/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ ╚──────────────────────────────────────────────────────────────────────────────╝ │ │ │ The author of this software is David M. Gay. │ │ Please send bug reports to David M. Gay │ │ or Justine Tunney │ │ │ │ Copyright (C) 1998, 1999 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. │ │ │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/runtime/fenv.h" #include "third_party/gdtoa/gdtoa.internal.h" /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string. * * Inspired by "How to Print Floating-Point Numbers Accurately" by * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126]. * * Modifications: * 1. Rather than iterating, we use a simple numeric overestimate * to determine k = floor(log10(d)). We scale relevant * quantities using O(log2(k)) rather than O(k) __gdtoa_multiplications. * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't * try to generate digits strictly left to right. Instead, we * compute with fewer bits and propagate the carry if necessary * when rounding the final digit up. This is often faster. * 3. Under the as__gdtoa_sumption that input will be rounded nearest, * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22. * That is, we allow equality in stopping tests when the * round-nearest rule will give the same floating-point value * as would satisfaction of the stopping test with strict * inequality. * 4. We remove common factors of powers of 2 from relevant * quantities. * 5. When converting floating-point integers less than 1e16, * we use floating-point arithmetic rather than resorting * to __gdtoa_multiple-precision integers. * 6. When asked to produce fewer than 15 digits, we first try * to get by with floating-point arithmetic; we resort to * __gdtoa_multiple-precision integer arithmetic only if we cannot * guarantee that the floating-point calculation has given * the correctly rounded result. For k requested digits and * "uniformly" distributed input, the probability is * something like 10^(k-15) that we must resort to the Long * calculation. */ char * dtoa(double d0, int mode, int ndigits, int *decpt, int *sign, char **rve) { /* Arguments ndigits, decpt, sign are similar to those of ecvt and fcvt; trailing zeros are suppressed from the returned string. If not null, *rve is set to point to the end of the return value. If d is +-Infinity or NaN, then *decpt is set to 9999. mode: 0 ==> shortest string that yields d when read in and rounded to nearest. 1 ==> like 0, but with Steele & White stopping rule; e.g. with IEEE P754 arithmetic , mode 0 gives 1e23 whereas mode 1 gives 9.999999999999999e22. 2 ==> max(1,ndigits) significant digits. This gives a return value similar to that of ecvt, except that trailing zeros are suppressed. 3 ==> through ndigits past the decimal point. This gives a return value similar to that from fcvt, except that trailing zeros are suppressed, and ndigits can be negative. 4,5 ==> similar to 2 and 3, respectively, but (in round-nearest mode) with the tests of mode 0 to possibly return a shorter string that rounds to d. With IEEE arithmetic and compilation with -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same as modes 2 and 3 when FLT_ROUNDS != 1. 