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1 // The following is adapted from fdlibm (http://www.netlib.org/fdlibm). | |
2 // | |
3 // ==================================================== | |
4 // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. | |
5 // | |
6 // Developed at SunSoft, a Sun Microsystems, Inc. business. | |
7 // Permission to use, copy, modify, and distribute this | |
8 // software is freely granted, provided that this notice | |
9 // is preserved. | |
10 // ==================================================== | |
11 // | |
12 // The original source code covered by the above license above has been | |
13 // modified significantly by Google Inc. | |
14 // Copyright 2014 the V8 project authors. All rights reserved. | |
15 | |
16 #include "src/third_party/fdlibm/fdlibm.h" | |
17 | |
18 #include <stdint.h> | |
19 #include <cmath> | |
20 #include <limits> | |
21 | |
22 #include "src/base/macros.h" | |
23 #include "src/double.h" | |
24 | |
25 namespace v8 { | |
26 namespace fdlibm { | |
27 | |
28 #ifdef _MSC_VER | |
29 inline double scalbn(double x, int y) { return _scalb(x, y); } | |
30 #endif // _MSC_VER | |
31 | |
32 | |
33 // Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi | |
34 static const int two_over_pi[] = { | |
35 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, | |
36 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, | |
37 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44, | |
38 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, | |
39 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, | |
40 0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, | |
41 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, | |
42 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08, | |
43 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA, | |
44 0x73A8C9, 0x60E27B, 0xC08C6B}; | |
45 | |
46 static const double zero = 0.0; | |
47 static const double two24 = 1.6777216e+07; | |
48 static const double one = 1.0; | |
49 static const double twon24 = 5.9604644775390625e-08; | |
50 | |
51 static const double PIo2[] = { | |
52 1.57079625129699707031e+00, // 0x3FF921FB, 0x40000000 | |
53 7.54978941586159635335e-08, // 0x3E74442D, 0x00000000 | |
54 5.39030252995776476554e-15, // 0x3CF84698, 0x80000000 | |
55 3.28200341580791294123e-22, // 0x3B78CC51, 0x60000000 | |
56 1.27065575308067607349e-29, // 0x39F01B83, 0x80000000 | |
57 1.22933308981111328932e-36, // 0x387A2520, 0x40000000 | |
58 2.73370053816464559624e-44, // 0x36E38222, 0x80000000 | |
59 2.16741683877804819444e-51 // 0x3569F31D, 0x00000000 | |
60 }; | |
61 | |
62 | |
63 INLINE(int __kernel_rem_pio2(double* x, double* y, int e0, int nx)) { | |
64 static const int32_t jk = 3; | |
65 double fw; | |
66 int32_t jx = nx - 1; | |
67 int32_t jv = (e0 - 3) / 24; | |
68 if (jv < 0) jv = 0; | |
69 int32_t q0 = e0 - 24 * (jv + 1); | |
70 int32_t m = jx + jk; | |
71 | |
72 double f[20]; | |
73 for (int i = 0, j = jv - jx; i <= m; i++, j++) { | |
74 f[i] = (j < 0) ? zero : static_cast<double>(two_over_pi[j]); | |
75 } | |
76 | |
77 double q[20]; | |
78 for (int i = 0; i <= jk; i++) { | |
79 fw = 0.0; | |
80 for (int j = 0; j <= jx; j++) fw += x[j] * f[jx + i - j]; | |
81 q[i] = fw; | |
82 } | |
83 | |
84 int32_t jz = jk; | |
85 | |
86 recompute: | |
87 | |
88 int32_t iq[20]; | |
89 double z = q[jz]; | |
90 for (int i = 0, j = jz; j > 0; i++, j--) { | |
91 fw = static_cast<double>(static_cast<int32_t>(twon24 * z)); | |
92 iq[i] = static_cast<int32_t>(z - two24 * fw); | |
93 z = q[j - 1] + fw; | |
94 } | |
95 | |
96 z = scalbn(z, q0); | |
