/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ │ vi: set noet ft=c ts=8 sw=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 "third_party/gdtoa/gdtoa.internal.h" static Bigint * bitstob(ULong *bits, int nbits, int *bbits, ThInfo **PTI) { int i, k; Bigint *b; ULong *be, *x, *x0; i = ULbits; k = 0; while(i < nbits) { i <<= 1; k++; } b = __gdtoa_Balloc(k, PTI); be = bits + ((nbits - 1) >> kshift); x = x0 = b->x; do { *x++ = *bits & ALL_ON; } while(++bits <= be); i = x - x0; while(!x0[--i]) if (!i) { b->wds = 0; *bbits = 0; goto ret; } b->wds = i + 1; *bbits = i*ULbits + 32 - hi0bits(b->x[i]); ret: return b; } /* 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 * gdtoa(const FPI *fpi, int be, ULong *bits, int *kindp, int mode, int ndigits, int *decpt, char **rve) { /* Arguments ndigits and decpt are similar to the second and third arguments 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. be = exponent: value = (integer represented by bits) * (2 to the power of be). 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. 4-9 should give the same return values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode 2 + (mode & 1). These modes are mainly for debugging; often they run slower but sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right digit gene__gdtoa_ration. 6-9 ==> 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, be0, dig, i, ieps, ilim, ilim0, ilim1, inex; int j, j1, k, k0, k_check, kind, leftright, m2, m5, nbits; int rdir, s2, s5, spec_case, try_quick; Long L; Bigint *b, *b1, *delta, *mlo, *mhi, *mhi1, *S; double d2, ds; char *s, *s0; U d, eps; inex = 0; kind = *kindp &= ~STRTOG_Inexact; switch(kind & STRTOG_Retmask) { case STRTOG_Zero: goto ret_zero; case STRTOG_Normal: case STRTOG_Denormal: break; case STRTOG_Infinite: *decpt = -32768; return __gdtoa_nrv_alloc("Infinity", rve, 8, &TI); case STRTOG_NaN: *decpt = -32768; return __gdtoa_nrv_alloc("NaN", rve, 3, &TI); default: return 0; } b = bitstob(bits, nbits = fpi->nbits, &bbits, &TI); be0 = be; if ( (i = __gdtoa_trailz(b)) !=0) { __gdtoa_rshift(b, i); be += i; bbits -= i; } if (!b->wds) { __gdtoa_Bfree(b, &TI); ret_zero: *decpt = 1; return __gdtoa_nrv_alloc("0", rve, 1, &TI); } dval(&d) = __gdtoa_b2d(b, &i); i = be + bbits - 1; word0(&d) &= Frac_mask1; word0(&d) |= 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.) */ ds = (dval(&d)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981; /* correct as__gdtoa_sumption about exponent range */ if ((j = i) < 0) j = -j; if ((j -= 1077) > 0) ds += j * 7e-17; k = (int)ds; if (ds < 0. && ds != k) k--; /* want k = floor(ds) */ k_check = 1; // TODO: word0(&d) += (be + bbits - 1) << Exp_shift; // error: third_party/gdtoa/gdtoa.c:244: left shift of negative value -6 'int' 20 'int' // 4161d8: __die at libc/log/die.c:33 // 463165: __ubsan_abort at libc/intrin/ubsan.c:270 // 4632d6: __ubsan_handle_shift_out_of_bounds at libc/intrin/ubsan.c:299 // 421d42: gdtoa at third_party/gdtoa/gdtoa.c:244 // 420449: g_dfmt_p at third_party/gdtoa/g_dfmt_p.c:105 // 413947: ConvertMatrixToStringTable at tool/viz/lib/formatmatrix-double.c:40 // 413a5f: FormatMatrixDouble at tool/viz/lib/formatmatrix-double.c:55 // 413b13: StringifyMatrixDouble at tool/viz/lib/formatmatrix-double.c:65 // 464923: GetChromaticAdaptationMatrix_testD65ToD50_soWeCanCieLab at test/dsp/core/illumination_test.c:39 // 4650c2: testlib_runtestcases at libc/testlib/testrunner.c:94 // 464676: testlib_runalltests at libc/testlib/runner.c:37 // 46455e: main at libc/testlib/testmain.c:84 // 401d30: cosmo at libc/runtime/cosmo.S:65 // 401173: _start at libc/crt/crt.S:67 word0(&d) += (unsigned)(be + bbits - 1) << Exp_shift; 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 = 1; if (mode > 5) { mode -= 4; try_quick = 0; } else if (i >= -4 - Emin || i < Emin) 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 = (int)(nbits * .30103) + 3; 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) rdir = 0; else if ( (rdir = fpi->rounding - 1) !