libm.h

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/*
 * erf function: Copyright (c) 2006 John Maddock
 * This file is part of FFmpeg.
 *
 * FFmpeg is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * FFmpeg is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with FFmpeg; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 */

#ifndef AVUTIL_LIBM_H
#define AVUTIL_LIBM_H

#include <math.h>
#include "config.h"
#include "attributes.h"
#include "intfloat.h"
#include "mathematics.h"

#if HAVE_MIPSFPU && HAVE_INLINE_ASM
#include "libavutil/mips/libm_mips.h"
#endif /* HAVE_MIPSFPU && HAVE_INLINE_ASM*/

#if !HAVE_ATANF
#undef atanf
#define atanf(x) ((float)atan(x))
#endif /* HAVE_ATANF */

#if !HAVE_ATAN2F
#undef atan2f
#define atan2f(y, x) ((float)atan2(y, x))
#endif /* HAVE_ATAN2F */

#if !HAVE_POWF
#undef powf
#define powf(x, y) ((float)pow(x, y))
#endif /* HAVE_POWF */

#if !HAVE_CBRT
static av_always_inline double cbrt(double x)
{
    return x < 0 ? -pow(-x, 1.0 / 3.0) : pow(x, 1.0 / 3.0);
}
#endif /* HAVE_CBRT */

#if !HAVE_CBRTF
static av_always_inline float cbrtf(float x)
{
    return x < 0 ? -powf(-x, 1.0 / 3.0) : powf(x, 1.0 / 3.0);
}
#endif /* HAVE_CBRTF */

#if !HAVE_COPYSIGN
static av_always_inline double copysign(double x, double y)
{
    uint64_t vx = av_double2int(x);
    uint64_t vy = av_double2int(y);
    return av_int2double((vx & UINT64_C(0x7fffffffffffffff)) | (vy & UINT64_C(0x8000000000000000)));
}
#endif /* HAVE_COPYSIGN */

#if !HAVE_COSF
#undef cosf
#define cosf(x) ((float)cos(x))
#endif /* HAVE_COSF */

#if !HAVE_ERF
static inline double ff_eval_poly(const double *coeff, int size, double x) {
    double sum = coeff[size-1];
    int i;
    for (i = size-2; i >= 0; --i) {
        sum *= x;
        sum += coeff[i];
    }
    return sum;
}

static inline double erf(double z)
{
#ifndef FF_ARRAY_ELEMS
#define FF_ARRAY_ELEMS(a) (sizeof(a) / sizeof((a)[0]))
#endif
    double result;

    /* handle the symmetry: erf(-x) = -erf(x) */
    if (z < 0)
        return -erf(-z);

    /* branch based on range of z, and pick appropriate approximation */
    if (z == 0)
        return 0;
    else if (z < 1e-10)
        return z * 1.125 + z * 0.003379167095512573896158903121545171688;
    else if (z < 0.5) {
        // Maximum Deviation Found:                     1.561e-17
        // Expected Error Term:                         1.561e-17
        // Maximum Relative Change in Control Points:   1.155e-04
        // Max Error found at double precision =        2.961182e-17