6-9 ==> Debugging modes similar to mode - 4: don't try fast floating-point estimate (if applicable). Values of mode other than 0-9 are treated as mode 0. Sufficient space is allocated to the return value to hold the suppressed trailing zeros. */ ThInfo *TI = 0; int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1, j, j1, k, k0, k_check, leftright, m2, m5, s2, s5, spec_case, try_quick; Long L; int denorm; ULong x; Bigint *b, *b1, *delta, *mlo, *mhi, *S; U d, d2, eps, eps1; double ds; char *s, *s0; int Rounding; Rounding = FLT_ROUNDS; d.d = d0; if (word0(&d) & Sign_bit) { /* set sign for everything, including 0's and NaNs */ *sign = 1; word0(&d) &= ~Sign_bit; /* clear sign bit */ } else *sign = 0; if ((word0(&d) & Exp_mask) == Exp_mask) { /* Infinity or NaN */ *decpt = 9999; if (!word1(&d) && !(word0(&d) & 0xfffff)) return __gdtoa_nrv_alloc("Infinity", rve, 8, &TI); return __gdtoa_nrv_alloc("NaN", rve, 3, &TI); } if (!dval(&d)) { *decpt = 1; return __gdtoa_nrv_alloc("0", rve, 1, &TI); } if (Rounding >= 2) { if (*sign) Rounding = Rounding == 2 ? 0 : 2; else if (Rounding != 2) Rounding = 0; } b = __gdtoa_d2b(dval(&d), &be, &bbits, &TI); if (( i = (int)(word0(&d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)) )!=0) { dval(&d2) = dval(&d); word0(&d2) &= Frac_mask1; word0(&d2) |= Exp_11; /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 * log10(x) = log(x) / log(10) * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) * log10(&d) = (i-Bias)*log(2)/log(10) + log10(&d2) * * This suggests computing an approximation k to log10(&d) by * * k = (i - Bias)*0.301029995663981 * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 ); * * We want k to be too large rather than too small. * The error in the first-order Taylor series approximation * is in our favor, so we just round up the constant enough * to compensate for any error in the __gdtoa_multiplication of * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077, * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14, * adding 1e-13 to the constant term more than suffices. * Hence we adjust the constant term to 0.1760912590558. * (We could get a more accurate k by invoking log10, * but this is probably not worthwhile.) */ i -= Bias; denorm = 0; } else { /* d is denormalized */ i = bbits + be + (Bias + (P-1) - 1); x = i > 32 ? word0(&d) << (64 - i) | word1(&d) >> (i - 32) : word1(&d) << (32 - i); dval(&d2) = x; word0(&d2) -= 31*Exp_msk1; /* adjust exponent */ i -= (Bias + (P-1) - 1) + 1; denorm = 1; } ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; k = (int)ds; if (ds < 0. && ds != k) k--; /* want k = floor(ds) */ k_check = 1; if (k >= 0 && k <= Ten_pmax) { if (dval(&d) < __gdtoa_tens[k]) k--; k_check = 0; } j = bbits - i - 1; if (j >= 0) { b2 = 0; s2 = j; } else { b2 = -j; s2 = 0; } if (k >= 0) { b5 = 0; s5 = k; s2 += k; } else { b2 -= k; b5 = -k; s5 = 0; } if (mode < 0 || mode > 9) mode = 0; try_quick = Rounding == 1; if (mode > 5) { mode -= 4; try_quick = 0; } leftright = 1; ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */ /* silence erroneous "gcc -Wall" warning. */ switch(mode) { case 0: case 1: i = 18; ndigits = 0; break; case 2: leftright = 0; /* no break */ case 4: if (ndigits <= 0) ndigits = 1; ilim = ilim1 = i = ndigits; break; case 3: leftright = 0; /* no break */ case 5: i = ndigits + k + 1; ilim = i; ilim1 = i - 1; if (i <= 0) i = 1; } s = s0 = __gdtoa_rv_alloc(i, &TI); if (mode > 1 && Rounding != 1) leftright = 0; if (ilim >= 0 && ilim <= Quick_max && try_quick) { /* Try to get by with floating-point arithmetic. */ i = 0; j1 = 0; dval(&d2) = dval(&d); k0 = k; ilim0 = ilim; ieps = 2; /* conservative */ if (k > 0) { ds = __gdtoa_tens[k&0xf]; j = k >> 4; if (j & Bletch) { /* prevent overflows */ j &= Bletch - 1; dval(&d) /= __gdtoa_bigtens[n___gdtoa_bigtens-1]; ieps++; } for(; j; j >>= 1, i++) if (j & 1) { ieps++; ds *= __gdtoa_bigtens[i]; } dval(&d) /= ds; } else if (( j1 = -k )!