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fa20edc44d
- Remove most __ASSEMBLER__ __LINKER__ ifdefs - Rename libc/intrin/bits.h to libc/serialize.h - Block pthread cancelation in fchmodat() polyfill - Remove `clang-format off` statements in third_party
622 lines
17 KiB
C
622 lines
17 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ The author of this software is David M. Gay. │
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│ Please send bug reports to David M. Gay <dmg@acm.org> │
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│ or Justine Tunney <jtunney@gmail.com> │
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│ │
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│ Copyright (C) 1998, 1999 by Lucent Technologies │
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│ All Rights Reserved │
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│ │
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│ Permission to use, copy, modify, and distribute this software and │
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│ its documentation for any purpose and without fee is hereby │
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│ granted, provided that the above copyright notice appear in all │
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│ copies and that both that the copyright notice and this │
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│ permission notice and warranty disclaimer appear in supporting │
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│ documentation, and that the name of Lucent or any of its entities │
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│ not be used in advertising or publicity pertaining to │
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│ distribution of the software without specific, written prior │
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│ permission. │
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│ │
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│ LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, │
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│ INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. │
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│ IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY │
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│ SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES │
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│ WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER │
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│ IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, │
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│ ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF │
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│ THIS SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/runtime/fenv.h"
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#include "third_party/gdtoa/gdtoa.internal.h"
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/* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
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*
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* Inspired by "How to Print Floating-Point Numbers Accurately" by
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* Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
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*
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* Modifications:
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* 1. Rather than iterating, we use a simple numeric overestimate
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* to determine k = floor(log10(d)). We scale relevant
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* quantities using O(log2(k)) rather than O(k) __gdtoa_multiplications.
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* 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
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* try to generate digits strictly left to right. Instead, we
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* compute with fewer bits and propagate the carry if necessary
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* when rounding the final digit up. This is often faster.
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* 3. Under the as__gdtoa_sumption that input will be rounded nearest,
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* mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
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* That is, we allow equality in stopping tests when the
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* round-nearest rule will give the same floating-point value
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* as would satisfaction of the stopping test with strict
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* inequality.
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* 4. We remove common factors of powers of 2 from relevant
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* quantities.
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* 5. When converting floating-point integers less than 1e16,
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* we use floating-point arithmetic rather than resorting
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* to __gdtoa_multiple-precision integers.
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* 6. When asked to produce fewer than 15 digits, we first try
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* to get by with floating-point arithmetic; we resort to
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* __gdtoa_multiple-precision integer arithmetic only if we cannot
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* guarantee that the floating-point calculation has given
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* the correctly rounded result. For k requested digits and
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* "uniformly" distributed input, the probability is
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* something like 10^(k-15) that we must resort to the Long
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* calculation.
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*/
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char *
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dtoa(double d0, int mode, int ndigits, int *decpt, int *sign, char **rve)
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{
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/* Arguments ndigits, decpt, sign are similar to those
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of ecvt and fcvt; trailing zeros are suppressed from
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the returned string. If not null, *rve is set to point
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to the end of the return value. If d is +-Infinity or NaN,
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then *decpt is set to 9999.
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mode:
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0 ==> shortest string that yields d when read in
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and rounded to nearest.
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1 ==> like 0, but with Steele & White stopping rule;
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e.g. with IEEE P754 arithmetic , mode 0 gives
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1e23 whereas mode 1 gives 9.999999999999999e22.
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2 ==> max(1,ndigits) significant digits. This gives a
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return value similar to that of ecvt, except
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that trailing zeros are suppressed.
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3 ==> through ndigits past the decimal point. This
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gives a return value similar to that from fcvt,
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except that trailing zeros are suppressed, and
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ndigits can be negative.
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4,5 ==> similar to 2 and 3, respectively, but (in
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round-nearest mode) with the tests of mode 0 to
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possibly return a shorter string that rounds to d.
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With IEEE arithmetic and compilation with
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-DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
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as modes 2 and 3 when FLT_ROUNDS != 1.
