1 /* $NetBSD: hdtoa.c,v 1.14 2024/06/09 15:06:07 jakllsch Exp $ */
2
3 /*-
4 * Copyright (c) 2004, 2005 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 <sys/cdefs.h>
30 #if 0
31 __FBSDID("$FreeBSD: src/lib/libc/gdtoa/_hdtoa.c,v 1.4 2007/01/03 04:57:58 das Exp $");
32 #else
33 __RCSID("$NetBSD: hdtoa.c,v 1.14 2024/06/09 15:06:07 jakllsch Exp $");
34 #endif
35
36 #include <float.h>
37 #include <limits.h>
38 #include <math.h>
39 #ifndef __vax__
40 #include <machine/ieee.h>
41 #else
42 #include <machine/vaxfp.h>
43 #define ieee_double_u vax_dfloating_u
44 #define dblu_d dfltu_d
45 #define dblu_dbl dfltu_dflt
46 #define dbl_sign dflt_sign
47 #define dbl_exp dflt_exp
48 #define dbl_frach dflt_frach
49 #define dbl_fracm dflt_fracm
50 #define dbl_fracl dflt_fracl
51 #define DBL_FRACHBITS DFLT_FRACHBITS
52 #define DBL_FRACMBITS DFLT_FRACMBITS
53 #define DBL_FRACLBITS DFLT_FRACLBITS
54 #define DBL_EXPBITS DFLT_EXPBITS
55 #endif
56 #include "gdtoaimp.h"
57
58 /* Strings values used by dtoa() */
59 #define INFSTR "Infinity"
60 #define NANSTR "NaN"
61
62 #ifndef __vax__
63 #define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
64 #define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
65 #else /* __vax__ */
66 #define DBL_ADJ (DBL_MAX_EXP + 4 + ((DBL_MANT_DIG) % 4))
67 #endif
68
69 /*
70 * Round up the given digit string. If the digit string is fff...f,
71 * this procedure sets it to 100...0 and returns 1 to indicate that
72 * the exponent needs to be bumped. Otherwise, 0 is returned.
73 */
74 static int
roundup(char * s0,int ndigits)75 roundup(char *s0, int ndigits)
76 {
77 char *s;
78
79 for (s = s0 + ndigits - 1; *s == 0xf; s--) {
80 if (s == s0) {
81 *s = 1;
82 return (1);
83 }
84 *s = 0;
85 }
86 ++*s;
87 return (0);
88 }
89
90 /*
91 * Round the given digit string to ndigits digits according to the
92 * current rounding mode. Note that this could produce a string whose
93 * value is not representable in the corresponding floating-point
94 * type. The exponent pointed to by decpt is adjusted if necessary.
95 */
96 static void
dorounding(char * s0,int ndigits,int sign,int * decpt)97 dorounding(char *s0, int ndigits, int sign, int *decpt)
98 {
99 int adjust = 0; /* do we need to adjust the exponent? */
100
101 switch (FLT_ROUNDS) {
102 case 0: /* toward zero */
103 default: /* implementation-defined */
104 break;
105 case 1: /* to nearest, halfway rounds to even */
106 if ((s0[ndigits] > 8) ||
107 (s0[ndigits] == 8 && s0[ndigits - 1] & 1))
108 adjust = roundup(s0, ndigits);
109 break;
110 case 2: /* toward +inf */
111 if (sign == 0)
112 adjust = roundup(s0, ndigits);
113 break;
114 case 3: /* toward -inf */
115 if (sign != 0)
116 adjust = roundup(s0, ndigits);
117 break;
118 }
119
120 if (adjust)
121 *decpt += 4;
122 }
123
124 /*
125 * This procedure converts a double-precision number in IEEE format
126 * into a string of hexadecimal digits and an exponent of 2. Its
127 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
128 * following exceptions:
129 *
130 * - An ndigits < 0 causes it to use as many digits as necessary to
131 * represent the number exactly.
132 * - The additional xdigs argument should point to either the string
133 * "0123456789ABCDEF" or the string "0123456789abcdef", depending on
134 * which case is desired.
135 * - This routine does not repeat dtoa's mistake of setting decpt
136 * to 9999 in the case of an infinity or NaN. INT_MAX is used
137 * for this purpose instead.
