| 1 | /* $NetBSD: dtoa.c,v 1.3.4.1.4.1 2008/04/08 21:10:55 jdc Exp $ */
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| 2 |
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| 3 | /****************************************************************
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| 4 |
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| 5 | The author of this software is David M. Gay.
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| 6 |
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| 7 | Copyright (C) 1998, 1999 by Lucent Technologies
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| 8 | All Rights Reserved
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| 9 |
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| 10 | Permission to use, copy, modify, and distribute this software and
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| 11 | its documentation for any purpose and without fee is hereby
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| 12 | granted, provided that the above copyright notice appear in all
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| 13 | copies and that both that the copyright notice and this
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| 14 | permission notice and warranty disclaimer appear in supporting
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| 15 | documentation, and that the name of Lucent or any of its entities
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| 16 | not be used in advertising or publicity pertaining to
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| 17 | distribution of the software without specific, written prior
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| 18 | permission.
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| 19 |
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| 20 | LUCENT DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE,
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| 21 | INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS.
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| 22 | IN NO EVENT SHALL LUCENT OR ANY OF ITS ENTITIES BE LIABLE FOR ANY
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| 23 | SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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| 24 | WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
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| 25 | IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
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| 26 | ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
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| 27 | THIS SOFTWARE.
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| 28 |
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| 29 | ****************************************************************/
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| 30 |
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| 31 | /* Please send bug reports to David M. Gay (dmg at acm dot org,
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| 32 | * with " at " changed at "@" and " dot " changed to "."). */
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| 33 | #include <LibConfig.h>
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| 34 |
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| 35 | #include "gdtoaimp.h"
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| 36 |
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| 37 | /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
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| 38 | *
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| 39 | * Inspired by "How to Print Floating-Point Numbers Accurately" by
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| 40 | * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 112-126].
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| 41 | *
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| 42 | * Modifications:
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| 43 | * 1. Rather than iterating, we use a simple numeric overestimate
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| 44 | * to determine k = floor(log10(d)). We scale relevant
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| 45 | * quantities using O(log2(k)) rather than O(k) multiplications.
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| 46 | * 2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
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| 47 | * try to generate digits strictly left to right. Instead, we
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| 48 | * compute with fewer bits and propagate the carry if necessary
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| 49 | * when rounding the final digit up. This is often faster.
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| 50 | * 3. Under the assumption that input will be rounded nearest,
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| 51 | * mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
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| 52 | * That is, we allow equality in stopping tests when the
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| 53 | * round-nearest rule will give the same floating-point value
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| 54 | * as would satisfaction of the stopping test with strict
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| 55 | * inequality.
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| 56 | * 4. We remove common factors of powers of 2 from relevant
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| 57 | * quantities.
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| 58 | * 5. When converting floating-point integers less than 1e16,
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| 59 | * we use floating-point arithmetic rather than resorting
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| 60 | * to multiple-precision integers.
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| 61 | * 6. When asked to produce fewer than 15 digits, we first try
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| 62 | * to get by with floating-point arithmetic; we resort to
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| 63 | * multiple-precision integer arithmetic only if we cannot
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| 64 | * guarantee that the floating-point calculation has given
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| 65 | * the correctly rounded result. For k requested digits and
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| 66 | * "uniformly" distributed input, the probability is
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| 67 | * something like 10^(k-15) that we must resort to the Long
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| 68 | * calculation.
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| 69 | */
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| 70 |
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| 71 | #ifdef Honor_FLT_ROUNDS
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| 72 | #define Rounding rounding
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| 73 | #undef Check_FLT_ROUNDS
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| 74 | #define Check_FLT_ROUNDS
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| 75 | #else
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| 76 | #define Rounding Flt_Rounds
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| 77 | #endif
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| 78 |
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| 79 | #if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */
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| 80 | // Disable: warning C4700: uninitialized local variable 'xx' used
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| 81 | #pragma warning ( disable : 4700 )
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| 82 | #endif /* defined(_MSC_VER) */
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| 83 |
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| 84 | char *
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| 85 | dtoa
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| 86 | #ifdef KR_headers
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| 87 | (d, mode, ndigits, decpt, sign, rve)
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| 88 | double d; int mode, ndigits, *decpt, *sign; char **rve;
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| 89 | #else
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| 90 | (double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
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| 91 | #endif
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| 92 | {
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| 93 | /* Arguments ndigits, decpt, sign are similar to those
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| 94 | of ecvt and fcvt; trailing zeros are suppressed from
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| 95 | the returned string. If not null, *rve is set to point
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| 96 | to the end of the return value. If d is +-Infinity or NaN,
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| 97 | then *decpt is set to 9999.
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| 98 |
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| 99 | mode:
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| 100 | 0 ==> shortest string that yields d when read in
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| 101 | and rounded to nearest.
