mirror of
https://gcc.gnu.org/git/gcc.git
synced 2024-12-29 05:55:44 +08:00
168 lines
6.6 KiB
C
168 lines
6.6 KiB
C
/* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
|
|
Copyright (C) 1999 Free Software Foundation, Inc.
|
|
This file is part of the GNU C Library.
|
|
Contributed by Jakub Jelinek <jj@ultra.linux.cz>
|
|
|
|
The GNU C Library is free software; you can redistribute it and/or
|
|
modify it under the terms of the GNU Lesser General Public
|
|
License as published by the Free Software Foundation; either
|
|
version 2.1 of the License, or (at your option) any later version.
|
|
|
|
The GNU C Library is distributed in the hope that it will be useful,
|
|
but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
|
|
Lesser General Public License for more details.
|
|
|
|
You should have received a copy of the GNU Lesser General Public
|
|
License along with the GNU C Library; if not, write to the Free
|
|
Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
|
|
02111-1307 USA. */
|
|
|
|
#include "quadmath-imp.h"
|
|
|
|
static const __float128 c[] = {
|
|
#define ONE c[0]
|
|
1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
|
|
|
|
/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
|
|
x in <0,1/256> */
|
|
#define SCOS1 c[1]
|
|
#define SCOS2 c[2]
|
|
#define SCOS3 c[3]
|
|
#define SCOS4 c[4]
|
|
#define SCOS5 c[5]
|
|
-5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */
|
|
4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */
|
|
-1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */
|
|
2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
|
|
-2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */
|
|
|
|
/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
|
|
x in <0,0.1484375> */
|
|
#define COS1 c[6]
|
|
#define COS2 c[7]
|
|
#define COS3 c[8]
|
|
#define COS4 c[9]
|
|
#define COS5 c[10]
|
|
#define COS6 c[11]
|
|
#define COS7 c[12]
|
|
#define COS8 c[13]
|
|
-4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */
|
|
4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */
|
|
-1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */
|
|
2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
|
|
-2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */
|
|
2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */
|
|
-1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */
|
|
4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
|
|
|
|
/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
|
|
x in <0,1/256> */
|
|
#define SSIN1 c[14]
|
|
#define SSIN2 c[15]
|
|
#define SSIN3 c[16]
|
|
#define SSIN4 c[17]
|
|
#define SSIN5 c[18]
|
|
-1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */
|
|
8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
|
|
-1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
|
|
2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
|
|
-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
|
|
|
|
/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
|
|
x in <0,0.1484375> */
|
|
#define SIN1 c[19]
|
|
#define SIN2 c[20]
|
|
#define SIN3 c[21]
|
|
#define SIN4 c[22]
|
|
#define SIN5 c[23]
|
|
#define SIN6 c[24]
|
|
#define SIN7 c[25]
|
|
#define SIN8 c[26]
|
|
-1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
|
|
8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
|
|
-1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
|
|
2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
|
|
-2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
|
|
1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
|
|
-7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
|
|
2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
|
|
};
|
|
|
|
#define SINCOSQ_COS_HI 0
|
|
#define SINCOSQ_COS_LO 1
|
|
#define SINCOSQ_SIN_HI 2
|
|
#define SINCOSQ_SIN_LO 3
|
|
extern const __float128 __sincosq_table[];
|
|
|
|
void
|
|
__quadmath_kernel_sincosq(__float128 x, __float128 y, __float128 *sinx,
|
|
__float128 *cosx, int iy)
|
|
{
|
|
__float128 h, l, z, sin_l, cos_l_m1;
|
|
int64_t ix;
|
|
uint32_t tix, hix, index;
|
|
GET_FLT128_MSW64 (ix, x);
|
|
tix = ((uint64_t)ix) >> 32;
|
|
tix &= ~0x80000000; /* tix = |x|'s high 32 bits */
|
|
if (tix < 0x3ffc3000) /* |x| < 0.1484375 */
|
|
{
|
|
/* Argument is small enough to approximate it by a Chebyshev
|
|
polynomial of degree 16(17). */
|
|
if (tix < 0x3fc60000) /* |x| < 2^-57 */
|
|
if (!((int)x)) /* generate inexact */
|
|
{
|
|
*sinx = x;
|
|
*cosx = ONE;
|
|
return;
|
|
}
|
|
z = x * x;
|
|
*sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
|
|
z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
|
|
*cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
|
|
z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
|
|
}
|
|
else
|
|
{
|
|
/* So that we don't have to use too large polynomial, we find
|
|
l and h such that x = l + h, where fabsl(l) <= 1.0/256 with 83
|
|
possible values for h. We look up cosq(h) and sinq(h) in
|
|
pre-computed tables, compute cosq(l) and sinq(l) using a
|
|
Chebyshev polynomial of degree 10(11) and compute
|
|
sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l) and
|
|
cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l). */
|
|
index = 0x3ffe - (tix >> 16);
|
|
hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
|
|
if (signbitq (x))
|
|
{
|
|
x = -x;
|
|
y = -y;
|
|
}
|
|
switch (index)
|
|
{
|
|
case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
|
|
case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
|
|
default:
|
|
case 2: index = (hix - 0x3ffc3000) >> 10; break;
|
|
}
|
|
|
|
SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
|
|
if (iy)
|
|
l = y - (h - x);
|
|
else
|
|
l = x - h;
|
|
z = l * l;
|
|
sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
|
|
cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
|
|
z = __sincosq_table [index + SINCOSQ_SIN_HI]
|
|
+ (__sincosq_table [index + SINCOSQ_SIN_LO]
|
|
+ (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
|
|
+ (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
|
|
*sinx = (ix < 0) ? -z : z;
|
|
*cosx = __sincosq_table [index + SINCOSQ_COS_HI]
|
|
+ (__sincosq_table [index + SINCOSQ_COS_LO]
|
|
- (__sincosq_table [index + SINCOSQ_SIN_HI] * sin_l
|
|
- __sincosq_table [index + SINCOSQ_COS_HI] * cos_l_m1));
|
|
}
|
|
}
|