1/* Quad-precision floating point sine on <-pi/4,pi/4>.
2   Copyright (C) 1999 Free Software Foundation, Inc.
3   This file is part of the GNU C Library.
4   Contributed by Jakub Jelinek <jj@ultra.linux.cz>
5
6   The GNU C Library is free software; you can redistribute it and/or
7   modify it under the terms of the GNU Lesser General Public
8   License as published by the Free Software Foundation; either
9   version 2.1 of the License, or (at your option) any later version.
10
11   The GNU C Library is distributed in the hope that it will be useful,
12   but WITHOUT ANY WARRANTY; without even the implied warranty of
13   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
14   Lesser General Public License for more details.
15
16   You should have received a copy of the GNU Lesser General Public
17   License along with the GNU C Library; if not, write to the Free
18   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
19   02111-1307 USA.  */
20
21#include "quadmath-imp.h"
22
23static const __float128 c[] = {
24#define ONE c[0]
25 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
26
27/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
28   x in <0,1/256>  */
29#define SCOS1 c[1]
30#define SCOS2 c[2]
31#define SCOS3 c[3]
32#define SCOS4 c[4]
33#define SCOS5 c[5]
34-5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */
35 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */
36-1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */
37 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
38-2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */
39
40/* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
41   x in <0,0.1484375>  */
42#define SIN1 c[6]
43#define SIN2 c[7]
44#define SIN3 c[8]
45#define SIN4 c[9]
46#define SIN5 c[10]
47#define SIN6 c[11]
48#define SIN7 c[12]
49#define SIN8 c[13]
50-1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
51 8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
52-1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
53 2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
54-2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
55 1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
56-7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
57 2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
58
59/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
60   x in <0,1/256>  */
61#define SSIN1 c[14]
62#define SSIN2 c[15]
63#define SSIN3 c[16]
64#define SSIN4 c[17]
65#define SSIN5 c[18]
66-1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */
67 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
68-1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
69 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
70-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
71};
72
73#define SINCOSQ_COS_HI 0
74#define SINCOSQ_COS_LO 1
75#define SINCOSQ_SIN_HI 2
76#define SINCOSQ_SIN_LO 3
77extern const __float128 __sincosq_table[];
78
79__float128
80__quadmath_kernel_sinq (__float128 x, __float128 y, int iy)
81{
82  __float128 h, l, z, sin_l, cos_l_m1;
83  int64_t ix;
84  uint32_t tix, hix, index;
85  GET_FLT128_MSW64 (ix, x);
86  tix = ((uint64_t)ix) >> 32;
87  tix &= ~0x80000000;			/* tix = |x|'s high 32 bits */
88  if (tix < 0x3ffc3000)			/* |x| < 0.1484375 */
89    {
90      /* Argument is small enough to approximate it by a Chebyshev
91	 polynomial of degree 17.  */
92      if (tix < 0x3fc60000)		/* |x| < 2^-57 */
93	if (!((int)x)) return x;	/* generate inexact */
94      z = x * x;
95      return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
96		       z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
97    }
98  else
99    {
100      /* So that we don't have to use too large polynomial,  we find
101	 l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
102	 possible values for h.  We look up cosq(h) and sinq(h) in
103	 pre-computed tables,  compute cosq(l) and sinq(l) using a
104	 Chebyshev polynomial of degree 10(11) and compute
105	 sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l).  */
106      index = 0x3ffe - (tix >> 16);
107      hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
108      x = fabsq (x);
109      switch (index)
110	{
111	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
112	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
113	default:
114	case 2: index = (hix - 0x3ffc3000) >> 10; break;
115	}
116
117      SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
118      if (iy)
119	l = (ix < 0 ? -y : y) - (h - x);
120      else
121	l = x - h;
122      z = l * l;
123      sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
124      cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
125      z = __sincosq_table [index + SINCOSQ_SIN_HI]
126	  + (__sincosq_table [index + SINCOSQ_SIN_LO]
127	     + (__sincosq_table [index + SINCOSQ_SIN_HI] * cos_l_m1)
128	     + (__sincosq_table [index + SINCOSQ_COS_HI] * sin_l));
129      return (ix < 0) ? -z : z;
130    }
131}
132