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59e0d9fe 1/*-
31185420 2 * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
59e0d9fe
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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>
ad3c9f2a 28__FBSDID("$FreeBSD: src/lib/libc/gdtoa/_hdtoa.c,v 1.5 2007/05/08 02:59:37 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
31185420
A
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 }
ad3c9f2a 58 *s = 0;
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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) ||
ad3c9f2a 81 (s0[ndigits] == 8 && s0[ndigits + 1] & 1))
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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;
ad3c9f2a 129 int bufsize, f;
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130
131 u.d = d;
132 *sign = u.bits.sign;
133
ad3c9f2a 134 switch (f = fpclassify(d)) {
59e0d9fe 135 case FP_NORMAL:
31185420 136 *decpt = u.bits.exp - DBL_ADJ;
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137 break;
138 case FP_ZERO:
ad3c9f2a 139return_zero:
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140 *decpt = 1;
141 return (nrv_alloc("0", rve, 1));
142 case FP_SUBNORMAL:
ad3c9f2a
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143 /*
144 * For processors that treat subnormals as zero, comparison
145 * with zero will be equal, so we jump to the FP_ZERO case.
146 */
147 if(u.d == 0.0) goto return_zero;
31185420
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148 u.d *= 0x1p514;
149 *decpt = u.bits.exp - (514 + DBL_ADJ);
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150 break;
151 case FP_INFINITE:
152 *decpt = INT_MAX;
153 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
154 case FP_NAN:
155 *decpt = INT_MAX;
156 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
157 default:
ad3c9f2a 158 LIBC_ABORT("fpclassify returned %d", f);
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159 }
160
161 /* FP_NORMAL or FP_SUBNORMAL */
162
163 if (ndigits == 0) /* dtoa() compatibility */
164 ndigits = 1;
165
166 /*
167 * For simplicity, we generate all the digits even if the
168 * caller has requested fewer.
169 */
170 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
171 s0 = rv_alloc(bufsize);
172
173 /*
174 * We work from right to left, first adding any requested zero
175 * padding, then the least significant portion of the
176 * mantissa, followed by the most significant. The buffer is
177 * filled with the byte values 0x0 through 0xf, which are
178 * converted to xdigs[0x0] through xdigs[0xf] after the
179 * rounding phase.
180 */
181 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
182 *s = 0;
183 for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
184 *s = u.bits.manl & 0xf;
185 u.bits.manl >>= 4;
186 }
187 for (; s > s0; s--) {
188 *s = u.bits.manh & 0xf;
189 u.bits.manh >>= 4;
190 }
191
192 /*
193 * At this point, we have snarfed all the bits in the
194 * mantissa, with the possible exception of the highest-order
195 * (partial) nibble, which is dealt with by the next
31185420 196 * statement. We also tack on the implicit normalization bit.
59e0d9fe 197 */
31185420 198 *s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4));
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199
200 /* If ndigits < 0, we are expected to auto-size the precision. */
201 if (ndigits < 0) {
202 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
203 ;
204 }
205
206 if (sigfigs > ndigits && s0[ndigits] != 0)
207 dorounding(s0, ndigits, u.bits.sign, decpt);
208
209 s = s0 + ndigits;
210 if (rve != NULL)
211 *rve = s;
212 *s-- = '\0';
213 for (; s >= s0; s--)
214 *s = xdigs[(unsigned int)*s];
215
216 return (s0);
217}
218
219#if (LDBL_MANT_DIG > DBL_MANT_DIG)
220
221/*
222 * This is the long double version of __hdtoa().
59e0d9fe
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223 */
224char *
225__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
226 char **rve)
227{
31185420 228 static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
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229 union IEEEl2bits u;
230 char *s, *s0;
ad3c9f2a 231 int bufsize, f;
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232
233 u.e = e;
234 *sign = u.bits.sign;
235
ad3c9f2a 236 switch (f = fpclassify(e)) {
59e0d9fe 237 case FP_NORMAL:
ad3c9f2a 238 case FP_SUPERNORMAL:
31185420 239 *decpt = u.bits.exp - LDBL_ADJ;
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240 break;
241 case FP_ZERO:
242 *decpt = 1;
243 return (nrv_alloc("0", rve, 1));
244 case FP_SUBNORMAL:
31185420
A
245 u.e *= 0x1p514L;
246 *decpt = u.bits.exp - (514 + LDBL_ADJ);
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247 break;
248 case FP_INFINITE:
249 *decpt = INT_MAX;
250 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
251 case FP_NAN:
252 *decpt = INT_MAX;
253 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
254 default:
ad3c9f2a 255 LIBC_ABORT("fpclassify returned %d", f);
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256 }
257
258 /* FP_NORMAL or FP_SUBNORMAL */
259
260 if (ndigits == 0) /* dtoa() compatibility */
261 ndigits = 1;
262
263 /*
264 * For simplicity, we generate all the digits even if the
265 * caller has requested fewer.
266 */
267 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
268 s0 = rv_alloc(bufsize);
269
270 /*
271 * We work from right to left, first adding any requested zero
272 * padding, then the least significant portion of the
273 * mantissa, followed by the most significant. The buffer is
274 * filled with the byte values 0x0 through 0xf, which are
275 * converted to xdigs[0x0] through xdigs[0xf] after the
276 * rounding phase.
277 */
278 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
279 *s = 0;
280 for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
281 *s = u.bits.manl & 0xf;
282 u.bits.manl >>= 4;
283 }
284 for (; s > s0; s--) {
285 *s = u.bits.manh & 0xf;
286 u.bits.manh >>= 4;
287 }
288
289 /*
290 * At this point, we have snarfed all the bits in the
291 * mantissa, with the possible exception of the highest-order
292 * (partial) nibble, which is dealt with by the next
31185420 293 * statement. We also tack on the implicit normalization bit.
59e0d9fe 294 */
31185420 295 *s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
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296
297 /* If ndigits < 0, we are expected to auto-size the precision. */
298 if (ndigits < 0) {
299 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
300 ;
301 }
302
303 if (sigfigs > ndigits && s0[ndigits] != 0)
304 dorounding(s0, ndigits, u.bits.sign, decpt);
305
306 s = s0 + ndigits;
307 if (rve != NULL)
308 *rve = s;
309 *s-- = '\0';
310 for (; s >= s0; s--)
311 *s = xdigs[(unsigned int)*s];
312
313 return (s0);
314}
315
316#else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
317
318char *
319__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
320 char **rve)
321{
322
323 return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
324}
325
326#endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */