1/*
2 This Software is provided under the Zope Public License (ZPL) Version 2.1.
3
4 Copyright (c) 2009, 2010 by the mingw-w64 project
5
6 See the AUTHORS file for the list of contributors to the mingw-w64 project.
7
8 This license has been certified as open source. It has also been designated
9 as GPL compatible by the Free Software Foundation (FSF).
10
11 Redistribution and use in source and binary forms, with or without
12 modification, are permitted provided that the following conditions are met:
13
14 1. Redistributions in source code must retain the accompanying copyright
15 notice, this list of conditions, and the following disclaimer.
16 2. Redistributions in binary form must reproduce the accompanying
17 copyright notice, this list of conditions, and the following disclaimer
18 in the documentation and/or other materials provided with the
19 distribution.
20 3. Names of the copyright holders must not be used to endorse or promote
21 products derived from this software without prior written permission
22 from the copyright holders.
23 4. The right to distribute this software or to use it for any purpose does
24 not give you the right to use Servicemarks (sm) or Trademarks (tm) of
25 the copyright holders. Use of them is covered by separate agreement
26 with the copyright holders.
27 5. If any files are modified, you must cause the modified files to carry
28 prominent notices stating that you changed the files and the date of
29 any change.
30
31 Disclaimer
32
33 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY EXPRESSED
34 OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
35 OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
36 EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY DIRECT, INDIRECT,
37 INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
38 LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA,
39 OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
40 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
41 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE,
42 EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
43*/
44
45/* IEEE 754 - Elementary Functions - Special Cases
46 * pow(+/-0, oo) is +0
47 * pow(+/-0, -oo) is +oo
48 * pow (x, +/-0) is 1 for any x (even a zero, quiet NaN, or infinity)
49 * pow (+1, y) is 1 for any y (even a quiet NaN)
50 * pow (+/-0, y) is +/-oo and signals the divideByZero exception for y an odd integer < 0
51 * pow (+/-0, y) is +oo and signals the divideByZero exception for finite y < 0 and not an odd integer
52 * pow (+/-0, y) is +/-0 for finite y > 0 an odd integer
53 * pow (+/-0, y) is +0 for finite y > 0 and not an odd integer
54 * pow (-1, +/-oo) is 1 with no exception
55 pow( -inf, y) = +0 for y<0 and not an odd integer
56 pow( -inf, y) = -inf for y an odd integer > 0
57 pow( -inf, y) = +inf for y>0 and not an odd integer
58 pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0
59 pow (+/-inf, -inf) is +0 with no exception
60 pow (+/-inf, +inf) is +inf with no exception
61 pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer
62 pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer
63 pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer
64 pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y.
65
66 For x /= 0: lim y->oo (1/x)^y results as: for |x| < 1 that sgn(x)*0 and for |x| > 0 that sgn(x)*Infinity
67
68*/
69#include "../complex/complex_internal.h"
70#include <errno.h>
71#include <limits.h>
72#include <math.h>
73#include <errno.h>
74
75static __FLT_TYPE
76internal_modf (__FLT_TYPE value, __FLT_TYPE *iptr)
77{
78 __FLT_TYPE int_part = (__FLT_TYPE) 0.0;
79 /* truncate */
80 /* truncate */
81#ifdef __x86_64__
82 asm volatile ("pushq %%rax\n\tsubq $8, %%rsp\n"
83 "fnstcw 4(%%rsp)\n"
84 "movzwl 4(%%rsp), %%eax\n"
85 "orb $12, %%ah\n"
86 "movw %%ax, (%%rsp)\n"
87 "fldcw (%%rsp)\n"
88 "frndint\n"
89 "fldcw 4(%%rsp)\n"
90 "addq $8, %%rsp\npopq %%rax" : "=t" (int_part) : "0" (value)); /* round */