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6-9 ==> Debugging modes similar to mode - 4: don't try
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fast floating-point estimate (if applicable).
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Values of mode other than 0-9 are treated as mode 0.
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Sufficient space is allocated to the return value
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to hold the suppressed trailing zeros.
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*/
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ThInfo *TI = 0;
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int bbits, b2, b5, be, dig, i, ieps, ilim, ilim0, ilim1,
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j, j1, k, k0, k_check, leftright, m2, m5, s2, s5,
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spec_case, try_quick;
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Long L;
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int denorm;
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ULong x;
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Bigint *b, *b1, *delta, *mlo, *mhi, *S;
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U d, d2, eps, eps1;
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double ds;
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char *s, *s0;
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int Rounding;
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Rounding = FLT_ROUNDS;
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d.d = d0;
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if (word0(&d) & Sign_bit) {
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/* set sign for everything, including 0's and NaNs */
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*sign = 1;
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word0(&d) &= ~Sign_bit; /* clear sign bit */
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}
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else
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*sign = 0;
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if ((word0(&d) & Exp_mask) == Exp_mask)
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{
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/* Infinity or NaN */
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*decpt = 9999;
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if (!word1(&d) && !(word0(&d) & 0xfffff))
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return __gdtoa_nrv_alloc("Infinity", rve, 8, &TI);
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return __gdtoa_nrv_alloc("NaN", rve, 3, &TI);
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}
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if (!dval(&d)) {
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*decpt = 1;
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return __gdtoa_nrv_alloc("0", rve, 1, &TI);
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}
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if (Rounding >= 2) {
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if (*sign)
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Rounding = Rounding == 2 ? 0 : 2;
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else
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if (Rounding != 2)
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Rounding = 0;
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}
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b = __gdtoa_d2b(dval(&d), &be, &bbits, &TI);
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if (( i = (int)(word0(&d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)) )!=0) {
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dval(&d2) = dval(&d);
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word0(&d2) &= Frac_mask1;
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word0(&d2) |= Exp_11;
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/* log(x) ~=~ log(1.5) + (x-1.5)/1.5
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* log10(x) = log(x) / log(10)
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* ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
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* log10(&d) = (i-Bias)*log(2)/log(10) + log10(&d2)
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*
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* This suggests computing an approximation k to log10(&d) by
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*
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* k = (i - Bias)*0.301029995663981
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* + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
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*
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* We want k to be too large rather than too small.
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* The error in the first-order Taylor series approximation
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* is in our favor, so we just round up the constant enough
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* to compensate for any error in the __gdtoa_multiplication of
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* (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
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* and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
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* adding 1e-13 to the constant term more than suffices.
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* Hence we adjust the constant term to 0.1760912590558.
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* (We could get a more accurate k by invoking log10,
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* but this is probably not worthwhile.)
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*/
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i -= Bias;
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denorm = 0;
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}
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else {
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/* d is denormalized */
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i = bbits + be + (Bias + (P-1) - 1);
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x = i > 32 ? word0(&d) << (64 - i) | word1(&d) >> (i - 32)
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: word1(&d) << (32 - i);
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dval(&d2) = x;
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word0(&d2) -= 31*Exp_msk1; /* adjust exponent */
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i -= (Bias + (P-1) - 1) + 1;
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denorm = 1;
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}
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ds = (dval(&d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
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k = (int)ds;
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if (ds < 0. && ds != k)
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k--; /* want k = floor(ds) */
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k_check = 1;
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if (k >= 0 && k <= Ten_pmax) {
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if (dval(&d) < __gdtoa_tens[k])
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k--;
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k_check = 0;
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}
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j = bbits - i - 1;
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if (j >= 0) {
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b2 = 0;
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s2 = j;
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}
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else {
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b2 = -j;
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s2 = 0;
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}
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if (k >= 0) {
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b5 = 0;
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s5 = k;
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s2 += k;
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}
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else {
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b2 -= k;
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b5 = -k;
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s5 = 0;
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}
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if (mode < 0 || mode > 9)
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mode = 0;
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try_quick = Rounding == 1;
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if (mode > 5) {
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mode -= 4;
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try_quick = 0;
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}
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leftright = 1;
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ilim = ilim1 = -1; /* Values for cases 0 and 1; done here to */
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/* silence erroneous "gcc -Wall" warning. */
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switch(mode) {
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case 0:
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case 1:
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i = 18;
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ndigits = 0;
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break;
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case 2:
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leftright = 0;
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/* no break */
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case 4:
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if (ndigits <= 0)
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ndigits = 1;
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ilim = ilim1 = i = ndigits;
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break;
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case 3:
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leftright = 0;
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/* no break */
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case 5:
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i = ndigits + k + 1;
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ilim = i;
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ilim1 = i - 1;
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if (i <= 0)
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i = 1;
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}
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s = s0 = __gdtoa_rv_alloc(i, &TI);
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if (mode > 1 && Rounding != 1)
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leftright = 0;
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if (ilim >= 0 && ilim <= Quick_max && try_quick) {
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/* Try to get by with floating-point arithmetic. */
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i = 0;
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j1 = 0;
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dval(&d2) = dval(&d);
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k0 = k;
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ilim0 = ilim;
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ieps = 2; /* conservative */
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if (k > 0) {
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ds = __gdtoa_tens[k&0xf];
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j = k >> 4;
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if (j & Bletch) {
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/* prevent overflows */
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j &= Bletch - 1;
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dval(&d) /= __gdtoa_bigtens[n___gdtoa_bigtens-1];
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ieps++;
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}
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for(; j; j >>= 1, i++)
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if (j & 1) {
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ieps++;
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ds *= __gdtoa_bigtens[i];
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}
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dval(&d) /= ds;
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}
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else if (( j1 = -k )!=0) {
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dval(&d) *= __gdtoa_tens[j1 & 0xf];
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for(j = j1 >> 4; j; j >>= 1, i++)
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if (j & 1) {
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ieps++;
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dval(&d) *= __gdtoa_bigtens[i];
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}
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}
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if (k_check && dval(&d) < 1. && ilim > 0) {
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if (ilim1 <= 0)
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goto fast_failed;
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ilim = ilim1;
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k--;
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dval(&d) *= 10.;
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ieps++;
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}
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dval(&eps) = ieps*dval(&d) + 7.;
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word0(&eps) -= (P-1)*Exp_msk1;
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if (ilim == 0) {
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S = mhi = 0;
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dval(&d) -= 5.;
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if (dval(&d) > dval(&eps))
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goto one_digit;
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if (dval(&d) < -dval(&eps))
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goto no_digits;
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goto fast_failed;
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}
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if (leftright) {
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/* Use Steele & White method of only
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* generating digits needed.
