1/*	$NetBSD: hdtoa.c,v 1.8 2011/03/21 23:37:42 enami 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 1.8 2011/03/21 23:37:42 enami 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#define	DBL_ADJ		(DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4))
63#define	LDBL_ADJ	(LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4))
64
65/*
66 * Round up the given digit string.  If the digit string is fff...f,
67 * this procedure sets it to 100...0 and returns 1 to indicate that
68 * the exponent needs to be bumped.  Otherwise, 0 is returned.
69 */
70static int
71roundup(char *s0, int ndigits)
72{
73	char *s;
74
75	for (s = s0 + ndigits - 1; *s == 0xf; s--) {
76		if (s == s0) {
77			*s = 1;
78			return (1);
79		}
80		*s = 0;
81	}
82	++*s;
83	return (0);
84}
85
86/*
87 * Round the given digit string to ndigits digits according to the
88 * current rounding mode.  Note that this could produce a string whose
89 * value is not representable in the corresponding floating-point
90 * type.  The exponent pointed to by decpt is adjusted if necessary.
91 */
92static void
93dorounding(char *s0, int ndigits, int sign, int *decpt)
94{
95	int adjust = 0;	/* do we need to adjust the exponent? */
96
97	switch (FLT_ROUNDS) {
98	case 0:		/* toward zero */
99	default:	/* implementation-defined */
100		break;
101	case 1:		/* to nearest, halfway rounds to even */
102		if ((s0[ndigits] > 8) ||
103		    (s0[ndigits] == 8 && s0[ndigits - 1] & 1))
104			adjust = roundup(s0, ndigits);
105		break;
106	case 2:		/* toward +inf */
107		if (sign == 0)
108			adjust = roundup(s0, ndigits);
109		break;
110	case 3:		/* toward -inf */
111		if (sign != 0)
112			adjust = roundup(s0, ndigits);
113		break;
114	}
115
116	if (adjust)
117		*decpt += 4;
118}
119
120/*
121 * This procedure converts a double-precision number in IEEE format
122 * into a string of hexadecimal digits and an exponent of 2.  Its
123 * behavior is bug-for-bug compatible with dtoa() in mode 2, with the
124 * following exceptions:
125 *
126 * - An ndigits < 0 causes it to use as many digits as necessary to
127 *   represent the number exactly.
128 * - The additional xdigs argument should point to either the string
129 *   "0123456789ABCDEF" or the string "0123456789abcdef", depending on
130 *   which case is desired.
131 * - This routine does not repeat dtoa's mistake of setting decpt
132 *   to 9999 in the case of an infinity or NaN.  INT_MAX is used
133 *   for this purpose instead.
134 *
135 * Note that the C99 standard does not specify what the leading digit
136 * should be for non-zero numbers.  For instance, 0x1.3p3 is the same
137 * as 0x2.6p2 is the same as 0x4.cp3.  This implementation chooses the
138 * first digit so that subsequent digits are aligned on nibble
139 * boundaries (before rounding).
140 *
141 * Inputs:	d, xdigs, ndigits
142 * Outputs:	decpt, sign, rve
143 */
144char *
145hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
146    char **rve)
147{
148	static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
149	union ieee_double_u u;
150	char *s, *s0;
151	size_t bufsize;
152
153	u.dblu_d = d;
154	*sign = u.dblu_dbl.dbl_sign;
155
156	switch (fpclassify(d)) {
157	case FP_NORMAL:
158		*decpt = u.dblu_dbl.dbl_exp - DBL_ADJ;
159		break;
160	case FP_ZERO:
161		*decpt = 1;
162		return (nrv_alloc("0", rve, 1));
163	case FP_SUBNORMAL:
164#ifdef __vax__
165		/* (DBL_MAX_EXP=127 / 2) + 2 = 65? */
166		u.dblu_d *= 0x1p65;
167		*decpt = u.dblu_dbl.dbl_exp - (65 + DBL_ADJ);
168#else
169		/* (DBL_MAX_EXP=1024 / 2) + 2 = 514? */
170		u.dblu_d *= 0x1p514;
171		*decpt = u.dblu_dbl.dbl_exp - (514 + DBL_ADJ);
172#endif
173		break;
174	case FP_INFINITE:
175		*decpt = INT_MAX;
176		return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
177	case FP_NAN:
178		*decpt = INT_MAX;
179		return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
180	default:
181		abort();
182	}
183
184	/* FP_NORMAL or FP_SUBNORMAL */
185
186	if (ndigits == 0)		/* dtoa() compatibility */
187		ndigits = 1;
188
189	/*
190	 * For simplicity, we generate all the digits even if the
191	 * caller has requested fewer.
192	 */
193	bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
194	s0 = rv_alloc(bufsize);
195	if (s0 == NULL)
196		return NULL;
197
198	/*
199	 * We work from right to left, first adding any requested zero
200	 * padding, then the least significant portion of the
201	 * mantissa, followed by the most significant.  The buffer is
202	 * filled with the byte values 0x0 through 0xf, which are
203	 * converted to xdigs[0x0] through xdigs[0xf] after the
204	 * rounding phase.
205	 */
206	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
207		*s = 0;
208	for (; s > s0 + sigfigs - (DBL_FRACLBITS / 4) - 1 && s > s0; s--) {
209		*s = u.dblu_dbl.dbl_fracl & 0xf;
210		u.dblu_dbl.dbl_fracl >>= 4;
211	}
212#ifdef DBL_FRACMBITS
213	for (; s > s0; s--) {
214		*s = u.dblu_dbl.dbl_fracm & 0xf;
215		u.dblu_dbl.dbl_fracm >>= 4;
216	}
217#endif
218	for (; s > s0; s--) {
219		*s = u.dblu_dbl.dbl_frach & 0xf;
220		u.dblu_dbl.dbl_frach >>= 4;
221	}
222
223	/*
224	 * At this point, we have snarfed all the bits in the
225	 * mantissa, with the possible exception of the highest-order
226	 * (partial) nibble, which is dealt with by the next
227	 * statement.  We also tack on the implicit normalization bit.
228	 */
229	*s = u.dblu_dbl.dbl_frach | (1U << ((DBL_MANT_DIG - 1) % 4));
230
231	/* If ndigits < 0, we are expected to auto-size the precision. */
232	if (ndigits < 0) {
233		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
234			continue;
235	}
236
237	if (sigfigs > ndigits && s0[ndigits] != 0)
238		dorounding(s0, ndigits, u.dblu_dbl.dbl_sign, decpt);
239
240	s = s0 + ndigits;
241	if (rve != NULL)
242		*rve = s;
243	*s-- = '\0';
244	for (; s >= s0; s--)
245		*s = xdigs[(unsigned int)*s];
246
247	return (s0);
248}
249
250#if (LDBL_MANT_DIG > DBL_MANT_DIG)
251
252/*
253 * This is the long double version of hdtoa().
254 */
255char *
256hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
257    char **rve)
258{
259	static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
260	union ieee_ext_u u;
261	char *s, *s0;
262	size_t bufsize;
263
264	memset(&u, 0, sizeof u);
265	u.extu_ld = e;
266	*sign = u.extu_ext.ext_sign;
267
268	switch (fpclassify(e)) {
269	case FP_NORMAL:
270		*decpt = u.extu_ext.ext_exp - LDBL_ADJ;
271		break;
272	case FP_ZERO:
273		*decpt = 1;
274		return (nrv_alloc("0", rve, 1));
275	case FP_SUBNORMAL:
276		u.extu_ld *= 0x1p514L;
277		*decpt = u.extu_ext.ext_exp - (514 + LDBL_ADJ);
278		break;
279	case FP_INFINITE:
280		*decpt = INT_MAX;
281		return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
282	case FP_NAN:
283		*decpt = INT_MAX;
284		return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
285	default:
286		abort();
287	}
288
289	/* FP_NORMAL or FP_SUBNORMAL */
290
291	if (ndigits == 0)		/* dtoa() compatibility */
292		ndigits = 1;
293
294	/*
295	 * For simplicity, we generate all the digits even if the
296	 * caller has requested fewer.
297	 */
298	bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
299	s0 = rv_alloc(bufsize);
300	if (s0 == NULL)
301		return NULL;
302
303	/*
304	 * We work from right to left, first adding any requested zero
305	 * padding, then the least significant portion of the
306	 * mantissa, followed by the most significant.  The buffer is
307	 * filled with the byte values 0x0 through 0xf, which are
308	 * converted to xdigs[0x0] through xdigs[0xf] after the
309	 * rounding phase.
310	 */
311	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
312		*s = 0;
313	for (; s > s0 + sigfigs - (EXT_FRACLBITS / 4) - 1 && s > s0; s--) {
314		*s = u.extu_ext.ext_fracl & 0xf;
315		u.extu_ext.ext_fracl >>= 4;
316	}
317#ifdef EXT_FRACHMBITS
318	for (; s > s0; s--) {
319		*s = u.extu_ext.ext_frachm & 0xf;
320		u.extu_ext.ext_frachm >>= 4;
321	}
322#endif
323#ifdef EXT_FRACLMBITS
324	for (; s > s0; s--) {
325		*s = u.extu_ext.ext_fraclm & 0xf;
326		u.extu_ext.ext_fraclm >>= 4;
327	}
328#endif
329	for (; s > s0; s--) {
330		*s = u.extu_ext.ext_frach & 0xf;
331		u.extu_ext.ext_frach >>= 4;
332	}
333
334	/*
335	 * At this point, we have snarfed all the bits in the
336	 * mantissa, with the possible exception of the highest-order
337	 * (partial) nibble, which is dealt with by the next
338	 * statement.  We also tack on the implicit normalization bit.
339	 */
340	*s = u.extu_ext.ext_frach | (1U << ((LDBL_MANT_DIG - 1) % 4));
341
342	/* If ndigits < 0, we are expected to auto-size the precision. */
343	if (ndigits < 0) {
344		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
345			continue;
346	}
347
348	if (sigfigs > ndigits && s0[ndigits] != 0)
349		dorounding(s0, ndigits, u.extu_ext.ext_sign, decpt);
350
351	s = s0 + ndigits;
352	if (rve != NULL)
353		*rve = s;
354	*s-- = '\0';
355	for (; s >= s0; s--)
356		*s = xdigs[(unsigned int)*s];
357
358	return (s0);
359}
360
361#else	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
362
363char *
364hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
365    char **rve)
366{
367
368	return (hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
369}
370
371#endif	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
372