/*
+ * erf function: Copyright (c) 2006 John Maddock
* This file is part of FFmpeg.
*
* FFmpeg is free software; you can redistribute it and/or
#include "config.h"
#include "attributes.h"
#include "intfloat.h"
+#include "mathematics.h"
#if HAVE_MIPSFPU && HAVE_INLINE_ASM
#include "libavutil/mips/libm_mips.h"
#if !HAVE_ATANF
#undef atanf
#define atanf(x) ((float)atan(x))
-#endif
+#endif /* HAVE_ATANF */
#if !HAVE_ATAN2F
#undef atan2f
#define atan2f(y, x) ((float)atan2(y, x))
-#endif
+#endif /* HAVE_ATAN2F */
#if !HAVE_POWF
#undef powf
#define powf(x, y) ((float)pow(x, y))
-#endif
+#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
+#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
+#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;
+}
+
+/**
+ * erf function
+ * Algorithm taken from the Boost project, source:
+ * http://www.boost.org/doc/libs/1_46_1/boost/math/special_functions/erf.hpp
+ * Use, modification and distribution are subject to the
+ * Boost Software License, Version 1.0 (see notice below).
+ * Boost Software License - Version 1.0 - August 17th, 2003
+Permission is hereby granted, free of charge, to any person or organization
+obtaining a copy of the software and accompanying documentation covered by
+this license (the "Software") to use, reproduce, display, distribute,
+execute, and transmit the Software, and to prepare derivative works of the
+Software, and to permit third-parties to whom the Software is furnished to
+do so, all subject to the following:
+
+The copyright notices in the Software and this entire statement, including
+the above license grant, this restriction and the following disclaimer,
+must be included in all copies of the Software, in whole or in part, and
+all derivative works of the Software, unless such copies or derivative
+works are solely in the form of machine-executable object code generated by
+a source language processor.
+
+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, TITLE AND NON-INFRINGEMENT. IN NO EVENT
+SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
+FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN 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 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
+#endif /* HAVE_EXPF */
#if !HAVE_EXP2
#undef exp2
-#define exp2(x) exp((x) * 0.693147180559945)
+#define exp2(x) exp((x) * M_LN2)
#endif /* HAVE_EXP2 */
#if !HAVE_EXP2F
#endif /* HAVE_ISNAN */
#if !HAVE_HYPOT
-#undef hypot
static inline av_const double hypot(double x, double y)
{
double ret, temp;
#if !HAVE_LDEXPF
#undef ldexpf
#define ldexpf(x, exp) ((float)ldexp(x, exp))
-#endif
+#endif /* HAVE_LDEXPF */
#if !HAVE_LLRINT
#undef llrint
#if !HAVE_LOG10F
#undef log10f
#define log10f(x) ((float)log10(x))
-#endif
+#endif /* HAVE_LOG10F */
#if !HAVE_SINF
#undef sinf
#define sinf(x) ((float)sin(x))
-#endif
+#endif /* HAVE_SINF */
#if !HAVE_RINT
static inline double rint(double x)
projects / ffmpeg / blobdiff