138 *
139 * Note that the C99 standard does not specify what the leading digit
140 * should be for non-zero numbers. For instance, 0x1.3p3 is the same
141 * as 0x2.6p2 is the same as 0x4.cp3. This implementation chooses the
142 * first digit so that subsequent digits are aligned on nibble
143 * boundaries (before rounding).
144 *
145 * Inputs: d, xdigs, ndigits
146 * Outputs: decpt, sign, rve
147 */
148 char *
hdtoa(double d,const char * xdigs,int ndigits,int * decpt,int * sign,char ** rve)149 hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
150 char **rve)
151 {
152 static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
153 union ieee_double_u u;
154 char *s, *s0;
155 size_t bufsize;
156
157 u.dblu_d = d;
158 *sign = u.dblu_dbl.dbl_sign;
159 #ifdef __vax__
160 u.dfltu_dflt.dflt_fracl =
161 ((u.dfltu_dflt.dflt_fracl >> 16) & 0xFFFF) |
162 ((u.dfltu_dflt.dflt_fracl & 0xffff) << 16);
163 #endif
164
165 switch (fpclassify(d)) {
166 case FP_NORMAL:
167 *decpt = u.dblu_dbl.dbl_exp - DBL_ADJ;
168 break;
169 case FP_ZERO:
170 *decpt = 1;
171 return (nrv_alloc("0", rve, 1));
172 #ifndef __vax__
173 case FP_SUBNORMAL:
174 /* (DBL_MAX_EXP=1024 / 2) + 2 = 514? */
175 u.dblu_d *= 0x1p514;
176 *decpt = u.dblu_dbl.dbl_exp - (514 + DBL_ADJ);
177 break;
178 case FP_INFINITE:
179 *decpt = INT_MAX;
180 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
181 case FP_NAN:
182 *decpt = INT_MAX;
183 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
184 #endif
185 default:
186 abort();
187 }
188
189 /* FP_NORMAL or FP_SUBNORMAL */
190
191 if (ndigits == 0) /* dtoa() compatibility */
192 ndigits = 1;
193
194 /*
195 * For simplicity, we generate all the digits even if the
196 * caller has requested fewer.
197 */
198 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
199 s0 = rv_alloc(bufsize);
200 if (s0 == NULL)
201 return NULL;
202
203 /*
204 * We work from right to left, first adding any requested zero
205 * padding, then the least significant portion of the
206 * mantissa, followed by the most significant. The buffer is
207 * filled with the byte values 0x0 through 0xf, which are
208 * converted to xdigs[0x0] through xdigs[0xf] after the
209 * rounding phase.
210 */
211 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
212 *s = 0;
213 for (; s > s0 + sigfigs - (DBL_FRACLBITS / 4) - 1 && s > s0; s--) {
214 *s = u.dblu_dbl.dbl_fracl & 0xf;
215 u.dblu_dbl.dbl_fracl >>= 4;
216 }
217 #ifdef DBL_FRACMBITS
218 for (; s > s0 + sigfigs - ((DBL_FRACLBITS + DBL_FRACMBITS) / 4) - 1
219 && s > s0; s--) {
220 *s = u.dblu_dbl.dbl_fracm & 0xf;
221 u.dblu_dbl.dbl_fracm >>= 4;
222 }
223 #endif
224 for (; s > s0; s--) {
225 *s = u.dblu_dbl.dbl_frach & 0xf;
226 u.dblu_dbl.dbl_frach >>= 4;
227 }
228
229 /*
230 * At this point, we have snarfed all the bits in the
231 * mantissa, with the possible exception of the highest-order
232 * (partial) nibble, which is dealt with by the next
233 * statement. We also tack on the implicit normalization bit.
234 */
235 *s = u.dblu_dbl.dbl_frach | (1U << ((DBL_MANT_DIG - 1) % 4));
236
237 /* If ndigits < 0, we are expected to auto-size the precision. */
238 if (ndigits < 0) {
239 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
240 continue;
241 }
242
243 if (sigfigs > ndigits && s0[ndigits] != 0)
244 dorounding(s0, ndigits, u.dblu_dbl.dbl_sign, decpt);
245
246 s = s0 + ndigits;
247 if (rve != NULL)
248 *rve = s;
249 *s-- = '\0';
250 for (; s >= s0; s--)
251 *s = xdigs[(unsigned int)*s];
252
253 return (s0);
254 }
255
256 #if (LDBL_MANT_DIG > DBL_MANT_DIG)
257
258 /*
259 * This is the long double version of hdtoa().
