amd-builtins/math32/expm1F.cl

/*
 * 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.
 */

#include "math32.h"

/* Refer exp routine for algorithm */

__attribute__((overloadable)) float
expm1(float x)
{
    USE_TABLE(float2, p_tbl, EXP_TBL_EP);

    const float X_MAX = 0x1.62e42ep+6f;  // 128*log2 : 88.722839111673
    const float X_MIN = -0x1.9d1da0p+6f; // -149*log2 : -103.27892990343184

    const float R_64_BY_LOG2 = 0x1.715476p+6f;     // 64/log2 : 92.332482616893657
    const float R_LOG2_BY_64_LD = 0x1.620000p-7f;  // log2/64 lead: 0.0108032227
    const float R_LOG2_BY_64_TL = 0x1.c85fdep-16f; // log2/64 tail: 0.0000272020388

    uint xi = as_uint(x);
    int n = (int)(x * R_64_BY_LOG2);
    float fn = (float)n;

    int j = n & 0x3f;
    int m = n >> 6;

    float r = mad(fn, -R_LOG2_BY_64_TL, mad(fn, -R_LOG2_BY_64_LD, x));

    // Truncated Taylor series
    float z2 = mad(r*r, mad(r, mad(r, 0x1.555556p-5f,  0x1.555556p-3f), 0.5f), r);

    float m2 = as_float((m + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
    float2 tv = p_tbl[j];
    float two_to_jby64_h = tv.s0 * m2;
    float two_to_jby64_t = tv.s1 * m2;
    float two_to_jby64 = two_to_jby64_h + two_to_jby64_t;

    z2 = mad(z2, two_to_jby64, two_to_jby64_t) + (two_to_jby64_h - 1.0f);
	//Make subnormals work
	z2 = x == 0. ? x : z2;
    z2 = x < X_MIN | m < -24 ? -1.0f : z2;
    z2 = x > X_MAX ? as_float(PINFBITPATT_SP32) : z2;
    z2 = isnan(x) ? x : z2;

    return z2;
}