2010-05-12 01:44:00 +08:00
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/*M///////////////////////////////////////////////////////////////////////////////////////
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//
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// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
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//
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// By downloading, copying, installing or using the software you agree to this license.
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// If you do not agree to this license, do not download, install,
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// copy or use the software.
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//
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//
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// License Agreement
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// For Open Source Computer Vision Library
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//
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// Copyright (C) 2000-2008, Intel Corporation, all rights reserved.
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// Copyright (C) 2009, Willow Garage Inc., all rights reserved.
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// Third party copyrights are property of their respective owners.
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//
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// Redistribution and use in source and binary forms, with or without modification,
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// are permitted provided that the following conditions are met:
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//
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// * Redistribution's of source code must retain the above copyright notice,
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// this list of conditions and the following disclaimer.
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//
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// * Redistribution's in binary form must reproduce the above copyright notice,
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// this list of conditions and the following disclaimer in the documentation
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// and/or other materials provided with the distribution.
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//
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// * The name of the copyright holders may not be used to endorse or promote products
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// derived from this software without specific prior written permission.
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//
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// This software is provided by the copyright holders and contributors "as is" and
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// any express or implied warranties, including, but not limited to, the implied
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// warranties of merchantability and fitness for a particular purpose are disclaimed.
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// In no event shall the Intel Corporation or contributors be liable for any direct,
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// indirect, incidental, special, exemplary, or consequential damages
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// (including, but not limited to, procurement of substitute goods or services;
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// loss of use, data, or profits; or business interruption) however caused
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// and on any theory of liability, whether in contract, strict liability,
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// or tort (including negligence or otherwise) arising in any way out of
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// the use of this software, even if advised of the possibility of such damage.
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//
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//M*/
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#include "precomp.hpp"
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namespace cv
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{
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static const int MAX_BLOCK_SIZE = 1024;
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typedef CvStatus (CV_STDCALL * MathFunc)(const void* src, void* dst, int len);
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#define ICV_MATH_BLOCK_SIZE 256
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#define _CV_SQRT_MAGIC 0xbe6f0000
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#define _CV_SQRT_MAGIC_DBL CV_BIG_UINT(0xbfcd460000000000)
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#define _CV_ATAN_CF0 (-15.8131890796f)
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#define _CV_ATAN_CF1 (61.0941945596f)
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#define _CV_ATAN_CF2 0.f /*(-0.140500406322f)*/
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static const float icvAtanTab[8] = { 0.f + _CV_ATAN_CF2, 90.f - _CV_ATAN_CF2,
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180.f - _CV_ATAN_CF2, 90.f + _CV_ATAN_CF2,
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360.f - _CV_ATAN_CF2, 270.f + _CV_ATAN_CF2,
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180.f + _CV_ATAN_CF2, 270.f - _CV_ATAN_CF2
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};
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static const int icvAtanSign[8] =
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{ 0, 0x80000000, 0x80000000, 0, 0x80000000, 0, 0, 0x80000000 };
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float fastAtan2( float y, float x )
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{
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double a, x2 = (double)x*x, y2 = (double)y*y;
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if( y2 <= x2 )
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{
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a = (180./CV_PI)*x*y/(x2 + 0.28*y2 + DBL_EPSILON);
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return (float)(x < 0 ? a + 180 : y >= 0 ? a : 360+a);
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}
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a = (180./CV_PI)*x*y/(y2 + 0.28*x2 + DBL_EPSILON);
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return (float)(y >= 0 ? 90 - a : 270 - a);
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}
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static CvStatus CV_STDCALL FastAtan2_32f(const float *Y, const float *X, float *angle, int len, bool angleInDegrees=true )
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{
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if( !Y || !X || !angle || len < 0 )
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return CV_BADFACTOR_ERR;
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int i = 0;
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float scale = angleInDegrees ? (float)(180/CV_PI) : 1.f;
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#if CV_SSE2
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if( checkHardwareSupport(CV_CPU_SSE) )
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{
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Cv32suf iabsmask; iabsmask.i = 0x7fffffff;
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__m128 eps = _mm_set1_ps((float)DBL_EPSILON), absmask = _mm_set1_ps(iabsmask.f);
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__m128 _90 = _mm_set1_ps((float)(CV_PI*0.5)), _180 = _mm_set1_ps((float)CV_PI), _360 = _mm_set1_ps((float)(CV_PI*2));
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__m128 zero = _mm_setzero_ps(), _0_28 = _mm_set1_ps(0.28f), scale4 = _mm_set1_ps(scale);
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for( ; i <= len - 4; i += 4 )
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{
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__m128 x4 = _mm_loadu_ps(X + i), y4 = _mm_loadu_ps(Y + i);
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__m128 xq4 = _mm_mul_ps(x4, x4), yq4 = _mm_mul_ps(y4, y4);
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__m128 xly = _mm_cmplt_ps(xq4, yq4);
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__m128 z4 = _mm_div_ps(_mm_mul_ps(x4, y4), _mm_add_ps(_mm_add_ps(_mm_max_ps(xq4, yq4),
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_mm_mul_ps(_mm_min_ps(xq4, yq4), _0_28)), eps));
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// a4 <- x < y ? 90 : 0;
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__m128 a4 = _mm_and_ps(xly, _90);
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// a4 <- (y < 0 ? 360 - a4 : a4) == ((x < y ? y < 0 ? 270 : 90) : (y < 0 ? 360 : 0))
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__m128 mask = _mm_cmplt_ps(y4, zero);
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a4 = _mm_or_ps(_mm_and_ps(_mm_sub_ps(_360, a4), mask), _mm_andnot_ps(mask, a4));
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// a4 <- (x < 0 && !(x < y) ? 180 : a4)
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mask = _mm_andnot_ps(xly, _mm_cmplt_ps(x4, zero));
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a4 = _mm_or_ps(_mm_and_ps(_180, mask), _mm_andnot_ps(mask, a4));
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// a4 <- (x < y ? a4 - z4 : a4 + z4)
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a4 = _mm_mul_ps(_mm_add_ps(_mm_xor_ps(z4, _mm_andnot_ps(absmask, xly)), a4), scale4);
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_mm_storeu_ps(angle + i, a4);
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}
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}
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#endif
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for( ; i < len; i++ )
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{
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float x = X[i], y = Y[i];
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float a, x2 = x*x, y2 = y*y;
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if( y2 <= x2 )
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a = x*y/(x2 + 0.28f*y2 + (float)DBL_EPSILON) + (float)(x < 0 ? CV_PI : y >= 0 ? 0 : CV_PI*2);
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else
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a = (float)(y >= 0 ? CV_PI*0.5 : CV_PI*1.5) - x*y/(y2 + 0.28f*x2 + (float)DBL_EPSILON);
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angle[i] = a*scale;
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}