=0) { if (rdir < 0) rdir = 2; if (kind & STRTOG_Neg) rdir = 3 - rdir; } /* Now rdir = 0 ==> round near, 1 ==> round up, 2 ==> round down. */ if (ilim >= 0 && ilim <= Quick_max && try_quick && !rdir && k == 0) { /* Try to get by with floating-point arithmetic. */ i = 0; 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]; } } else { ds = 1.; 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) = ds*0.5/__gdtoa_tens[ilim-1] - dval(&eps); for(i = 0;;) { L = (Long)(dval(&d)/ds); dval(&d) -= L*ds; *s++ = '0' + (int)L; if (dval(&d) < dval(&eps)) { if (dval(&d)) inex = STRTOG_Inexlo; goto ret1; } if (ds - 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.) { if ( (L = (Long)(dval(&d)/ds)) !=0) dval(&d) -= L*ds; *s++ = '0' + (int)L; if (i == ilim) { ds *= 0.5; if (dval(&d) > ds + dval(&eps)) goto bump_up; else if (dval(&d) < ds - dval(&eps)) { if (dval(&d)) inex = STRTOG_Inexlo; goto ret1; } break; } } } fast_failed: s = s0; dval(&d) = d2; k = k0; ilim = ilim0; } /* Do we have a "small" integer? */ if (be >= 0 && k <= fpi->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 = 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) == 0.) break; if (i == ilim) { if (rdir) { if (rdir == 1) goto bump_up; inex = STRTOG_Inexlo; goto ret1; } dval(&d) += dval(&d); if (dval(&d) > ds || (dval(&d) == ds && L & 1)) { bump_up: inex = STRTOG_Inexhi; while(*--s == '9') if (s == s0) { k++; *s = '0'; break; } ++*s++; } else inex = STRTOG_Inexlo; break; } } goto ret1; } m2 = b2; m5 = b5; mhi = mlo = 0; if (leftright) { i = nbits - bbits; if (be - i++ < fpi->emin && mode != 3 && mode != 5) { /* denormal */ i = be - fpi->emin + 1; if (mode >= 2 && ilim > 0 && ilim < i) goto small_ilim; } else if (mode >= 2) { small_ilim: j = ilim - 1; if (m5 >= j) m5 -= j; else { s5 += j -= m5; b5 += j; m5 = 0; } if ((i = ilim) < 0) { m2 -= i; i = 0; } } 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) { if (bbits == 1 && be0 > fpi->emin + 1) { /* The special case */ b2++; s2++; 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. */ i = ((s5 ? hi0bits(S->x[S->wds-1]) : ULbits - 1) - s2 - 4) & kmask; m2 += i; if ((b2 += i) > 0) b = __gdtoa_lshift(b, b2, &TI); if ((s2 += i) > 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 > 2) { if (ilim < 0 || __gdtoa_cmp(b,S = __gdtoa_multadd(S,5,0,&TI)) <= 0) { /* no digits, fcvt style */ no_digits: k = -1 - ndigits; inex = STRTOG_Inexlo; goto ret; } one_digit: inex = STRTOG_Inexhi; *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, 1, &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 && !(bits[0] & 1) && !rdir) { if (dig == '9') goto round_9_up; if (j <= 0) { if (b->wds > 1 || b->x[0]) inex = STRTOG_Inexlo; } else { dig++; inex = STRTOG_Inexhi; } *s++ = dig; goto ret; } if (j < 0 || (j == 0 && !mode && !(bits[0] & 1))) { if (rdir && (b->wds > 1 || b->x[0])) { if (rdir == 2) { inex = STRTOG_Inexlo; goto accept; } while (__gdtoa_cmp(S,mhi) > 0) { *s++ = dig; mhi1 = __gdtoa_multadd(mhi, 10, 0, &TI); if (mlo == mhi) mlo = mhi1; mhi = mhi1; b = __gdtoa_multadd(b, 10, 0, &TI); dig = __gdtoa_quorem(b,S) + '0'; } if (dig++ == '9') goto round_9_up; inex = STRTOG_Inexhi; goto accept; } 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; inex = STRTOG_Inexhi; } if (b->wds > 1 || b->x[0]) inex = STRTOG_Inexlo; accept: *s++ = dig; goto ret; } if (j1 > 0 && rdir != 2) { if (dig == '9') { /* possible if i == 1 */ round_9_up: *s++ = '9'; inex = STRTOG_Inexhi; goto roundoff; } inex = STRTOG_Inexhi; *s++ = dig + 1; goto ret; } *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 (i >= ilim) break; b = __gdtoa_multadd(b, 10, 0, &TI); } /* Round off last digit */ if (rdir) { if (rdir == 2 || (b->wds <= 1 && !b->x[0])) goto chopzeros; goto roundoff; } b = __gdtoa_lshift(b, 1, &TI); j = __gdtoa_cmp(b, S); if (j > 0 || (j == 0 && dig & 1)) { roundoff: inex = STRTOG_Inexhi; while(*--s == '9') if (s == s0) { k++; *s++ = '1'; goto ret; } ++*s++; } else { chopzeros: if (b->wds > 1 || b->x[0]) inex = STRTOG_Inexlo; } ret: __gdtoa_Bfree(S, &TI); if (mhi) { if (mlo && mlo != mhi) __gdtoa_Bfree(mlo, &TI); __gdtoa_Bfree(mhi, &TI); } ret1: while(s > s0 && s[-1] == '0') --s; __gdtoa_Bfree(b, &TI); *s = 0; *decpt = k + 1; if (rve) *rve = s; *kindp |= inex; return s0; }