mirror of https://github.com/PrimeDecomp/prime.git
135 lines
4.2 KiB
C
135 lines
4.2 KiB
C
/* @(#)k_tan.c 1.2 95/01/04 */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* 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 "fdlibm.h"
|
|
|
|
#ifdef __STDC__
|
|
static const double
|
|
#else
|
|
static double
|
|
#endif
|
|
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
|
|
pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
|
|
pio4lo = 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */
|
|
T[] = {
|
|
3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */
|
|
1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */
|
|
5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */
|
|
2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */
|
|
8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */
|
|
3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */
|
|
1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */
|
|
5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */
|
|
2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */
|
|
7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */
|
|
7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */
|
|
-1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */
|
|
2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */
|
|
};
|
|
|
|
#ifdef __STDC__
|
|
double __kernel_tan(double x, double y, _INT32 iy)
|
|
#else
|
|
double __kernel_tan(x, y, iy)
|
|
double x, y;
|
|
_INT32 iy;
|
|
#endif
|
|
{
|
|
double z, r, v, w, s;
|
|
_INT32 ix, hx;
|
|
hx = __HI(x); /* high word of x */
|
|
ix = hx & 0x7fffffff; /* high word of |x| */
|
|
if (ix < 0x3e300000) /* x < 2**-28 */
|
|
{
|
|
if ((_INT32)x == 0) { /* generate inexact */
|
|
if (((ix | __LO(x)) | (iy + 1)) == 0)
|
|
return one / fabs(x);
|
|
else
|
|
return (iy == 1) ? x : -one / x;
|
|
}
|
|
}
|
|
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;
|
|
__LO(z) = 0;
|
|
v = r - (z - x); /* z+v = r+x */
|
|
t = a = -1.0 / w; /* a = -1.0/w */
|
|
__LO(t) = 0;
|
|
s = 1.0 + t * z;
|
|
return t + a * (s + t * v);
|
|
}
|
|
}
|