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