+++ /dev/null
-/* @(#)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);
- }
-}
projects / musl / blobdiff