/**************************************************************** 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 "."). */ #include "gdtoaimp.h" #ifndef NO_FENV_H #include #endif #ifdef USE_LOCALE #include "locale.h" #endif #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, 1e-64, 1e-128, 9007199254740992.*9007199254740992.e-256 }; #endif #endif #ifdef Honor_FLT_ROUNDS #undef Check_FLT_ROUNDS #define Check_FLT_ROUNDS #else #define Rounding Flt_Rounds #endif double strtod #ifdef KR_headers (s00, se) CONST char *s00; char **se; #else (CONST char *s00, char **se) #endif { #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 = NULL, *bs, *delta; #ifdef SET_INEXACT int inexact, oldinexact; #endif #ifdef USE_LOCALE #ifdef NO_LOCALE_CACHE char *decimalpoint = localeconv()->decimal_point; #else char *decimalpoint; static char *decimalpoint_cache; if (!(s0 = decimalpoint_cache)) { size_t len; s0 = localeconv()->decimal_point; len = strlen(s0) + 1; if ((decimalpoint_cache = (char*)malloc(len))) { strlcpy(decimalpoint_cache, s0, len); s0 = decimalpoint_cache; } } decimalpoint = (char*)s0; #endif #endif #ifdef Honor_FLT_ROUNDS /*{*/ int Rounding; #ifdef Trust_FLT_ROUNDS /*{{ only define this if FLT_ROUNDS really works! */ Rounding = Flt_Rounds; #else /*}{*/ Rounding = 1; switch(fegetround()) { case FE_TOWARDZERO: Rounding = 0; break; case FE_UPWARD: Rounding = 2; break; case FE_DOWNWARD: Rounding = 3; } #endif /*}}*/ #endif /*}*/ 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; #ifdef Honor_FLT_ROUNDS /*{{*/ fpi1.rounding = Rounding; #else /*}{*/ switch(fegetround()) { case FE_TOWARDZERO: fpi1.rounding = 0; break; case FE_UPWARD: fpi1.rounding = 2; break; case FE_DOWNWARD: fpi1.rounding = 3; } #endif /*}}*/ #else /*}{*/ #define fpi1 fpi #endif /*}}*/ switch((i = gethex(&s, &fpi1, &exp, &bb, sign)) & STRTOG_Retmask) { case STRTOG_NoNumber: s = s00; sign = 0; case STRTOG_Zero: break; case STRTOG_NoMemory: goto ovfl; default: if (bb) { copybits(bits, fpi.nbits, bb); Bfree(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 == *decimalpoint) { for(i = 1; decimalpoint[i]; ++i) if (s[i] != decimalpoint[i]) goto dig_done; s += i; c = *s; #else if (c == '.') { c = *++s; #endif decpt = 1; 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; word0(rv) = 0x7ff00000; word1(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) { word0(rv) = 0x7ff00000 | bits[1]; word1(rv) = bits[0]; } else { #endif word0(rv) = NAN_WORD0; word1(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; } 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) { 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. */ #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 = */ rounded_product(dval(rv), tens[e]); if ((word0(rv) & Exp_mask) > Exp_msk1*(DBL_MAX_EXP+Bias-1-P)) goto ovfl; word0(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) { rv = -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 >= 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 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 */ word0(rv) = Big0; word1(rv) = Big1; break; default: word0(rv) = Exp_mask; word1(rv) = 0; } #else /*Honor_FLT_ROUNDS*/ word0(rv) = Exp_mask; word1(rv) = 0; #endif /*Honor_FLT_ROUNDS*/ #ifdef SET_INEXACT /* set overflow bit */ dval(rv0) = 1e300; dval(rv0) *= dval(rv0); #endif #else /*IEEE_Arith*/ word0(rv) = Big0; word1(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. */ word0(rv) -= P*Exp_msk1; dval(rv) *= 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; word1(rv) = Big1; } else word0(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 - ((word0(rv) & Exp_mask) >> Exp_shift)) > 0) { /* scaled rv is denormal; zap j low bits */ if (j >= 32) { word1(rv) = 0; if (j >= 53) word0(rv) = (P+2)*Exp_msk1; else word0(rv) &= 0xffffffff << j-32; } else word1(rv) &= 0xffffffff << j; } #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 errno = ERANGE; #endif if (bd0) goto retfree; goto ret; } #ifndef Avoid_Underflow word0(rv) = Tiny0; word1(rv) = Tiny1; /* 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(s0, nd0, nd, y); if (bd0 == NULL) goto ovfl; for(;;) { bd = Balloc(bd0->k); if (bd == NULL) goto ovfl; Bcopy(bd, bd0); bb = d2b(dval(rv), &bbe, &bbbits); /* rv = bb * 2^bbe */ if (bb == NULL) goto ovfl; bs = i2b(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 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 #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(bs, bb5); if (bs == NULL) goto ovfl; bb1 = mult(bs, bb); if (bb1 == NULL) goto ovfl; Bfree(bb); bb = bb1; } if (bb2 > 0) { bb = lshift(bb, bb2); if (bb == NULL) goto ovfl; } if (bd5 > 0) { bd = pow5mult(bd, bd5); if (bd == NULL) goto ovfl; } if (bd2 > 0) { bd = lshift(bd, bd2); if (bd == NULL) goto ovfl; } if (bs2 > 0) { bs = lshift(bs, bs2); if (bs == NULL) goto ovfl; } delta = diff(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 (!word1(rv) && !