| // The following is adapted from fdlibm (http://www.netlib.org/fdlibm). |
| // |
| // ==================================================== |
| // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| // |
| // Developed at SunSoft, a Sun Microsystems, Inc. business. |
| // Permission to use, copy, modify, and distribute this |
| // software is freely granted, provided that this notice |
| // is preserved. |
| // ==================================================== |
| // |
| // The original source code covered by the above license above has been |
| // modified significantly by Google Inc. |
| // Copyright 2014 the V8 project authors. All rights reserved. |
| |
| #include "src/third_party/fdlibm/fdlibm.h" |
| |
| #include <stdint.h> |
| #include <cmath> |
| #include <limits> |
| |
| #include "src/base/macros.h" |
| #include "src/double.h" |
| |
| namespace v8 { |
| namespace fdlibm { |
| |
| #ifdef _MSC_VER |
| inline double scalbn(double x, int y) { return _scalb(x, y); } |
| #endif // _MSC_VER |
| |
| |
| // Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| static const int two_over_pi[] = { |
| 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, |
| 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, |
| 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44, |
| 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, |
| 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, |
| 0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
| 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, |
| 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08, |
| 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA, |
| 0x73A8C9, 0x60E27B, 0xC08C6B}; |
| |
| static const double zero = 0.0; |
| static const double two24 = 1.6777216e+07; |
| static const double one = 1.0; |
| static const double twon24 = 5.9604644775390625e-08; |
| |
| static const double PIo2[] = { |
| 1.57079625129699707031e+00, // 0x3FF921FB, 0x40000000 |
| 7.54978941586159635335e-08, // 0x3E74442D, 0x00000000 |
| 5.39030252995776476554e-15, // 0x3CF84698, 0x80000000 |
| 3.28200341580791294123e-22, // 0x3B78CC51, 0x60000000 |
| 1.27065575308067607349e-29, // 0x39F01B83, 0x80000000 |
| 1.22933308981111328932e-36, // 0x387A2520, 0x40000000 |
| 2.73370053816464559624e-44, // 0x36E38222, 0x80000000 |
| 2.16741683877804819444e-51 // 0x3569F31D, 0x00000000 |
| }; |
| |
| |
| INLINE(int __kernel_rem_pio2(double* x, double* y, int e0, int nx)) { |
| static const int32_t jk = 3; |
| double fw; |
| int32_t jx = nx - 1; |
| int32_t jv = (e0 - 3) / 24; |
| if (jv < 0) jv = 0; |
| int32_t q0 = e0 - 24 * (jv + 1); |
| int32_t m = jx + jk; |
| |
| double f[20]; |
| for (int i = 0, j = jv - jx; i <= m; i++, j++) { |
| f[i] = (j < 0) ? zero : static_cast<double>(two_over_pi[j]); |
| } |
| |
| double q[20]; |
| for (int i = 0; i <= jk; i++) { |
| fw = 0.0; |
| for (int j = 0; j <= jx; j++) fw += x[j] * f[jx + i - j]; |
| q[i] = fw; |
| } |
| |
| int32_t jz = jk; |
| |
| recompute: |
| |
| int32_t iq[20]; |
| double z = q[jz]; |
| for (int i = 0, j = jz; j > 0; i++, j--) { |
| fw = static_cast<double>(static_cast<int32_t>(twon24 * z)); |
