a0ee07829a
This brings us up to date with FreeBSD HEAD, fixes various bugs, unifies the set of functions we support on ARM, MIPS, and x86, fixes "long double", adds ISO C99 support, and adds basic unit tests. It turns out that our "long double" functions have always been broken for non-normal numbers. This patch fixes that by not using the upstream implementations and just forwarding to the regular "double" implementation instead (since "long double" on Android is just "double" anyway, which is what BSD doesn't support). All the tests pass on ARM, MIPS, and x86, plus glibc on x86-64. Bug: 3169850 Bug: 8012787 Bug: https://code.google.com/p/android/issues/detail?id=6697 Change-Id: If0c343030959c24bfc50d4d21c9530052c581837
133 lines
3.9 KiB
C
133 lines
3.9 KiB
C
/* @(#)k_tan.c 1.5 04/04/22 SMI */
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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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/* INDENT OFF */
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/* __kernel_tan( x, y, k )
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* kernel tan function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
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* Input x is assumed to be bounded by ~pi/4 in magnitude.
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* Input y is the tail of x.
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* Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned.
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*
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* Algorithm
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* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
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* 2. Callers must return tan(-0) = -0 without calling here since our
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* odd polynomial is not evaluated in a way that preserves -0.
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* Callers may do the optimization tan(x) ~ x for tiny x.
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* 3. tan(x) is approximated by a odd polynomial of degree 27 on
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* [0,0.67434]
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* 3 27
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* tan(x) ~ x + T1*x + ... + T13*x
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* where
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*
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* |tan(x) 2 4 26 | -59.2
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* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
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* | x |
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*
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* Note: tan(x+y) = tan(x) + tan'(x)*y
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* ~ tan(x) + (1+x*x)*y
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* Therefore, for better accuracy in computing tan(x+y), let
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* 3 2 2 2 2
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* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
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* then
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* 3 2
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* tan(x+y) = x + (T1*x + (x *(r+y)+y))
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*
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* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
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* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
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* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
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*/
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#include "math.h"
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#include "math_private.h"
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static const double xxx[] = {
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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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/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
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/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
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/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
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};
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#define one xxx[13]
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#define pio4 xxx[14]
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#define pio4lo xxx[15]
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#define T xxx
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/* INDENT ON */
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double
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__kernel_tan(double x, double y, int iy) {
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double z, r, v, w, s;
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int32_t ix, hx;
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GET_HIGH_WORD(hx,x);
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ix = hx & 0x7fffffff; /* high word of |x| */
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if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
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if (hx < 0) {
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x = -x;
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y = -y;
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}
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z = pio4 - x;
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w = pio4lo - y;
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x = z + w;
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y = 0.0;
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}
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z = x * x;
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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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r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
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w * T[11]))));
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v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
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w * T[12])))));
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s = z * x;
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r = y + z * (s * (r + v) + y);
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r += T[0] * s;
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w = x + r;
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if (ix >= 0x3FE59428) {
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v = (double) iy;
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return (double) (1 - ((hx >> 30) & 2)) *
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(v - 2.0 * (x - (w * w / (w + v) - r)));
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}
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if (iy == 1)
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return w;
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else {
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/*
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* if allow error up to 2 ulp, simply return
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* -1.0 / (x+r) here
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*/
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/* compute -1.0 / (x+r) accurately */
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double a, t;
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z = w;
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SET_LOW_WORD(z,0);
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v = r - (z - x); /* z+v = r+x */
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t = a = -1.0 / w; /* a = -1.0/w */
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SET_LOW_WORD(t,0);
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s = 1.0 + t * z;
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return t + a * (s + t * v);
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}
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}
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