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 */
74static int
75roundup(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 */
96static void
97dorounding(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 */
148char *
149hdtoa(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 */
261char *
262hldtoa(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
369char *
370hldtoa(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