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comparison libquadmath/math/fmaq.c @ 68:561a7518be6b

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update gcc-4.6
author Nobuyasu Oshiro <dimolto@cr.ie.u-ryukyu.ac.jp>
date Sun, 21 Aug 2011 07:07:55 +0900
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children 04ced10e8804
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67:f6334be47118 68:561a7518be6b
1 /* Compute x * y + z as ternary operation.
2 Copyright (C) 2010 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
5
6 The GNU C Library is free software; you can redistribute it and/or
7 modify it under the terms of the GNU Lesser General Public
8 License as published by the Free Software Foundation; either
9 version 2.1 of the License, or (at your option) any later version.
10
11 The GNU C Library is distributed in the hope that it will be useful,
12 but WITHOUT ANY WARRANTY; without even the implied warranty of
13 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
14 Lesser General Public License for more details.
15
16 You should have received a copy of the GNU Lesser General Public
17 License along with the GNU C Library; if not, write to the Free
18 Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
19 02111-1307 USA. */
20
21 #include "quadmath-imp.h"
22 #include <math.h>
23 #include <float.h>
24 #ifdef HAVE_FENV_H
25 # include <fenv.h>
26 # if defined HAVE_FEHOLDEXCEPT && defined HAVE_FESETROUND \
27 && defined HAVE_FEUPDATEENV && defined HAVE_FETESTEXCEPT \
28 && defined FE_TOWARDZERO && defined FE_INEXACT
29 # define USE_FENV_H
30 # endif
31 #endif
32
33 /* This implementation uses rounding to odd to avoid problems with
34 double rounding. See a paper by Boldo and Melquiond:
35 http://www.lri.fr/~melquion/doc/08-tc.pdf */
36
37 __float128
38 fmaq (__float128 x, __float128 y, __float128 z)
39 {
40 ieee854_float128 u, v, w;
41 int adjust = 0;
42 u.value = x;
43 v.value = y;
44 w.value = z;
45 if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
46 >= 0x7fff + IEEE854_FLOAT128_BIAS
47 - FLT128_MANT_DIG, 0)
48 || __builtin_expect (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
49 || __builtin_expect (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
50 || __builtin_expect (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG, 0)
51 || __builtin_expect (u.ieee.exponent + v.ieee.exponent
52 <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG, 0))
53 {
54 /* If z is Inf, but x and y are finite, the result should be
55 z rather than NaN. */
56 if (w.ieee.exponent == 0x7fff
57 && u.ieee.exponent != 0x7fff
58 && v.ieee.exponent != 0x7fff)
59 return (z + x) + y;
60 /* If x or y or z is Inf/NaN, or if fma will certainly overflow,
61 or if x * y is less than half of FLT128_DENORM_MIN,
62 compute as x * y + z. */
63 if (u.ieee.exponent == 0x7fff
64 || v.ieee.exponent == 0x7fff
65 || w.ieee.exponent == 0x7fff
66 || u.ieee.exponent + v.ieee.exponent
67 > 0x7fff + IEEE854_FLOAT128_BIAS
68 || u.ieee.exponent + v.ieee.exponent
69 < IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG - 2)
70 return x * y + z;
71 if (u.ieee.exponent + v.ieee.exponent
72 >= 0x7fff + IEEE854_FLOAT128_BIAS - FLT128_MANT_DIG)
73 {
74 /* Compute 1p-113 times smaller result and multiply
75 at the end. */
76 if (u.ieee.exponent > v.ieee.exponent)
77 u.ieee.exponent -= FLT128_MANT_DIG;
78 else
79 v.ieee.exponent -= FLT128_MANT_DIG;
80 /* If x + y exponent is very large and z exponent is very small,
81 it doesn't matter if we don't adjust it. */
82 if (w.ieee.exponent > FLT128_MANT_DIG)
83 w.ieee.exponent -= FLT128_MANT_DIG;
84 adjust = 1;
85 }
86 else if (w.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
87 {
88 /* Similarly.