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return CV_OK;
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}
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/* ************************************************************************** *\
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Fast cube root by Ken Turkowski
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(http://www.worldserver.com/turk/computergraphics/papers.html)
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\* ************************************************************************** */
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float cubeRoot( float value )
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{
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float fr;
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Cv32suf v, m;
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int ix, s;
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int ex, shx;
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v.f = value;
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ix = v.i & 0x7fffffff;
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s = v.i & 0x80000000;
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ex = (ix >> 23) - 127;
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shx = ex % 3;
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shx -= shx >= 0 ? 3 : 0;
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ex = (ex - shx) / 3; /* exponent of cube root */
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v.i = (ix & ((1<<23)-1)) | ((shx + 127)<<23);
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fr = v.f;
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/* 0.125 <= fr < 1.0 */
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/* Use quartic rational polynomial with error < 2^(-24) */
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fr = (float)(((((45.2548339756803022511987494 * fr +
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192.2798368355061050458134625) * fr +
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119.1654824285581628956914143) * fr +
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13.43250139086239872172837314) * fr +
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0.1636161226585754240958355063)/
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((((14.80884093219134573786480845 * fr +
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151.9714051044435648658557668) * fr +
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168.5254414101568283957668343) * fr +
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33.9905941350215598754191872) * fr +
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1.0));
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/* fr *= 2^ex * sign */
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m.f = value;
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v.f = fr;
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v.i = (v.i + (ex << 23) + s) & (m.i*2 != 0 ? -1 : 0);
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return v.f;
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}
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static CvStatus CV_STDCALL
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Magnitude_32f(const float* x, const float* y, float* mag, int len)
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{
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int i = 0;
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#if CV_SSE
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if( checkHardwareSupport(CV_CPU_SSE) )
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{
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for( ; i <= len - 8; i += 8 )
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{
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__m128 x0 = _mm_loadu_ps(x + i), x1 = _mm_loadu_ps(x + i + 4);
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__m128 y0 = _mm_loadu_ps(y + i), y1 = _mm_loadu_ps(y + i + 4);
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x0 = _mm_add_ps(_mm_mul_ps(x0, x0), _mm_mul_ps(y0, y0));
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x1 = _mm_add_ps(_mm_mul_ps(x1, x1), _mm_mul_ps(y1, y1));
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x0 = _mm_sqrt_ps(x0); x1 = _mm_sqrt_ps(x1);
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_mm_storeu_ps(mag + i, x0); _mm_storeu_ps(mag + i + 4, x1);
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}
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}
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#endif
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for( ; i < len; i++ )
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{
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float x0 = x[i], y0 = y[i];
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mag[i] = std::sqrt(x0*x0 + y0*y0);
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}
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return CV_OK;
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}
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static CvStatus CV_STDCALL
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Magnitude_64f(const double* x, const double* y, double* mag, int len)
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{
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int i = 0;
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#if CV_SSE2
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if( checkHardwareSupport(CV_CPU_SSE2) )
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{
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for( ; i <= len - 4; i += 4 )
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{
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__m128d x0 = _mm_loadu_pd(x + i), x1 = _mm_loadu_pd(x + i + 2);
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__m128d y0 = _mm_loadu_pd(y + i), y1 = _mm_loadu_pd(y + i + 2);
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x0 = _mm_add_pd(_mm_mul_pd(x0, x0), _mm_mul_pd(y0, y0));
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x1 = _mm_add_pd(_mm_mul_pd(x1, x1), _mm_mul_pd(y1, y1));
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x0 = _mm_sqrt_pd(x0); x1 = _mm_sqrt_pd(x1);
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_mm_storeu_pd(mag + i, x0); _mm_storeu_pd(mag + i + 2, x1);
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}
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}
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#endif
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for( ; i < len; i++ )
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{
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double x0 = x[i], y0 = y[i];
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mag[i] = std::sqrt(x0*x0 + y0*y0);
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}
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return CV_OK;
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}
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static CvStatus CV_STDCALL InvSqrt_32f(const float* src, float* dst, int len)
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{
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int i = 0;
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#if CV_SSE
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if( checkHardwareSupport(CV_CPU_SSE) )
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{
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__m128 _0_5 = _mm_set1_ps(0.5f), _1_5 = _mm_set1_ps(1.5f);
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if( (((size_t)src|(size_t)dst) & 15) == 0 )
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for( ; i <= len - 8; i += 8 )
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{
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__m128 t0 = _mm_load_ps(src + i), t1 = _mm_load_ps(src + i + 4);
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__m128 h0 = _mm_mul_ps(t0, _0_5), h1 = _mm_mul_ps(t1, _0_5);
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t0 = _mm_rsqrt_ps(t0); t1 = _mm_rsqrt_ps(t1);
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t0 = _mm_mul_ps(t0, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t0,t0),h0)));
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t1 = _mm_mul_ps(t1, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t1,t1),h1)));
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_mm_store_ps(dst + i, t0); _mm_store_ps(dst + i + 4, t1);
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}
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else
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for( ; i <= len - 8; i += 8 )
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{
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__m128 t0 = _mm_loadu_ps(src + i), t1 = _mm_loadu_ps(src + i + 4);
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__m128 h0 = _mm_mul_ps(t0, _0_5), h1 = _mm_mul_ps(t1, _0_5);
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t0 = _mm_rsqrt_ps(t0); t1 = _mm_rsqrt_ps(t1);
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t0 = _mm_mul_ps(t0, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t0,t0),h0)));
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t1 = _mm_mul_ps(t1, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t1,t1),h1)));
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_mm_storeu_ps(dst + i, t0); _mm_storeu_ps(dst + i + 4, t1);
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}
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}
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#endif
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for( ; i < len; i++ )
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dst[i] = 1/std::sqrt(src[i]);
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return CV_OK;
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}
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static CvStatus CV_STDCALL InvSqrt_64f(const double* src, double* dst, int len)
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{
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for( int i = 0; i < len; i++ )
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dst[i] = 1/std::sqrt(src[i]);
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return CV_OK;
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}
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static CvStatus CV_STDCALL Sqrt_32f(const float* src, float* dst, int len)
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{
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int i = 0;
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#if CV_SSE
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if( checkHardwareSupport(CV_CPU_SSE) )
