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59e0d9fe 1/*-
31185420 2 * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
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3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27#include <sys/cdefs.h>
31185420 28__FBSDID("$FreeBSD: src/lib/libc/gdtoa/_hdtoa.c,v 1.3 2005/01/18 18:44:07 das Exp $");
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29
30#include <float.h>
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31#include <limits.h>
32#include <math.h>
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33#include "fpmath.h"
34#include "gdtoaimp.h"
35
36/* Strings values used by dtoa() */
37#define INFSTR "Infinity"
38#define NANSTR "NaN"
39
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40#define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
41#define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
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42
43/*
44 * Round up the given digit string. If the digit string is fff...f,
45 * this procedure sets it to 100...0 and returns 1 to indicate that
46 * the exponent needs to be bumped. Otherwise, 0 is returned.
47 */
48static int
49roundup(char *s0, int ndigits)
50{
51 char *s;
52
53 for (s = s0 + ndigits - 1; *s == 0xf; s--) {
54 if (s == s0) {
55 *s = 1;
56 return (1);
57 }
58 ++*s;
59 }
60 ++*s;
61 return (0);
62}
63
64/*
65 * Round the given digit string to ndigits digits according to the
66 * current rounding mode. Note that this could produce a string whose
67 * value is not representable in the corresponding floating-point
68 * type. The exponent pointed to by decpt is adjusted if necessary.
69 */
70static void
71dorounding(char *s0, int ndigits, int sign, int *decpt)
72{
73 int adjust = 0; /* do we need to adjust the exponent? */
74
75 switch (FLT_ROUNDS) {
76 case 0: /* toward zero */
77 default: /* implementation-defined */
78 break;
79 case 1: /* to nearest, halfway rounds to even */
80 if ((s0[ndigits] > 8) ||
81 (s0[ndigits] == 8 && s0[ndigits - 1] & 1))
82 adjust = roundup(s0, ndigits);
83 break;
84 case 2: /* toward +inf */
85 if (sign == 0)
86 adjust = roundup(s0, ndigits);
87 break;
88 case 3: /* toward -inf */
89 if (sign != 0)
90 adjust = roundup(s0, ndigits);
91 break;
92 }
93
94 if (adjust)
95 *decpt += 4;
96}
97
98/*
99 * This procedure converts a double-precision number in IEEE format
100 * into a string of hexadecimal digits and an exponent of 2. Its
101 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
102 * following exceptions:
103 *
104 * - An ndigits < 0 causes it to use as many digits as necessary to
105 * represent the number exactly.
106 * - The additional xdigs argument should point to either the string
107 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
108 * which case is desired.
109 * - This routine does not repeat dtoa's mistake of setting decpt
110 * to 9999 in the case of an infinity or NaN. INT_MAX is used
111 * for this purpose instead.
112 *
113 * Note that the C99 standard does not specify what the leading digit
114 * should be for non-zero numbers. For instance, 0x1.3p3 is the same
115 * as 0x2.6p2 is the same as 0x4.cp3. This implementation chooses the
116 * first digit so that subsequent digits are aligned on nibble
117 * boundaries (before rounding).
118 *
119 * Inputs: d, xdigs, ndigits
120 * Outputs: decpt, sign, rve
121 */
122char *
123__hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
124 char **rve)
125{
31185420 126 static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
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127 union IEEEd2bits u;
128 char *s, *s0;
129 int bufsize;
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130
131 u.d = d;
132 *sign = u.bits.sign;
133
134 switch (fpclassify(d)) {
135 case FP_NORMAL:
31185420 136 *decpt = u.bits.exp - DBL_ADJ;
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137 break;
138 case FP_ZERO:
139 *decpt = 1;
140 return (nrv_alloc("0", rve, 1));
141 case FP_SUBNORMAL:
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142 u.d *= 0x1p514;
143 *decpt = u.bits.exp - (514 + DBL_ADJ);
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144 break;
145 case FP_INFINITE:
146 *decpt = INT_MAX;
147 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
148 case FP_NAN:
149 *decpt = INT_MAX;
150 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
151 default:
152 abort();
153 }
154
155 /* FP_NORMAL or FP_SUBNORMAL */
156
157 if (ndigits == 0) /* dtoa() compatibility */
158 ndigits = 1;
159
160 /*
161 * For simplicity, we generate all the digits even if the
162 * caller has requested fewer.
