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      1 /* Quad-precision floating point sine 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 (at) 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 
     22 static 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 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
     40    x in <0,0.1484375>  */
     41 #define SIN1 c[6]
     42 #define SIN2 c[7]
     43 #define SIN3 c[8]
     44 #define SIN4 c[9]
     45 #define SIN5 c[10]
     46 #define SIN6 c[11]
     47 #define SIN7 c[12]
     48 #define SIN8 c[13]
     49 -1.66666666666666666666666666666666538e-01Q, /* bffc5555555555555555555555555550 */
     50  8.33333333333333333333333333307532934e-03Q, /* 3ff811111111111111111111110e7340 */
     51 -1.98412698412698412698412534478712057e-04Q, /* bff2a01a01a01a01a01a019e7a626296 */
     52  2.75573192239858906520896496653095890e-06Q, /* 3fec71de3a556c7338fa38527474b8f5 */
     53 -2.50521083854417116999224301266655662e-08Q, /* bfe5ae64567f544e16c7de65c2ea551f */
     54  1.60590438367608957516841576404938118e-10Q, /* 3fde6124613a811480538a9a41957115 */
     55 -7.64716343504264506714019494041582610e-13Q, /* bfd6ae7f3d5aef30c7bc660b060ef365 */
     56  2.81068754939739570236322404393398135e-15Q, /* 3fce9510115aabf87aceb2022a9a9180 */
     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
     76 extern const __float128 __sincosq_table[];
     77 
     78 __float128
     79 __quadmath_kernel_sinq(__float128 x, __float128 y, int iy)
     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 17.  */
     91       if (tix < 0x3fc60000)		/* |x| < 2^-57 */
     92 	{
     93 	  math_check_force_underflow (x);
     94 	  if (!((int)x)) return x;	/* generate inexact */
     95 	}
     96       z = x * x;
     97       return x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
     98 		       z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
     99     }
    100   else
    101     {
    102       /* So that we don't have to use too large polynomial,  we find
    103 	 l and h such that x = l + h,  where fabsq(l) <= 1.0/256 with 83
    104 	 possible values for h.  We look up cosq(h) and sinq(h) in
    105 	 pre-computed tables,  compute cosq(l) and sinq(l) using a
    106 	 Chebyshev polynomial of degree 10(11) and compute
    107 	 sinq(h+l) = sinq(h)cosq(l) + cosq(h)sinq(l).  */
    108       index = 0x3ffe - (tix >> 16);
    109       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
    110       x = fabsq (x);
    111       switch (index)
    112 	{
    113 	case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
    114 	case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
    115 	default:
    116 	case 2: index = (hix - 0x3ffc3000) >> 10; break;
    117 	}
    118 
    119       SET_FLT128_WORDS64(h, ((uint64_t)hix) << 32, 0);
    120       if (iy)
    121 	l = (ix < 0 ? -y : y) - (h - x);
    122       else
    123 	l = x - h;
    124       z = l * l;
    125       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
    126       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
    127       z = __sincosq_table [index + SINCOSL_SIN_HI]
    128 	  + (__sincosq_table [index + SINCOSL_SIN_LO]
    129 	     + (__sincosq_table [index + SINCOSL_SIN_HI] * cos_l_m1)
    130 	     + (__sincosq_table [index + SINCOSL_COS_HI] * sin_l));
    131       return (ix < 0) ? -z : z;
    132     }
    133 }
    134