sysdeps/ieee754/ldbl-128/k_cosl.c

   1 /* Quad-precision floating point cosine on <-pi/4,pi/4>.
   2    Copyright (C) 1999-2017 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 <math.h>
  21 #include <math_private.h>
  22
  23 static const _Float128 c[] = {
  24 #define ONE c[0]
  25  L(1.00000000000000000000000000000000000E+00), /* 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 L(-5.00000000000000000000000000000000000E-01), /* bffe0000000000000000000000000000 */
  35  L(4.16666666666666666666666666556146073E-02), /* 3ffa5555555555555555555555395023 */
  36 L(-1.38888888888888888888309442601939728E-03), /* bff56c16c16c16c16c16a566e42c0375 */
  37  L(2.48015873015862382987049502531095061E-05), /* 3fefa01a01a019ee02dcf7da2d6d5444 */
  38 L(-2.75573112601362126593516899592158083E-07), /* bfe927e4f5dce637cb0b54908754bde0 */
  39
  40 /* cos x ~ ONE + x^2 ( COS1 + COS2 * x^2 + ... + COS7 * x^12 + COS8 * x^14 )
  41    x in <0,0.1484375>  */
  42 #define COS1 c[6]
  43 #define COS2 c[7]
  44 #define COS3 c[8]
  45 #define COS4 c[9]
  46 #define COS5 c[10]
  47 #define COS6 c[11]
  48 #define COS7 c[12]
  49 #define COS8 c[13]
  50 L(-4.99999999999999999999999999999999759E-01), /* bffdfffffffffffffffffffffffffffb */
  51  L(4.16666666666666666666666666651287795E-02), /* 3ffa5555555555555555555555516f30 */
  52 L(-1.38888888888888888888888742314300284E-03), /* bff56c16c16c16c16c16c16a463dfd0d */
  53  L(2.48015873015873015867694002851118210E-05), /* 3fefa01a01a01a01a0195cebe6f3d3a5 */
  54 L(-2.75573192239858811636614709689300351E-07), /* bfe927e4fb7789f5aa8142a22044b51f */
  55  L(2.08767569877762248667431926878073669E-09), /* 3fe21eed8eff881d1e9262d7adff4373 */
  56 L(-1.14707451049343817400420280514614892E-11), /* bfda9397496922a9601ed3d4ca48944b */
  57  L(4.77810092804389587579843296923533297E-14), /* 3fd2ae5f8197cbcdcaf7c3fb4523414c */
  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 L(-1.66666666666666666666666666666666659E-01), /* bffc5555555555555555555555555555 */
  67  L(8.33333333333333333333333333146298442E-03), /* 3ff81111111111111111111110fe195d */
  68 L(-1.98412698412698412697726277416810661E-04), /* bff2a01a01a01a01a019e7121e080d88 */
  69  L(2.75573192239848624174178393552189149E-06), /* 3fec71de3a556c640c6aaa51aa02ab41 */
  70 L(-2.50521016467996193495359189395805639E-08), /* bfe5ae644ee90c47dc71839de75b2787 */
  71 };
  72
  73 #define SINCOSL_COS_HI 0
  74 #define SINCOSL_COS_LO 1
  75 #define SINCOSL_SIN_HI 2
  76 #define SINCOSL_SIN_LO 3
  77 extern const _Float128 __sincosl_table[];
  78
  79 _Float128
  80 __kernel_cosl(_Float128 x, _Float128 y)
  81 {
  82   _Float128 h, l, z, sin_l, cos_l_m1;
  83   int64_t ix;
  84   uint32_t tix, hix, index;
  85   GET_LDOUBLE_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 16.  */
  92       if (tix < 0x3fc60000)             /* |x| < 2^-57 */
  93         if (!((int)x)) return ONE;      /* generate inexact */
  94       z = x * x;
  95       return ONE + (z*(COS1+z*(COS2+z*(COS3+z*(COS4+
  96                     z*(COS5+z*(COS6+z*(COS7+z*COS8))))))));
  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 cosl(h) and sinl(h) in
 103          pre-computed tables,  compute cosl(l) and sinl(l) using a
 104          Chebyshev polynomial of degree 10(11) and compute
 105          cosl(h+l) = cosl(h)cosl(l) - sinl(h)sinl(l).  */
 106       index = 0x3ffe - (tix >> 16);
 107       hix = (tix + (0x200 << index)) & (0xfffffc00 << index);
 108       if (signbit (x))
 109         {
 110           x = -x;
 111           y = -y;
 112         }
 113       switch (index)
 114         {
 115         case 0: index = ((45 << 10) + hix - 0x3ffe0000) >> 8; break;
 116         case 1: index = ((13 << 11) + hix - 0x3ffd0000) >> 9; break;
 117         default:
 118         case 2: index = (hix - 0x3ffc3000) >> 10; break;
 119         }
 120
 121       SET_LDOUBLE_WORDS64(h, ((uint64_t)hix) << 32, 0);
 122       l = y - (h - x);
 123       z = l * l;
 124       sin_l = l*(ONE+z*(SSIN1+z*(SSIN2+z*(SSIN3+z*(SSIN4+z*SSIN5)))));
 125       cos_l_m1 = z*(SCOS1+z*(SCOS2+z*(SCOS3+z*(SCOS4+z*SCOS5))));
 126       return __sincosl_table [index + SINCOSL_COS_HI]
 127              + (__sincosl_table [index + SINCOSL_COS_LO]
 128                 - (__sincosl_table [index + SINCOSL_SIN_HI] * sin_l
 129                    - __sincosl_table [index + SINCOSL_COS_HI] * cos_l_m1));
 130     }
 131 }