(word0(rv) & Frac_mask)) { y = word0(rv) & Exp_mask; #ifdef Avoid_Underflow if (!scale || y > 2*P*Exp_msk1) #else if (y) #endif { delta = lshift(delta,Log2P); if (delta == NULL) goto ovfl; if (cmp(delta, bs) <= 0) adj = -0.5; } } apply_adj: #ifdef Avoid_Underflow if (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) word0(adj) += (2*P+1)*Exp_msk1 - y; #else #ifdef Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { word0(rv) += P*Exp_msk1; dval(rv) += adj*ulp(dval(rv)); word0(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 = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) word0(adj) += (2*P+1)*Exp_msk1 - y; #else #ifdef Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { word0(rv) += P*Exp_msk1; adj *= ulp(dval(rv)); if (dsign) dval(rv) += adj; else dval(rv) -= adj; word0(rv) -= P*Exp_msk1; goto cont; } #endif /*Sudden_Underflow*/ #endif /*Avoid_Underflow*/ adj *= ulp(dval(rv)); if (dsign) { if (word0(rv) == Big0 && word1(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 || word1(rv) || word0(rv) & Bndry_mask #ifdef IEEE_Arith #ifdef Avoid_Underflow || (word0(rv) & Exp_mask) <= (2*P+1)*Exp_msk1 #else || (word0(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(delta,Log2P); if (delta == NULL) goto ovfl; 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) == ( #ifdef Avoid_Underflow (scale && (y = word0(rv) & Exp_mask) <= 2*P*Exp_msk1) ? (0xffffffff & (0xffffffff << (2*P+1-(y>>Exp_shift)))) : #endif 0xffffffff)) { /*boundary case -- increment exponent*/ word0(rv) = (word0(rv) & Exp_mask) + Exp_msk1 #ifdef IBM | Exp_msk1 >> 4 #endif ; word1(rv) = 0; #ifdef Avoid_Underflow dsign = 0; #endif break; } } else if (!(word0(rv) & Bndry_mask) && !word1(rv)) { drop_down: /* boundary case -- decrement exponent */ #ifdef Sudden_Underflow /*{{*/ L = word0(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 = word0(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 = (word0(rv) & Exp_mask) - Exp_msk1; #endif /*Sudden_Underflow}}*/ word0(rv) = L | Bndry_mask1; word1(rv) = 0xffffffff; #ifdef IBM goto cont; #else break; #endif } #ifndef ROUND_BIASED if (!(word1(rv) & LSB)) break; #endif if (dsign) dval(rv) += ulp(dval(rv)); #ifndef ROUND_BIASED else { dval(rv) -= ulp(dval(rv)); #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 = 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(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 /*Check_FLT_ROUNDS*/ } y = word0(rv) & Exp_mask; /* Check for overflow */ if (y == Exp_msk1*(DBL_MAX_EXP+Bias-1)) { dval(rv0) = dval(rv); word0(rv) -= P*Exp_msk1; adj = aadj1 * ulp(dval(rv)); dval(rv) += adj; if ((word0(rv) & Exp_mask) >= Exp_msk1*(DBL_MAX_EXP+Bias-P)) { if (word0(rv0) == Big0 && word1(rv0) == Big1) goto ovfl; word0(rv) = Big0; word1(rv) = Big1; goto cont; } else word0(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; } word0(aadj1) += (2*P+1)*Exp_msk1 - y; } adj = aadj1 * ulp(dval(rv)); dval(rv) += adj; #else #ifdef Sudden_Underflow if ((word0(rv) & Exp_mask) <= P*Exp_msk1) { dval(rv0) = dval(rv); word0(rv) += P*Exp_msk1; adj = aadj1 * ulp(dval(rv)); dval(rv) += 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(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 = word0(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 || word1(rv) || word0(rv) & Bndry_mask) { if (aadj < .4999999 || aadj > .5000001) break; } else if (aadj < .4999999/FLT_RADIX) break; } #endif cont: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(delta); } #ifdef SET_INEXACT if (inexact) { if (!oldinexact) { word0(rv0) = Exp_1 + (70 << Exp_shift); word1(rv0) = 0; dval(rv0) += 1.; } } else if (!oldinexact) clear_inexact(); #endif #ifdef Avoid_Underflow if (scale) { word0(rv0) = Exp_1 - 2*P*Exp_msk1; word1(rv0) = 0; dval(rv) *= dval(rv0); #ifndef NO_ERRNO /* try to avoid the bug of testing an 8087 register value */ #ifdef IEEE_Arith if (!(word0(rv) & Exp_mask)) #else if (word0(rv) == 0 && word1(rv) == 0) #endif errno = ERANGE; #endif } #endif /* Avoid_Underflow */ #ifdef SET_INEXACT if (inexact && !(word0(rv) & Exp_mask)) { /* set underflow bit */ dval(rv0) = 1e-300; dval(rv0) *= dval(rv0); } #endif retfree: Bfree(bb); Bfree(bd); Bfree(bs); Bfree(bd0); Bfree(delta); ret: if (se) *se = (char *)s; return sign ? -dval(rv) : dval(rv); }