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{
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if( (((size_t)src|(size_t)dst) & 15) == 0 )
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for( ; i <= len - 8; i += 8 )
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{
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__m128 t0 = _mm_load_ps(src + i), t1 = _mm_load_ps(src + i + 4);
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t0 = _mm_sqrt_ps(t0); t1 = _mm_sqrt_ps(t1);
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_mm_store_ps(dst + i, t0); _mm_store_ps(dst + i + 4, t1);
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}
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else
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for( ; i <= len - 8; i += 8 )
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{
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__m128 t0 = _mm_loadu_ps(src + i), t1 = _mm_loadu_ps(src + i + 4);
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t0 = _mm_sqrt_ps(t0); t1 = _mm_sqrt_ps(t1);
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_mm_storeu_ps(dst + i, t0); _mm_storeu_ps(dst + i + 4, t1);
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}
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}
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#endif
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for( ; i < len; i++ )
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dst[i] = std::sqrt(src[i]);
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return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
static CvStatus CV_STDCALL Sqrt_64f(const double* src, double* dst, int len)
|
|
|
|
{
|
|
|
|
int i = 0;
|
|
|
|
|
|
|
|
#if CV_SSE2
|
|
|
|
if( checkHardwareSupport(CV_CPU_SSE2) )
|
|
|
|
{
|
|
|
|
if( (((size_t)src|(size_t)dst) & 15) == 0 )
|
|
|
|
for( ; i <= len - 4; i += 4 )
|
|
|
|
{
|
|
|
|
__m128d t0 = _mm_load_pd(src + i), t1 = _mm_load_pd(src + i + 2);
|
|
|
|
t0 = _mm_sqrt_pd(t0); t1 = _mm_sqrt_pd(t1);
|
|
|
|
_mm_store_pd(dst + i, t0); _mm_store_pd(dst + i + 2, t1);
|
|
|
|
}
|
|
|
|
else
|
|
|
|
for( ; i <= len - 4; i += 4 )
|
|
|
|
{
|
|
|
|
__m128d t0 = _mm_loadu_pd(src + i), t1 = _mm_loadu_pd(src + i + 2);
|
|
|
|
t0 = _mm_sqrt_pd(t0); t1 = _mm_sqrt_pd(t1);
|
|
|
|
_mm_storeu_pd(dst + i, t0); _mm_storeu_pd(dst + i + 2, t1);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
#endif
|
|
|
|
|
|
|
|
for( ; i < len; i++ )
|
|
|
|
dst[i] = std::sqrt(src[i]);
|
|
|
|
return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/****************************************************************************************\
|
|
|
|
* Cartezian -> Polar *
|
|
|
|
\****************************************************************************************/
|
|
|
|
|
|
|
|
void magnitude( const Mat& X, const Mat& Y, Mat& Mag )
|
|
|
|
{
|
|
|
|
int type = X.type(), depth = X.depth(), cn = X.channels();
|
|
|
|
CV_Assert( X.size() == Y.size() && type == Y.type() && (depth == CV_32F || depth == CV_64F));
|
|
|
|
Mag.create( X.size(), type );
|
|
|
|
|
|
|
|
Size size = getContinuousSize( X, Y, Mag, cn );
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
{
|
|
|
|
const float *x = (const float*)X.data, *y = (const float*)Y.data;
|
|
|
|
float *mag = (float*)Mag.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t mstep = Mag.step/sizeof(mag[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, mag += mstep )
|
|
|
|
Magnitude_32f( x, y, mag, size.width );
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
const double *x = (const double*)X.data, *y = (const double*)Y.data;
|
|
|
|
double *mag = (double*)Mag.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t mstep = Mag.step/sizeof(mag[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, mag += mstep )
|
|
|
|
Magnitude_64f( x, y, mag, size.width );
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
void phase( const Mat& X, const Mat& Y, Mat& Angle, bool angleInDegrees )
|
|
|
|
{
|
|
|
|
float buf[2][MAX_BLOCK_SIZE];
|
|
|
|
int i, j, type = X.type(), depth = X.depth(), cn = X.channels();
|
|
|
|
|
|
|
|
CV_Assert( X.size() == Y.size() && type == Y.type() && (depth == CV_32F || depth == CV_64F));
|
|
|
|
Angle.create( X.size(), type );
|
|
|
|
|
|
|
|
Size size = getContinuousSize( X, Y, Angle, cn );
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
{
|
|
|
|
const float *x = (const float*)X.data, *y = (const float*)Y.data;
|
|
|
|
float *angle = (float*)Angle.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t astep = Angle.step/sizeof(angle[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, angle += astep )
|
|
|
|
FastAtan2_32f( y, x, angle, size.width, angleInDegrees );
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
const double *x = (const double*)X.data, *y = (const double*)Y.data;
|
|
|
|
double *angle = (double*)Angle.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t astep = Angle.step/sizeof(angle[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, angle += astep )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i += MAX_BLOCK_SIZE )
|
|
|
|
{
|
|
|
|
int block_size = std::min(MAX_BLOCK_SIZE, size.width - i);
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
{
|
|
|
|
buf[0][j] = (float)x[i + j];
|
|
|
|
buf[1][j] = (float)y[i + j];
|
|
|
|
}
|
|
|
|
FastAtan2_32f( buf[1], buf[0], buf[0], block_size, angleInDegrees );
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
angle[i + j] = buf[0][j];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
void cartToPolar( const Mat& X, const Mat& Y, Mat& Mag, Mat& Angle, bool angleInDegrees )
|
|
|
|
{
|
|
|
|
float buf[2][MAX_BLOCK_SIZE];
|
|
|
|
int i, j, type = X.type(), depth = X.depth(), cn = X.channels();
|
|
|
|
|
|
|
|
CV_Assert( X.size() == Y.size() && type == Y.type() && (depth == CV_32F || depth == CV_64F));
|
|
|
|
Mag.create( X.size(), type );
|
|
|
|
Angle.create( X.size(), type );
|
|
|
|
|
|
|
|
Size size = getContinuousSize( X, Y, Mag, Angle, cn );
|
|
|
|
bool inplace = Mag.data == X.data || Mag.data == Y.data;
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
{
|
|
|
|
const float *x = (const float*)X.data, *y = (const float*)Y.data;
|
|
|
|
float *mag = (float*)Mag.data, *angle = (float*)Angle.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t mstep = Mag.step/sizeof(mag[0]), astep = Angle.step/sizeof(angle[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, mag += mstep, angle += astep )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i += MAX_BLOCK_SIZE )
|
|
|
|
{
|
|
|
|
int block_size = std::min(MAX_BLOCK_SIZE, size.width - i);
|
|
|
|
Magnitude_32f( x + i, y + i, inplace ? buf[0] : mag + i, block_size );
|
|
|
|
FastAtan2_32f( y + i, x + i, angle + i, block_size, angleInDegrees );
|
|
|
|
if( inplace )
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
mag[i + j] = buf[0][j];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
const double *x = (const double*)X.data, *y = (const double*)Y.data;
|
|
|
|
double *mag = (double*)Mag.data, *angle = (double*)Angle.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t mstep = Mag.step/sizeof(mag[0]), astep = Angle.step/sizeof(angle[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, mag += mstep, angle += astep )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i += MAX_BLOCK_SIZE )
|
|
|
|
{
|
|
|
|
int block_size = std::min(MAX_BLOCK_SIZE, size.width - i);
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
{
|
|
|
|
buf[0][j] = (float)x[i + j];
|
|
|
|
buf[1][j] = (float)y[i + j];
|
|
|
|
}
|
|
|
|
FastAtan2_32f( buf[1], buf[0], buf[0], block_size, angleInDegrees );
|
|
|
|
Magnitude_64f( x + i, y + i, mag + i, block_size );
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
angle[i + j] = buf[0][j];
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/****************************************************************************************\
|
|
|
|
* Polar -> Cartezian *
|
|
|
|
\****************************************************************************************/
|
|
|
|
|
|
|
|
static CvStatus CV_STDCALL
|
|
|
|
SinCos_32f( const float *angle,float *sinval, float* cosval,
|
|
|
|
int len, int angle_in_degrees )
|
|
|
|
{
|
|
|
|
const int N = 64;
|
|
|
|
|
|
|
|
static const double sin_table[] =
|
|
|
|
{
|
|
|
|
0.00000000000000000000, 0.09801714032956060400,
|
|
|
|
0.19509032201612825000, 0.29028467725446233000,
|
|
|
|
0.38268343236508978000, 0.47139673682599764000,
|
|
|
|
0.55557023301960218000, 0.63439328416364549000,
|
|
|
|
0.70710678118654746000, 0.77301045336273699000,
|
|
|
|
0.83146961230254524000, 0.88192126434835494000,
|
|
|
|
0.92387953251128674000, 0.95694033573220894000,
|
|
|
|
0.98078528040323043000, 0.99518472667219682000,
|
|
|
|
1.00000000000000000000, 0.99518472667219693000,
|
|
|
|
0.98078528040323043000, 0.95694033573220894000,
|
|
|
|
0.92387953251128674000, 0.88192126434835505000,
|
|
|
|
0.83146961230254546000, 0.77301045336273710000,
|
|
|
|
0.70710678118654757000, 0.63439328416364549000,
|
|
|
|
0.55557023301960218000, 0.47139673682599786000,
|
|
|
|
0.38268343236508989000, 0.29028467725446239000,
|
|
|
|
0.19509032201612861000, 0.09801714032956082600,
|
|
|
|
0.00000000000000012246, -0.09801714032956059000,
|
|
|
|
-0.19509032201612836000, -0.29028467725446211000,
|
|
|
|
-0.38268343236508967000, -0.47139673682599764000,
|
|
|
|
-0.55557023301960196000, -0.63439328416364527000,
|
|
|
|
-0.70710678118654746000, -0.77301045336273666000,
|
|
|
|
-0.83146961230254524000, -0.88192126434835494000,
|
|
|
|
-0.92387953251128652000, -0.95694033573220882000,
|
|
|
|
-0.98078528040323032000, -0.99518472667219693000,
|
|
|
|
-1.00000000000000000000, -0.99518472667219693000,
|
|
|
|
-0.98078528040323043000, -0.95694033573220894000,
|
|
|
|
-0.92387953251128663000, -0.88192126434835505000,
|
|
|
|
-0.83146961230254546000, -0.77301045336273688000,
|
|
|
|
-0.70710678118654768000, -0.63439328416364593000,
|
|
|
|
-0.55557023301960218000, -0.47139673682599792000,
|
|
|
|
-0.38268343236509039000, -0.29028467725446250000,
|
|
|
|
-0.19509032201612872000, -0.09801714032956050600,
|
|
|
|
};
|
|
|
|
|
|
|
|
static const double k2 = (2*CV_PI)/N;
|
|
|
|
|
|
|
|
static const double sin_a0 = -0.166630293345647*k2*k2*k2;
|
|
|
|
static const double sin_a2 = k2;
|
|
|
|
|
|
|
|
static const double cos_a0 = -0.499818138450326*k2*k2;
|
|
|
|
/*static const double cos_a2 = 1;*/
|
|
|
|
|
|
|
|
double k1;
|
|
|
|
int i;
|
|
|
|
|
|
|
|
if( !angle_in_degrees )
|
|
|
|
k1 = N/(2*CV_PI);
|
|
|
|
else
|
|
|
|
k1 = N/360.;
|
|
|
|
|
|
|
|
for( i = 0; i < len; i++ )
|
|
|
|
{
|
|
|
|
double t = angle[i]*k1;
|
|
|
|
int it = cvRound(t);
|
|
|
|
t -= it;
|
|
|
|
int sin_idx = it & (N - 1);
|
|
|
|
int cos_idx = (N/4 - sin_idx) & (N - 1);
|
|
|
|
|
|
|
|
double sin_b = (sin_a0*t*t + sin_a2)*t;
|
|
|
|
double cos_b = cos_a0*t*t + 1;
|
|
|
|
|
|
|
|
double sin_a = sin_table[sin_idx];
|
|
|
|
double cos_a = sin_table[cos_idx];
