forked from Lephenixnoir/OpenLibm
81053b7fcb
- Align DLLEXPORT in definitions and declations. There is still a few cases left, where the declation in the compiler's complex.h disagrees with the implementation here. For now we can't do anything about that, but maybe should be revisited in the future. - Fix the syntax on an .ascii directive that gcc accepted mistakingly, but clang does not.
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 "cdefs-compat.h"
|
|
//__FBSDID("$FreeBSD: src/lib/msun/ld80/k_cosl.c,v 1.1 2008/02/17 07:32:14 das Exp $");
|
|
|
|
/*
|
|
* 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));
|
|
}
|