97 z -= 8.0 * std::floor(z * 0.125); | |
98 int32_t n = static_cast<int32_t>(z); | |
99 z -= static_cast<double>(n); | |
100 int32_t ih = 0; | |
101 if (q0 > 0) { | |
102 int32_t i = (iq[jz - 1] >> (24 - q0)); | |
103 n += i; | |
104 iq[jz - 1] -= i << (24 - q0); | |
105 ih = iq[jz - 1] >> (23 - q0); | |
106 } else if (q0 == 0) { | |
107 ih = iq[jz - 1] >> 23; | |
108 } else if (z >= 0.5) { | |
109 ih = 2; | |
110 } | |
111 | |
112 if (ih > 0) { | |
113 n += 1; | |
114 int32_t carry = 0; | |
115 for (int i = 0; i < jz; i++) { | |
116 int32_t j = iq[i]; | |
117 if (carry == 0) { | |
118 if (j != 0) { | |
119 carry = 1; | |
120 iq[i] = 0x1000000 - j; | |
121 } | |
122 } else { | |
123 iq[i] = 0xffffff - j; | |
124 } | |
125 } | |
126 if (q0 == 1) { | |
127 iq[jz - 1] &= 0x7fffff; | |
128 } else if (q0 == 2) { | |
129 iq[jz - 1] &= 0x3fffff; | |
130 } | |
131 if (ih == 2) { | |
132 z = one - z; | |
133 if (carry != 0) z -= scalbn(one, q0); | |
134 } | |
135 } | |
136 | |
137 if (z == zero) { | |
138 int32_t j = 0; | |
139 for (int i = jz - 1; i >= jk; i--) j |= iq[i]; | |
140 if (j == 0) { | |
141 int32_t k = 1; | |
142 while (iq[jk - k] == 0) k++; | |
143 for (int i = jz + 1; i <= jz + k; i++) { | |
144 f[jx + i] = static_cast<double>(two_over_pi[jv + i]); | |
145 for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j]; | |
146 q[i] = fw; | |
147 } | |
148 jz += k; | |
149 goto recompute; | |
150 } | |
151 } | |
152 | |
153 if (z == 0.0) { | |
154 jz -= 1; | |
155 q0 -= 24; | |
156 while (iq[jz] == 0) { | |
157 jz--; | |
158 q0 -= 24; | |
159 } | |
160 } else { | |
161 z = scalbn(z, -q0); | |
162 if (z >= two24) { | |
163 fw = static_cast<double>(static_cast<int32_t>(twon24 * z)); | |
164 iq[jz] = static_cast<int32_t>(z - two24 * fw); | |
165 jz += 1; | |
166 q0 += 24; | |
167 iq[jz] = static_cast<int32_t>(fw); | |
168 } else { | |
169 iq[jz] = static_cast<int32_t>(z); | |
170 } | |
171 } | |
172 | |
173 fw = scalbn(one, q0); | |
174 for (int i = jz; i >= 0; i--) { | |
175 q[i] = fw * static_cast<double>(iq[i]); | |
176 fw *= twon24; | |
177 } | |
178 | |
179 double fq[20]; | |
180 for (int i = jz; i >= 0; i--) { | |
181 fw = 0.0; | |
182 for (int k = 0; k <= jk && k <= jz - i; k++) fw += PIo2[k] * q[i + k]; | |
183 fq[jz - i] = fw; | |
184 } | |
185 | |
186 fw = 0.0; | |
187 for (int i = jz; i >= 0; i--) fw += fq[i]; | |
188 y[0] = (ih == 0) ? fw : -fw; | |
189 fw = fq[0] - fw; | |
190 for (int i = 1; i <= jz; i++) fw += fq[i]; | |
191 y[1] = (ih == 0) ? fw : -fw; | |
192 return n & 7; | |
193 } | |
194 | |
195 | |
196 int rempio2(double x, double* y) { | |
197 int32_t hx = static_cast<int32_t>(internal::double_to_uint64(x) >> 32); | |
198 int32_t ix = hx & 0x7fffffff; | |
199 | |
200 if (ix >= 0x7ff00000) { | |
201 *y = std::numeric_limits<double>::quiet_NaN(); | |
202 return 0; | |
203 } | |
204 | |
205 int32_t e0 = (ix >> 20) - 1046; | |
206 uint64_t zi = internal::double_to_uint64(x) & 0xFFFFFFFFu; | |
207 zi |= static_cast<uint64_t>(ix - (e0 << 20)) << 32; | |
208 double z = internal::uint64_to_double(zi); | |
209 | |
210 double tx[3]; | |
211 for (int i = 0; i < 2; i++) { | |
212 tx[i] = static_cast<double>(static_cast<int32_t>(z)); | |
213 z = (z - tx[i]) * two24; | |
214 } | |
215 tx[2] = z; | |
216 | |
217 int nx = 3; | |
218 while (tx[nx - 1] == zero) nx--; | |
219 int n = __kernel_rem_pio2(tx, y, e0, nx); | |
220 if (hx < 0) { | |
221 y[0] = -y[0]; | |
222 y[1] = -y[1]; | |
223 return -n; | |
224 } | |
225 return n; | |
226 } | |
227 } // namespace internal | |
228 } // namespace v8 | |
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