libclc/generic/lib/math/sincospiF_piby4.h

   1 /*
   2  * Copyright (c) 2014 Advanced Micro Devices, Inc.
   3  *
   4  * Permission is hereby granted, free of charge, to any person obtaining a copy
   5  * of this software and associated documentation files (the "Software"), to deal
   6  * in the Software without restriction, including without limitation the rights
   7  * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
   8  * copies of the Software, and to permit persons to whom the Software is
   9  * furnished to do so, subject to the following conditions:
  10  *
  11  * The above copyright notice and this permission notice shall be included in
  12  * all copies or substantial portions of the Software.
  13  *
  14  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  15  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  16  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  17  * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  18  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  19  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
  20  * THE SOFTWARE.
  21  */
  22 #include <clc/math/clc_mad.h>
  23
  24 // Evaluate single precisions in and cos of value in interval [-pi/4, pi/4]
  25 _CLC_INLINE float2 __libclc__sincosf_piby4(float x) {
  26   // Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
  27   // = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
  28   // = x * f(w)
  29   // where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
  30   // We use a minimax approximation of (f(w) - 1) / w
  31   // because this produces an expansion in even powers of x.
  32
  33   // Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
  34   // = f(w)
  35   // where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
  36   // We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
  37   // because this produces an expansion in even powers of x.
  38
  39   const float sc1 = -0.166666666638608441788607926e0F;
  40   const float sc2 = 0.833333187633086262120839299e-2F;
  41   const float sc3 = -0.198400874359527693921333720e-3F;
  42   const float sc4 = 0.272500015145584081596826911e-5F;
  43
  44   const float cc1 = 0.41666666664325175238031e-1F;
  45   const float cc2 = -0.13888887673175665567647e-2F;
  46   const float cc3 = 0.24800600878112441958053e-4F;
  47   const float cc4 = -0.27301013343179832472841e-6F;
  48
  49   float x2 = x * x;
  50
  51   float2 ret;
  52   ret.x = __clc_mad(
  53       x * x2, __clc_mad(x2, __clc_mad(x2, __clc_mad(x2, sc4, sc3), sc2), sc1),
  54       x);
  55   ret.y = __clc_mad(
  56       x2 * x2, __clc_mad(x2, __clc_mad(x2, __clc_mad(x2, cc4, cc3), cc2), cc1),
  57       __clc_mad(x2, -0.5f, 1.0f));
  58   return ret;
  59 }