[builtins] Introduce proper Float64Tan operator.

src/third_party/fdlibm/fdlibm.cc

-// 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