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 <fenv.h>
73 #include <math.h>
74 #include <errno.h>
75 #define FE_ROUNDING_MASK \
76 (FE_TONEAREST | FE_DOWNWARD | FE_UPWARD | FE_TOWARDZERO)
77
78 static __FLT_TYPE
internal_modf(__FLT_TYPE value,__FLT_TYPE * iptr)79 internal_modf (__FLT_TYPE value, __FLT_TYPE *iptr)
80 {
81 __FLT_TYPE int_part = (__FLT_TYPE) 0.0;
82 /* truncate */
83 /* truncate */
84 #ifdef __x86_64__
85 asm volatile ("pushq %%rax\n\tsubq $8, %%rsp\n"
86 "fnstcw 4(%%rsp)\n"
87 "movzwl 4(%%rsp), %%eax\n"
88 "orb $12, %%ah\n"
89 "movw %%ax, (%%rsp)\n"
90 "fldcw (%%rsp)\n"
91 "frndint\n"
92 "fldcw 4(%%rsp)\n"
93 "addq $8, %%rsp\npopq %%rax" : "=t" (int_part) : "0" (value)); /* round */
94 #else
95 asm volatile ("push %%eax\n\tsubl $8, %%esp\n"
96 "fnstcw 4(%%esp)\n"
97 "movzwl 4(%%esp), %%eax\n"
98 "orb $12, %%ah\n"
99 "movw %%ax, (%%esp)\n"
100 "fldcw (%%esp)\n"
101 "frndint\n"
102 "fldcw 4(%%esp)\n"
103 "addl $8, %%esp\n\tpop %%eax\n" : "=t" (int_part) : "0" (value)); /* round */
104 #endif
105 if (iptr)
106 *iptr = int_part;
107 return (isinf (value) ? (__FLT_TYPE) 0.0 : value - int_part);
108 }
109
110 __FLT_TYPE __cdecl __FLT_ABI(__powi) (__FLT_TYPE x, int n);
111
112 __FLT_TYPE __cdecl
__FLT_ABI(pow)113 __FLT_ABI(pow) (__FLT_TYPE x, __FLT_TYPE y)
114 {
115 int x_class = fpclassify (x);
116 int y_class = fpclassify (y);
117 long odd_y = 0;
118 __FLT_TYPE d, rslt;
119
120 if (y_class == FP_ZERO || x == __FLT_CST(1.0))
121 return __FLT_CST(1.0);
122 else if (x_class == FP_NAN || y_class == FP_NAN)
123 {
124 if (x_class == FP_NAN) {
125 __FLT_RPT_DOMAIN ("pow", x, y, x);
126 return x;
127 } else {
128 __FLT_RPT_DOMAIN ("pow", x, y, y);
129 return y;
130 }
131 }
132 else if (x_class == FP_ZERO)
133 {
134 if (y_class == FP_INFINITE)
135 return (signbit(y) ? __FLT_HUGE_VAL : __FLT_CST(0.0));
136
137 if (signbit(x) && internal_modf (y, &d) != 0.0)
138 {
139 return signbit (y) ? (1.0 / -x) : __FLT_CST (0.0);
140 /*__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
141 return -__FLT_NAN; */
142 }
143 odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
144 if (!signbit(y))
145 {
146 if (!odd_y || !signbit (x))
147 return __FLT_CST (0.0);
148 return -__FLT_CST(0.0);
149 }
150
151 if (!odd_y || !signbit (x))
152 return __FLT_HUGE_VAL;
153 return (signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
154 }
155 else if (y_class == FP_INFINITE)
156 {
157 __FLT_TYPE a_x;
158
159 if (x_class == FP_INFINITE)
160 return (signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
161 a_x = (signbit (x) ? -x : x);
162 if (a_x == 1.0)
163 return __FLT_CST (1.0);
164 if (a_x > 1.0)
165 return (signbit (y) == 0 ? __FLT_HUGE_VAL : __FLT_CST (0.0));
166 return (!signbit (y) ? __FLT_CST (0.0) : __FLT_HUGE_VAL);
167 }
168 else if (x_class == FP_INFINITE)
169 {
170 /* pow (x, y) signals the invalid operation exception for finite x < 0 and finite non-integer y. */
171 if (signbit(x) && internal_modf (y, &d) != 0.0)
172 {
173 return signbit(y) ? 1.0 / -x : -x;
174 /*__FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
175 return -__FLT_NAN;*/
176 }
177 odd_y = (internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0) ? 1 : 0;
178 /* pow( -inf, y) = +0 for y<0 and not an odd integer, */
179 if (signbit(x) && signbit(y) && !odd_y)
180 return __FLT_CST(0.0);
181 /* pow( -inf, y) = -inf for y an odd integer > 0. */
182 if (signbit(x) && !signbit(y) && odd_y)
183 return -__FLT_HUGE_VAL;
184 /* pow( -inf, y) = +inf for y>0 and not an odd integer. */
185 if (signbit(x) && !signbit(y) && !odd_y)
186 return __FLT_HUGE_VAL;
187 /* pow (+/-inf, y) is +/-0 with no exception for y an odd integer < 0. */
188 if (signbit(y))
189 {
190 /* pow (+/-inf, y) is +0 with no exception for finite y < 0 and not an odd integer. */
191 return (odd_y && signbit(x) ? -__FLT_CST(0.0) : __FLT_CST(0.0));
192 }
193 /* pow (+/-inf, y) is +/-inf with no exception for finite y > 0 an odd integer. */
194 /* pow (+/-inf, y) is +inf with no exception for finite y > 0 and not an odd integer. */
195 return (odd_y && signbit(x) ? -__FLT_HUGE_VAL : __FLT_HUGE_VAL);
196 }
197
198 if (internal_modf (y, &d) != 0.0)
199 {
200 if (signbit (x))
201 {
202 __FLT_RPT_DOMAIN ("pow", x, y, -__FLT_NAN);
203 return -__FLT_NAN;
204 }
205 if (y == __FLT_CST(0.5))
206 {
207 asm volatile ("fsqrt" : "=t" (rslt) : "0" (x));
208 return rslt;
209 }
210 }
211 else if ((d <= (__FLT_TYPE) INT_MAX && d >= (__FLT_TYPE) INT_MIN))
212 return __FLT_ABI (__powi) (x, (int) y);
213 /* As exp already checks for minlog and maxlog no further checks are necessary. */
214 rslt = (__FLT_TYPE) exp2l ((long double) y * log2l ((long double) __FLT_ABI(fabs) (x)));
215
216 if (signbit (x) && internal_modf (__FLT_ABI (ldexp) (y, -1), &d) != 0.0)
217 rslt = -rslt;
218 return rslt;
219 }
220