amd-builtins/math32/tanF_piby4.h

/*
 * Copyright (c) 2014 Advanced Micro Devices, Inc.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

static inline float
tanf_piby4_new(float x, int regn)
{
    // Core Remez [1,2] approximation to tan(x) on the interval [0,pi/4].
    float r = x * x;

    float a = mad(r, -0.0172032480471481694693109f, 0.385296071263995406715129f);

    float b = mad(r,
	          mad(r, 0.01844239256901656082986661f, -0.51396505478854532132342f),
	          1.15588821434688393452299f);

    float t = mad(x*r, __amdil_improved_div_f32(a, b), x);
    float tr = -MATH_RECIP(t);

    return regn & 1 ? tr : t;
}