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*/
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dval(&eps) = 0.5/__gdtoa_tens[ilim-1] - dval(&eps);
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if (k0 < 0 && j1 >= 307) {
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eps1.d = 1.01e256; /* 1.01 allows roundoff in the next few lines */
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word0(&eps1) -= Exp_msk1 * (Bias+P-1);
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dval(&eps1) *= __gdtoa_tens[j1 & 0xf];
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for(i = 0, j = (j1-256) >> 4; j; j >>= 1, i++)
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if (j & 1)
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dval(&eps1) *= __gdtoa_bigtens[i];
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if (eps.d < eps1.d)
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eps.d = eps1.d;
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if (10. - d.d < 10.*eps.d && eps.d < 1.) {
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/* eps.d < 1. excludes trouble with the tiniest denormal */
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*s++ = '1';
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++k;
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goto ret1;
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}
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}
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for(i = 0;;) {
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L = dval(&d);
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dval(&d) -= L;
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*s++ = '0' + (int)L;
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if (dval(&d) < dval(&eps))
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goto retc;
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if (1. - dval(&d) < dval(&eps))
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goto bump_up;
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if (++i >= ilim)
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break;
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dval(&eps) *= 10.;
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dval(&d) *= 10.;
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}
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}
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else {
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/* Generate ilim digits, then fix them up. */
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dval(&eps) *= __gdtoa_tens[ilim-1];
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for(i = 1;; i++, dval(&d) *= 10.) {
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L = (Long)(dval(&d));
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if (!(dval(&d) -= L))
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ilim = i;
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*s++ = '0' + (int)L;
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if (i == ilim) {
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if (dval(&d) > 0.5 + dval(&eps))
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goto bump_up;
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else if (dval(&d) < 0.5 - dval(&eps))
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goto retc;
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break;
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}
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}
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}
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fast_failed:
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s = s0;
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dval(&d) = dval(&d2);
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k = k0;
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ilim = ilim0;
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}
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/* Do we have a "small" integer? */
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if (be >= 0 && k <= Int_max) {
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/* Yes. */
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ds = __gdtoa_tens[k];
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if (ndigits < 0 && ilim <= 0) {
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S = mhi = 0;
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if (ilim < 0 || dval(&d) <= 5*ds)
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goto no_digits;
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goto one_digit;
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}
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for(i = 1;; i++, dval(&d) *= 10.) {
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L = (Long)(dval(&d) / ds);
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dval(&d) -= L*ds;
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/* If FLT_ROUNDS == 2, L will usually be high by 1 */
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if (dval(&d) < 0) {
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L--;
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dval(&d) += ds;
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}
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*s++ = '0' + (int)L;
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if (!dval(&d)) {
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break;
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}
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if (i == ilim) {
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if (mode > 1)
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switch(Rounding) {
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case 0: goto retc;
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case 2: goto bump_up;
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}
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dval(&d) += dval(&d);
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if (dval(&d) > ds || (dval(&d) == ds && L & 1)) {
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bump_up:
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while(*--s == '9')
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if (s == s0) {
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k++;
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*s = '0';
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break;
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}
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++*s++;
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}
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break;
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}
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}
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goto retc;
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}
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m2 = b2;
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m5 = b5;
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mhi = mlo = 0;
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if (leftright) {
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i = denorm ? be + (Bias + (P-1) - 1 + 1) : 1 + P - bbits;
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b2 += i;
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s2 += i;
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mhi = __gdtoa_i2b(1, &TI);
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}
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if (m2 > 0 && s2 > 0) {
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i = m2 < s2 ? m2 : s2;
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b2 -= i;
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m2 -= i;
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s2 -= i;
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}
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if (b5 > 0) {
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if (leftright) {
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if (m5 > 0) {
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mhi = __gdtoa_pow5mult(mhi, m5, &TI);
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b1 = __gdtoa_mult(mhi, b, &TI);
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__gdtoa_Bfree(b, &TI);
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b = b1;
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}
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if (( j = b5 - m5 )!=0)
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b = __gdtoa_pow5mult(b, j, &TI);
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}
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else
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b = __gdtoa_pow5mult(b, b5, &TI);
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}
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S = __gdtoa_i2b(1, &TI);
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if (s5 > 0)
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S = __gdtoa_pow5mult(S, s5, &TI);
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/* Check for special case that d is a normalized power of 2. */
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spec_case = 0;
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if ((mode < 2 || leftright) && Rounding == 1) {
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if (!word1(&d) && !(word0(&d) & Bndry_mask) &&
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word0(&d) & (Exp_mask & ~Exp_msk1)) {
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/* The special case */
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b2 += Log2P;
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s2 += Log2P;
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spec_case = 1;
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}
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}
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/* Arrange for convenient computation of quotients:
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* shift left if necessary so divisor has 4 leading 0 bits.
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*
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* Perhaps we should just compute leading 28 bits of S once
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* and for all and pass them and a shift to __gdtoa_quorem, so it
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* can do shifts and ors to compute the numerator for q.
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*/
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if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f )!=0)
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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;
|
|
}
|