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| 102 | 1 ==> like 0, but with Steele & White stopping rule;
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| 103 | e.g. with IEEE P754 arithmetic , mode 0 gives
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| 104 | 1e23 whereas mode 1 gives 9.999999999999999e22.
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| 105 | 2 ==> max(1,ndigits) significant digits. This gives a
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| 106 | return value similar to that of ecvt, except
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| 107 | that trailing zeros are suppressed.
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| 108 | 3 ==> through ndigits past the decimal point. This
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| 109 | gives a return value similar to that from fcvt,
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| 110 | except that trailing zeros are suppressed, and
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| 111 | ndigits can be negative.
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| 112 | 4,5 ==> similar to 2 and 3, respectively, but (in
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| 113 | round-nearest mode) with the tests of mode 0 to
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| 114 | possibly return a shorter string that rounds to d.
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| 115 | With IEEE arithmetic and compilation with
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| 116 | -DHonor_FLT_ROUNDS, modes 4 and 5 behave the same
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| 117 | as modes 2 and 3 when FLT_ROUNDS != 1.
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| 118 | 6-9 ==> Debugging modes similar to mode - 4: don't try
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| 119 | fast floating-point estimate (if applicable).
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| 120 |
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| 121 | Values of mode other than 0-9 are treated as mode 0.
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| 122 |
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| 123 | Sufficient space is allocated to the return value
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| 124 | to hold the suppressed trailing zeros.
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| 125 | */
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| 126 |
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| 127 | int bbits, b2, b5, be, dig, i, ieps, ilim0,
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| 128 | j, jj1, k, k0, k_check, leftright, m2, m5, s2, s5,
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| 129 | spec_case, try_quick;
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| 130 | int ilim = 0, ilim1 = 0; /* pacify gcc */
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| 131 | Long L;
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| 132 | #ifndef Sudden_Underflow
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| 133 | int denorm;
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| 134 | ULong x;
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| 135 | #endif
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| 136 | Bigint *b, *b1, *delta, *mhi, *S;
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| 137 | Bigint *mlo = NULL; /* pacify gcc */
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| 138 | double d2, ds, eps;
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| 139 | char *s, *s0;
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| 140 | #ifdef Honor_FLT_ROUNDS
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| 141 | int rounding;
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| 142 | #endif
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| 143 | #ifdef SET_INEXACT
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| 144 | int inexact, oldinexact;
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| 145 | #endif
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| 146 |
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| 147 | #ifndef MULTIPLE_THREADS
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| 148 | if (dtoa_result) {
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| 149 | freedtoa(dtoa_result);
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| 150 | dtoa_result = 0;
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| 151 | }
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| 152 | #endif
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| 153 |
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| 154 | if (word0(d) & Sign_bit) {
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| 155 | /* set sign for everything, including 0's and NaNs */
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| 156 | *sign = 1;
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| 157 | word0(d) &= ~Sign_bit; /* clear sign bit */
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| 158 | }
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| 159 | else
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| 160 | *sign = 0;
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| 161 |
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| 162 | #if defined(IEEE_Arith) + defined(VAX)
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| 163 | #ifdef IEEE_Arith
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| 164 | if ((word0(d) & Exp_mask) == Exp_mask)
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| 165 | #else
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| 166 | if (word0(d) == 0x8000)
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| 167 | #endif
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| 168 | {
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| 169 | /* Infinity or NaN */
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| 170 | *decpt = 9999;
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| 171 | #ifdef IEEE_Arith
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| 172 | if (!word1(d) && !(word0(d) & 0xfffff))
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| 173 | return nrv_alloc("Infinity", rve, 8);
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| 174 | #endif
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| 175 | return nrv_alloc("NaN", rve, 3);
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| 176 | }
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| 177 | #endif
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| 178 | #ifdef IBM
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| 179 | dval(d) += 0; /* normalize */
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| 180 | #endif
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| 181 | if (!dval(d)) {
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| 182 | *decpt = 1;
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| 183 | return nrv_alloc("0", rve, 1);
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| 184 | }
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| 185 |
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| 186 | #ifdef SET_INEXACT
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| 187 | try_quick = oldinexact = get_inexact();
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| 188 | inexact = 1;
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| 189 | #endif
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| 190 | #ifdef Honor_FLT_ROUNDS
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| 191 | if ((rounding = Flt_Rounds) >= 2) {
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| 192 | if (*sign)
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| 193 | rounding = rounding == 2 ? 0 : 2;
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| 194 | else
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| 195 | if (rounding != 2)
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| 196 | rounding = 0;
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| 197 | }
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| 198 | #endif
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| 199 |
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| 200 | b = d2b(dval(d), &be, &bbits);
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| 201 | if (b == NULL)
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| 202 | return NULL;
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| 203 | #ifdef Sudden_Underflow
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| 204 | i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1));
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| 205 | #else
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| 206 | if (( i = (int)(word0(d) >> Exp_shift1 & (Exp_mask>>Exp_shift1)) )!=0) {
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| 207 | #endif
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| 208 | dval(d2) = dval(d);
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| 209 | word0(d2) &= Frac_mask1;
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| 210 | word0(d2) |= Exp_11;
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| 211 | #ifdef IBM
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| 212 | if (( j = 11 - hi0bits(word0(d2) & Frac_mask) )!=0)
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| 213 | dval(d2) /= 1 << j;
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| 214 | #endif
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| 215 |
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| 216 | /* log(x) ~=~ log(1.5) + (x-1.5)/1.5
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| 217 | * log10(x) = log(x) / log(10)
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| 218 | * ~=~ log(1.5)/log(10) + (x-1.5)/(1.5*log(10))
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| 219 | * log10(d) = (i-Bias)*log(2)/log(10) + log10(d2)
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| 220 | *
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| 221 | * This suggests computing an approximation k to log10(d) by
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| 222 | *
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| 223 | * k = (i - Bias)*0.301029995663981
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| 224 | * + ( (d2-1.5)*0.289529654602168 + 0.176091259055681 );
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| 225 | *
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| 226 | * We want k to be too large rather than too small.
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| 227 | * The error in the first-order Taylor series approximation
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| 228 | * is in our favor, so we just round up the constant enough
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| 229 | * to compensate for any error in the multiplication of
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| 230 | * (i - Bias) by 0.301029995663981; since |i - Bias| <= 1077,
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| 231 | * and 1077 * 0.30103 * 2^-52 ~=~ 7.2e-14,
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| 232 | * adding 1e-13 to the constant term more than suffices.
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| 233 | * Hence we adjust the constant term to 0.1760912590558.
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| 234 | * (We could get a more accurate k by invoking log10,
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| 235 | * but this is probably not worthwhile.)
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| 236 | */
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| 237 |
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| 238 | i -= Bias;
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| 239 | #ifdef IBM
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| 240 | i <<= 2;
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| 241 | i += j;
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| 242 | #endif
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| 243 | #ifndef Sudden_Underflow
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| 244 | denorm = 0;
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| 245 | }
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| 246 | else {
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| 247 | /* d is denormalized */
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| 248 |
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| 249 | i = bbits + be + (Bias + (P-1) - 1);
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| 250 | x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
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| 251 | : word1(d) << (32 - i);
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| 252 | dval(d2) = (double)x;
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| 253 | word0(d2) -= 31*Exp_msk1; /* adjust exponent */
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| 254 | i -= (Bias + (P-1) - 1) + 1;
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| 255 | denorm = 1;
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| 256 | }
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| 257 | #endif
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| 258 | ds = (dval(d2)-1.5)*0.289529654602168 + 0.1760912590558 + i*0.301029995663981;
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| 259 | k = (int)ds;
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| 260 | if (ds < 0. && ds != k)
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| 261 | k--; /* want k = floor(ds) */
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| 262 | k_check = 1;
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| 263 | if (k >= 0 && k <= Ten_pmax) {
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| 264 | if (dval(d) < tens[k])
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| 265 | k--;
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| 266 | k_check = 0;
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| 267 | }
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| 268 | j = bbits - i - 1;
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| 269 | if (j >= 0) {
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| 270 | b2 = 0;
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| 271 | s2 = j;
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| 272 | }
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| 273 | else {
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| 274 | b2 = -j;
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| 275 | s2 = 0;
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| 276 | }
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| 277 | if (k >= 0) {
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| 278 | b5 = 0;
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| 279 | s5 = k;
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| 280 | s2 += k;
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| 281 | }
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| 282 | else {
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| 283 | b2 -= k;
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| 284 | b5 = -k;
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| 285 | s5 = 0;
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| 286 | }
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| 287 | if (mode < 0 || mode > 9)
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| 288 | mode = 0;
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| 289 |
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| 290 | #ifndef SET_INEXACT
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| 291 | #ifdef Check_FLT_ROUNDS
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| 292 | try_quick = Rounding == 1;
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| 293 | #else
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| 294 | try_quick = 1;
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| 295 | #endif
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| 296 | #endif /*SET_INEXACT*/
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| 297 |
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| 298 | if (mode > 5) {
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| 299 | mode -= 4;
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| 300 | try_quick = 0;
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| 301 | }
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| 302 | leftright = 1;
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| 303 | switch(mode) {
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| 304 | case 0:
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| 305 | case 1:
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| 306 | ilim = ilim1 = -1;
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| 307 | i = 18;
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| 308 | ndigits = 0;
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| 309 | break;
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| 310 | case 2:
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| 311 | leftright = 0;
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| 312 | /* FALLTHROUGH */
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| 313 | case 4:
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| 314 | if (ndigits <= 0)
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| 315 | ndigits = 1;
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| 316 | ilim = ilim1 = i = ndigits;
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| 317 | break;
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| 318 | case 3:
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| 319 | leftright = 0;
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| 320 | /* FALLTHROUGH */
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| 321 | case 5:
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| 322 | i = ndigits + k + 1;
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| 323 | ilim = i;
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| 324 | ilim1 = i - 1;
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| 325 | if (i <= 0)
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| 326 | i = 1;
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| 327 | }
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| 328 | s = s0 = rv_alloc((size_t)i);
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| 329 | if (s == NULL)
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| 330 | return NULL;
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| 331 |
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| 332 | #ifdef Honor_FLT_ROUNDS
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| 333 | if (mode > 1 && rounding != 1)
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| 334 | leftright = 0;
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| 335 | #endif
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| 336 |
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| 337 | if (ilim >= 0 && ilim <= Quick_max && try_quick) {
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| 338 |
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| 339 | /* Try to get by with floating-point arithmetic. */
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| 340 |
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| 341 | i = 0;
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| 342 | dval(d2) = dval(d);
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| 343 | k0 = k;
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| 344 | ilim0 = ilim;
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| 345 | ieps = 2; /* conservative */
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| 346 | if (k > 0) {
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| 347 | ds = tens[k&0xf];
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| 348 | j = (unsigned int)k >> 4;
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| 349 | if (j & Bletch) {
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| 350 | /* prevent overflows */
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| 351 | j &= Bletch - 1;
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| 352 | dval(d) /= bigtens[n_bigtens-1];
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| 353 | ieps++;
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| 354 | }
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| 355 | for(; j; j = (unsigned int)j >> 1, i++)
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| 356 | if (j & 1) {
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| 357 | ieps++;
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| 358 | ds *= bigtens[i];
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| 359 | }
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| 360 | dval(d) /= ds;
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| 361 | }
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| 362 | else if (( jj1 = -k )!=0) {
