amd-builtins/math64/ep_logD.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
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 * 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
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 * THE SOFTWARE.
 */

#define LN0 8.33333333333317923934e-02
#define LN1 1.25000000037717509602e-02
#define LN2 2.23213998791944806202e-03
#define LN3 4.34887777707614552256e-04

#define LF0 8.33333333333333593622e-02
#define LF1 1.24999999978138668903e-02
#define LF2 2.23219810758559851206e-03

static inline void
ep_log(double x, int *xexp, double *r1, double *r2)
{
    USE_TABLE(double2, p_tbl, LN_TBL);

    // Computes natural log(x). Algorithm based on:
    // Ping-Tak Peter Tang
    // "Table-driven implementation of the logarithm function in IEEE
    // floating-point arithmetic"
    // ACM Transactions on Mathematical Software (TOMS)
    // Volume 16, Issue 4 (December 1990)
    int near_one = x >= 0x1.e0faap-1 & x <= 0x1.1082cp+0;

    ulong ux = as_ulong(x);
    ulong uxs = as_ulong(as_double(0x03d0000000000000UL | ux) - 0x1.0p-962);
    int c = ux < IMPBIT_DP64;
    ux = c ? uxs : ux;
    int expadjust = c ? 60 : 0;

    // Store the exponent of x in xexp and put f into the range [0.5,1)
    int xexp1 = ((as_int2(ux).hi >> 20) & 0x7ff) - EXPBIAS_DP64 - expadjust;
    double f = as_double(HALFEXPBITS_DP64 | (ux & MANTBITS_DP64));
    *xexp = near_one ? 0 : xexp1;

    double r = x - 1.0;
    double u1 = MATH_DIVIDE(r, 2.0 + r);
    double ru1 = -r * u1;
    u1 = u1 + u1;

    int index = as_int2(ux).hi >> 13;
    index = ((0x80 | (index & 0x7e)) >> 1) + (index & 0x1);

    double f1 = index * 0x1.0p-7;
    double f2 = f - f1;
    double u2 = MATH_DIVIDE(f2, fma(0.5, f2, f1));

    double2 tv = p_tbl[index - 64];
    double z1 = tv.s0;
    double q = tv.s1;

    z1 = near_one ? r : z1;
    q = near_one ? 0.0 : q;
    double u = near_one ? u1 : u2;
    double v = u*u;

    double cc = near_one ? ru1 : u2;

    double z21 = fma(v, fma(v, fma(v, LN3, LN2), LN1), LN0);
    double z22 = fma(v, fma(v, LF2, LF1), LF0);
    double z2 = near_one ? z21 : z22;
    z2 = fma(u*v, z2, cc) + q;

    *r1 = z1;
    *r2 = z2;
}