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
scalbn(double x,int y)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
INLINE(int __kernel_rem_pio2 (double * x,double * y,int e0,int nx))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
rempio2(double x,double * y)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
229