163 */
164 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
165 s0 = rv_alloc(bufsize);
166
167 /*
168 * We work from right to left, first adding any requested zero
169 * padding, then the least significant portion of the
170 * mantissa, followed by the most significant. The buffer is
171 * filled with the byte values 0x0 through 0xf, which are
172 * converted to xdigs[0x0] through xdigs[0xf] after the
173 * rounding phase.
174 */
175 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
176 *s = 0;
177 for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
178 *s = u.bits.manl & 0xf;
179 u.bits.manl >>= 4;
180 }
181 for (; s > s0; s--) {
182 *s = u.bits.manh & 0xf;
183 u.bits.manh >>= 4;
184 }
185
186 /*
187 * At this point, we have snarfed all the bits in the
188 * mantissa, with the possible exception of the highest-order
189 * (partial) nibble, which is dealt with by the next
31185420 190 * statement. We also tack on the implicit normalization bit.
59e0d9fe 191 */
31185420 192 *s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4));
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193
194 /* If ndigits < 0, we are expected to auto-size the precision. */
195 if (ndigits < 0) {
196 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
197 ;
198 }
199
200 if (sigfigs > ndigits && s0[ndigits] != 0)
201 dorounding(s0, ndigits, u.bits.sign, decpt);
202
203 s = s0 + ndigits;
204 if (rve != NULL)
205 *rve = s;
206 *s-- = '\0';
207 for (; s >= s0; s--)
208 *s = xdigs[(unsigned int)*s];
209
210 return (s0);
211}
212
213#if (LDBL_MANT_DIG > DBL_MANT_DIG)
214
215/*
216 * This is the long double version of __hdtoa().
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217 */
218char *
219__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
220 char **rve)
221{
31185420 222 static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
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223 union IEEEl2bits u;
224 char *s, *s0;
225 int bufsize;
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226
227 u.e = e;
228 *sign = u.bits.sign;
229
230 switch (fpclassify(e)) {
231 case FP_NORMAL:
31185420 232 *decpt = u.bits.exp - LDBL_ADJ;
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233 break;
234 case FP_ZERO:
235 *decpt = 1;
236 return (nrv_alloc("0", rve, 1));
237 case FP_SUBNORMAL:
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238 u.e *= 0x1p514L;
239 *decpt = u.bits.exp - (514 + LDBL_ADJ);
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240 break;
241 case FP_INFINITE:
242 *decpt = INT_MAX;
243 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
244 case FP_NAN:
245 *decpt = INT_MAX;
246 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
247 default:
248 abort();
249 }
250
251 /* FP_NORMAL or FP_SUBNORMAL */
252
253 if (ndigits == 0) /* dtoa() compatibility */
254 ndigits = 1;
255
256 /*
257 * For simplicity, we generate all the digits even if the
258 * caller has requested fewer.
259 */
260 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
261 s0 = rv_alloc(bufsize);
262
263 /*
264 * We work from right to left, first adding any requested zero
265 * padding, then the least significant portion of the
266 * mantissa, followed by the most significant. The buffer is
267 * filled with the byte values 0x0 through 0xf, which are
268 * converted to xdigs[0x0] through xdigs[0xf] after the
269 * rounding phase.
270 */
271 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
272 *s = 0;
273 for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
274 *s = u.bits.manl & 0xf;
275 u.bits.manl >>= 4;
276 }
277 for (; s > s0; s--) {
278 *s = u.bits.manh & 0xf;
279 u.bits.manh >>= 4;
280 }
281
282 /*
283 * At this point, we have snarfed all the bits in the
284 * mantissa, with the possible exception of the highest-order
285 * (partial) nibble, which is dealt with by the next
31185420 286 * statement. We also tack on the implicit normalization bit.
59e0d9fe 287 */
31185420 288 *s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
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289
290 /* If ndigits < 0, we are expected to auto-size the precision. */
291 if (ndigits < 0) {
292 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
293 ;
294 }
295
296 if (sigfigs > ndigits && s0[ndigits] != 0)
297 dorounding(s0, ndigits, u.bits.sign, decpt);
298
299 s = s0 + ndigits;
300 if (rve != NULL)
301 *rve = s;
302 *s-- = '\0';
303 for (; s >= s0; s--)
304 *s = xdigs[(unsigned int)*s];
305
306 return (s0);
307}
308
309#else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
310
311char *
312__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
313 char **rve)
314{
315
316 return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
317}
318
319#endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */