1 /*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2004-2008 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29 #include <float.h>
30 #include <limits.h>
31 #include <math.h>
32
33 #include "../stdio/floatio.h"
34 #include "fpmath.h"
35 #include "gdtoaimp.h"
36
37 /* Strings values used by dtoa() */
38 #define INFSTR "Infinity"
39 #define NANSTR "NaN"
40
41 #define DBL_ADJ (DBL_MAX_EXP - 2)
42 #define SIGFIGS ((DBL_MANT_DIG + 3) / 4 + 1)
43 #define MAX_HEX_DIGITS ((DBL_MANT_DIG + 3 - 1) / 4 + 1)
44
45 static const float one[] = { 1.0f, -1.0f };
46
47 /*
48 * This procedure converts a double-precision number in IEEE format
49 * into a string of hexadecimal digits and an exponent of 2. Its
50 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
51 * following exceptions:
52 *
53 * - An ndigits < 0 causes it to use as many digits as necessary to
54 * represent the number exactly.
55 * - The additional xdigs argument should point to either the string
56 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
57 * which case is desired.
58 * - This routine does not repeat dtoa's mistake of setting decpt
59 * to 9999 in the case of an infinity or NaN. INT_MAX is used
60 * for this purpose instead.
61 *
62 * Note that the C99 standard does not specify what the leading digit
63 * should be for non-zero numbers. For instance, 0x1.3p3 is the same
64 * as 0x2.6p2 is the same as 0x4.cp3. This implementation always makes
65 * the leading digit a 1. This ensures that the exponent printed is the
66 * actual base-2 exponent, i.e., ilogb(d).
67 *
68 * Inputs: d, xdigs, ndigits
69 * Outputs: decpt, sign, rve
70 */
71 char *
__hdtoa(double d,const char * xdigs,int ndigits,int * decpt,int * sign,char ** rve)72 __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
73 char **rve)
74 {
75 union IEEEd2bits u;
76 char *s, *s0;
77 int bufsize;
78 uint32_t manh, manl;
79
80 u.d = d;
81 *sign = u.bits.sign;
82
83 switch (fpclassify(d)) {
84 case FP_NORMAL:
85 *decpt = u.bits.exp - DBL_ADJ;
86 break;
87 case FP_ZERO:
88 *decpt = 1;
89 return (nrv_alloc("0", rve, 1));
90 case FP_SUBNORMAL:
91 u.d *= 0x1p514;
92 *decpt = u.bits.exp - (514 + DBL_ADJ);
93 break;
94 case FP_INFINITE:
95 *decpt = INT_MAX;
96 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
97 default: /* FP_NAN or unrecognized */
98 *decpt = INT_MAX;
99 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
100 }
101
102 /* FP_NORMAL or FP_SUBNORMAL */
103
104 if (ndigits == 0) /* dtoa() compatibility */
105 ndigits = 1;
106
107 /*
108 * If ndigits < 0, we are expected to auto-size, so we allocate
109 * enough space for all the digits.
110 */
111 bufsize = (ndigits > 0) ? ndigits : SIGFIGS;
112 s0 = rv_alloc(bufsize);
113
114 /* Round to the desired number of digits. */
115 if (MAX_HEX_DIGITS > ndigits && ndigits > 0) {
116 float redux = one[u.bits.sign];
117 int offset = 4 * ndigits + DBL_MAX_EXP - 4 - DBL_MANT_DIG;
118 u.bits.exp = offset;
119 u.d += redux;
120 u.d -= redux;
121 *decpt += u.bits.exp - offset;
122 }
123
124 manh = u.bits.manh;
125 manl = u.bits.manl;
126 *s0 = '1';
127 for (s = s0 + 1; s < s0 + bufsize; s++) {
128 *s = xdigs[(manh >> (DBL_MANH_SIZE - 4)) & 0xf];
129 manh = (manh << 4) | (manl >> (DBL_MANL_SIZE - 4));
130 manl <<= 4;
131 }
132
133 /* If ndigits < 0, we are expected to auto-size the precision. */
134 if (ndigits < 0) {
135 for (ndigits = SIGFIGS; s0[ndigits - 1] == '0'; ndigits--)
136 ;
137 }
138
139 s = s0 + ndigits;
140 *s = '\0';
141 if (rve != NULL)
142 *rve = s;
143 return (s0);
144 }
145