xref: /freebsd/lib/libc/gdtoa/_hdtoa.c (revision 1e413cf93298b5b97441a21d9a50fdcd0ee9945e)
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("$FreeBSD$");
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  */
48 static int
49 roundup(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  */
70 static void
71 dorounding(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  */
122 char *
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  */
218 char *
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 
311 char *
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