| iq[i] = static_cast<int32_t>(z - two24 * fw); |
| z = q[j - 1] + fw; |
| } |
| |
| z = scalbn(z, q0); |
| z -= 8.0 * std::floor(z * 0.125); |
| int32_t n = static_cast<int32_t>(z); |
| z -= static_cast<double>(n); |
| int32_t ih = 0; |
| if (q0 > 0) { |
| int32_t i = (iq[jz - 1] >> (24 - q0)); |
| n += i; |
| iq[jz - 1] -= i << (24 - q0); |
| ih = iq[jz - 1] >> (23 - q0); |
| } else if (q0 == 0) { |
| ih = iq[jz - 1] >> 23; |
| } else if (z >= 0.5) { |
| ih = 2; |
| } |
| |
| if (ih > 0) { |
| n += 1; |
| int32_t carry = 0; |
| for (int i = 0; i < jz; i++) { |
| int32_t j = iq[i]; |
| if (carry == 0) { |
| if (j != 0) { |
| carry = 1; |
| iq[i] = 0x1000000 - j; |
| } |
| } else { |
| iq[i] = 0xffffff - j; |
| } |
| } |
| if (q0 == 1) { |
| iq[jz - 1] &= 0x7fffff; |
| } else if (q0 == 2) { |
| iq[jz - 1] &= 0x3fffff; |
| } |
| if (ih == 2) { |
| z = one - z; |
| if (carry != 0) z -= scalbn(one, q0); |
| } |
| } |
| |
| if (z == zero) { |
| int32_t j = 0; |
| for (int i = jz - 1; i >= jk; i--) j |= iq[i]; |
| if (j == 0) { |
| int32_t k = 1; |
| while (iq[jk - k] == 0) k++; |
| for (int i = jz + 1; i <= jz + k; i++) { |
| f[jx + i] = static_cast<double>(two_over_pi[jv + i]); |
| for (j = 0, fw = 0.0; j <= jx; j++) fw += x[j] * f[jx + i - j]; |
| q[i] = fw; |
| } |
| jz += k; |
| goto recompute; |
| } |
| } |
| |
| if (z == 0.0) { |
| jz -= 1; |
| q0 -= 24; |
| while (iq[jz] == 0) { |
| jz--; |
| q0 -= 24; |
| } |
| } else { |
| z = scalbn(z, -q0); |
| if (z >= two24) { |
| fw = static_cast<double>(static_cast<int32_t>(twon24 * z)); |
| iq[jz] = static_cast<int32_t>(z - two24 * fw); |
| jz += 1; |
| q0 += 24; |
| iq[jz] = static_cast<int32_t>(fw); |
| } else { |
| iq[jz] = static_cast<int32_t>(z); |
| } |
| } |
| |
| fw = scalbn(one, q0); |
| for (int i = jz; i >= 0; i--) { |
| q[i] = fw * static_cast<double>(iq[i]); |
| fw *= twon24; |
| } |
| |
| double fq[20]; |
| for (int i = jz; i >= 0; i--) { |
| fw = 0.0; |
| for (int k = 0; k <= jk && k <= jz - i; k++) fw += PIo2[k] * q[i + k]; |
| fq[jz - i] = fw; |
| } |
| |
| fw = 0.0; |
| for (int i = jz; i >= 0; i--) fw += fq[i]; |
| y[0] = (ih == 0) ? fw : -fw; |
| fw = fq[0] - fw; |
| for (int i = 1; i <= jz; i++) fw += fq[i]; |
| y[1] = (ih == 0) ? fw : -fw; |
| return n & 7; |
| } |
| |
| |
| int rempio2(double x, double* y) { |
| int32_t hx = static_cast<int32_t>(internal::double_to_uint64(x) >> 32); |
| int32_t ix = hx & 0x7fffffff; |
| |
| if (ix >= 0x7ff00000) { |
| *y = std::numeric_limits<double>::quiet_NaN(); |
| return 0; |
| } |
| |
| int32_t e0 = (ix >> 20) - 1046; |
| uint64_t zi = internal::double_to_uint64(x) & 0xFFFFFFFFu; |
| zi |= static_cast<uint64_t>(ix - (e0 << 20)) << 32; |
| double z = internal::uint64_to_double(zi); |
| |
| double tx[3]; |
| for (int i = 0; i < 2; i++) { |
| tx[i] = static_cast<double>(static_cast<int32_t>(z)); |
| z = (z - tx[i]) * two24; |
| } |
| tx[2] = z; |
| |
| int nx = 3; |
| while (tx[nx - 1] == zero) nx--; |
| int n = __kernel_rem_pio2(tx, y, e0, nx); |
| if (hx < 0) { |
| y[0] = -y[0]; |
| y[1] = -y[1]; |
| return -n; |
| } |
| return n; |
| } |
| } // namespace internal |
| } // namespace v8 |