=0) { dval(&d) *= __gdtoa_tens[j1 & 0xf]; for(j = j1 >> 4; j; j >>= 1, i++) if (j & 1) { ieps++; dval(&d) *= __gdtoa_bigtens[i]; } } if (k_check && dval(&d) < 1. && ilim > 0) { if (ilim1 <= 0) goto fast_failed; ilim = ilim1; k--; dval(&d) *= 10.; ieps++; } dval(&eps) = ieps*dval(&d) + 7.; word0(&eps) -= (P-1)*Exp_msk1; if (ilim == 0) { S = mhi = 0; dval(&d) -= 5.; if (dval(&d) > dval(&eps)) goto one_digit; if (dval(&d) < -dval(&eps)) goto no_digits; goto fast_failed; } if (leftright) { /* Use Steele & White method of only * generating digits needed. */ dval(&eps) = 0.5/__gdtoa_tens[ilim-1] - dval(&eps); if (k0 < 0 && j1 >= 307) { eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */ word0(&eps1) -= Exp_msk1 * (Bias+P-1); dval(&eps1) *= __gdtoa_tens[j1 & 0xf]; for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++) if (j & 1) dval(&eps1) *= __gdtoa_bigtens[i]; if (eps.d < eps1.d) eps.d = eps1.d; if (10. - d.d < 10.*eps.d && eps.d < 1.) { /* eps.d < 1. excludes trouble with the tiniest denormal */ *s++ = '1'; ++k; goto ret1; } } for(i = 0;;) { L = dval(&d); dval(&d) -= L; *s++ = '0' + (int)L; if (dval(&d) < dval(&eps)) goto retc; if (1. - dval(&d) < dval(&eps)) goto bump_up; if (++i >= ilim) break; dval(&eps) *= 10.; dval(&d) *= 10.; } } else { /* Generate ilim digits, then fix them up. */ dval(&eps) *= __gdtoa_tens[ilim-1]; for(i = 1;; i++, dval(&d) *= 10.) { L = (Long)(dval(&d)); if (!(dval(&d) -= L)) ilim = i; *s++ = '0' + (int)L; if (i == ilim) { if (dval(&d) > 0.5 + dval(&eps)) goto bump_up; else if (dval(&d) < 0.5 - dval(&eps)) goto retc; break; } } } fast_failed: s = s0; dval(&d) = dval(&d2); k = k0; ilim = ilim0; } /* Do we have a "small" integer? */ if (be >= 0 && k <= Int_max) { /* Yes. */ ds = __gdtoa_tens[k]; if (ndigits < 0 && ilim <= 0) { S = mhi = 0; if (ilim < 0 || dval(&d) <= 5*ds) goto no_digits; goto one_digit; } for(i = 1;; i++, dval(&d) *= 10.) { L = (Long)(dval(&d) / ds); dval(&d) -= L*ds; /* If FLT_ROUNDS == 2, L will usually be high by 1 */ if (dval(&d) < 0) { L--; dval(&d) += ds; } *s++ = '0' + (int)L; if (!dval(&d)) { break; } if (i == ilim) { if (mode > 1) switch(Rounding) { case 0: goto retc; case 2: goto bump_up; } dval(&d) += dval(&d); if (dval(&d) > ds || (dval(&d) == ds && L & 1)) { bump_up: while(*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } break; } } goto retc; } m2 = b2; m5 = b5; mhi = mlo = 0; if (leftright) { i = denorm ? be + (Bias + (P-1) - 1 + 1) : 1 + P - bbits; b2 += i; s2 += i; mhi = __gdtoa_i2b(1, &TI); } if (m2 > 0 && s2 > 0) { i = m2 < s2 ? m2 : s2; b2 -= i; m2 -= i; s2 -= i; } if (b5 > 0) { if (leftright) { if (m5 > 0) { mhi = __gdtoa_pow5mult(mhi, m5, &TI); b1 = __gdtoa_mult(mhi, b, &TI); __gdtoa_Bfree(b, &TI); b = b1; } if (( j = b5 - m5 )!=0) b = __gdtoa_pow5mult(b, j, &TI); } else b = __gdtoa_pow5mult(b, b5, &TI); } S = __gdtoa_i2b(1, &TI); if (s5 > 0) S = __gdtoa_pow5mult(S, s5, &TI); /* Check for special case that d is a normalized power of 2. */ spec_case = 0; if ((mode < 2 || leftright) && Rounding == 1) { if (!word1(&d) && !