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| 363 | dval(d) *= tens[jj1 & 0xf];
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| 364 | for(j = jj1 >> 4; j; j >>= 1, i++)
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| 365 | if (j & 1) {
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| 366 | ieps++;
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| 367 | dval(d) *= bigtens[i];
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| 368 | }
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| 369 | }
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| 370 | if (k_check && dval(d) < 1. && ilim > 0) {
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| 371 | if (ilim1 <= 0)
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| 372 | goto fast_failed;
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| 373 | ilim = ilim1;
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| 374 | k--;
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| 375 | dval(d) *= 10.;
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| 376 | ieps++;
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| 377 | }
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| 378 | dval(eps) = ieps*dval(d) + 7.;
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| 379 | word0(eps) -= (P-1)*Exp_msk1;
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| 380 | if (ilim == 0) {
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| 381 | S = mhi = 0;
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| 382 | dval(d) -= 5.;
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| 383 | if (dval(d) > dval(eps))
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| 384 | goto one_digit;
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| 385 | if (dval(d) < -dval(eps))
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| 386 | goto no_digits;
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| 387 | goto fast_failed;
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| 388 | }
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| 389 | #ifndef No_leftright
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| 390 | if (leftright) {
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| 391 | /* Use Steele & White method of only
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| 392 | * generating digits needed.
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| 393 | */
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| 394 | dval(eps) = 0.5/tens[ilim-1] - dval(eps);
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| 395 | for(i = 0;;) {
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| 396 | L = (INT32)dval(d);
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| 397 | dval(d) -= L;
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| 398 | *s++ = (char)('0' + (int)L);
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| 399 | if (dval(d) < dval(eps))
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| 400 | goto ret1;
|
|---|
| 401 | if (1. - dval(d) < dval(eps))
|
|---|
| 402 | goto bump_up;
|
|---|
| 403 | if (++i >= ilim)
|
|---|
| 404 | break;
|
|---|
| 405 | dval(eps) *= 10.;
|
|---|
| 406 | dval(d) *= 10.;
|
|---|
| 407 | }
|
|---|
| 408 | }
|
|---|
| 409 | else {
|
|---|
| 410 | #endif
|
|---|
| 411 | /* Generate ilim digits, then fix them up. */
|
|---|
| 412 | dval(eps) *= tens[ilim-1];
|
|---|
| 413 | for(i = 1;; i++, dval(d) *= 10.) {
|
|---|
| 414 | L = (Long)(dval(d));
|
|---|
| 415 | if (!(dval(d) -= L))
|
|---|
| 416 | ilim = i;
|
|---|
| 417 | *s++ = (char)('0' + (int)L);
|
|---|
| 418 | if (i == ilim) {
|
|---|
| 419 | if (dval(d) > 0.5 + dval(eps))
|
|---|
| 420 | goto bump_up;
|
|---|
| 421 | else if (dval(d) < 0.5 - dval(eps)) {
|
|---|
| 422 | while(*--s == '0');
|
|---|
| 423 | s++;
|
|---|
| 424 | goto ret1;
|
|---|
| 425 | }
|
|---|
| 426 | break;
|
|---|
| 427 | }
|
|---|
| 428 | }
|
|---|
| 429 | #ifndef No_leftright
|
|---|
| 430 | }
|
|---|
| 431 | #endif
|
|---|
| 432 | fast_failed:
|
|---|
| 433 | s = s0;
|
|---|
| 434 | dval(d) = dval(d2);
|
|---|
| 435 | k = k0;
|
|---|
| 436 | ilim = ilim0;
|
|---|
| 437 | }
|
|---|
| 438 |
|
|---|
| 439 | /* Do we have a "small" integer? */
|
|---|
| 440 |
|
|---|
| 441 | if (be >= 0 && k <= Int_max) {
|
|---|
| 442 | /* Yes. */
|
|---|
| 443 | ds = tens[k];
|
|---|
| 444 | if (ndigits < 0 && ilim <= 0) {
|
|---|
| 445 | S = mhi = 0;
|
|---|
| 446 | if (ilim < 0 || dval(d) <= 5*ds)
|
|---|
| 447 | goto no_digits;
|
|---|
| 448 | goto one_digit;
|
|---|
| 449 | }
|
|---|
| 450 | for(i = 1;; i++, dval(d) *= 10.) {
|
|---|
| 451 | L = (Long)(dval(d) / ds);
|
|---|
| 452 | dval(d) -= L*ds;
|
|---|
| 453 | #ifdef Check_FLT_ROUNDS
|
|---|
| 454 | /* If FLT_ROUNDS == 2, L will usually be high by 1 */
|
|---|
| 455 | if (dval(d) < 0) {
|
|---|
| 456 | L--;
|
|---|
| 457 | dval(d) += ds;
|
|---|
| 458 | }
|
|---|
| 459 | #endif
|
|---|
| 460 | *s++ = (char)('0' + (int)L);
|
|---|
| 461 | if (!dval(d)) {
|
|---|
| 462 | #ifdef SET_INEXACT
|
|---|
| 463 | inexact = 0;
|
|---|
| 464 | #endif
|
|---|
| 465 | break;
|
|---|
| 466 | }
|
|---|
| 467 | if (i == ilim) {
|
|---|
| 468 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 469 | if (mode > 1)
|
|---|
| 470 | switch(rounding) {
