rv) = Big1; #endif /*!_DOUBLE_IS_32BITS*/ } else dword0(rv) += P*Exp_msk1; } } 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) { #ifndef _DOUBLE_IS_32BITS dword1(rv) = 0; #endif /*!_DOUBLE_IS_32BITS*/ if (j >= 53) dword0(rv) = (P+2)*Exp_msk1; else dword0(rv) &= 0xffffffff << (j-32); } #ifndef _DOUBLE_IS_32BITS else dword1(rv) &= 0xffffffff << j; #endif /*!_DOUBLE_IS_32BITS*/ } #else 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 if (!dval(rv)) { undfl: dval(rv) = 0.; #ifndef NO_ERRNO ptr->_errno = ERANGE; #endif if (bd0) goto retfree; goto ret; } #ifndef Avoid_Underflow #ifndef _DOUBLE_IS_32BITS dword0(rv) = Tiny0; dword1(rv) = Tiny1; #else dword0(rv) = Tiny1; #endif /*_DOUBLE_IS_32BITS*/ /* The refinement below will clean * this approximation up. */ } #endif } } /* 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); if (bd0 == NULL) goto ovfl; for(;;) { bd = Balloc(ptr,bd0->_k); if (bd == NULL) goto ovfl; Bcopy(bd, bd0); bb = d2b(ptr,dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ if (bb == NULL) goto ovfl; bs = i2b(ptr,1); if (bs == NULL) goto ovfl; 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 Lsb = LSB; Lsb1 = 0; j = bbe - scale; i = j + bbbits - 1; /* logb(rv) */ j = P + 1 - bbbits; if (i < Emin) { /* denormal */ i = Emin - i; j -= i; if (i < 32) Lsb <<= i; else Lsb1 = Lsb << (i-32); } #else /*Avoid_Underflow*/ #ifdef Sudden_Underflow #ifdef IBM j = 1 + 4*P - 3 - bbbits + ((bbe + bbbits - 1) & 3); #else 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); if (bs == NULL) goto ovfl; bb1 = mult(ptr, bs, bb); if (bb1 == NULL) goto ovfl; Bfree(ptr, bb); bb = bb1; } if (bb2 > 0) { bb = lshift(ptr, bb, bb2); if (bb == NULL) goto ovfl; } if (bd5 > 0) { bd = pow5mult(ptr, bd, bd5); if (bd == NULL) goto ovfl; } if (bd2 > 0) { bd = lshift(ptr, bd, bd2); if (bd == NULL) goto ovfl; } if (bs2 > 0) { bs = lshift(ptr, bs, bs2); if (bs == NULL) goto ovfl; } delta = diff(ptr, bb, bd); if (delta == NULL) goto ovfl; 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 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 if (y) #endif { 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) { if (dword0(rv) == Big0 && dword1(rv) == Big1) goto ovfl; 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*/ if (dword0(rv) == Big0 && dword1(rv) == Big1) goto ovfl; dword0(rv) = (dword0(rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ; #ifndef _DOUBLE_IS_32BITS dword1(rv) = 0; #endif /*!_DOUBLE_IS_32BITS*/ #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; #ifndef _DOUBLE_IS_32BITS dword1(rv) = 0xffffffff; #endif /*!_DOUBLE_IS_32BITS*/ #ifdef IBM goto cont; #else break; #endif } #ifndef ROUND_BIASED #ifdef Avoid_Underflow if (Lsb1) { if (!(dword0(rv) & Lsb1)) break; } else if (!(dword1(rv) & Lsb)) break; #else if (!