(word0(&d) & Bndry_mask) && word0(&d) & (Exp_mask & ~Exp_msk1)) { /* The special case */ b2 += Log2P; s2 += Log2P; spec_case = 1; } } /* Arrange for convenient computation of quotients: * shift left if necessary so divisor has 4 leading 0 bits. * * Perhaps we should just compute leading 28 bits of S once * and for all and pass them and a shift to __gdtoa_quorem, so it * can do shifts and ors to compute the numerator for q. */ if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f )!=0) i = 32 - i; if (i > 4) { i -= 4; b2 += i; m2 += i; s2 += i; } else if (i < 4) { i += 28; b2 += i; m2 += i; s2 += i; } if (b2 > 0) b = __gdtoa_lshift(b, b2, &TI); if (s2 > 0) S = __gdtoa_lshift(S, s2, &TI); if (k_check) { if (__gdtoa_cmp(b,S) < 0) { k--; b = __gdtoa_multadd(b, 10, 0, &TI); /* we botched the k estimate */ if (leftright) mhi = __gdtoa_multadd(mhi, 10, 0, &TI); ilim = ilim1; } } if (ilim <= 0 && (mode == 3 || mode == 5)) { if (ilim < 0 || __gdtoa_cmp(b,S = __gdtoa_multadd(S,5,0,&TI)) <= 0) { /* no digits, fcvt style */ no_digits: k = -1 - ndigits; goto ret; } one_digit: *s++ = '1'; k++; goto ret; } if (leftright) { if (m2 > 0) mhi = __gdtoa_lshift(mhi, m2, &TI); /* Compute mlo -- check for special case * that d is a normalized power of 2. */ mlo = mhi; if (spec_case) { mhi = __gdtoa_Balloc(mhi->k, &TI); Bcopy(mhi, mlo); mhi = __gdtoa_lshift(mhi, Log2P, &TI); } for(i = 1;;i++) { dig = __gdtoa_quorem(b,S) + '0'; /* Do we yet have the shortest decimal string * that will round to d? */ j = __gdtoa_cmp(b, mlo); delta = __gdtoa_diff(S, mhi, &TI); j1 = delta->sign ? 1 : __gdtoa_cmp(b, delta); __gdtoa_Bfree(delta, &TI); if (j1 == 0 && mode != 1 && !(word1(&d) & 1) && Rounding >= 1) { if (dig == '9') goto round_9_up; if (j > 0) dig++; *s++ = dig; goto ret; } if (j < 0 || (j == 0 && mode != 1 && !(word1(&d) & 1) )) { if (!b->x[0] && b->wds <= 1) { goto accept_dig; } if (mode > 1) switch(Rounding) { case 0: goto accept_dig; case 2: goto keep_dig; } if (j1 > 0) { b = __gdtoa_lshift(b, 1, &TI); j1 = __gdtoa_cmp(b, S); if ((j1 > 0 || (j1 == 0 && dig & 1)) && dig++ == '9') goto round_9_up; } accept_dig: *s++ = dig; goto ret; } if (j1 > 0) { if (!Rounding && mode > 1) goto accept_dig; if (dig == '9') { /* possible if i == 1 */ round_9_up: *s++ = '9'; goto roundoff; } *s++ = dig + 1; goto ret; } keep_dig: *s++ = dig; if (i == ilim) break; b = __gdtoa_multadd(b, 10, 0, &TI); if (mlo == mhi) mlo = mhi = __gdtoa_multadd(mhi, 10, 0, &TI); else { mlo = __gdtoa_multadd(mlo, 10, 0, &TI); mhi = __gdtoa_multadd(mhi, 10, 0, &TI); } } } else { for(i = 1;; i++) { *s++ = dig = __gdtoa_quorem(b,S) + '0'; if (!b->x[0] && b->wds <= 1) { goto ret; } if (i >= ilim) break; b = __gdtoa_multadd(b, 10, 0, &TI); } } /* Round off last digit */ switch(Rounding) { case 0: goto trimzeros; case 2: goto roundoff; } b = __gdtoa_lshift(b, 1, &TI); j = __gdtoa_cmp(b, S); if (j > 0 || (j == 0 && dig & 1)) { roundoff: while(*--s == '9') if (s == s0) { k++; *s++ = '1'; goto ret; } ++*s++; } else { trimzeros: while(*--s == '0'); s++; } ret: __gdtoa_Bfree(S, &TI); if (mhi) { if (mlo && mlo != mhi) __gdtoa_Bfree(mlo, &TI); __gdtoa_Bfree(mhi, &TI); } retc: while(s > s0 && s[-1] == '0') --s; ret1: __gdtoa_Bfree(b, &TI); *s = 0; *decpt = k + 1; if (rve) *rve = s; return s0; }