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Diffstat (limited to 'src/math/k_tan.c')
| -rw-r--r-- | src/math/k_tan.c | 149 |
1 files changed, 0 insertions, 149 deletions
diff --git a/src/math/k_tan.c b/src/math/k_tan.c deleted file mode 100644 index f721ae6d..00000000 --- a/src/math/k_tan.c +++ /dev/null @@ -1,149 +0,0 @@ -/* @(#)k_tan.c 1.5 04/04/22 SMI */ - -/* - * ==================================================== - * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. - * - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -/* __kernel_tan( x, y, k ) - * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. - * - * Algorithm - * 1. Since tan(-x) = -tan(x), we need only to consider positive x. - * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. - * 3. tan(x) is approximated by a odd polynomial of degree 27 on - * [0,0.67434] - * 3 27 - * tan(x) ~ x + T1*x + ... + T13*x - * where - * - * |tan(x) 2 4 26 | -59.2 - * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 - * | x | - * - * Note: tan(x+y) = tan(x) + tan'(x)*y - * ~ tan(x) + (1+x*x)*y - * Therefore, for better accuracy in computing tan(x+y), let - * 3 2 2 2 2 - * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) - * then - * 3 2 - * tan(x+y) = x + (T1*x + (x *(r+y)+y)) - * - * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then - * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) - * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) - */ - -#include <math.h> -#include "math_private.h" -static const double xxx[] = { - 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ - 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ - 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ - 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ - 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ - 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ - 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ - 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ - 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ - 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ - 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ - -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ - 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ -/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ -/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ -/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ -}; -#define one xxx[13] -#define pio4 xxx[14] -#define pio4lo xxx[15] -#define T xxx -/* INDENT ON */ - -double -__kernel_tan(double x, double y, int iy) { - double z, r, v, w, s; - int32_t ix, hx; - - GET_HIGH_WORD(hx,x); - ix = hx & 0x7fffffff; /* high word of |x| */ - if (ix < 0x3e300000) { /* x < 2**-28 */ - if ((int) x == 0) { /* generate inexact */ - uint32_t low; - GET_LOW_WORD(low,x); - if (((ix | low) | (iy + 1)) == 0) - return one / fabs(x); - else { - if (iy == 1) - return x; - else { /* compute -1 / (x+y) carefully */ - double a, t; - - z = w = x + y; - SET_LOW_WORD(z, 0); - v = y - (z - x); - t = a = -one / w; - SET_LOW_WORD(t, 0); - s = one + t * z; - return t + a * (s + t * v); - } - } - } - } - if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ - if (hx < 0) { - x = -x; - y = -y; - } - z = pio4 - x; - w = pio4lo - y; - x = z + w; - y = 0.0; - } - z = x * x; - w = z * z; - /* - * Break x^5*(T[1]+x^2*T[2]+...) into - * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + - * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) - */ - r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + - w * T[11])))); - v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + - w * T[12]))))); - s = z * x; - r = y + z * (s * (r + v) + y); - r += T[0] * s; - w = x + r; - if (ix >= 0x3FE59428) { - v = (double) iy; - return (double) (1 - ((hx >> 30) & 2)) * - (v - 2.0 * (x - (w * w / (w + v) - r))); - } - if (iy == 1) - return w; - else { - /* - * if allow error up to 2 ulp, simply return - * -1.0 / (x+r) here - */ - /* compute -1.0 / (x+r) accurately */ - double a, t; - z = w; - SET_LOW_WORD(z,0); - v = r - (z - x); /* z+v = r+x */ - t = a = -1.0 / w; /* a = -1.0/w */ - SET_LOW_WORD(t,0); - s = 1.0 + t * z; - return t + a * (s + t * v); - } -} |