|
|---|
| 471 | case 0: goto ret1;
|
|---|
| 472 | case 2: goto bump_up;
|
|---|
| 473 | }
|
|---|
| 474 | #endif
|
|---|
| 475 | dval(d) += dval(d);
|
|---|
| 476 | if (dval(d) > ds || (dval(d) == ds && L & 1)) {
|
|---|
| 477 | bump_up:
|
|---|
| 478 | while(*--s == '9')
|
|---|
| 479 | if (s == s0) {
|
|---|
| 480 | k++;
|
|---|
| 481 | *s = '0';
|
|---|
| 482 | break;
|
|---|
| 483 | }
|
|---|
| 484 | ++*s++;
|
|---|
| 485 | }
|
|---|
| 486 | break;
|
|---|
| 487 | }
|
|---|
| 488 | }
|
|---|
| 489 | goto ret1;
|
|---|
| 490 | }
|
|---|
| 491 |
|
|---|
| 492 | m2 = b2;
|
|---|
| 493 | m5 = b5;
|
|---|
| 494 | mhi = mlo = 0;
|
|---|
| 495 | if (leftright) {
|
|---|
| 496 | i =
|
|---|
| 497 | #ifndef Sudden_Underflow
|
|---|
| 498 | denorm ? be + (Bias + (P-1) - 1 + 1) :
|
|---|
| 499 | #endif
|
|---|
| 500 | #ifdef IBM
|
|---|
| 501 | 1 + 4*P - 3 - bbits + ((bbits + be - 1) & 3);
|
|---|
| 502 | #else
|
|---|
| 503 | 1 + P - bbits;
|
|---|
| 504 | #endif
|
|---|
| 505 | b2 += i;
|
|---|
| 506 | s2 += i;
|
|---|
| 507 | mhi = i2b(1);
|
|---|
| 508 | if (mhi == NULL)
|
|---|
| 509 | return NULL;
|
|---|
| 510 | }
|
|---|
| 511 | if (m2 > 0 && s2 > 0) {
|
|---|
| 512 | i = m2 < s2 ? m2 : s2;
|
|---|
| 513 | b2 -= i;
|
|---|
| 514 | m2 -= i;
|
|---|
| 515 | s2 -= i;
|
|---|
| 516 | }
|
|---|
| 517 | if (b5 > 0) {
|
|---|
| 518 | if (leftright) {
|
|---|
| 519 | if (m5 > 0) {
|
|---|
| 520 | mhi = pow5mult(mhi, m5);
|
|---|
| 521 | if (mhi == NULL)
|
|---|
| 522 | return NULL;
|
|---|
| 523 | b1 = mult(mhi, b);
|
|---|
| 524 | if (b1 == NULL)
|
|---|
| 525 | return NULL;
|
|---|
| 526 | Bfree(b);
|
|---|
| 527 | b = b1;
|
|---|
| 528 | }
|
|---|
| 529 | if (( j = b5 - m5 )!=0)
|
|---|
| 530 | b = pow5mult(b, j);
|
|---|
| 531 | if (b == NULL)
|
|---|
| 532 | return NULL;
|
|---|
| 533 | }
|
|---|
| 534 | else
|
|---|
| 535 | b = pow5mult(b, b5);
|
|---|
| 536 | if (b == NULL)
|
|---|
| 537 | return NULL;
|
|---|
| 538 | }
|
|---|
| 539 | S = i2b(1);
|
|---|
| 540 | if (S == NULL)
|
|---|
| 541 | return NULL;
|
|---|
| 542 | if (s5 > 0) {
|
|---|
| 543 | S = pow5mult(S, s5);
|
|---|
| 544 | if (S == NULL)
|
|---|
| 545 | return NULL;
|
|---|
| 546 | }
|
|---|
| 547 |
|
|---|
| 548 | /* Check for special case that d is a normalized power of 2. */
|
|---|
| 549 |
|
|---|
| 550 | spec_case = 0;
|
|---|
| 551 | if ((mode < 2 || leftright)
|
|---|
| 552 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 553 | && rounding == 1
|
|---|
| 554 | #endif
|
|---|
| 555 | ) {
|
|---|
| 556 | if (!word1(d) && !(word0(d) & Bndry_mask)
|
|---|
| 557 | #ifndef Sudden_Underflow
|
|---|
| 558 | && word0(d) & (Exp_mask & ~Exp_msk1)
|
|---|
| 559 | #endif
|
|---|
| 560 | ) {
|
|---|
| 561 | /* The special case */
|
|---|
| 562 | b2 += Log2P;
|
|---|
| 563 | s2 += Log2P;
|
|---|
| 564 | spec_case = 1;
|
|---|
| 565 | }
|
|---|
| 566 | }
|
|---|
| 567 |
|
|---|
| 568 | /* Arrange for convenient computation of quotients:
|
|---|
| 569 | * shift left if necessary so divisor has 4 leading 0 bits.
|
|---|
| 570 | *
|
|---|
| 571 | * Perhaps we should just compute leading 28 bits of S once
|
|---|
| 572 | * and for all and pass them and a shift to quorem, so it
|
|---|
| 573 | * can do shifts and ors to compute the numerator for q.
|
|---|
| 574 | */
|
|---|
| 575 | #ifdef Pack_32
|
|---|
| 576 | if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0x1f )!=0)
|
|---|
| 577 | i = 32 - i;
|
|---|
| 578 | #else
|
|---|
| 579 | if (( i = ((s5 ? 32 - hi0bits(S->x[S->wds-1]) : 1) + s2) & 0xf )!=0)
|
|---|
| 580 | i = 16 - i;
|
|---|
| 581 | #endif
|
|---|
| 582 | if (i > 4) {
|
|---|
| 583 | i -= 4;
|
|---|
| 584 | b2 += i;
|
|---|
| 585 | m2 += i;
|
|---|
| 586 | s2 += i;
|
|---|
| 587 | }
|
|---|
| 588 | else if (i < 4) {
|
|---|
| 589 | i += 28;
|
|---|
| 590 | b2 += i;
|
|---|
| 591 | m2 += i;
|
|---|
| 592 | s2 += i;
|
|---|
| 593 | }
|
|---|
| 594 | if (b2 > 0) {
|
|---|
| 595 | b = lshift(b, b2);
|
|---|
| 596 | if (b == NULL)
|
|---|
| 597 | return NULL;
|
|---|
| 598 | }
|
|---|
| 599 | if (s2 > 0) {
|
|---|
| 600 | S = lshift(S, s2);
|
|---|
| 601 | if (S == NULL)
|
|---|
| 602 | return NULL;
|
|---|
| 603 | }
|
|---|
| 604 | if (k_check) {
|
|---|
| 605 | if (cmp(b,S) < 0) {
|
|---|
| 606 | k--;
|
|---|
| 607 | b = multadd(b, 10, 0); /* we botched the k estimate */
|
|---|
| 608 | if (b == NULL)
|
|---|
| 609 | return NULL;
|
|---|
| 610 | if (leftright) {
|
|---|
| 611 | mhi = multadd(mhi, 10, 0);
|
|---|
| 612 | if (mhi == NULL)
|
|---|
| 613 | return NULL;
|
|---|
| 614 | }
|
|---|
| 615 | ilim = ilim1;
|
|---|
| 616 | }
|
|---|
| 617 | }
|
|---|
| 618 | if (ilim <= 0 && (mode == 3 || mode == 5)) {
|
|---|
| 619 | if (ilim < 0 || cmp(b,S = multadd(S,5,0)) <= 0) {
|
|---|
| 620 | /* no digits, fcvt style */
|
|---|
| 621 | no_digits:
|
|---|
| 622 | k = -1 - ndigits;
|
|---|
| 623 | goto ret;
|
|---|
| 624 | }
|
|---|
| 625 | one_digit:
|
|---|
| 626 | *s++ = '1';
|
|---|
| 627 | k++;
|
|---|
| 628 | goto ret;
|
|---|
| 629 | }
|
|---|
| 630 | if (leftright) {
|
|---|
| 631 | if (m2 > 0) {
|
|---|
| 632 | mhi = lshift(mhi, m2);
|
|---|
| 633 | if (mhi == NULL)
|
|---|
| 634 | return NULL;
|
|---|
| 635 | }
|
|---|
| 636 |
|
|---|
| 637 | /* Compute mlo -- check for special case
|
|---|
| 638 | * that d is a normalized power of 2.
