1/*	$OpenBSD: hdtoa.c,v 1.2 2009/10/16 12:15:03 martynas Exp $	*/
2/*-
3 * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
4 * All rights reserved.
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 * 1. Redistributions of source code must retain the above copyright
10 *    notice, this list of conditions and the following disclaimer.
11 * 2. Redistributions in binary form must reproduce the above copyright
12 *    notice, this list of conditions and the following disclaimer in the
13 *    documentation and/or other materials provided with the distribution.
14 *
15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
18 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
25 * SUCH DAMAGE.
26 */
27
28#include <sys/types.h>
29#include <machine/ieee.h>
30#include <float.h>
31#include <limits.h>
32#include <math.h>
33
34#include "gdtoaimp.h"
35
36/* Strings values used by dtoa() */
37#define	INFSTR	"Infinity"
38#define	NANSTR	"NaN"
39
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))
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 = 0;
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{
126	static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
127	struct ieee_double *p = (struct ieee_double *)&d;
128	char *s, *s0;
129	int bufsize;
130
131	*sign = p->dbl_sign;
132
133	switch (fpclassify(d)) {
134	case FP_NORMAL:
135		*decpt = p->dbl_exp - DBL_ADJ;
136		break;
137	case FP_ZERO:
138		*decpt = 1;
139		return (nrv_alloc("0", rve, 1));
140	case FP_SUBNORMAL:
141		d *= 0x1p514;
142		*decpt = p->dbl_exp - (514 + DBL_ADJ);
143		break;
144	case FP_INFINITE:
145		*decpt = INT_MAX;
146		return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
147	case FP_NAN:
148		*decpt = INT_MAX;
149		return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
150	default:
151		abort();
152	}
153
154	/* FP_NORMAL or FP_SUBNORMAL */
155
156	if (ndigits == 0)		/* dtoa() compatibility */
157		ndigits = 1;
158
159	/*
160	 * For simplicity, we generate all the digits even if the
161	 * caller has requested fewer.
162	 */
163	bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
164	s0 = rv_alloc(bufsize);
165	if (s0 == NULL)
166		return (NULL);
167
168	/*
169	 * We work from right to left, first adding any requested zero
170	 * padding, then the least significant portion of the
171	 * mantissa, followed by the most significant.  The buffer is
172	 * filled with the byte values 0x0 through 0xf, which are
173	 * converted to xdigs[0x0] through xdigs[0xf] after the
174	 * rounding phase.
175	 */
176	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
177		*s = 0;
178	for (; s > s0 + sigfigs - (DBL_FRACLBITS / 4) - 1 && s > s0; s--) {
179		*s = p->dbl_fracl & 0xf;
180		p->dbl_fracl >>= 4;
181	}
182	for (; s > s0; s--) {
183		*s = p->dbl_frach & 0xf;
184		p->dbl_frach >>= 4;
185	}
186
187	/*
188	 * At this point, we have snarfed all the bits in the
189	 * mantissa, with the possible exception of the highest-order
190	 * (partial) nibble, which is dealt with by the next
191	 * statement.  We also tack on the implicit normalization bit.
192	 */
193	*s = p->dbl_frach | (1U << ((DBL_MANT_DIG - 1) % 4));
194
195	/* If ndigits < 0, we are expected to auto-size the precision. */
196	if (ndigits < 0) {
197		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
198			;
199	}
200
201	if (sigfigs > ndigits && s0[ndigits] != 0)
202		dorounding(s0, ndigits, p->dbl_sign, decpt);
203
204	s = s0 + ndigits;
205	if (rve != NULL)
206		*rve = s;
207	*s-- = '\0';
208	for (; s >= s0; s--)
209		*s = xdigs[(unsigned int)*s];
210
211	return (s0);
212}
213
214#if (LDBL_MANT_DIG > DBL_MANT_DIG)
215
216/*
217 * This is the long double version of __hdtoa().
218 */
219char *
220__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
221    char **rve)
222{
223	static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
224	struct ieee_ext *p = (struct ieee_ext *)&e;
225	char *s, *s0;
226	int bufsize;
227
228	*sign = p->ext_sign;
229
230	switch (fpclassify(e)) {
231	case FP_NORMAL:
232		*decpt = p->ext_exp - LDBL_ADJ;
233		break;
234	case FP_ZERO:
235		*decpt = 1;
236		return (nrv_alloc("0", rve, 1));
237	case FP_SUBNORMAL:
238		e *= 0x1p514L;
239		*decpt = p->ext_exp - (514 + LDBL_ADJ);
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	if (s0 == NULL)
263		return (NULL);
264
265	/*
266	 * We work from right to left, first adding any requested zero
267	 * padding, then the least significant portion of the
268	 * mantissa, followed by the most significant.  The buffer is
269	 * filled with the byte values 0x0 through 0xf, which are
270	 * converted to xdigs[0x0] through xdigs[0xf] after the
271	 * rounding phase.
272	 */
273	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
274		*s = 0;
275	for (; s > s0 + sigfigs - (EXT_FRACLBITS / 4) - 1 && s > s0; s--) {
276		*s = p->ext_fracl & 0xf;
277		p->ext_fracl >>= 4;
278	}
279#ifdef EXT_FRACHMBITS
280	for (; s > s0; s--) {
281		*s = p->ext_frachm & 0xf;
282		p->ext_frachm >>= 4;
283	}
284#endif
285#ifdef EXT_FRACLMBITS
286	for (; s > s0; s--) {
287		*s = p->ext_fraclm & 0xf;
288		p->ext_fraclm >>= 4;
289	}
290#endif
291	for (; s > s0; s--) {
292		*s = p->ext_frach & 0xf;
293		p->ext_frach >>= 4;
294	}
295
296	/*
297	 * At this point, we have snarfed all the bits in the
298	 * mantissa, with the possible exception of the highest-order
299	 * (partial) nibble, which is dealt with by the next
300	 * statement.  We also tack on the implicit normalization bit.
301	 */
302	*s = p->ext_frach | (1U << ((LDBL_MANT_DIG - 1) % 4));
303
304	/* If ndigits < 0, we are expected to auto-size the precision. */
305	if (ndigits < 0) {
306		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
307			;
308	}
309
310	if (sigfigs > ndigits && s0[ndigits] != 0)
311		dorounding(s0, ndigits, p->ext_sign, decpt);
312
313	s = s0 + ndigits;
314	if (rve != NULL)
315		*rve = s;
316	*s-- = '\0';
317	for (; s >= s0; s--)
318		*s = xdigs[(unsigned int)*s];
319
320	return (s0);
321}
322
323#else	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
324
325char *
326__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
327    char **rve)
328{
329	return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
330}
331
332#endif	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
333