        static const double y = 1.044948577880859375;
        static const double p[] = {
            0.0834305892146531832907,
            -0.338165134459360935041,
            -0.0509990735146777432841,
            -0.00772758345802133288487,
            -0.000322780120964605683831,
        };
        static const double q[] = {
            1,
            0.455004033050794024546,
            0.0875222600142252549554,
            0.00858571925074406212772,
            0.000370900071787748000569,
        };
        double zz = z * z;
        return z * (y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), zz) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), zz));
    }
    /* here onwards compute erfc */
    else if (z < 1.5) {
        // Maximum Deviation Found:                     3.702e-17
        // Expected Error Term:                         3.702e-17
        // Maximum Relative Change in Control Points:   2.845e-04
        // Max Error found at double precision =        4.841816e-17
        static const double y = 0.405935764312744140625;
        static const double p[] = {
            -0.098090592216281240205,
            0.178114665841120341155,
            0.191003695796775433986,
            0.0888900368967884466578,
            0.0195049001251218801359,
            0.00180424538297014223957,
        };
        static const double q[] = {
            1,
            1.84759070983002217845,
            1.42628004845511324508,
            0.578052804889902404909,
            0.12385097467900864233,
            0.0113385233577001411017,
            0.337511472483094676155e-5,
        };
        result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), z - 0.5) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), z - 0.5);
        result *= exp(-z * z) / z;
        return 1 - result;
    }
    else if (z < 2.5) {
        // Max Error found at double precision =        6.599585e-18
        // Maximum Deviation Found:                     3.909e-18
        // Expected Error Term:                         3.909e-18
        // Maximum Relative Change in Control Points:   9.886e-05
        static const double y = 0.50672817230224609375;
        static const double p[] = {
            -0.0243500476207698441272,
            0.0386540375035707201728,
            0.04394818964209516296,
            0.0175679436311802092299,
            0.00323962406290842133584,
            0.000235839115596880717416,
        };
        static const double q[] = {
            1,
            1.53991494948552447182,
            0.982403709157920235114,
            0.325732924782444448493,
            0.0563921837420478160373,
            0.00410369723978904575884,
        };
        result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), z - 1.5) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), z - 1.5);
        result *= exp(-z * z) / z;
        return 1 - result;
    }
    else if (z < 4.5) {
        // Maximum Deviation Found:                     1.512e-17
        // Expected Error Term:                         1.512e-17
        // Maximum Relative Change in Control Points:   2.222e-04
        // Max Error found at double precision =        2.062515e-17
        static const double y = 0.5405750274658203125;
        static const double p[] = {
            0.00295276716530971662634,
            0.0137384425896355332126,
            0.00840807615555585383007,
            0.00212825620914618649141,
            0.000250269961544794627958,
            0.113212406648847561139e-4,
        };
        static const double q[] = {
            1,
            1.04217814166938418171,
            0.442597659481563127003,
            0.0958492726301061423444,
            0.0105982906484876531489,
            0.000479411269521714493907,
        };
        result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), z - 3.5) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), z - 3.5);
        result *= exp(-z * z) / z;
        return 1 - result;
    }
    /* differ from Boost here, the claim of underflow of erfc(x) past 5.8 is
     * slightly incorrect, change to 5.92
     * (really somewhere between 5.9125 and 5.925 is when it saturates) */
    else if (z < 5.92) {
        // Max Error found at double precision =        2.997958e-17
        // Maximum Deviation Found:                     2.860e-17
        // Expected Error Term:                         2.859e-17
        // Maximum Relative Change in Control Points:   1.357e-05
        static const double y = 0.5579090118408203125;
        static const double p[] = {
            0.00628057170626964891937,
            0.0175389834052493308818,
            -0.212652252872804219852,
            -0.687717681153649930619,
            -2.5518551727311523996,
            -3.22729451764143718517,
            -2.8175401114513378771,
        };
        static const double q[] = {
            1,
            2.79257750980575282228,
            11.0567237927800161565,
            15.930646027911794143,
            22.9367376522880577224,
            13.5064170191802889145,
            5.48409182238641741584,
        };
        result = y + ff_eval_poly(p, FF_ARRAY_ELEMS(p), 1 / z) / ff_eval_poly(q, FF_ARRAY_ELEMS(q), 1 / z);
        result *= exp(-z * z) / z;
        return 1 - result;
    }
    /* handle the nan case, but don't use isnan for max portability */
    else if (z != z)
        return z;
    /* finally return saturated result */
    else
        return 1;
}
#endif /* HAVE_ERF */

#if !HAVE_EXPF
#undef expf
#define expf(x) ((float)exp(x))
#endif /* HAVE_EXPF */

#if !HAVE_EXP2
#undef exp2
#define exp2(x) exp((x) * M_LN2)
#endif /* HAVE_EXP2 */

#if !HAVE_EXP2F
#undef exp2f
#define exp2f(x) ((float)exp2(x))
#endif /* HAVE_EXP2F */

#if !HAVE_ISINF
#undef isinf
/* Note: these do not follow the BSD/Apple/GNU convention of returning -1 for
-Inf, +1 for Inf, 0 otherwise, but merely follow the POSIX/ISO mandated spec of
returning a non-zero value for +/-Inf, 0 otherwise. */
static av_always_inline av_const int avpriv_isinff(float x)
{
    uint32_t v = av_float2int(x);
    if ((v & 0x7f800000) != 0x7f800000)
        return 0;
    return !(v & 0x007fffff);
}

static av_always_inline av_const int avpriv_isinf(double x)
{
    uint64_t v = av_double2int(x);
    if ((v & 0x7ff0000000000000) != 0x7ff0000000000000)
        return 0;
    return !(v & 0x000fffffffffffff);
}

