1/* Quad-precision floating point cosine on <-pi/4,pi/4>.
2   Copyright (C) 1999-2018 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, see
18   <http://www.gnu.org/licenses/>.  */
19
20#include "quadmath-imp.h"
21
22static const __float128 c[] = {
23#define ONE c[0]
24 1.00000000000000000000000000000000000E+00Q, /* 3fff0000000000000000000000000000 */
25
26/* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
27   x in <0,1/256>  */
28#define SCOS1 c[1]
29#define SCOS2 c[2]
30#define SCOS3 c[3]
31#define SCOS4 c[4]
32#define SCOS5 c[5]
33-5.00000000000000000000000000000000000E-01Q, /* bffe0000000000000000000000000000 */
34 4.16666666666666666666666666556146073E-02Q, /* 3ffa5555555555555555555555395023 */
35-1.38888888888888888888309442601939728E-03Q, /* bff56c16c16c16c16c16a566e42c0375 */
36 2.48015873015862382987049502531095061E-05Q, /* 3fefa01a01a019ee02dcf7da2d6d5444 */
37-2.75573112601362126593516899592158083E-07Q, /* bfe927e4f5dce637cb0b54908754bde0 */
38
39/* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
40   x in <0,0.1484375>  */
41#define COS1 c[6]
42#define COS2 c[7]
43#define COS3 c[8]
44#define COS4 c[9]
45#define COS5 c[10]
46#define COS6 c[11]
47#define COS7 c[12]
48#define COS8 c[13]
49-4.99999999999999999999999999999999759E-01Q, /* bffdfffffffffffffffffffffffffffb */
50 4.16666666666666666666666666651287795E-02Q, /* 3ffa5555555555555555555555516f30 */
51-1.38888888888888888888888742314300284E-03Q, /* bff56c16c16c16c16c16c16a463dfd0d */
52 2.48015873015873015867694002851118210E-05Q, /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
53-2.75573192239858811636614709689300351E-07Q, /* bfe927e4fb7789f5aa8142a22044b51f */
54 2.08767569877762248667431926878073669E-09Q, /* 3fe21eed8eff881d1e9262d7adff4373 */
55-1.14707451049343817400420280514614892E-11Q, /* bfda9397496922a9601ed3d4ca48944b */
56 4.77810092804389587579843296923533297E-14Q, /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
57
58/* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
59   x in <0,1/256>  */
60#define SSIN1 c[14]
61#define SSIN2 c[15]
62#define SSIN3 c[16]
63#define SSIN4 c[17]
64#define SSIN5 c[18]
65-1.66666666666666666666666666666666659E-01Q, /* bffc5555555555555555555555555555 */
66 8.33333333333333333333333333146298442E-03Q, /* 3ff81111111111111111111110fe195d */
67-1.98412698412698412697726277416810661E-04Q, /* bff2a01a01a01a01a019e7121e080d88 */
68 2.75573192239848624174178393552189149E-06Q, /* 3fec71de3a556c640c6aaa51aa02ab41 */
69-2.50521016467996193495359189395805639E-08Q, /* bfe5ae644ee90c47dc71839de75b2787 */
70};
71
72#define SINCOSL_COS_HI 0
73#define SINCOSL_COS_LO 1
74#define SINCOSL_SIN_HI 2
75#define SINCOSL_SIN_LO 3
76extern const __float128 __sincosq_table[];
77
78__float128
79__quadmath_kernel_cosq(__float128 x, __float128 y)
80{
81  __float128 h, l, z, sin_l, cos_l_m1;
82  int64_t ix;
83  uint32_t tix, hix, index;
84  GET_FLT128_MSW64 (ix, x);
85  tix = ((uint64_t)ix) >> 32;
86  tix &= ~0x80000000;			/* tix = |x|'s high 32 bits */
87  if (tix < 0x3ffc3000)			/* |x| < 0.1484375 */
88    {
89      /* Argument is small enough to approximate it by a Chebyshev
90	 polynomial of degree 16.  */
91      if (tix < 0x3fc60000)		/* |x| < 2^-57 */
92	if (!((int)x)) return ONE;	/* generate inexact */
93      z = x * x;
94      return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
95		    z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
96    }
97  else
98    {
99      /* So that we don't have to use too large polynomial,  we find
100	 l and h such that x = l + h,  where fabsq(l) <= 1.0/256 with 83
101	 possible values for h.  We look up cosq(h) and sinq(h) in
102	 pre-computed tables,  compute cosq(l) and sinq(l) using a
103	 Chebyshev polynomial of degree 10(11) and compute
104	 cosq(h+l) = cosq(h)cosq(l) - sinq(h)sinq(l).  */
105      index = 0x3ffe - (tix >> 16);
106      hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
107      if (signbitq (x))
108	{
109	  x = -x;
110	  y = -y;
111	}
112      switch (index)
113	{
114	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
115	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
116	default:
117	case 2: index = (hix - 0x3ffc3000) >> 10; break;
118	}
119
120      SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
121      l = y - (h - x);
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      return __sincosq_table [index + SINCOSL_COS_HI]
126	     + (__sincosq_table [index + SINCOSL_COS_LO]
127		- (__sincosq_table [index + SINCOSL_SIN_HI] * sin_l
128		   - __sincosq_table [index + SINCOSL_COS_HI] * cos_l_m1));
129    }
130}
131