Implement trigonometric functions using a fdlibm port.

src/rempio2.cc

+// Copyright 2014 the V8 project authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// 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.
+// ====================================================
+
+
+#include "src/v8.h"
+
+#include "src/double.h"
+#include "src/rempio2.h"
+
+
+namespace v8 {
+namespace internal {
+
+const double TrigonometricConstants::constants[] = {
+    6.36619772367581382433e-01,   // invpio2   0
+    1.57079632673412561417e+00,   // pio2_1    1
+    6.07710050650619224932e-11,   // pio2_1t   2
+    6.07710050630396597660e-11,   // pio2_2    3
+    2.02226624879595063154e-21,   // pio2_2t   4
+    2.02226624871116645580e-21,   // pio2_3    5
+    8.47842766036889956997e-32,   // pio2_3t   6
+    -1.66666666666666324348e-01,  // S1        7
+    8.33333333332248946124e-03,   //           8
+    -1.98412698298579493134e-04,  //           9
+    2.75573137070700676789e-06,   //          10
+    -2.50507602534068634195e-08,  //          11
+    1.58969099521155010221e-10,   // S6       12
+    4.16666666666666019037e-02,   // C1       13
+    -1.38888888888741095749e-03,  //          14
+    2.48015872894767294178e-05,   //          15
+    -2.75573143513906633035e-07,  //          16
+    2.08757232129817482790e-09,   //          17
+    -1.13596475577881948265e-11,  // C6       18
+    3.33333333333334091986e-01,   // T0       19
+    1.33333333333201242699e-01,   //          20
+    5.39682539762260521377e-02,   //          21
+    2.18694882948595424599e-02,   //          22
+    8.86323982359930005737e-03,   //          23
+    3.59207910759131235356e-03,   //          24
+    1.45620945432529025516e-03,   //          25
+    5.88041240820264096874e-04,   //          26
+    2.46463134818469906812e-04,   //          27
+    7.81794442939557092300e-05,   //          28
+    7.14072491382608190305e-05,   //          29
+    -1.85586374855275456654e-05,  //          30
+    2.59073051863633712884e-05,   // T12      31
+    7.85398163397448278999e-01,   // pio4     32
+    3.06161699786838301793e-17,   // pio4lo   33
+};

[Raymond Toy, 2014/07/24 16:51:12]

I think readability would be vastly improved if you didn't smash all of these
constants into one giant array.  At the very least, the S1-S6, C1-C6 and T0-T12
values should be in their own arrays.

[Yang, 2014/07/28 11:29:00]

Like previously mentioned. This should all go away once we have constant pools
for all platforms.

+
+
+// 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
+};
+
+
+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[10];
+  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[10];
+  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[10];
+  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[10];
+  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>(double_to_uint64(x) >> 32);
+  int32_t ix = hx & 0x7fffffff;
+
+  ASSERT(ix > 0x413921fb);  // Handling of lower ix has been omitted.
+  if (ix >= 0x7ff00000) {
+    *y = base::OS::nan_value();
+    return 0;
+  }
+
+  int32_t e0 = (ix >> 20) - 1046;
+  uint64_t zi = double_to_uint64(x) & 0xFFFFFFFFu;
+  zi |= static_cast<uint64_t>(ix - (e0 << 20)) << 32;
+  double z = 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 v8::internal