sysdeps/ieee754/ldbl-128/k_sincosl.c

   1 /* Quad-precision floating point sine and cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2019 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    <https://www.gnu.org/licenses/>.  */
  19
  20 #include <float.h>
  21 #include <math.h>
  22 #include <math_private.h>
  23 #include <math-underflow.h>
  24
  25 static const _Float128 c[] = {
  26 #define ONE c[0]
  27  L(1.00000000000000000000000000000000000E+00), /* 3fff0000000000000000000000000000 */
  28
  29 /* cos x ~ ONE + x^2 ( SCOS1 + SCOS2 * x^2 + ... + SCOS4 * x^6 + SCOS5 * x^8 )
  30    x in <0,1/256>  */
  31 #define SCOS1 c[1]
  32 #define SCOS2 c[2]
  33 #define SCOS3 c[3]
  34 #define SCOS4 c[4]
  35 #define SCOS5 c[5]
  36 L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */
  37  L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */
  38 L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */
  39  L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  40 L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */
  41
  42 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  43    x in <0,0.1484375>  */
  44 #define COS1 c[6]
  45 #define COS2 c[7]
  46 #define COS3 c[8]
  47 #define COS4 c[9]
  48 #define COS5 c[10]
  49 #define COS6 c[11]
  50 #define COS7 c[12]
  51 #define COS8 c[13]
  52 L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */
  53  L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */
  54 L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */
  55  L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  56 L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */
  57  L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */
  58 L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */
  59  L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
  60
  61 /* sin x ~ ONE * x + x^3 ( SSIN1 + SSIN2 * x^2 + ... + SSIN4 * x^6 + SSIN5 * x^8 )
  62    x in <0,1/256>  */
  63 #define SSIN1 c[14]
  64 #define SSIN2 c[15]
  65 #define SSIN3 c[16]
  66 #define SSIN4 c[17]
  67 #define SSIN5 c[18]
  68 L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */
  69  L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */
  70 L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */
  71  L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */
  72 L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */
  73
  74 /* sin x ~ ONE * x + x^3 ( SIN1 + SIN2 * x^2 + ... + SIN7 * x^12 + SIN8 * x^14 )
  75    x in <0,0.1484375>  */
  76 #define SIN1 c[19]
  77 #define SIN2 c[20]
  78 #define SIN3 c[21]
  79 #define SIN4 c[22]
  80 #define SIN5 c[23]
  81 #define SIN6 c[24]
  82 #define SIN7 c[25]
  83 #define SIN8 c[26]
  84 L(-1.66666666666666666666666666666666538e-01), /* bffc5555555555555555555555555550 */
  85  L(8.33333333333333333333333333307532934e-03), /* 3ff811111111111111111111110e7340 */
  86 L(-1.98412698412698412698412534478712057e-04), /* bff2a01a01a01a01a01a019e7a626296 */
  87  L(2.75573192239858906520896496653095890e-06), /* 3fec71de3a556c7338fa38527474b8f5 */
  88 L(-2.50521083854417116999224301266655662e-08), /* bfe5ae64567f544e16c7de65c2ea551f */
  89  L(1.60590438367608957516841576404938118e-10), /* 3fde6124613a811480538a9a41957115 */
  90 L(-7.64716343504264506714019494041582610e-13), /* bfd6ae7f3d5aef30c7bc660b060ef365 */
  91  L(2.81068754939739570236322404393398135e-15), /* 3fce9510115aabf87aceb2022a9a9180 */
  92 };
  93
  94 #define SINCOSL_COS_HI 0
  95 #define SINCOSL_COS_LO 1
  96 #define SINCOSL_SIN_HI 2
  97 #define SINCOSL_SIN_LO 3
  98 extern const _Float128 __sincosl_table[];
  99
 100 void
 101 __kernel_sincosl(_Float128 x, _Float128 y, _Float128 *sinx, _Float128 *cosx, int iy)
 102 {
 103   _Float128 h, l, z, sin_l, cos_l_m1;
 104   int64_t ix;
 105   uint32_t tix, hix, index;
 106   GET_LDOUBLE_MSW64 (ix, x);
 107   tix = ((uint64_t)ix) >> 32;
 108   tix &= ~0x80000000;                   /* tix = |x|'s high 32 bits */
 109   if (tix < 0x3ffc3000)                 /* |x| < 0.1484375 */
 110     {
 111       /* Argument is small enough to approximate it by a Chebyshev
 112          polynomial of degree 16(17).  */
 113       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
 114         {
 115           math_check_force_underflow (x);
 116           if (!((int)x))                        /* generate inexact */
 117             {
 118               *sinx = x;
 119               *cosx = ONE;
 120               return;
 121             }
 122         }
 123       z = x * x;
 124       *sinx = x + (x * (z*(SIN1+z*(SIN2+z*(SIN3+z*(SIN4+
 125                         z*(SIN5+z*(SIN6+z*(SIN7+z*SIN8)))))))));
 126       *cosx = ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
 127                      z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
 128     }
 129   else
 130     {
 131       /* So that we don't have to use too large polynomial,  we find
 132          l and h such that x = l + h,  where fabsl(l) <= 1.0/256 with 83
 133          possible values for h.  We look up cosl(h) and sinl(h) in
 134          pre-computed tables,  compute cosl(l) and sinl(l) using a
 135          Chebyshev polynomial of degree 10(11) and compute
 136          sinl(h+l) = sinl(h)cosl(l) + cosl(h)sinl(l) and
 137          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 138       index = 0x3ffe - (tix >> 16);
 139       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 140       if (signbit (x))
 141         {
 142           x = -x;
 143           y = -y;
 144         }
 145       switch (index)
 146         {
 147         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 148         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 149         default:
 150         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 151         }
 152
 153       SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0);
 154       if (iy)
 155         l = y - (h - x);
 156       else
 157         l = x - h;
 158       z = l * l;
 159       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 160       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 161       z = __sincosl_table [index + SINCOSL_SIN_HI]
 162           + (__sincosl_table [index + SINCOSL_SIN_LO]
 163              + (__sincosl_table [index + SINCOSL_SIN_HI] * cos_l_m1)
 164              + (__sincosl_table [index + SINCOSL_COS_HI] * sin_l));
 165       *sinx = (ix < 0) ? -z : z;
 166       *cosx = __sincosl_table [index + SINCOSL_COS_HI]
 167               + (__sincosl_table [index + SINCOSL_COS_LO]
 168                  - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 169                     - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 170     }
 171 }