#define isinf(x)                  \
    (sizeof(x) == sizeof(float)   \
        ? avpriv_isinff(x)        \
        : avpriv_isinf(x))
#endif /* HAVE_ISINF */

#if !HAVE_ISNAN
static av_always_inline av_const int avpriv_isnanf(float x)
{
    uint32_t v = av_float2int(x);
    if ((v & 0x7f800000) != 0x7f800000)
        return 0;
    return v & 0x007fffff;
}

static av_always_inline av_const int avpriv_isnan(double x)
{
    uint64_t v = av_double2int(x);
    if ((v & 0x7ff0000000000000) != 0x7ff0000000000000)
        return 0;
    return (v & 0x000fffffffffffff) && 1;
}

#define isnan(x)                  \
    (sizeof(x) == sizeof(float)   \
        ? avpriv_isnanf(x)        \
        : avpriv_isnan(x))
#endif /* HAVE_ISNAN */

#if !HAVE_ISFINITE
static av_always_inline av_const int avpriv_isfinitef(float x)
{
    uint32_t v = av_float2int(x);
    return (v & 0x7f800000) != 0x7f800000;
}

static av_always_inline av_const int avpriv_isfinite(double x)
{
    uint64_t v = av_double2int(x);
    return (v & 0x7ff0000000000000) != 0x7ff0000000000000;
}

#define isfinite(x)                  \
    (sizeof(x) == sizeof(float)      \
        ? avpriv_isfinitef(x)        \
        : avpriv_isfinite(x))
#endif /* HAVE_ISFINITE */

#if !HAVE_HYPOT
static inline av_const double hypot(double x, double y)
{
    double ret, temp;
    x = fabs(x);
    y = fabs(y);

    if (isinf(x) || isinf(y))
        return av_int2double(0x7ff0000000000000);
    if (x == 0 || y == 0)
        return x + y;
    if (x < y) {
        temp = x;
        x = y;
        y = temp;
    }

    y = y/x;
    return x*sqrt(1 + y*y);
}
#endif /* HAVE_HYPOT */

#if !HAVE_LDEXPF
#undef ldexpf
#define ldexpf(x, exp) ((float)ldexp(x, exp))
#endif /* HAVE_LDEXPF */

#if !HAVE_LLRINT
#undef llrint
#define llrint(x) ((long long)rint(x))
#endif /* HAVE_LLRINT */

#if !HAVE_LLRINTF
#undef llrintf
#define llrintf(x) ((long long)rint(x))
#endif /* HAVE_LLRINT */

#if !HAVE_LOG2
#undef log2
#define log2(x) (log(x) * 1.44269504088896340736)
#endif /* HAVE_LOG2 */

#if !HAVE_LOG2F
#undef log2f
#define log2f(x) ((float)log2(x))
#endif /* HAVE_LOG2F */

#if !HAVE_LOG10F
#undef log10f
#define log10f(x) ((float)log10(x))
#endif /* HAVE_LOG10F */

#if !HAVE_SINF
#undef sinf
#define sinf(x) ((float)sin(x))
#endif /* HAVE_SINF */

#if !HAVE_RINT
static inline double rint(double x)
{
    return x >= 0 ? floor(x + 0.5) : ceil(x - 0.5);
}
#endif /* HAVE_RINT */

#if !HAVE_LRINT
static av_always_inline av_const long int lrint(double x)
{
    return rint(x);
}
#endif /* HAVE_LRINT */

#if !HAVE_LRINTF
static av_always_inline av_const long int lrintf(float x)
{
    return (int)(rint(x));
}
#endif /* HAVE_LRINTF */

#if !HAVE_ROUND
static av_always_inline av_const double round(double x)
{
    return (x > 0) ? floor(x + 0.5) : ceil(x - 0.5);
}
#endif /* HAVE_ROUND */

#if !HAVE_ROUNDF
static av_always_inline av_const float roundf(float x)
{
    return (x > 0) ? floor(x + 0.5) : ceil(x - 0.5);
}
#endif /* HAVE_ROUNDF */

#if !HAVE_TRUNC
static av_always_inline av_const double trunc(double x)
{
    return (x > 0) ? floor(x) : ceil(x);
}
#endif /* HAVE_TRUNC */

#if !HAVE_TRUNCF
static av_always_inline av_const float truncf(float x)
{
    return (x > 0) ? floor(x) : ceil(x);
}
#endif /* HAVE_TRUNCF */

#endif /* AVUTIL_LIBM_H */