260 */
261 char *
hldtoa(long double e,const char * xdigs,int ndigits,int * decpt,int * sign,char ** rve)262 hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
263 char **rve)
264 {
265 static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
266 union ieee_ext_u u;
267 char *s, *s0;
268 size_t bufsize;
269
270 memset(&u, 0, sizeof u);
271 u.extu_ld = e;
272 *sign = u.extu_ext.ext_sign;
273
274 switch (fpclassify(e)) {
275 case FP_NORMAL:
276 *decpt = u.extu_ext.ext_exp - LDBL_ADJ;
277 break;
278 case FP_ZERO:
279 *decpt = 1;
280 return (nrv_alloc("0", rve, 1));
281 case FP_SUBNORMAL:
282 u.extu_ld *= 0x1p514L;
283 *decpt = u.extu_ext.ext_exp - (514 + LDBL_ADJ);
284 break;
285 case FP_INFINITE:
286 *decpt = INT_MAX;
287 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
288 case FP_NAN:
289 *decpt = INT_MAX;
290 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
291 default:
292 abort();
293 }
294
295 /* FP_NORMAL or FP_SUBNORMAL */
296
297 if (ndigits == 0) /* dtoa() compatibility */
298 ndigits = 1;
299
300 /*
301 * For simplicity, we generate all the digits even if the
302 * caller has requested fewer.
303 */
304 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
305 s0 = rv_alloc(bufsize);
306 if (s0 == NULL)
307 return NULL;
308
309 /*
310 * We work from right to left, first adding any requested zero
311 * padding, then the least significant portion of the
312 * mantissa, followed by the most significant. The buffer is
313 * filled with the byte values 0x0 through 0xf, which are
314 * converted to xdigs[0x0] through xdigs[0xf] after the
315 * rounding phase.
316 */
317 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
318 *s = 0;
319 for (; s > s0 + sigfigs - (EXT_FRACLBITS / 4) - 1 && s > s0; s--) {
320 *s = u.extu_ext.ext_fracl & 0xf;
321 u.extu_ext.ext_fracl >>= 4;
322 }
323 #ifdef EXT_FRACHMBITS
324 for (; s > s0; s--) {
325 *s = u.extu_ext.ext_frachm & 0xf;
326 u.extu_ext.ext_frachm >>= 4;
327 }
328 #endif
329 #ifdef EXT_FRACLMBITS
330 for (; s > s0; s--) {
331 *s = u.extu_ext.ext_fraclm & 0xf;
332 u.extu_ext.ext_fraclm >>= 4;
333 }
334 #endif
335 for (; s > s0; s--) {
336 *s = u.extu_ext.ext_frach & 0xf;
337 u.extu_ext.ext_frach >>= 4;
338 }
339
340 /*
341 * At this point, we have snarfed all the bits in the
342 * mantissa, with the possible exception of the highest-order
343 * (partial) nibble, which is dealt with by the next
344 * statement. We also tack on the implicit normalization bit.
345 */
346 *s = u.extu_ext.ext_frach | (1U << ((LDBL_MANT_DIG - 1) % 4));
347
348 /* If ndigits < 0, we are expected to auto-size the precision. */
349 if (ndigits < 0) {
350 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
351 continue;
352 }
353
354 if (sigfigs > ndigits && s0[ndigits] != 0)
355 dorounding(s0, ndigits, u.extu_ext.ext_sign, decpt);
356
357 s = s0 + ndigits;
358 if (rve != NULL)
359 *rve = s;
360 *s-- = '\0';
361 for (; s >= s0; s--)
362 *s = xdigs[(unsigned int)*s];
363
364 return (s0);
365 }
366
367 #else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
368
369 char *
hldtoa(long double e,const char * xdigs,int ndigits,int * decpt,int * sign,char ** rve)370 hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
371 char **rve)
372 {
373
374 return (hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
375 }
376
377 #endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
378