_hdtoa.c revision 165742 
1/*-
2 * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
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>
28__FBSDID("$FreeBSD: head/lib/libc/gdtoa/_hdtoa.c 165742 2007-01-03 04:57:58Z das $");
29
30#include <float.h>
31#include <limits.h>
32#include <math.h>
33#include "fpmath.h"
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	union IEEEd2bits u;
128	char *s, *s0;
129	int bufsize;
130
131	u.d = d;
132	*sign = u.bits.sign;
133
134	switch (fpclassify(d)) {
135	case FP_NORMAL:
136		*decpt = u.bits.exp - DBL_ADJ;
137		break;
138	case FP_ZERO:
139		*decpt = 1;
140		return (nrv_alloc("0", rve, 1));
141	case FP_SUBNORMAL:
142		u.d *= 0x1p514;
143		*decpt = u.bits.exp - (514 + DBL_ADJ);
144		break;
145	case FP_INFINITE:
146		*decpt = INT_MAX;
147		return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
148	case FP_NAN:
149		*decpt = INT_MAX;
150		return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
151	default:
152		abort();
153	}
154
155	/* FP_NORMAL or FP_SUBNORMAL */
156
157	if (ndigits == 0)		/* dtoa() compatibility */
158		ndigits = 1;
159
160	/*
161	 * For simplicity, we generate all the digits even if the
162	 * caller has requested fewer.
163	 */
164	bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
165	s0 = rv_alloc(bufsize);
166
167	/*
168	 * We work from right to left, first adding any requested zero
169	 * padding, then the least significant portion of the
170	 * mantissa, followed by the most significant.  The buffer is
171	 * filled with the byte values 0x0 through 0xf, which are
172	 * converted to xdigs[0x0] through xdigs[0xf] after the
173	 * rounding phase.
174	 */
175	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
176		*s = 0;
177	for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
178		*s = u.bits.manl & 0xf;
179		u.bits.manl >>= 4;
180	}
181	for (; s > s0; s--) {
182		*s = u.bits.manh & 0xf;
183		u.bits.manh >>= 4;
184	}
185
186	/*
187	 * At this point, we have snarfed all the bits in the
188	 * mantissa, with the possible exception of the highest-order
189	 * (partial) nibble, which is dealt with by the next
190	 * statement.  We also tack on the implicit normalization bit.
191	 */
192	*s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4));
193
194	/* If ndigits < 0, we are expected to auto-size the precision. */
195	if (ndigits < 0) {
196		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
197			;
198	}
199
200	if (sigfigs > ndigits && s0[ndigits] != 0)
201		dorounding(s0, ndigits, u.bits.sign, decpt);
202
203	s = s0 + ndigits;
204	if (rve != NULL)
205		*rve = s;
206	*s-- = '\0';
207	for (; s >= s0; s--)
208		*s = xdigs[(unsigned int)*s];
209
210	return (s0);
211}
212
213#if (LDBL_MANT_DIG > DBL_MANT_DIG)
214
215/*
216 * This is the long double version of __hdtoa().
217 */
218char *
219__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
220    char **rve)
221{
222	static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
223	union IEEEl2bits u;
224	char *s, *s0;
225	int bufsize;
226
227	u.e = e;
228	*sign = u.bits.sign;
229
230	switch (fpclassify(e)) {
231	case FP_NORMAL:
232		*decpt = u.bits.exp - LDBL_ADJ;
233		break;
234	case FP_ZERO:
235		*decpt = 1;
236		return (nrv_alloc("0", rve, 1));
237	case FP_SUBNORMAL:
238		u.e *= 0x1p514L;
239		*decpt = u.bits.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
263	/*
264	 * We work from right to left, first adding any requested zero
265	 * padding, then the least significant portion of the
266	 * mantissa, followed by the most significant.  The buffer is
267	 * filled with the byte values 0x0 through 0xf, which are
268	 * converted to xdigs[0x0] through xdigs[0xf] after the
269	 * rounding phase.
270	 */
271	for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
272		*s = 0;
273	for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
274		*s = u.bits.manl & 0xf;
275		u.bits.manl >>= 4;
276	}
277	for (; s > s0; s--) {
278		*s = u.bits.manh & 0xf;
279		u.bits.manh >>= 4;
280	}
281
282	/*
283	 * At this point, we have snarfed all the bits in the
284	 * mantissa, with the possible exception of the highest-order
285	 * (partial) nibble, which is dealt with by the next
286	 * statement.  We also tack on the implicit normalization bit.
287	 */
288	*s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
289
290	/* If ndigits < 0, we are expected to auto-size the precision. */
291	if (ndigits < 0) {
292		for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
293			;
294	}
295
296	if (sigfigs > ndigits && s0[ndigits] != 0)
297		dorounding(s0, ndigits, u.bits.sign, decpt);
298
299	s = s0 + ndigits;
300	if (rve != NULL)
301		*rve = s;
302	*s-- = '\0';
303	for (; s >= s0; s--)
304		*s = xdigs[(unsigned int)*s];
305
306	return (s0);
307}
308
309#else	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
310
311char *
312__hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
313    char **rve)
314{
315
316	return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
317}
318
319#endif	/* (LDBL_MANT_DIG == DBL_MANT_DIG) */
320