|
|---|
| 639 | */
|
|---|
| 640 |
|
|---|
| 641 | mlo = mhi;
|
|---|
| 642 | if (spec_case) {
|
|---|
| 643 | mhi = Balloc(mhi->k);
|
|---|
| 644 | if (mhi == NULL)
|
|---|
| 645 | return NULL;
|
|---|
| 646 | Bcopy(mhi, mlo);
|
|---|
| 647 | mhi = lshift(mhi, Log2P);
|
|---|
| 648 | if (mhi == NULL)
|
|---|
| 649 | return NULL;
|
|---|
| 650 | }
|
|---|
| 651 |
|
|---|
| 652 | for(i = 1;;i++) {
|
|---|
| 653 | dig = quorem(b,S) + '0';
|
|---|
| 654 | /* Do we yet have the shortest decimal string
|
|---|
| 655 | * that will round to d?
|
|---|
| 656 | */
|
|---|
| 657 | j = cmp(b, mlo);
|
|---|
| 658 | delta = diff(S, mhi);
|
|---|
| 659 | if (delta == NULL)
|
|---|
| 660 | return NULL;
|
|---|
| 661 | jj1 = delta->sign ? 1 : cmp(b, delta);
|
|---|
| 662 | Bfree(delta);
|
|---|
| 663 | #ifndef ROUND_BIASED
|
|---|
| 664 | if (jj1 == 0 && mode != 1 && !(word1(d) & 1)
|
|---|
| 665 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 666 | && rounding >= 1
|
|---|
| 667 | #endif
|
|---|
| 668 | ) {
|
|---|
| 669 | if (dig == '9')
|
|---|
| 670 | goto round_9_up;
|
|---|
| 671 | if (j > 0)
|
|---|
| 672 | dig++;
|
|---|
| 673 | #ifdef SET_INEXACT
|
|---|
| 674 | else if (!b->x[0] && b->wds <= 1)
|
|---|
| 675 | inexact = 0;
|
|---|
| 676 | #endif
|
|---|
| 677 | *s++ = (char)dig;
|
|---|
| 678 | goto ret;
|
|---|
| 679 | }
|
|---|
| 680 | #endif
|
|---|
| 681 | if (j < 0 || (j == 0 && mode != 1
|
|---|
| 682 | #ifndef ROUND_BIASED
|
|---|
| 683 | && !(word1(d) & 1)
|
|---|
| 684 | #endif
|
|---|
| 685 | )) {
|
|---|
| 686 | if (!b->x[0] && b->wds <= 1) {
|
|---|
| 687 | #ifdef SET_INEXACT
|
|---|
| 688 | inexact = 0;
|
|---|
| 689 | #endif
|
|---|
| 690 | goto accept_dig;
|
|---|
| 691 | }
|
|---|
| 692 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 693 | if (mode > 1)
|
|---|
| 694 | switch(rounding) {
|
|---|
| 695 | case 0: goto accept_dig;
|
|---|
| 696 | case 2: goto keep_dig;
|
|---|
| 697 | }
|
|---|
| 698 | #endif /*Honor_FLT_ROUNDS*/
|
|---|
| 699 | if (jj1 > 0) {
|
|---|
| 700 | b = lshift(b, 1);
|
|---|
| 701 | if (b == NULL)
|
|---|
| 702 | return NULL;
|
|---|
| 703 | jj1 = cmp(b, S);
|
|---|
| 704 | if ((jj1 > 0 || (jj1 == 0 && dig & 1))
|
|---|
| 705 | && dig++ == '9')
|
|---|
| 706 | goto round_9_up;
|
|---|
| 707 | }
|
|---|
| 708 | accept_dig:
|
|---|
| 709 | *s++ = (char)dig;
|
|---|
| 710 | goto ret;
|
|---|
| 711 | }
|
|---|
| 712 | if (jj1 > 0) {
|
|---|
| 713 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 714 | if (!rounding)
|
|---|
| 715 | goto accept_dig;
|
|---|
| 716 | #endif
|
|---|
| 717 | if (dig == '9') { /* possible if i == 1 */
|
|---|
| 718 | round_9_up:
|
|---|
| 719 | *s++ = '9';
|
|---|
| 720 | goto roundoff;
|
|---|
| 721 | }
|
|---|
| 722 | *s++ = (char)(dig + 1);
|
|---|
| 723 | goto ret;
|
|---|
| 724 | }
|
|---|
| 725 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 726 | keep_dig:
|
|---|
| 727 | #endif
|
|---|
| 728 | *s++ = (char)dig;
|
|---|
| 729 | if (i == ilim)
|
|---|
| 730 | break;
|
|---|
| 731 | b = multadd(b, 10, 0);
|
|---|
| 732 | if (b == NULL)
|
|---|
| 733 | return NULL;
|
|---|
| 734 | if (mlo == mhi) {
|
|---|
| 735 | mlo = mhi = multadd(mhi, 10, 0);
|
|---|
| 736 | if (mlo == NULL)
|
|---|
| 737 | return NULL;
|
|---|
| 738 | }
|
|---|
| 739 | else {
|
|---|
| 740 | mlo = multadd(mlo, 10, 0);
|
|---|
| 741 | if (mlo == NULL)
|
|---|
| 742 | return NULL;
|
|---|
| 743 | mhi = multadd(mhi, 10, 0);
|
|---|
| 744 | if (mhi == NULL)
|
|---|
| 745 | return NULL;
|
|---|
| 746 | }
|
|---|
| 747 | }
|
|---|
| 748 | }
|
|---|
| 749 | else
|
|---|
| 750 | for(i = 1;; i++) {
|
|---|
| 751 | *s++ = (char)(dig = (int)(quorem(b,S) + '0'));
|
|---|
| 752 | if (!b->x[0] && b->wds <= 1) {
|
|---|
| 753 | #ifdef SET_INEXACT
|
|---|
| 754 | inexact = 0;
|
|---|
| 755 | #endif
|
|---|
| 756 | goto ret;
|
|---|
| 757 | }
|
|---|
| 758 | if (i >= ilim)
|
|---|
| 759 | break;
|
|---|
| 760 | b = multadd(b, 10, 0);
|
|---|
| 761 | if (b == NULL)
|
|---|
| 762 | return NULL;
|
|---|
| 763 | }
|
|---|
| 764 |
|
|---|
| 765 | /* Round off last digit */
|
|---|
| 766 |
|
|---|
| 767 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 768 | switch(rounding) {
|
|---|
| 769 | case 0: goto trimzeros;
|
|---|
| 770 | case 2: goto roundoff;
|
|---|
| 771 | }
|
|---|
| 772 | #endif
|
|---|
| 773 | b = lshift(b, 1);
|
|---|
| 774 | j = cmp(b, S);
|
|---|
| 775 | if (j > 0 || (j == 0 && dig & 1)) {
|
|---|
| 776 | roundoff:
|
|---|
| 777 | while(*--s == '9')
|
|---|
| 778 | if (s == s0) {
|
|---|
| 779 | k++;
|
|---|
| 780 | *s++ = '1';
|
|---|
| 781 | goto ret;
|
|---|
| 782 | }
|
|---|
| 783 | ++*s++;
|
|---|
| 784 | }
|
|---|
| 785 | else {
|
|---|
| 786 | #ifdef Honor_FLT_ROUNDS
|
|---|
| 787 | trimzeros:
|
|---|
| 788 | #endif
|
|---|
| 789 | while(*--s == '0');
|
|---|
| 790 | s++;
|
|---|
| 791 | }
|
|---|
| 792 | ret:
|
|---|
| 793 | Bfree(S);
|
|---|
| 794 | if (mhi) {
|
|---|
| 795 | if (mlo && mlo != mhi)
|
|---|
| 796 | Bfree(mlo);
|
|---|
| 797 | Bfree(mhi);
|
|---|
| 798 | }
|
|---|
| 799 | ret1:
|
|---|
| 800 | #ifdef SET_INEXACT
|
|---|
| 801 | if (inexact) {
|
|---|
| 802 | if (!oldinexact) {
|
|---|
| 803 | word0(d) = Exp_1 + (70 << Exp_shift);
|
|---|
| 804 | word1(d) = 0;
|
|---|
| 805 | dval(d) += 1.;
|
|---|
| 806 | }
|
|---|
| 807 | }
|
|---|
| 808 | else if (!oldinexact)
|
|---|
| 809 | clear_inexact();
|
|---|
| 810 | #endif
|
|---|
| 811 | Bfree(b);
|
|---|
| 812 | if (s == s0) { /* don't return empty string */
|
|---|
| 813 | *s++ = '0';
|
|---|
| 814 | k = 0;
|
|---|
| 815 | }
|
|---|
| 816 | *s = 0;
|
|---|
| 817 | *decpt = k + 1;
|
|---|
| 818 | if (rve)
|
|---|
| 819 | *rve = s;
|
|---|
| 820 | return s0;
|
|---|
| 821 | }
|
|---|
