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/v8.h"
17
18 #include "src/double.h"
19 #include "third_party/fdlibm/fdlibm.h"
20
21
22 namespace v8 {
23 namespace fdlibm {
24
25 #ifdef _MSC_VER
scalbn(double x,int y)26 inline double scalbn(double x, int y) { return _scalb(x, y); }
27 #endif // _MSC_VER
28
29 const double MathConstants::constants[] = {
30 6.36619772367581382433e-01, // invpio2 0
31 1.57079632673412561417e+00, // pio2_1 1
32 6.07710050650619224932e-11, // pio2_1t 2
33 6.07710050630396597660e-11, // pio2_2 3
34 2.02226624879595063154e-21, // pio2_2t 4
35 2.02226624871116645580e-21, // pio2_3 5
36 8.47842766036889956997e-32, // pio2_3t 6
37 -1.66666666666666324348e-01, // S1 7 coefficients for sin
38 8.33333333332248946124e-03, // 8
39 -1.98412698298579493134e-04, // 9
40 2.75573137070700676789e-06, // 10
41 -2.50507602534068634195e-08, // 11
42 1.58969099521155010221e-10, // S6 12
43 4.16666666666666019037e-02, // C1 13 coefficients for cos
44 -1.38888888888741095749e-03, // 14
45 2.48015872894767294178e-05, // 15
46 -2.75573143513906633035e-07, // 16
47 2.08757232129817482790e-09, // 17
48 -1.13596475577881948265e-11, // C6 18
49 3.33333333333334091986e-01, // T0 19 coefficients for tan
50 1.33333333333201242699e-01, // 20
51 5.39682539762260521377e-02, // 21
52 2.18694882948595424599e-02, // 22
53 8.86323982359930005737e-03, // 23
54 3.59207910759131235356e-03, // 24
55 1.45620945432529025516e-03, // 25
56 5.88041240820264096874e-04, // 26
57 2.46463134818469906812e-04, // 27
58 7.81794442939557092300e-05, // 28
59 7.14072491382608190305e-05, // 29
60 -1.85586374855275456654e-05, // 30
61 2.59073051863633712884e-05, // T12 31
62 7.85398163397448278999e-01, // pio4 32
63 3.06161699786838301793e-17, // pio4lo 33
64 6.93147180369123816490e-01, // ln2_hi 34
65 1.90821492927058770002e-10, // ln2_lo 35
66 1.80143985094819840000e+16, // 2^54 36
67 6.666666666666666666e-01, // 2/3 37
68 6.666666666666735130e-01, // LP1 38 coefficients for log1p
69 3.999999999940941908e-01, // 39
70 2.857142874366239149e-01, // 40
71 2.222219843214978396e-01, // 41
72 1.818357216161805012e-01, // 42
73 1.531383769920937332e-01, // 43
74 1.479819860511658591e-01, // LP7 44
75 7.09782712893383973096e+02, // 45 overflow threshold for expm1
76 1.44269504088896338700e+00, // 1/ln2 46
77 -3.33333333333331316428e-02, // Q1 47 coefficients for expm1
78 1.58730158725481460165e-03, // 48
79 -7.93650757867487942473e-05, // 49
80 4.00821782732936239552e-06, // 50
81 -2.01099218183624371326e-07, // Q5 51
82 710.4758600739439 // 52 overflow threshold sinh, cosh
83 };
84
85
86 // Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
87 static const int two_over_pi[] = {
88 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C,
89 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649,
90 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44,
91 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B,
92 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D,
93 0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
94 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330,
95 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08,
96 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA,
97 0x73A8C9, 0x60E27B, 0xC08C6B};
98
99 static const double zero = 0.0;
100 static const double two24 = 1.6777216e+07;
101 static const double one = 1.0;
102 static const double twon24 = 5.9604644775390625e-08;
103
104 static const double PIo2[] = {
105 1.57079625129699707031e+00, // 0x3FF921FB, 0x40000000
106 7.54978941586159635335e-08, // 0x3E74442D, 0x00000000
107 5.39030252995776476554e-15, // 0x3CF84698, 0x80000000
108 3.28200341580791294123e-22, // 0x3B78CC51, 0x60000000
109 1.27065575308067607349e-29, // 0x39F01B83, 0x80000000
110 1.22933308981111328932e-36, // 0x387A2520, 0x40000000
111 2.73370053816464559624e-44, // 0x36E38222, 0x80000000
112 2.16741683877804819444e-51 // 0x3569F31D, 0x00000000
113 };
114
115
__kernel_rem_pio2(double * x,double * y,int e0,int nx)116 int __kernel_rem_pio2(double* x, double* y, int e0, int nx) {
117 static const int32_t jk = 3;
118 double fw;
119 int32_t jx = nx - 1;
120 int32_t jv = (e0 - 3) / 24;
121 if (jv < 0) jv = 0;
122 int32_t q0 = e0 - 24 * (jv + 1);
123 int32_t m = jx + jk;
124
125 double f[10];
126 for (int i = 0, j = jv - jx; i <= m; i++, j++) {
127 f[i] = (j < 0) ? zero : static_cast<double>(two_over_pi[j]);
128 }
129
130 double q[10];
131 for (int i = 0; i <= jk; i++) {
132 fw = 0.0;
133 for (int j = 0; j <= jx; j++) fw += x[j] * f[jx + i - j];
134 q[i] = fw;
135 }
136
137 int32_t jz = jk;
138
139 recompute:
140
141 int32_t iq[10];
142 double z = q[jz];
143 for (int i = 0, j = jz; j > 0; i++, j--) {
144 fw = static_cast<double>(static_cast<int32_t>(twon24 * z));
145 iq[i] = static_cast<int32_t>(z - two24 * fw);
146 z = q[j - 1] + fw;
147 }
148
149 z = scalbn(z, q0);
150 z -= 8.0 * std::floor(z * 0.125);
151 int32_t n = static_cast<int32_t>(z);
152 z -= static_cast<double>(n);
153 int32_t ih = 0;
154 if (q0 > 0) {
155 int32_t i = (iq[jz - 1] >> (24 - q0));
156 n += i;
157 iq[jz - 1] -= i << (24 - q0);
158 ih = iq[jz - 1] >> (23 - q0);
159 } else if (q0 == 0) {
160 ih = iq[jz - 1] >> 23;
161 } else if (z >= 0.5) {
162 ih = 2;
163 }
164
165 if (ih > 0) {
166 n += 1;
167 int32_t carry = 0;
168 for (int i = 0; i < jz; i++) {
169 int32_t j = iq[i];
170 if (carry == 0) {
171 if (j != 0) {
172 carry = 1;
173 iq[i] = 0x1000000 - j;
174 }
175 } else {
176 iq[i] = 0xffffff - j;
177 }
178 }
179 if (q0 == 1) {
180 iq[jz - 1] &= 0x7fffff;
181 } else if (q0 == 2) {
182 iq[jz - 1] &= 0x3fffff;
183 }
184 if (ih == 2) {
185 z = one - z;
186 if (carry != 0) z -= scalbn(one, q0);
187 }
188 }
189
190 if (z == zero) {
191 int32_t j = 0;
192 for (int i = jz - 1; i >= jk; i--) j |= iq[i];
193 if (j == 0) {
194 int32_t k = 1;
195 while (iq[jk - k] == 0) k++;
196 for (int i = jz + 1; i <= jz + k; i++) {
197 f[jx + i] = static_cast<double>(two_over_pi[jv + i]);
198 for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j];
199 q[i] = fw;
200 }
201 jz += k;
202 goto recompute;
203 }
204 }
205
206 if (z == 0.0) {
207 jz -= 1;
208 q0 -= 24;
209 while (iq[jz] == 0) {
210 jz--;
211 q0 -= 24;
212 }
213 } else {
214 z = scalbn(z, -q0);
215 if (z >= two24) {
216 fw = static_cast<double>(static_cast<int32_t>(twon24 * z));
217 iq[jz] = static_cast<int32_t>(z - two24 * fw);
218 jz += 1;
219 q0 += 24;
220 iq[jz] = static_cast<int32_t>(fw);
221 } else {
222 iq[jz] = static_cast<int32_t>(z);
223 }
224 }
225
226 fw = scalbn(one, q0);
227 for (int i = jz; i >= 0; i--) {
228 q[i] = fw * static_cast<double>(iq[i]);
229 fw *= twon24;
230 }
231
232 double fq[10];
233 for (int i = jz; i >= 0; i--) {
234 fw = 0.0;
235 for (int k = 0; k <= jk && k <= jz - i; k++) fw += PIo2[k] * q[i + k];
236 fq[jz - i] = fw;
237 }
238
239 fw = 0.0;
240 for (int i = jz; i >= 0; i--) fw += fq[i];
241 y[0] = (ih == 0) ? fw : -fw;
242 fw = fq[0] - fw;
243 for (int i = 1; i <= jz; i++) fw += fq[i];
244 y[1] = (ih == 0) ? fw : -fw;
245 return n & 7;
246 }
247
248
rempio2(double x,double * y)249 int rempio2(double x, double* y) {
250 int32_t hx = static_cast<int32_t>(internal::double_to_uint64(x) >> 32);
251 int32_t ix = hx & 0x7fffffff;
252
253 if (ix >= 0x7ff00000) {
254 *y = base::OS::nan_value();
255 return 0;
256 }
257
258 int32_t e0 = (ix >> 20) - 1046;
259 uint64_t zi = internal::double_to_uint64(x) & 0xFFFFFFFFu;
260 zi |= static_cast<uint64_t>(ix - (e0 << 20)) << 32;
261 double z = internal::uint64_to_double(zi);
262
263 double tx[3];
264 for (int i = 0; i < 2; i++) {
265 tx[i] = static_cast<double>(static_cast<int32_t>(z));
266 z = (z - tx[i]) * two24;
267 }
268 tx[2] = z;
269
270 int nx = 3;
271 while (tx[nx - 1] == zero) nx--;
272 int n = __kernel_rem_pio2(tx, y, e0, nx);
273 if (hx < 0) {
274 y[0] = -y[0];
275 y[1] = -y[1];
276 return -n;
277 }
278 return n;
279 }
280 }
281 } // namespace v8::internal
282