91#else
92 asm volatile ("push %%eax\n\tsubl $8, %%esp\n"
93 "fnstcw 4(%%esp)\n"
94 "movzwl 4(%%esp), %%eax\n"
95 "orb $12, %%ah\n"
96 "movw %%ax, (%%esp)\n"
97 "fldcw (%%esp)\n"
98 "frndint\n"
99 "fldcw 4(%%esp)\n"
100 "addl $8, %%esp\n\tpop %%eax\n" : "=t" (int_part) : "0" (value)); /* round */
101#endif
102 if (iptr)
103 *iptr = int_part;
104 return (isinf (value) ? (__FLT_TYPE) 0.0 : value - int_part);
105}
106
107__FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int n);
108
109__FLT_TYPE __cdecl
110__FLT_ABI(pow) (__FLT_TYPE x, __FLT_TYPE y)
111{
112 int x_class = fpclassify (x);
113 int y_class = fpclassify (y);
114 long odd_y = 0;
115 __FLT_TYPE d, rslt;
116
117 if (y_class == FP_ZERO || x == __FLT_CST(1.0))
118 return __FLT_CST(1.0);
119 else if (x_class == FP_NAN || y_class == FP_NAN)
120 {
121 if (x_class == FP_NAN) {
122 __FLT_RPT_DOMAIN ("pow", x, y, x);
123 return x;
124 } else {
125 __FLT_RPT_DOMAIN ("pow", x, y, y);
126 return y;
127 }
128 }
129 else if (x_class == FP_ZERO)
130 {
131 if (y_class == FP_INFINITE)
132 return (signbit(y) ? __FLT_HUGE_VAL : __FLT_CST(0.0));
133
134 if (signbit(x) && internal_modf (y, &d) != 0.0)
135 {
136 return signbit (y) ? (1.0 / -x) : __FLT_CST (0.0);
137 /*__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
138 return -__FLT_NAN; */
139 }
140 odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
141 if (!signbit(y))
142 {
143 if (!odd_y || !signbit (x))
144 return __FLT_CST (0.0);
145 return -__FLT_CST(0.0);
146 }
147
148 if (!odd_y || !signbit (x))
149 return __FLT_HUGE_VAL;
150 return (signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
151 }
152 else if (y_class == FP_INFINITE)
153 {
154 __FLT_TYPE a_x;
155
156 if (x_class == FP_INFINITE)
157 return (signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
158 a_x = (signbit (x) ? -x : x);
159 if (a_x == 1.0)
160 return __FLT_CST (1.0);
161 if (a_x > 1.0)
162 return (signbit (y) == 0 ? __FLT_HUGE_VAL : __FLT_CST (0.0));
163 return (!signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
164 }
165 else if (x_class == FP_INFINITE)
166 {
167 /* pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y. */
168 if (signbit(x) && internal_modf (y, &d) != 0.0)
169 {
170 return signbit(y) ? 1.0 / -x : -x;
171 /*__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
172 return -__FLT_NAN;*/
173 }
174 odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
175 /* pow( -inf, y) = +0 for y<0 and not an odd integer, */
176 if (signbit(x) && signbit(y) && !odd_y)
177 return __FLT_CST(0.0);
178 /* pow( -inf, y) = -inf for y an odd integer > 0. */
179 if (signbit(x) && !signbit(y) && odd_y)
180 return -__FLT_HUGE_VAL;
181 /* pow( -inf, y) = +inf for y>0 and not an odd integer. */
182 if (signbit(x) && !signbit(y) && !odd_y)
183 return __FLT_HUGE_VAL;
184 /* pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0. */
185 if (signbit(y))
186 {
187 /* pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer. */
188 return (odd_y && signbit(x) ? -__FLT_CST(0.0) : __FLT_CST(0.0));
189 }
190 /* pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer. */
191 /* pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer. */
192 return (odd_y && signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
193 }
194
195 if (internal_modf (y, &d) != 0.0)
196 {
197 if (signbit (x))
198 {
199 __FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
200 return -__FLT_NAN;
201 }
202 if (y == __FLT_CST(0.5))
203 {
204 asm volatile ("fsqrt" : "=t" (rslt) : "0" (x));
205 return rslt;
206 }
207 }
208 else if ((d <= (__FLT_TYPE) INT_MAX && d >= (__FLT_TYPE) INT_MIN))
209 return __FLT_ABI (__powi) (x, (int) y);
210 /* As exp already checks for minlog and maxlog no further checks are necessary. */
211 rslt = (__FLT_TYPE) exp2l ((long double) y * log2l ((long double) __FLT_ABI(fabs) (x)));
212
213 if (signbit (x) && internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0)
214 rslt = -rslt;
215 return rslt;
216}