mirror of https://github.com/n-hys/msun.git
79 lines
2.8 KiB
C
79 lines
2.8 KiB
C
/* From: @(#)k_cos.c 1.3 95/01/18 */
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
* Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
|
|
*
|
|
* Developed at SunSoft, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
#include <sys/cdefs.h>
|
|
__FBSDID("$FreeBSD$");
|
|
|
|
/*
|
|
* ld80 version of k_cos.c. See ../src/k_cos.c for most comments.
|
|
*/
|
|
|
|
#include "math_private.h"
|
|
|
|
/*
|
|
* Domain [-0.7854, 0.7854], range ~[-2.43e-23, 2.425e-23]:
|
|
* |cos(x) - c(x)| < 2**-75.1
|
|
*
|
|
* The coefficients of c(x) were generated by a pari-gp script using
|
|
* a Remez algorithm that searches for the best higher coefficients
|
|
* after rounding leading coefficients to a specified precision.
|
|
*
|
|
* Simpler methods like Chebyshev or basic Remez barely suffice for
|
|
* cos() in 64-bit precision, because we want the coefficient of x^2
|
|
* to be precisely -0.5 so that multiplying by it is exact, and plain
|
|
* rounding of the coefficients of a good polynomial approximation only
|
|
* gives this up to about 64-bit precision. Plain rounding also gives
|
|
* a mediocre approximation for the coefficient of x^4, but a rounding
|
|
* error of 0.5 ulps for this coefficient would only contribute ~0.01
|
|
* ulps to the final error, so this is unimportant. Rounding errors in
|
|
* higher coefficients are even less important.
|
|
*
|
|
* In fact, coefficients above the x^4 one only need to have 53-bit
|
|
* precision, and this is more efficient. We get this optimization
|
|
* almost for free from the complications needed to search for the best
|
|
* higher coefficients.
|
|
*/
|
|
static const double
|
|
one = 1.0;
|
|
|
|
#if defined(__amd64__) || defined(__i386__)
|
|
/* Long double constants are slow on these arches, and broken on i386. */
|
|
static const volatile double
|
|
C1hi = 0.041666666666666664, /* 0x15555555555555.0p-57 */
|
|
C1lo = 2.2598839032744733e-18; /* 0x14d80000000000.0p-111 */
|
|
#define C1 ((long double)C1hi + C1lo)
|
|
#else
|
|
static const long double
|
|
C1 = 0.0416666666666666666136L; /* 0xaaaaaaaaaaaaaa9b.0p-68 */
|
|
#endif
|
|
|
|
static const double
|
|
C2 = -0.0013888888888888874, /* -0x16c16c16c16c10.0p-62 */
|
|
C3 = 0.000024801587301571716, /* 0x1a01a01a018e22.0p-68 */
|
|
C4 = -0.00000027557319215507120, /* -0x127e4fb7602f22.0p-74 */
|
|
C5 = 0.0000000020876754400407278, /* 0x11eed8caaeccf1.0p-81 */
|
|
C6 = -1.1470297442401303e-11, /* -0x19393412bd1529.0p-89 */
|
|
C7 = 4.7383039476436467e-14; /* 0x1aac9d9af5c43e.0p-97 */
|
|
|
|
long double
|
|
__kernel_cosl(long double x, long double y)
|
|
{
|
|
long double hz,z,r,w;
|
|
|
|
z = x*x;
|
|
r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*C7))))));
|
|
hz = 0.5*z;
|
|
w = one-hz;
|
|
return w + (((one-w)-hz) + (z*r-x*y));
|
|
}
|