2 * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG>
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
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.
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
27 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD$");
36 /* Strings values used by dtoa() */
37 #define INFSTR "Infinity"
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))
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.
49 roundup(char *s0, int ndigits)
53 for (s = s0 + ndigits - 1; *s == 0xf; s--) {
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.
71 dorounding(char *s0, int ndigits, int sign, int *decpt)
73 int adjust = 0; /* do we need to adjust the exponent? */
76 case 0: /* toward zero */
77 default: /* implementation-defined */
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);
84 case 2: /* toward +inf */
86 adjust = roundup(s0, ndigits);
88 case 3: /* toward -inf */
90 adjust = roundup(s0, ndigits);
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:
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.
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).
119 * Inputs: d, xdigs, ndigits
120 * Outputs: decpt, sign, rve
123 __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign,
126 static const int sigfigs = (DBL_MANT_DIG + 3) / 4;
134 switch (fpclassify(d)) {
136 *decpt = u.bits.exp - DBL_ADJ;
140 return (nrv_alloc("0", rve, 1));
143 *decpt = u.bits.exp - (514 + DBL_ADJ);
147 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
150 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
155 /* FP_NORMAL or FP_SUBNORMAL */
157 if (ndigits == 0) /* dtoa() compatibility */
161 * For simplicity, we generate all the digits even if the
162 * caller has requested fewer.
164 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
165 s0 = rv_alloc(bufsize);
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
175 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
177 for (; s > s0 + sigfigs - (DBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
178 *s = u.bits.manl & 0xf;
181 for (; s > s0; s--) {
182 *s = u.bits.manh & 0xf;
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.
192 *s = u.bits.manh | (1U << ((DBL_MANT_DIG - 1) % 4));
194 /* If ndigits < 0, we are expected to auto-size the precision. */
196 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
200 if (sigfigs > ndigits && s0[ndigits] != 0)
201 dorounding(s0, ndigits, u.bits.sign, decpt);
208 *s = xdigs[(unsigned int)*s];
213 #if (LDBL_MANT_DIG > DBL_MANT_DIG)
216 * This is the long double version of __hdtoa().
219 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
222 static const int sigfigs = (LDBL_MANT_DIG + 3) / 4;
230 switch (fpclassify(e)) {
232 *decpt = u.bits.exp - LDBL_ADJ;
236 return (nrv_alloc("0", rve, 1));
239 *decpt = u.bits.exp - (514 + LDBL_ADJ);
243 return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1));
246 return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1));
251 /* FP_NORMAL or FP_SUBNORMAL */
253 if (ndigits == 0) /* dtoa() compatibility */
257 * For simplicity, we generate all the digits even if the
258 * caller has requested fewer.
260 bufsize = (sigfigs > ndigits) ? sigfigs : ndigits;
261 s0 = rv_alloc(bufsize);
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
271 for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--)
273 for (; s > s0 + sigfigs - (LDBL_MANL_SIZE / 4) - 1 && s > s0; s--) {
274 *s = u.bits.manl & 0xf;
277 for (; s > s0; s--) {
278 *s = u.bits.manh & 0xf;
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.
288 *s = u.bits.manh | (1U << ((LDBL_MANT_DIG - 1) % 4));
290 /* If ndigits < 0, we are expected to auto-size the precision. */
292 for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--)
296 if (sigfigs > ndigits && s0[ndigits] != 0)
297 dorounding(s0, ndigits, u.bits.sign, decpt);
304 *s = xdigs[(unsigned int)*s];
309 #else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
312 __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign,
316 return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve));
319 #endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */