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80 lines
2.7 KiB
Plaintext
80 lines
2.7 KiB
Plaintext
module std::math::nolibc @if(env::NO_LIBC);
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/* origin: FreeBSD /usr/src/lib/msun/src/k_tan.c */
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/*
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* ====================================================
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* Copyright 2004 Sun Microsystems, Inc. All Rights Reserved.
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*
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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const double[*] TAN_T = {
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3.33333333333334091986e-01, /* 3FD55555, 55555563 */
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1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
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5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
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2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
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8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
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3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
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1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
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5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
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2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
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7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
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7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
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-1.85586374855275456654e-05, /* BEF375CB, DB605373 */
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2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
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};
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fn double __tan(double x, double y, int odd) @extern("__tan") @weak @nostrip
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{
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const double PIO4 = 7.85398163397448278999e-01; /* 3FE921FB, 54442D18 */
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const double PIO4LO = 3.06161699786838301793e-17; /* 3C81A626, 33145C07 */
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uint hx = (uint)(bitcast(x, ulong) >> 32);
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bool big = (hx &0x7fffffff) >= 0x3FE59428; // |x| >= 0.6744
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int sign @noinit;
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if (big)
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{
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sign = hx >> 31;
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if (sign)
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{
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x = -x;
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y = -y;
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}
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x = (PIO4 - x) + (PIO4LO - y);
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y = 0.0;
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}
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double z = x * x;
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double w = z * z;
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/*
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* Break x^5*(T[1]+x^2*T[2]+...) into
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* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
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* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
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*/
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double r = TAN_T[1] + w * (TAN_T[3] + w * (TAN_T[5] + w * (TAN_T[7] + w * (TAN_T[9] + w * TAN_T[11]))));
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double v = z * (TAN_T[2] + w * (TAN_T[4] + w * (TAN_T[6] + w * (TAN_T[8] + w * (TAN_T[10] + w * TAN_T[12])))));
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double s = z * x;
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r = y + z * (s * (r + v) + y) + s * TAN_T[0];
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w = x + r;
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if (big)
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{
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s = (double)(1 - 2 * odd);
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v = s - 2.0 * (x + (r - w*w/(w + s)));
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return sign ? -v : v;
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}
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if (!odd) return w;
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// -1.0/(x+r) has up to 2ulp error, so compute it accurately
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// Clear low word
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ulong d = bitcast(w, ulong) & 0xFFFF_FFFF_0000_0000;
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double w0 = bitcast(d, double);
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v = r - (w0 - x); // w0+v = r+x
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double a = -1.0 / w;
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d = bitcast(a, ulong) & 0xFFFF_FFFF_0000_0000;
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double a0 = bitcast(d, double);
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return a0 + a * (1.0 + a0 * w0 + a0 * v);
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}
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