(dword1(rv) & LSB)) break; #endif #endif if (dsign) #ifdef Avoid_Underflow dval(rv) += sulp(rv, scale); #else dval(rv) += ulp(dval(rv)); #endif #ifndef ROUND_BIASED else { #ifdef Avoid_Underflow dval(rv) -= sulp(rv, scale); #else dval(rv) -= ulp(dval(rv)); #endif #ifndef Sudden_Underflow if (!dval(rv)) goto undfl; #endif } #ifdef Avoid_Underflow dsign = 1 - dsign; #endif #endif break; } if ((aadj = ratio(delta, bs)) <= 2.) { if (dsign) aadj = dval(aadj1) = 1.; else if (dword1(rv) || dword0(rv) & Bndry_mask) { #ifndef Sudden_Underflow if (dword1(rv) == Tiny1 && !dword0(rv)) goto undfl; #endif aadj = 1.; dval(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; dval(aadj1) = -aadj; } } else { aadj *= 0.5; dval(aadj1) = dsign ? aadj : -aadj; #ifdef Check_FLT_ROUNDS switch(Rounding) { case 2: /* towards +infinity */ dval(aadj1) -= 0.5; break; case 0: /* towards 0 */ case 3: /* towards -infinity */ dval(aadj1) += 0.5; } #else if (Flt_Rounds == 0) dval(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 = dval(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; #ifndef _DOUBLE_IS_32BITS dword1(rv) = Big1; #endif /*!_DOUBLE_IS_32BITS*/ 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; dval(aadj1) = dsign ? aadj : -aadj; } dword0(aadj1) += (2*P+1)*Exp_msk1 - y; } adj = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; #else #ifdef Sudden_Underflow if ((dword0(rv) & Exp_mask) <= P*Exp_msk1) { dval(rv0) = dval(rv); dword0(rv) += P*Exp_msk1; adj = dval(aadj1) * ulp(dval(rv)); dval(rv) += adj; #ifdef IBM if ((dword0(rv) & Exp_mask) < P*Exp_msk1) #else if ((dword0(rv) & Exp_mask) <= P*Exp_msk1) #endif { if (dword0(rv0) == Tiny0 && dword1(rv0) == Tiny1) goto undfl; #ifndef _DOUBLE_IS_32BITS dword0(rv) = Tiny0; dword1(rv) = Tiny1; #else dword0(rv) = Tiny1; #endif /*_DOUBLE_IS_32BITS*/ goto cont; } else dword0(rv) -= P*Exp_msk1; } else { adj = dval(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.) { dval(aadj1) = (double)(int)(aadj + 0.5); if (!dsign) dval(aadj1) = -dval(aadj1); } adj = dval(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); } #ifdef SET_INEXACT if (inexact) { if (!oldinexact) { dword0(rv0) = Exp_1 + (70 << Exp_shift); #ifndef _DOUBLE_IS_32BITS dword1(rv0) = 0; #endif /*!_DOUBLE_IS_32BITS*/ dval(rv0) += 1.; } } else if (!oldinexact) clear_inexact(); #endif #ifdef Avoid_Underflow if (scale) { dword0(rv0) = Exp_1 - 2*P*Exp_msk1; #ifndef _DOUBLE_IS_32BITS dword1(rv0) = 0; #endif /*!_DOUBLE_IS_32BITS*/ 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); } double _strtod_r (struct _reent *ptr, const char *__restrict s00, char **__restrict se) { return _strtod_l (ptr, s00, se, __get_current_locale ()); } #ifndef _REENT_ONLY double strtod_l (const char *__restrict s00, char **__restrict se, locale_t loc) { return _strtod_l (_REENT, s00, se, loc); } double strtod (const char *__restrict s00, char **__restrict se) { return _strtod_l (_REENT, s00, se, __get_current_locale ()); } float strtof_l (const char *__restrict s00, char **__restrict se, locale_t loc) { double val = _strtod_l (_REENT, s00, se, loc); if (isnan (val)) return nanf (NULL); float retval = (float) val; #ifndef NO_ERRNO if (isinf (retval) && !isinf (val)) _REENT->_errno = ERANGE; #endif return retval; } float strtof (const char *__restrict s00, char **__restrict se) { double val = _strtod_l (_REENT, s00, se, __get_current_locale ()); if (isnan (val)) return nanf (NULL); float retval = (float) val; #ifndef NO_ERRNO if (isinf (retval) && !isinf (val)) _REENT->_errno = ERANGE; #endif return retval; } #endif