89 If z exponent is very large and x and y exponents are
90 very small, it doesn't matter if we don't adjust it. */
91 if (u.ieee.exponent > v.ieee.exponent)
92 {
93 if (u.ieee.exponent > FLT128_MANT_DIG)
94 u.ieee.exponent -= FLT128_MANT_DIG;
95 }
96 else if (v.ieee.exponent > FLT128_MANT_DIG)
97 v.ieee.exponent -= FLT128_MANT_DIG;
98 w.ieee.exponent -= FLT128_MANT_DIG;
99 adjust = 1;
100 }
101 else if (u.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
102 {
103 u.ieee.exponent -= FLT128_MANT_DIG;
104 if (v.ieee.exponent)
105 v.ieee.exponent += FLT128_MANT_DIG;
106 else
107 v.value *= 0x1p113Q;
108 }
109 else if (v.ieee.exponent >= 0x7fff - FLT128_MANT_DIG)
110 {
111 v.ieee.exponent -= FLT128_MANT_DIG;
112 if (u.ieee.exponent)
113 u.ieee.exponent += FLT128_MANT_DIG;
114 else
115 u.value *= 0x1p113Q;
116 }
117 else /* if (u.ieee.exponent + v.ieee.exponent
118 <= IEEE854_FLOAT128_BIAS + FLT128_MANT_DIG) */
119 {
120 if (u.ieee.exponent > v.ieee.exponent)
121 u.ieee.exponent += 2 * FLT128_MANT_DIG;
122 else
123 v.ieee.exponent += 2 * FLT128_MANT_DIG;
124 if (w.ieee.exponent <= 4 * FLT128_MANT_DIG + 4)
125 {
126 if (w.ieee.exponent)
127 w.ieee.exponent += 2 * FLT128_MANT_DIG;
128 else
129 w.value *= 0x1p226Q;
130 adjust = -1;
131 }
132 /* Otherwise x * y should just affect inexact
133 and nothing else. */
134 }
135 x = u.value;
136 y = v.value;
137 z = w.value;
138 }
139 /* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
140 #define C ((1LL << (FLT128_MANT_DIG + 1) / 2) + 1)
141 __float128 x1 = x * C;
142 __float128 y1 = y * C;
143 __float128 m1 = x * y;
144 x1 = (x - x1) + x1;
145 y1 = (y - y1) + y1;
146 __float128 x2 = x - x1;
147 __float128 y2 = y - y1;
148 __float128 m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
149
150 /* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
151 __float128 a1 = z + m1;
152 __float128 t1 = a1 - z;
153 __float128 t2 = a1 - t1;
154 t1 = m1 - t1;
155 t2 = z - t2;
156 __float128 a2 = t1 + t2;
157
158 #ifdef USE_FENV_H
159 fenv_t env;
160 feholdexcept (&env);
161 fesetround (FE_TOWARDZERO);
162 #endif
163 /* Perform m2 + a2 addition with round to odd. */
164 u.value = a2 + m2;
165
166 if (__builtin_expect (adjust == 0, 1))
167 {
168 #ifdef USE_FENV_H
169 if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff)
170 u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
171 feupdateenv (&env);
172 #endif
173 /* Result is a1 + u.value. */
174 return a1 + u.value;
175 }
176 else if (__builtin_expect (adjust > 0, 1))
177 {
178 #ifdef USE_FENV_H
179 if ((u.ieee.mant_low & 1) == 0 && u.ieee.exponent != 0x7fff)
180 u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
181 feupdateenv (&env);
182 #endif
183 /* Result is a1 + u.value, scaled up. */
184 return (a1 + u.value) * 0x1p113Q;
185 }
186 else
187 {
188 #ifdef USE_FENV_H
189 if ((u.ieee.mant_low & 1) == 0)
190 u.ieee.mant_low |= fetestexcept (FE_INEXACT) != 0;
191 #endif
192 v.value = a1 + u.value;
193 /* Ensure the addition is not scheduled after fetestexcept call. */
194 asm volatile ("" : : "m" (v));
195 #ifdef USE_FENV_H
196 int j = fetestexcept (FE_INEXACT) != 0;
197 feupdateenv (&env);
198 #else
199 int j = 0;
200 #endif
201 /* Ensure the following computations are performed in default rounding
202 mode instead of just reusing the round to zero computation. */
203 asm volatile ("" : "=m" (u) : "m" (u));
204 /* If a1 + u.value is exact, the only rounding happens during
205 scaling down. */
206 if (j == 0)
207 return v.value * 0x1p-226Q;
208 /* If result rounded to zero is not subnormal, no double
209 rounding will occur. */
210 if (v.ieee.exponent > 226)
211 return (a1 + u.value) * 0x1p-226Q;
212 /* If v.value * 0x1p-226Q with round to zero is a subnormal above
213 or equal to FLT128_MIN / 2, then v.value * 0x1p-226Q shifts mantissa
214 down just by 1 bit, which means v.ieee.mant_low |= j would
215 change the round bit, not sticky or guard bit.
216 v.value * 0x1p-226Q never normalizes by shifting up,
217 so round bit plus sticky bit should be already enough
218 for proper rounding. */
219 if (v.ieee.exponent == 226)
220 {
221 /* v.ieee.mant_low & 2 is LSB bit of the result before rounding,
222 v.ieee.mant_low & 1 is the round bit and j is our sticky
223 bit. In round-to-nearest 001 rounds down like 00,
224 011 rounds up, even though 01 rounds down (thus we need
225 to adjust), 101 rounds down like 10 and 111 rounds up
226 like 11. */
227 if ((v.ieee.mant_low & 3) == 1)
228 {
229 v.value *= 0x1p-226Q;
230 if (v.ieee.negative)
231 return v.value - 0x1p-16494Q /* __FLT128_DENORM_MIN__ */;
232 else
233 return v.value + 0x1p-16494Q /* __FLT128_DENORM_MIN__ */;
234 }
235 else
236 return v.value * 0x1p-226Q;
237 }
238 v.ieee.mant_low |= j;
239 return v.value * 0x1p-226Q;
240 }
241 }