|
|
|
|
|
|
|
|
double sin_val = sin_a*cos_b + cos_a*sin_b;
|
|
|
|
double cos_val = cos_a*cos_b - sin_a*sin_b;
|
|
|
|
|
|
|
|
sinval[i] = (float)sin_val;
|
|
|
|
cosval[i] = (float)cos_val;
|
|
|
|
}
|
|
|
|
|
|
|
|
return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
void polarToCart( const Mat& Mag, const Mat& Angle, Mat& X, Mat& Y, bool angleInDegrees )
|
|
|
|
{
|
|
|
|
int i, j, type = Angle.type(), depth = Angle.depth();
|
|
|
|
Size size;
|
|
|
|
|
|
|
|
CV_Assert( depth == CV_32F || depth == CV_64F );
|
|
|
|
X.create( Angle.size(), type );
|
|
|
|
Y.create( Angle.size(), type );
|
|
|
|
|
|
|
|
if( Mag.data )
|
|
|
|
{
|
|
|
|
CV_Assert( Mag.size() == Angle.size() && Mag.type() == Angle.type() );
|
|
|
|
size = getContinuousSize( Mag, Angle, X, Y, Angle.channels() );
|
|
|
|
}
|
|
|
|
else
|
|
|
|
size = getContinuousSize( Angle, X, Y, Angle.channels() );
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
{
|
|
|
|
float *x = (float*)X.data, *y = (float*)Y.data;
|
|
|
|
const float *mag = (const float*)Mag.data, *angle = (const float*)Angle.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t mstep = Mag.step/sizeof(mag[0]), astep = Angle.step/sizeof(angle[0]);
|
|
|
|
float x_tmp[MAX_BLOCK_SIZE];
|
|
|
|
float y_tmp[MAX_BLOCK_SIZE];
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, mag += mstep, angle += astep )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i += MAX_BLOCK_SIZE )
|
|
|
|
{
|
|
|
|
int block_size = std::min(MAX_BLOCK_SIZE, size.width - i);
|
|
|
|
SinCos_32f( angle + i, y_tmp, x_tmp, block_size, angleInDegrees );
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
{
|
|
|
|
float m = mag ? mag[i + j] : 1.f;
|
|
|
|
float t0 = x_tmp[j]*m, t1 = y_tmp[j]*m;
|
|
|
|
x[i + j] = t0; y[i + j] = t1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
double *x = (double*)X.data, *y = (double*)Y.data;
|
|
|
|
const double *mag = (const double*)Mag.data, *angle = (const double*)Angle.data;
|
|
|
|
size_t xstep = X.step/sizeof(x[0]), ystep = Y.step/sizeof(y[0]);
|
|
|
|
size_t mstep = Mag.step/sizeof(mag[0]), astep = Angle.step/sizeof(angle[0]);
|
|
|
|
double ascale = angleInDegrees ? CV_PI/180. : 1;
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep, mag += mstep, angle += astep )
|
|
|
|
{
|
|
|
|
for( j = 0; j < size.width; j++ )
|
|
|
|
{
|
|
|
|
double alpha = angle[j]*ascale, m = mag ? mag[j] : 1.;
|
|
|
|
double a = cos(alpha), b = sin(alpha);
|
|
|
|
x[j] = m*a; y[j] = m*b;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
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/****************************************************************************************\
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* E X P *
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\****************************************************************************************/
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typedef union
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{
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struct {
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#if ( defined( WORDS_BIGENDIAN ) && !defined( OPENCV_UNIVERSAL_BUILD ) ) || defined( __BIG_ENDIAN__ )
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int hi;
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int lo;
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#else
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int lo;
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int hi;
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#endif
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} i;
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double d;
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}
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DBLINT;
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#ifndef HAVE_IPP
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#define EXPTAB_SCALE 6
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#define EXPTAB_MASK ((1 << EXPTAB_SCALE) - 1)
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#define EXPPOLY_32F_A0 .9670371139572337719125840413672004409288e-2
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static const double expTab[] = {
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1.0 * EXPPOLY_32F_A0,
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1.0108892860517004600204097905619 * EXPPOLY_32F_A0,
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1.0218971486541166782344801347833 * EXPPOLY_32F_A0,
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1.0330248790212284225001082839705 * EXPPOLY_32F_A0,
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1.0442737824274138403219664787399 * EXPPOLY_32F_A0,
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1.0556451783605571588083413251529 * EXPPOLY_32F_A0,
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1.0671404006768236181695211209928 * EXPPOLY_32F_A0,
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1.0787607977571197937406800374385 * EXPPOLY_32F_A0,
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1.0905077326652576592070106557607 * EXPPOLY_32F_A0,
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1.1023825833078409435564142094256 * EXPPOLY_32F_A0,
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1.1143867425958925363088129569196 * EXPPOLY_32F_A0,
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1.126521618608241899794798643787 * EXPPOLY_32F_A0,
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1.1387886347566916537038302838415 * EXPPOLY_32F_A0,
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1.151189229952982705817759635202 * EXPPOLY_32F_A0,
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1.1637248587775775138135735990922 * EXPPOLY_32F_A0,
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1.1763969916502812762846457284838 * EXPPOLY_32F_A0,
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1.1892071150027210667174999705605 * EXPPOLY_32F_A0,
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1.2021567314527031420963969574978 * EXPPOLY_32F_A0,
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1.2152473599804688781165202513388 * EXPPOLY_32F_A0,
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1.2284805361068700056940089577928 * EXPPOLY_32F_A0,
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1.2418578120734840485936774687266 * EXPPOLY_32F_A0,
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1.2553807570246910895793906574423 * EXPPOLY_32F_A0,
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1.2690509571917332225544190810323 * EXPPOLY_32F_A0,
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1.2828700160787782807266697810215 * EXPPOLY_32F_A0,
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1.2968395546510096659337541177925 * EXPPOLY_32F_A0,
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1.3109612115247643419229917863308 * EXPPOLY_32F_A0,
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1.3252366431597412946295370954987 * EXPPOLY_32F_A0,
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1.3396675240533030053600306697244 * EXPPOLY_32F_A0,
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1.3542555469368927282980147401407 * EXPPOLY_32F_A0,
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1.3690024229745906119296011329822 * EXPPOLY_32F_A0,
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1.3839098819638319548726595272652 * EXPPOLY_32F_A0,
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1.3989796725383111402095281367152 * EXPPOLY_32F_A0,
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1.4142135623730950488016887242097 * EXPPOLY_32F_A0,
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1.4296133383919700112350657782751 * EXPPOLY_32F_A0,
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1.4451808069770466200370062414717 * EXPPOLY_32F_A0,
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1.4609177941806469886513028903106 * EXPPOLY_32F_A0,
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1.476826145939499311386907480374 * EXPPOLY_32F_A0,
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1.4929077282912648492006435314867 * EXPPOLY_32F_A0,
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1.5091644275934227397660195510332 * EXPPOLY_32F_A0,
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1.5255981507445383068512536895169 * EXPPOLY_32F_A0,
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1.5422108254079408236122918620907 * EXPPOLY_32F_A0,
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1.5590044002378369670337280894749 * EXPPOLY_32F_A0,
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1.5759808451078864864552701601819 * EXPPOLY_32F_A0,
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1.5931421513422668979372486431191 * EXPPOLY_32F_A0,
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1.6104903319492543081795206673574 * EXPPOLY_32F_A0,
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1.628027421857347766848218522014 * EXPPOLY_32F_A0,
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1.6457554781539648445187567247258 * EXPPOLY_32F_A0,
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1.6636765803267364350463364569764 * EXPPOLY_32F_A0,
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1.6817928305074290860622509524664 * EXPPOLY_32F_A0,
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1.7001063537185234695013625734975 * EXPPOLY_32F_A0,
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1.7186192981224779156293443764563 * EXPPOLY_32F_A0,
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1.7373338352737062489942020818722 * EXPPOLY_32F_A0,
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1.7562521603732994831121606193753 * EXPPOLY_32F_A0,
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1.7753764925265212525505592001993 * EXPPOLY_32F_A0,
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1.7947090750031071864277032421278 * EXPPOLY_32F_A0,
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1.8142521755003987562498346003623 * EXPPOLY_32F_A0,
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1.8340080864093424634870831895883 * EXPPOLY_32F_A0,
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1.8539791250833855683924530703377 * EXPPOLY_32F_A0,
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1.8741676341102999013299989499544 * EXPPOLY_32F_A0,
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1.8945759815869656413402186534269 * EXPPOLY_32F_A0,
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1.9152065613971472938726112702958 * EXPPOLY_32F_A0,
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1.9360617934922944505980559045667 * EXPPOLY_32F_A0,
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1.9571441241754002690183222516269 * EXPPOLY_32F_A0,
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1.9784560263879509682582499181312 * EXPPOLY_32F_A0,
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};
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2010-10-04 06:45:04 +08:00
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2010-05-12 01:44:00 +08:00
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static const double exp_prescale = 1.4426950408889634073599246810019 * (1 << EXPTAB_SCALE);
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static const double exp_postscale = 1./(1 << EXPTAB_SCALE);
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static const double exp_max_val = 3000.*(1 << EXPTAB_SCALE); // log10(DBL_MAX) < 3000
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static CvStatus CV_STDCALL Exp_32f( const float *_x, float *y, int n )
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{
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2010-10-04 06:45:04 +08:00
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static const float
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A4 = (float)(1.000000000000002438532970795181890933776 / EXPPOLY_32F_A0),
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A3 = (float)(.6931471805521448196800669615864773144641 / EXPPOLY_32F_A0),
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A2 = (float)(.2402265109513301490103372422686535526573 / EXPPOLY_32F_A0),
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A1 = (float)(.5550339366753125211915322047004666939128e-1 / EXPPOLY_32F_A0);
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#undef EXPPOLY
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#define EXPPOLY(x) \
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(((((x) + A1)*(x) + A2)*(x) + A3)*(x) + A4)
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2010-05-12 01:44:00 +08:00
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int i = 0;
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const Cv32suf* x = (const Cv32suf*)_x;
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2010-10-04 06:45:04 +08:00
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Cv32suf buf[4];
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2010-05-12 01:44:00 +08:00
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2010-10-04 06:45:04 +08:00
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#if CV_SSE2
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if( n >= 8 && checkHardwareSupport(CV_CPU_SSE) )
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{
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static const __m128d prescale2 = _mm_set1_pd(exp_prescale);
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static const __m128 postscale4 = _mm_set1_ps((float)exp_postscale);
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static const __m128 maxval4 = _mm_set1_ps((float)(exp_max_val/exp_prescale));
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static const __m128 minval4 = _mm_set1_ps((float)(-exp_max_val/exp_prescale));
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static const __m128 mA1 = _mm_set1_ps(A1);
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static const __m128 mA2 = _mm_set1_ps(A2);
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static const __m128 mA3 = _mm_set1_ps(A3);
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static const __m128 mA4 = _mm_set1_ps(A4);
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bool y_aligned = (size_t)(void*)y % 16 == 0;
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ushort CV_DECL_ALIGNED(16) tab_idx[8];
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for( ; i <= n - 8; i += 8 )
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{
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__m128 xf0, xf1;
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xf0 = _mm_loadu_ps(&x[i].f);
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xf1 = _mm_loadu_ps(&x[i+4].f);
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__m128i xi0, xi1, xi2, xi3;
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xf0 = _mm_min_ps(_mm_max_ps(xf0, minval4), maxval4);
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xf1 = _mm_min_ps(_mm_max_ps(xf1, minval4), maxval4);
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__m128d xd0 = _mm_cvtps_pd(xf0);
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__m128d xd2 = _mm_cvtps_pd(_mm_movehl_ps(xf0, xf0));
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__m128d xd1 = _mm_cvtps_pd(xf1);
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__m128d xd3 = _mm_cvtps_pd(_mm_movehl_ps(xf1, xf1));
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xd0 = _mm_mul_pd(xd0, prescale2);
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xd2 = _mm_mul_pd(xd2, prescale2);
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xd1 = _mm_mul_pd(xd1, prescale2);
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xd3 = _mm_mul_pd(xd3, prescale2);
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xi0 = _mm_cvtpd_epi32(xd0);
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xi2 = _mm_cvtpd_epi32(xd2);
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xi1 = _mm_cvtpd_epi32(xd1);
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xi3 = _mm_cvtpd_epi32(xd3);
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xd0 = _mm_sub_pd(xd0, _mm_cvtepi32_pd(xi0));
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xd2 = _mm_sub_pd(xd2, _mm_cvtepi32_pd(xi2));
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xd1 = _mm_sub_pd(xd1, _mm_cvtepi32_pd(xi1));
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xd3 = _mm_sub_pd(xd3, _mm_cvtepi32_pd(xi3));
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xf0 = _mm_movelh_ps(_mm_cvtpd_ps(xd0), _mm_cvtpd_ps(xd2));
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xf1 = _mm_movelh_ps(_mm_cvtpd_ps(xd1), _mm_cvtpd_ps(xd3));
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xf0 = _mm_mul_ps(xf0, postscale4);
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xf1 = _mm_mul_ps(xf1, postscale4);
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xi0 = _mm_unpacklo_epi64(xi0, xi2);
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xi1 = _mm_unpacklo_epi64(xi1, xi3);
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xi0 = _mm_packs_epi32(xi0, xi1);
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_mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi16(EXPTAB_MASK)));
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xi0 = _mm_add_epi16(_mm_srai_epi16(xi0, EXPTAB_SCALE), _mm_set1_epi16(127));
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xi0 = _mm_max_epi16(xi0, _mm_setzero_si128());
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xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(255));
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xi1 = _mm_unpackhi_epi16(xi0, _mm_setzero_si128());
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xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128());
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__m128d yd0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1]));
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__m128d yd1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3]));
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__m128d yd2 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[4]), _mm_load_sd(expTab + tab_idx[5]));
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__m128d yd3 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[6]), _mm_load_sd(expTab + tab_idx[7]));
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__m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1));
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__m128 yf1 = _mm_movelh_ps(_mm_cvtpd_ps(yd2), _mm_cvtpd_ps(yd3));
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2010-05-12 01:44:00 +08:00
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2010-10-04 06:45:04 +08:00
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yf0 = _mm_mul_ps(yf0, _mm_castsi128_ps(_mm_slli_epi32(xi0, 23)));
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yf1 = _mm_mul_ps(yf1, _mm_castsi128_ps(_mm_slli_epi32(xi1, 23)));
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__m128 zf0 = _mm_add_ps(xf0, mA1);
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__m128 zf1 = _mm_add_ps(xf1, mA1);
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zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA2);
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zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA2);
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zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA3);
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zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA3);
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zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA4);
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zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA4);
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zf0 = _mm_mul_ps(zf0, yf0);
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zf1 = _mm_mul_ps(zf1, yf1);
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if( y_aligned )
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{
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_mm_store_ps(y + i, zf0);
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_mm_store_ps(y + i + 4, zf1);
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}
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else
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{
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_mm_storeu_ps(y + i, zf0);
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_mm_storeu_ps(y + i + 4, zf1);
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}
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}
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}
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else
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#endif
|
2010-05-12 01:44:00 +08:00
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for( ; i <= n - 4; i += 4 )
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{
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double x0 = x[i].f * exp_prescale;
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double x1 = x[i + 1].f * exp_prescale;
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double x2 = x[i + 2].f * exp_prescale;
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double x3 = x[i + 3].f * exp_prescale;
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int val0, val1, val2, val3, t;
|
2010-10-04 06:45:04 +08:00
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|
2010-05-12 01:44:00 +08:00
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if( ((x[i].i >> 23) & 255) > 127 + 10 )
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x0 = x[i].i < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
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|
2010-05-12 01:44:00 +08:00
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if( ((x[i+1].i >> 23) & 255) > 127 + 10 )
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x1 = x[i+1].i < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
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|
2010-05-12 01:44:00 +08:00
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if( ((x[i+2].i >> 23) & 255) > 127 + 10 )
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x2 = x[i+2].i < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
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|
2010-05-12 01:44:00 +08:00
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if( ((x[i+3].i >> 23) & 255) > 127 + 10 )
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x3 = x[i+3].i < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
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2010-05-12 01:44:00 +08:00
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val0 = cvRound(x0);
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val1 = cvRound(x1);
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val2 = cvRound(x2);
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val3 = cvRound(x3);
|
2010-10-04 06:45:04 +08:00
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|
2010-05-12 01:44:00 +08:00
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x0 = (x0 - val0)*exp_postscale;
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x1 = (x1 - val1)*exp_postscale;
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x2 = (x2 - val2)*exp_postscale;
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x3 = (x3 - val3)*exp_postscale;
|
2010-10-04 06:45:04 +08:00
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t = (val0 >> EXPTAB_SCALE) + 127;
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t = !(t & ~255) ? t : t < 0 ? 0 : 255;
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|
|
buf[0].i = t << 23;
|
|
|
|
|
|
|
|
t = (val1 >> EXPTAB_SCALE) + 127;
|
|
|
|
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
|
|
|
|
buf[1].i = t << 23;
|
|
|
|
|
|
|
|
t = (val2 >> EXPTAB_SCALE) + 127;
|
|
|
|
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
|
|
|
|
buf[2].i = t << 23;
|
|
|
|
|
|
|
|
t = (val3 >> EXPTAB_SCALE) + 127;
|
|
|
|
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
|
|
|
|
buf[3].i = t << 23;
|
|
|
|
|
|
|
|
x0 = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
|
|
|
|
x1 = buf[1].f * expTab[val1 & EXPTAB_MASK] * EXPPOLY( x1 );
|
|
|
|
|
|
|
|
y[i] = x0;
|
|
|
|
y[i + 1] = x1;
|
|
|
|
|
|
|
|
x2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
|
|
|
|
x3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 );
|
|
|
|
|
|
|
|
y[i + 2] = x2;
|
|
|
|
y[i + 3] = x3;
|
2010-05-12 01:44:00 +08:00
|
|
|
}
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
for( ; i < n; i++ )
|
|
|
|
{
|
|
|
|
double x0 = x[i].f * exp_prescale;
|
|
|
|
int val0, t;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
if( ((x[i].i >> 23) & 255) > 127 + 10 )
|
|
|
|
x0 = x[i].i < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
val0 = cvRound(x0);
|
2010-10-04 06:45:04 +08:00
|
|
|
t = (val0 >> EXPTAB_SCALE) + 127;
|
|
|
|
t = !(t & ~255) ? t : t < 0 ? 0 : 255;
|
|
|
|
|
|
|
|
buf[0].i = t << 23;
|
2010-05-12 01:44:00 +08:00
|
|
|
x0 = (x0 - val0)*exp_postscale;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
|
|
|
y[i] = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY(x0);
|
2010-05-12 01:44:00 +08:00
|
|
|
}
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
return CV_OK;
|
|
|
|
}
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
static CvStatus CV_STDCALL Exp_64f( const double *_x, double *y, int n )
|
|
|
|
{
|
|
|
|
static const double
|
2010-10-04 06:45:04 +08:00
|
|
|
A5 = .99999999999999999998285227504999 / EXPPOLY_32F_A0,
|
|
|
|
A4 = .69314718055994546743029643825322 / EXPPOLY_32F_A0,
|
|
|
|
A3 = .24022650695886477918181338054308 / EXPPOLY_32F_A0,
|
|
|
|
A2 = .55504108793649567998466049042729e-1 / EXPPOLY_32F_A0,
|
|
|
|
A1 = .96180973140732918010002372686186e-2 / EXPPOLY_32F_A0,
|
|
|
|
A0 = .13369713757180123244806654839424e-2 / EXPPOLY_32F_A0;
|
|
|
|
|
|
|
|
#undef EXPPOLY
|
|
|
|
#define EXPPOLY(x) (((((A0*(x) + A1)*(x) + A2)*(x) + A3)*(x) + A4)*(x) + A5)
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
int i = 0;
|
2010-10-04 06:45:04 +08:00
|
|
|
Cv64suf buf[4];
|
2010-05-12 01:44:00 +08:00
|
|
|
const Cv64suf* x = (const Cv64suf*)_x;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
|
|
|
#if CV_SSE2
|
|
|
|
if( checkHardwareSupport(CV_CPU_SSE) )
|
|
|
|
{
|
|
|
|
static const __m128d prescale2 = _mm_set1_pd(exp_prescale);
|
|
|
|
static const __m128d postscale2 = _mm_set1_pd(exp_postscale);
|
|
|
|
static const __m128d maxval2 = _mm_set1_pd(exp_max_val);
|
|
|
|
static const __m128d minval2 = _mm_set1_pd(-exp_max_val);
|
|
|
|
|
|
|
|
static const __m128d mA0 = _mm_set1_pd(A0);
|
|
|
|
static const __m128d mA1 = _mm_set1_pd(A1);
|
|
|
|
static const __m128d mA2 = _mm_set1_pd(A2);
|
|
|
|
static const __m128d mA3 = _mm_set1_pd(A3);
|
|
|
|
static const __m128d mA4 = _mm_set1_pd(A4);
|
|
|
|
static const __m128d mA5 = _mm_set1_pd(A5);
|
|
|
|
|
|
|
|
int CV_DECL_ALIGNED(16) tab_idx[4];
|
|
|
|
|
|
|
|
for( ; i <= n - 4; i += 4 )
|
|
|
|
{
|
|
|
|
__m128d xf0 = _mm_loadu_pd(&x[i].f), xf1 = _mm_loadu_pd(&x[i+2].f);
|
|
|
|
__m128i xi0, xi1;
|
|
|
|
xf0 = _mm_min_pd(_mm_max_pd(xf0, minval2), maxval2);
|
|
|
|
xf1 = _mm_min_pd(_mm_max_pd(xf1, minval2), maxval2);
|
|
|
|
xf0 = _mm_mul_pd(xf0, prescale2);
|
|
|
|
xf1 = _mm_mul_pd(xf1, prescale2);
|
|
|
|
|
|
|
|
xi0 = _mm_cvtpd_epi32(xf0);
|
|
|
|
xi1 = _mm_cvtpd_epi32(xf1);
|
|
|
|
xf0 = _mm_mul_pd(_mm_sub_pd(xf0, _mm_cvtepi32_pd(xi0)), postscale2);
|
|
|
|
xf1 = _mm_mul_pd(_mm_sub_pd(xf1, _mm_cvtepi32_pd(xi1)), postscale2);
|
|
|
|
|
|
|
|
xi0 = _mm_unpacklo_epi64(xi0, xi1);
|
|
|
|
_mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi32(EXPTAB_MASK)));
|
|
|
|
|
|
|
|
xi0 = _mm_add_epi32(_mm_srai_epi32(xi0, EXPTAB_SCALE), _mm_set1_epi32(1023));
|
|
|
|
xi0 = _mm_packs_epi32(xi0, xi0);
|
|
|
|
xi0 = _mm_max_epi16(xi0, _mm_setzero_si128());
|
|
|
|
xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(2047));
|
|
|
|
xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128());
|
|
|
|
xi1 = _mm_unpackhi_epi32(xi0, _mm_setzero_si128());
|
|
|
|
xi0 = _mm_unpacklo_epi32(xi0, _mm_setzero_si128());
|
|
|
|
|
|
|
|
__m128d yf0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1]));
|
|
|
|
__m128d yf1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3]));
|
|
|
|
yf0 = _mm_mul_pd(yf0, _mm_castsi128_pd(_mm_slli_epi64(xi0, 52)));
|
|
|
|
yf1 = _mm_mul_pd(yf1, _mm_castsi128_pd(_mm_slli_epi64(xi1, 52)));
|
|
|
|
|
|
|
|
__m128d zf0 = _mm_add_pd(_mm_mul_pd(mA0, xf0), mA1);
|
|
|
|
__m128d zf1 = _mm_add_pd(_mm_mul_pd(mA0, xf1), mA1);
|
|
|
|
|
|
|
|
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA2);
|
|
|
|
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA2);
|
|
|
|
|
|
|
|
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA3);
|
|
|
|
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA3);
|
|
|
|
|
|
|
|
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA4);
|
|
|
|
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA4);
|
|
|
|
|
|
|
|
zf0 = _mm_add_pd(_mm_mul_pd(zf0, xf0), mA5);
|
|
|
|
zf1 = _mm_add_pd(_mm_mul_pd(zf1, xf1), mA5);
|
|
|
|
|
|
|
|
zf0 = _mm_mul_pd(zf0, yf0);
|
|
|
|
zf1 = _mm_mul_pd(zf1, yf1);
|
|
|
|
|
|
|
|
_mm_storeu_pd(y + i, zf0);
|
|
|
|
_mm_storeu_pd(y + i + 2, zf1);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
#endif
|
2010-05-12 01:44:00 +08:00
|
|
|
for( ; i <= n - 4; i += 4 )
|
|
|
|
{
|
|
|
|
double x0 = x[i].f * exp_prescale;
|
|
|
|
double x1 = x[i + 1].f * exp_prescale;
|
|
|
|
double x2 = x[i + 2].f * exp_prescale;
|
|
|
|
double x3 = x[i + 3].f * exp_prescale;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
double y0, y1, y2, y3;
|
|
|
|
int val0, val1, val2, val3, t;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (int)(x[i].i >> 52);
|
|
|
|
if( (t & 2047) > 1023 + 10 )
|
|
|
|
x0 = t < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (int)(x[i+1].i >> 52);
|
|
|
|
if( (t & 2047) > 1023 + 10 )
|
|
|
|
x1 = t < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (int)(x[i+2].i >> 52);
|
|
|
|
if( (t & 2047) > 1023 + 10 )
|
|
|
|
x2 = t < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (int)(x[i+3].i >> 52);
|
|
|
|
if( (t & 2047) > 1023 + 10 )
|
|
|
|
x3 = t < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
val0 = cvRound(x0);
|
|
|
|
val1 = cvRound(x1);
|
|
|
|
val2 = cvRound(x2);
|
|
|
|
val3 = cvRound(x3);
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
x0 = (x0 - val0)*exp_postscale;
|
|
|
|
x1 = (x1 - val1)*exp_postscale;
|
|
|
|
x2 = (x2 - val2)*exp_postscale;
|
|
|
|
x3 = (x3 - val3)*exp_postscale;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (val0 >> EXPTAB_SCALE) + 1023;
|
2010-10-04 06:45:04 +08:00
|
|
|
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
|
|
|
|
buf[0].i = (int64)t << 52;
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (val1 >> EXPTAB_SCALE) + 1023;
|
2010-10-04 06:45:04 +08:00
|
|
|
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
|
|
|
|
buf[1].i = (int64)t << 52;
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (val2 >> EXPTAB_SCALE) + 1023;
|
2010-10-04 06:45:04 +08:00
|
|
|
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
|
|
|
|
buf[2].i = (int64)t << 52;
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (val3 >> EXPTAB_SCALE) + 1023;
|
2010-10-04 06:45:04 +08:00
|
|
|
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
|
|
|
|
buf[3].i = (int64)t << 52;
|
|
|
|
|
|
|
|
y0 = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
|
|
|
|
y1 = buf[1].f * expTab[val1 & EXPTAB_MASK] * EXPPOLY( x1 );
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
y[i] = y0;
|
|
|
|
y[i + 1] = y1;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
|
|
|
y2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 );
|
|
|
|
y3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 );
|
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
y[i + 2] = y2;
|
|
|
|
y[i + 3] = y3;
|
|
|
|
}
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
for( ; i < n; i++ )
|
|
|
|
{
|
|
|
|
double x0 = x[i].f * exp_prescale;
|
|
|
|
int val0, t;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
t = (int)(x[i].i >> 52);
|
|
|
|
if( (t & 2047) > 1023 + 10 )
|
|
|
|
x0 = t < 0 ? -exp_max_val : exp_max_val;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
val0 = cvRound(x0);
|
|
|
|
t = (val0 >> EXPTAB_SCALE) + 1023;
|
2010-10-04 06:45:04 +08:00
|
|
|
t = !(t & ~2047) ? t : t < 0 ? 0 : 2047;
|
|
|
|
|
|
|
|
buf[0].i = (int64)t << 52;
|
2010-05-12 01:44:00 +08:00
|
|
|
x0 = (x0 - val0)*exp_postscale;
|
2010-10-04 06:45:04 +08:00
|
|
|
|
|
|
|
y[i] = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 );
|
2010-05-12 01:44:00 +08:00
|
|
|
}
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
#undef EXPTAB_SCALE
|
|
|
|
#undef EXPTAB_MASK
|
|
|
|
#undef EXPPOLY_32F_A0
|
|
|
|
|
|
|
|
#else
|
|
|
|
|
|
|
|
#define Exp_32f ippsExp_32f_A21
|
|
|
|
#define Exp_64f ippsExp_64f_A50
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
void exp( const Mat& src, Mat& dst )
|
|
|
|
{
|
|
|
|
int depth = src.depth();
|
|
|
|
dst.create( src.size(), src.type() );
|
|
|
|
Size size = getContinuousSize( src, dst, src.channels() );
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
for( int y = 0; y < size.height; y++ )
|
|
|
|
Exp_32f( src.ptr<float>(y), dst.ptr<float>(y), size.width );
|
|
|
|
else if( depth == CV_64F )
|
|
|
|
for( int y = 0; y < size.height; y++ )
|
|
|
|
Exp_64f( src.ptr<double>(y), dst.ptr<double>(y), size.width );
|
|
|
|
else
|
|
|
|
CV_Error( CV_StsUnsupportedFormat, "" );
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/****************************************************************************************\
|
|
|
|
* L O G *
|
|
|
|
\****************************************************************************************/
|
|
|
|
|
|
|
|
#ifndef HAVE_IPP
|
|
|
|
|
|
|
|
#define LOGTAB_SCALE 8
|
|
|
|
#define LOGTAB_MASK ((1 << LOGTAB_SCALE) - 1)
|
|
|
|
#define LOGTAB_MASK2 ((1 << (20 - LOGTAB_SCALE)) - 1)
|
|
|
|
#define LOGTAB_MASK2_32F ((1 << (23 - LOGTAB_SCALE)) - 1)
|
|
|
|
|
2010-10-04 06:45:04 +08:00
|
|
|
static const double CV_DECL_ALIGNED(16) icvLogTab[] = {
|
2010-05-12 01:44:00 +08:00
|
|
|
0.0000000000000000000000000000000000000000, 1.000000000000000000000000000000000000000,
|
|
|
|
.00389864041565732288852075271279318258166, .9961089494163424124513618677042801556420,
|
|
|
|
.00778214044205494809292034119607706088573, .9922480620155038759689922480620155038760,
|
|
|
|
.01165061721997527263705585198749759001657, .9884169884169884169884169884169884169884,
|
|
|
|
.01550418653596525274396267235488267033361, .9846153846153846153846153846153846153846,
|
|
|
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.48790877731923892879351001283794175833480, .6139088729016786570743405275779376498801,
|
|
|
|
.49030398804519381705802061333088204264650, .6124401913875598086124401913875598086124,
|
|
|
|
.49269347544257524607047571407747454941280, .6109785202863961813842482100238663484487,
|
|
|
|
.49507726679785146739476431321236304938800, .6095238095238095238095238095238095238095,
|
|
|
|
.49745538920281889838648226032091770321130, .6080760095011876484560570071258907363420,
|
|
|
|
.49982786955644931126130359189119189977650, .6066350710900473933649289099526066350711,
|
|
|
|
.50219473456671548383667413872899487614650, .6052009456264775413711583924349881796690,
|
|
|
|
.50455601075239520092452494282042607665050, .6037735849056603773584905660377358490566,
|
|
|
|
.50691172444485432801997148999362252652650, .6023529411764705882352941176470588235294,
|
|
|
|
.50926190178980790257412536448100581765150, .6009389671361502347417840375586854460094,
|
|
|
|
.51160656874906207391973111953120678663250, .5995316159250585480093676814988290398126,
|
|
|
|
.51394575110223428282552049495279788970950, .5981308411214953271028037383177570093458,
|
|
|
|
.51627947444845445623684554448118433356300, .5967365967365967365967365967365967365967,
|
|
|
|
.51860776420804555186805373523384332656850, .5953488372093023255813953488372093023256,
|
|
|
|
.52093064562418522900344441950437612831600, .5939675174013921113689095127610208816705,
|
|
|
|
.52324814376454775732838697877014055848100, .5925925925925925925925925925925925925926,
|
|
|
|
.52556028352292727401362526507000438869000, .5912240184757505773672055427251732101617,
|
|
|
|
.52786708962084227803046587723656557500350, .5898617511520737327188940092165898617512,
|
|
|
|
.53016858660912158374145519701414741575700, .5885057471264367816091954022988505747126,
|
|
|
|
.53246479886947173376654518506256863474850, .5871559633027522935779816513761467889908,
|
|
|
|
.53475575061602764748158733709715306758900, .5858123569794050343249427917620137299771,
|
|
|
|
.53704146589688361856929077475797384977350, .5844748858447488584474885844748858447489,
|
|
|
|
.53932196859560876944783558428753167390800, .5831435079726651480637813211845102505695,
|
|
|
|
.54159728243274429804188230264117009937750, .5818181818181818181818181818181818181818,
|
|
|
|
.54386743096728351609669971367111429572100, .5804988662131519274376417233560090702948,
|
|
|
|
.54613243759813556721383065450936555862450, .5791855203619909502262443438914027149321,
|
|
|
|
.54839232556557315767520321969641372561450, .5778781038374717832957110609480812641084,
|
|
|
|
.55064711795266219063194057525834068655950, .5765765765765765765765765765765765765766,
|
|
|
|
.55289683768667763352766542084282264113450, .5752808988764044943820224719101123595506,
|
|
|
|
.55514150754050151093110798683483153581600, .5739910313901345291479820627802690582960,
|
|
|
|
.55738115013400635344709144192165695130850, .5727069351230425055928411633109619686801,
|
|
|
|
.55961578793542265941596269840374588966350, .5714285714285714285714285714285714285714,
|
|
|
|
.56184544326269181269140062795486301183700, .5701559020044543429844097995545657015590,
|
|
|
|
.56407013828480290218436721261241473257550, .5688888888888888888888888888888888888889,
|
|
|
|
.56628989502311577464155334382667206227800, .5676274944567627494456762749445676274945,
|
|
|
|
.56850473535266865532378233183408156037350, .5663716814159292035398230088495575221239,
|
|
|
|
.57071468100347144680739575051120482385150, .5651214128035320088300220750551876379691,
|
|
|
|
.57291975356178548306473885531886480748650, .5638766519823788546255506607929515418502,
|
|
|
|
.57511997447138785144460371157038025558000, .5626373626373626373626373626373626373626,
|
|
|
|
.57731536503482350219940144597785547375700, .5614035087719298245614035087719298245614,
|
|
|
|
.57950594641464214795689713355386629700650, .5601750547045951859956236323851203501094,
|
|
|
|
.58169173963462239562716149521293118596100, .5589519650655021834061135371179039301310,
|
|
|
|
.58387276558098266665552955601015128195300, .5577342047930283224400871459694989106754,
|
|
|
|
.58604904500357812846544902640744112432000, .5565217391304347826086956521739130434783,
|
|
|
|
.58822059851708596855957011939608491957200, .5553145336225596529284164859002169197397,
|
|
|
|
.59038744660217634674381770309992134571100, .5541125541125541125541125541125541125541,
|
|
|
|
.59254960960667157898740242671919986605650, .5529157667386609071274298056155507559395,
|
|
|
|
.59470710774669277576265358220553025603300, .5517241379310344827586206896551724137931,
|
|
|
|
.59685996110779382384237123915227130055450, .5505376344086021505376344086021505376344,
|
|
|
|
.59900818964608337768851242799428291618800, .5493562231759656652360515021459227467811,
|
|
|
|
.60115181318933474940990890900138765573500, .5481798715203426124197002141327623126338,
|
|
|
|
.60329085143808425240052883964381180703650, .5470085470085470085470085470085470085470,
|
|
|
|
.60542532396671688843525771517306566238400, .5458422174840085287846481876332622601279,
|
|
|
|
.60755525022454170969155029524699784815300, .5446808510638297872340425531914893617021,
|
|
|
|
.60968064953685519036241657886421307921400, .5435244161358811040339702760084925690021,
|
|
|
|
.61180154110599282990534675263916142284850, .5423728813559322033898305084745762711864,
|
|
|
|
.61391794401237043121710712512140162289150, .5412262156448202959830866807610993657505,
|
|
|
|
.61602987721551394351138242200249806046500, .5400843881856540084388185654008438818565,
|
|
|
|
.61813735955507864705538167982012964785100, .5389473684210526315789473684210526315789,
|
|
|
|
.62024040975185745772080281312810257077200, .5378151260504201680672268907563025210084,
|
|
|
|
.62233904640877868441606324267922900617100, .5366876310272536687631027253668763102725,
|
|
|
|
.62443328801189346144440150965237990021700, .5355648535564853556485355648535564853556,
|
|
|
|
.62652315293135274476554741340805776417250, .5344467640918580375782881002087682672234,
|
|
|
|
.62860865942237409420556559780379757285100, .5333333333333333333333333333333333333333,
|
|
|
|
.63068982562619868570408243613201193511500, .5322245322245322245322245322245322245322,
|
|
|
|
.63276666957103777644277897707070223987100, .5311203319502074688796680497925311203320,
|
|
|
|
.63483920917301017716738442686619237065300, .5300207039337474120082815734989648033126,
|
|
|
|
.63690746223706917739093569252872839570050, .5289256198347107438016528925619834710744,
|
|
|
|
.63897144645792069983514238629140891134750, .5278350515463917525773195876288659793814,
|
|
|
|
.64103117942093124081992527862894348800200, .5267489711934156378600823045267489711934,
|
|
|
|
.64308667860302726193566513757104985415950, .5256673511293634496919917864476386036961,
|
|
|
|
.64513796137358470073053240412264131009600, .5245901639344262295081967213114754098361,
|
|
|
|
.64718504499530948859131740391603671014300, .5235173824130879345603271983640081799591,
|
|
|
|
.64922794662510974195157587018911726772800, .5224489795918367346938775510204081632653,
|
|
|
|
.65126668331495807251485530287027359008800, .5213849287169042769857433808553971486762,
|
|
|
|
.65330127201274557080523663898929953575150, .5203252032520325203252032520325203252033,
|
|
|
|
.65533172956312757406749369692988693714150, .5192697768762677484787018255578093306288,
|
|
|
|
.65735807270835999727154330685152672231200, .5182186234817813765182186234817813765182,
|
|
|
|
.65938031808912778153342060249997302889800, .5171717171717171717171717171717171717172,
|
|
|
|
.66139848224536490484126716182800009846700, .5161290322580645161290322580645161290323,
|
|
|
|
.66341258161706617713093692145776003599150, .5150905432595573440643863179074446680080,
|
|
|
|
.66542263254509037562201001492212526500250, .5140562248995983935742971887550200803213,
|
|
|
|
.66742865127195616370414654738851822912700, .5130260521042084168336673346693386773547,
|
|
|
|
.66943065394262923906154583164607174694550, .5120000000000000000000000000000000000000,
|
|
|
|
.67142865660530226534774556057527661323550, .5109780439121756487025948103792415169661,
|
|
|
|
.67342267521216669923234121597488410770900, .5099601593625498007968127490039840637450,
|
|
|
|
.67541272562017662384192817626171745359900, .5089463220675944333996023856858846918489,
|
|
|
|
.67739882359180603188519853574689477682100, .5079365079365079365079365079365079365079,
|
|
|
|
.67938098479579733801614338517538271844400, .5069306930693069306930693069306930693069,
|
|
|
|
.68135922480790300781450241629499942064300, .5059288537549407114624505928853754940711,
|
|
|
|
.68333355911162063645036823800182901322850, .5049309664694280078895463510848126232742,
|
|
|
|
.68530400309891936760919861626462079584600, .5039370078740157480314960629921259842520,
|
|
|
|
.68727057207096020619019327568821609020250, .5029469548133595284872298624754420432220,
|
|
|
|
.68923328123880889251040571252815425395950, .5019607843137254901960784313725490196078,
|
|
|
|
.69314718055994530941723212145818, 5.0e-01,
|
|
|
|
};
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
#define LOGTAB_TRANSLATE(x,h) (((x) - 1.)*icvLogTab[(h)+1])
|
|
|
|
static const double ln_2 = 0.69314718055994530941723212145818;
|
|
|
|
|
|
|
|
static CvStatus CV_STDCALL Log_32f( const float *_x, float *y, int n )
|
|
|
|
{
|
2010-10-04 06:45:04 +08:00
|
|
|
static const float shift[] = { 0, -1.f/512 };
|
|
|
|
static const float
|
|
|
|
A0 = 0.3333333333333333333333333f,
|
|
|
|
A1 = -0.5f,
|
|
|
|
A2 = 1.f;
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
#undef LOGPOLY
|
2010-10-04 06:45:04 +08:00
|
|
|
#define LOGPOLY(x) (((A0*(x) + A1)*(x) + A2)*(x))
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
int i = 0;
|
2010-10-04 06:45:04 +08:00
|
|
|
Cv32suf buf[4];
|
2010-05-12 01:44:00 +08:00
|
|
|
const int* x = (const int*)_x;
|
|
|
|
|
2010-10-04 06:45:04 +08:00
|
|
|
#if CV_SSE2
|
|
|
|
if( checkHardwareSupport(CV_CPU_SSE) )
|
|
|
|
{
|
|
|
|
static const __m128d ln2_2 = _mm_set1_pd(ln_2);
|
|
|
|
static const __m128 _1_4 = _mm_set1_ps(1.f);
|
|
|
|
static const __m128 shift4 = _mm_set1_ps(-1.f/512);
|
|
|
|
|
|
|
|
static const __m128 mA0 = _mm_set1_ps(A0);
|
|
|
|
static const __m128 mA1 = _mm_set1_ps(A1);
|
|
|
|
static const __m128 mA2 = _mm_set1_ps(A2);
|
|
|
|
|
|
|
|
int CV_DECL_ALIGNED(16) idx[4];
|
|
|
|
|
|
|
|
for( ; i <= n - 4; i += 4 )
|
|
|
|
{
|
|
|
|
__m128i h0 = _mm_loadu_si128((const __m128i*)(x + i));
|
|
|
|
__m128i yi0 = _mm_sub_epi32(_mm_and_si128(_mm_srli_epi32(h0, 23), _mm_set1_epi32(255)), _mm_set1_epi32(127));
|
|
|
|
__m128d yd0 = _mm_mul_pd(_mm_cvtepi32_pd(yi0), ln2_2);
|
|
|
|
__m128d yd1 = _mm_mul_pd(_mm_cvtepi32_pd(_mm_unpackhi_epi64(yi0,yi0)), ln2_2);
|
|
|
|
|
|
|
|
__m128i xi0 = _mm_or_si128(_mm_and_si128(h0, _mm_set1_epi32(LOGTAB_MASK2_32F)), _mm_set1_epi32(127 << 23));
|
|
|
|
|
|
|
|
h0 = _mm_and_si128(_mm_srli_epi32(h0, 23 - LOGTAB_SCALE - 1), _mm_set1_epi32(LOGTAB_MASK*2));
|
|
|
|
_mm_store_si128((__m128i*)idx, h0);
|
|
|
|
h0 = _mm_cmpeq_epi32(h0, _mm_set1_epi32(510));
|
|
|
|
|
|
|
|
__m128d t0, t1, t2, t3, t4;
|
|
|
|
t0 = _mm_load_pd(icvLogTab + idx[0]);
|
|
|
|
t2 = _mm_load_pd(icvLogTab + idx[1]);
|
|
|
|
t1 = _mm_unpackhi_pd(t0, t2);
|
|
|
|
t0 = _mm_unpacklo_pd(t0, t2);
|
|
|
|
t2 = _mm_load_pd(icvLogTab + idx[2]);
|
|
|
|
t4 = _mm_load_pd(icvLogTab + idx[3]);
|
|
|
|
t3 = _mm_unpackhi_pd(t2, t4);
|
|
|
|
t2 = _mm_unpacklo_pd(t2, t4);
|
|
|
|
|
|
|
|
yd0 = _mm_add_pd(yd0, t0);
|
|
|
|
yd1 = _mm_add_pd(yd1, t2);
|
|
|
|
|
|
|
|
__m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1));
|
|
|
|
|
|
|
|
__m128 xf0 = _mm_sub_ps(_mm_castsi128_ps(xi0), _1_4);
|
|
|
|
xf0 = _mm_mul_ps(xf0, _mm_movelh_ps(_mm_cvtpd_ps(t1), _mm_cvtpd_ps(t3)));
|
|
|
|
xf0 = _mm_add_ps(xf0, _mm_and_ps(_mm_castsi128_ps(h0), shift4));
|
|
|
|
|
|
|
|
__m128 zf0 = _mm_mul_ps(xf0, mA0);
|
|
|
|
zf0 = _mm_mul_ps(_mm_add_ps(zf0, mA1), xf0);
|
|
|
|
zf0 = _mm_mul_ps(_mm_add_ps(zf0, mA2), xf0);
|
|
|
|
yf0 = _mm_add_ps(yf0, zf0);
|
|
|
|
|
|
|
|
_mm_storeu_ps(y + i, yf0);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
#endif
|
|
|
|
for( ; i <= n - 4; i += 4 )
|
2010-05-12 01:44:00 +08:00
|
|
|
{
|
|
|
|
double x0, x1, x2, x3;
|
|
|
|
double y0, y1, y2, y3;
|
|
|
|
int h0, h1, h2, h3;
|
|
|
|
|
|
|
|
h0 = x[i];
|
|
|
|
h1 = x[i+1];
|
|
|
|
buf[0].i = (h0 & LOGTAB_MASK2_32F) | (127 << 23);
|
|
|
|
buf[1].i = (h1 & LOGTAB_MASK2_32F) | (127 << 23);
|
|
|
|
|
|
|
|
y0 = (((h0 >> 23) & 0xff) - 127) * ln_2;
|
|
|
|
y1 = (((h1 >> 23) & 0xff) - 127) * ln_2;
|
|
|
|
|
|
|
|
h0 = (h0 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
h1 = (h1 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
|
|
|
|
y0 += icvLogTab[h0];
|
|
|
|
y1 += icvLogTab[h1];
|
|
|
|
|
|
|
|
h2 = x[i+2];
|
|
|
|
h3 = x[i+3];
|
|
|
|
|
|
|
|
x0 = LOGTAB_TRANSLATE( buf[0].f, h0 );
|
|
|
|
x1 = LOGTAB_TRANSLATE( buf[1].f, h1 );
|
|
|
|
|
|
|
|
buf[2].i = (h2 & LOGTAB_MASK2_32F) | (127 << 23);
|
|
|
|
buf[3].i = (h3 & LOGTAB_MASK2_32F) | (127 << 23);
|
|
|
|
|
|
|
|
y2 = (((h2 >> 23) & 0xff) - 127) * ln_2;
|
|
|
|
y3 = (((h3 >> 23) & 0xff) - 127) * ln_2;
|
|
|
|
|
|
|
|
h2 = (h2 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
h3 = (h3 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
|
|
|
|
y2 += icvLogTab[h2];
|
|
|
|
y3 += icvLogTab[h3];
|
|
|
|
|
|
|
|
x2 = LOGTAB_TRANSLATE( buf[2].f, h2 );
|
|
|
|
x3 = LOGTAB_TRANSLATE( buf[3].f, h3 );
|
|
|
|
|
2010-10-04 06:45:04 +08:00
|
|
|
x0 += shift[h0 == 510];
|
|
|
|
x1 += shift[h1 == 510];
|
|
|
|
y0 += LOGPOLY( x0 );
|
|
|
|
y1 += LOGPOLY( x1 );
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
y[i] = (float) y0;
|
|
|
|
y[i + 1] = (float) y1;
|
|
|
|
|
2010-10-04 06:45:04 +08:00
|
|
|
x2 += shift[h2 == 510];
|
|
|
|
x3 += shift[h3 == 510];
|
|
|
|
y2 += LOGPOLY( x2 );
|
|
|
|
y3 += LOGPOLY( x3 );
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
y[i + 2] = (float) y2;
|
|
|
|
y[i + 3] = (float) y3;
|
|
|
|
}
|
|
|
|
|
|
|
|
for( ; i < n; i++ )
|
|
|
|
{
|
|
|
|
int h0 = x[i];
|
2010-10-04 06:45:04 +08:00
|
|
|
double y0;
|
|
|
|
float x0;
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
y0 = (((h0 >> 23) & 0xff) - 127) * ln_2;
|
|
|
|
|
|
|
|
buf[0].i = (h0 & LOGTAB_MASK2_32F) | (127 << 23);
|
|
|
|
h0 = (h0 >> (23 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
|
|
|
|
y0 += icvLogTab[h0];
|
|
|
|
x0 = LOGTAB_TRANSLATE( buf[0].f, h0 );
|
2010-10-04 06:45:04 +08:00
|
|
|
x0 += shift[h0 == 510];
|
|
|
|
y0 += LOGPOLY( x0 );
|
2010-05-12 01:44:00 +08:00
|
|
|
|
|
|
|
y[i] = (float)y0;
|
|
|
|
}
|
|
|
|
|
|
|
|
return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
static CvStatus CV_STDCALL Log_64f( const double *x, double *y, int n )
|
|
|
|
{
|
|
|
|
static const double shift[] = { 0, -1./512 };
|
|
|
|
static const double
|
|
|
|
A7 = 1.0,
|
|
|
|
A6 = -0.5,
|
|
|
|
A5 = 0.333333333333333314829616256247390992939472198486328125,
|
|
|
|
A4 = -0.25,
|
|
|
|
A3 = 0.2,
|
|
|
|
A2 = -0.1666666666666666574148081281236954964697360992431640625,
|
|
|
|
A1 = 0.1428571428571428769682682968777953647077083587646484375,
|
|
|
|
A0 = -0.125;
|
|
|
|
|
|
|
|
#undef LOGPOLY
|
|
|
|
#define LOGPOLY(x,k) ((x)+=shift[k], xq = (x)*(x),\
|
|
|
|
(((A0*xq + A2)*xq + A4)*xq + A6)*xq + \
|
|
|
|
(((A1*xq + A3)*xq + A5)*xq + A7)*(x))
|
|
|
|
|
|
|
|
int i = 0;
|
|
|
|
DBLINT buf[4];
|
|
|
|
DBLINT *X = (DBLINT *) x;
|
|
|
|
|
2010-10-04 06:45:04 +08:00
|
|
|
#if CV_SSE2
|
|
|
|
if( checkHardwareSupport(CV_CPU_SSE) )
|
|
|
|
{
|
|
|
|
static const __m128d ln2_2 = _mm_set1_pd(ln_2);
|
|
|
|
static const __m128d _1_2 = _mm_set1_pd(1.);
|
|
|
|
static const __m128d shift2 = _mm_set1_pd(-1./512);
|
|
|
|
|
|
|
|
static const __m128i log_and_mask2 = _mm_set_epi32(LOGTAB_MASK2, 0xffffffff, LOGTAB_MASK2, 0xffffffff);
|
|
|
|
static const __m128i log_or_mask2 = _mm_set_epi32(1023 << 20, 0, 1023 << 20, 0);
|
|
|
|
|
|
|
|
static const __m128d mA0 = _mm_set1_pd(A0);
|
|
|
|
static const __m128d mA1 = _mm_set1_pd(A1);
|
|
|
|
static const __m128d mA2 = _mm_set1_pd(A2);
|
|
|
|
static const __m128d mA3 = _mm_set1_pd(A3);
|
|
|
|
static const __m128d mA4 = _mm_set1_pd(A4);
|
|
|
|
static const __m128d mA5 = _mm_set1_pd(A5);
|
|
|
|
static const __m128d mA6 = _mm_set1_pd(A6);
|
|
|
|
static const __m128d mA7 = _mm_set1_pd(A7);
|
|
|
|
|
|
|
|
int CV_DECL_ALIGNED(16) idx[4];
|
|
|
|
|
|
|
|
for( ; i <= n - 4; i += 4 )
|
|
|
|
{
|
|
|
|
__m128i h0 = _mm_loadu_si128((const __m128i*)(x + i));
|
|
|
|
__m128i h1 = _mm_loadu_si128((const __m128i*)(x + i + 2));
|
|
|
|
|
|
|
|
__m128d xd0 = _mm_castsi128_pd(_mm_or_si128(_mm_and_si128(h0, log_and_mask2), log_or_mask2));
|
|
|
|
__m128d xd1 = _mm_castsi128_pd(_mm_or_si128(_mm_and_si128(h1, log_and_mask2), log_or_mask2));
|
|
|
|
|
|
|
|
h0 = _mm_unpackhi_epi32(_mm_unpacklo_epi32(h0, h1), _mm_unpackhi_epi32(h0, h1));
|
|
|
|
|
|
|
|
__m128i yi0 = _mm_sub_epi32(_mm_and_si128(_mm_srli_epi32(h0, 20),
|
|
|
|
_mm_set1_epi32(2047)), _mm_set1_epi32(1023));
|
|
|
|
__m128d yd0 = _mm_mul_pd(_mm_cvtepi32_pd(yi0), ln2_2);
|
|
|
|
__m128d yd1 = _mm_mul_pd(_mm_cvtepi32_pd(_mm_unpackhi_epi64(yi0, yi0)), ln2_2);
|
|
|
|
|
|
|
|
h0 = _mm_and_si128(_mm_srli_epi32(h0, 20 - LOGTAB_SCALE - 1), _mm_set1_epi32(LOGTAB_MASK * 2));
|
|
|
|
_mm_store_si128((__m128i*)idx, h0);
|
|
|
|
h0 = _mm_cmpeq_epi32(h0, _mm_set1_epi32(510));
|
|
|
|
|
|
|
|
__m128d t0, t1, t2, t3, t4;
|
|
|
|
t0 = _mm_load_pd(icvLogTab + idx[0]);
|
|
|
|
t2 = _mm_load_pd(icvLogTab + idx[1]);
|
|
|
|
t1 = _mm_unpackhi_pd(t0, t2);
|
|
|
|
t0 = _mm_unpacklo_pd(t0, t2);
|
|
|
|
t2 = _mm_load_pd(icvLogTab + idx[2]);
|
|
|
|
t4 = _mm_load_pd(icvLogTab + idx[3]);
|
|
|
|
t3 = _mm_unpackhi_pd(t2, t4);
|
|
|
|
t2 = _mm_unpacklo_pd(t2, t4);
|
|
|
|
|
|
|
|
yd0 = _mm_add_pd(yd0, t0);
|
|
|
|
yd1 = _mm_add_pd(yd1, t2);
|
|
|
|
|
|
|
|
xd0 = _mm_mul_pd(_mm_sub_pd(xd0, _1_2), t1);
|
|
|
|
xd1 = _mm_mul_pd(_mm_sub_pd(xd1, _1_2), t3);
|
|
|
|
|
|
|
|
xd0 = _mm_add_pd(xd0, _mm_and_pd(_mm_castsi128_pd(_mm_unpacklo_epi32(h0, h0)), shift2));
|
|
|
|
xd1 = _mm_add_pd(xd1, _mm_and_pd(_mm_castsi128_pd(_mm_unpackhi_epi32(h0, h0)), shift2));
|
|
|
|
|
|
|
|
__m128d zd0 = _mm_mul_pd(xd0, mA0);
|
|
|
|
__m128d zd1 = _mm_mul_pd(xd1, mA0);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA1), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA1), xd1);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA2), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA2), xd1);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA3), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA3), xd1);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA4), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA4), xd1);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA5), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA5), xd1);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA6), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA6), xd1);
|
|
|
|
zd0 = _mm_mul_pd(_mm_add_pd(zd0, mA7), xd0);
|
|
|
|
zd1 = _mm_mul_pd(_mm_add_pd(zd1, mA7), xd1);
|
|
|
|
|
|
|
|
yd0 = _mm_add_pd(yd0, zd0);
|
|
|
|
yd1 = _mm_add_pd(yd1, zd1);
|
|
|
|
|
|
|
|
_mm_storeu_pd(y + i, yd0);
|
|
|
|
_mm_storeu_pd(y + i + 2, yd1);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
#endif
|
2010-05-12 01:44:00 +08:00
|
|
|
for( ; i <= n - 4; i += 4 )
|
|
|
|
{
|
|
|
|
double xq;
|
|
|
|
double x0, x1, x2, x3;
|
|
|
|
double y0, y1, y2, y3;
|
|
|
|
int h0, h1, h2, h3;
|
|
|
|
|
|
|
|
h0 = X[i].i.lo;
|
|
|
|
h1 = X[i + 1].i.lo;
|
|
|
|
buf[0].i.lo = h0;
|
|
|
|
buf[1].i.lo = h1;
|
|
|
|
|
|
|
|
h0 = X[i].i.hi;
|
|
|
|
h1 = X[i + 1].i.hi;
|
|
|
|
buf[0].i.hi = (h0 & LOGTAB_MASK2) | (1023 << 20);
|
|
|
|
buf[1].i.hi = (h1 & LOGTAB_MASK2) | (1023 << 20);
|
|
|
|
|
|
|
|
y0 = (((h0 >> 20) & 0x7ff) - 1023) * ln_2;
|
|
|
|
y1 = (((h1 >> 20) & 0x7ff) - 1023) * ln_2;
|
|
|
|
|
|
|
|
h2 = X[i + 2].i.lo;
|
|
|
|
h3 = X[i + 3].i.lo;
|
|
|
|
buf[2].i.lo = h2;
|
|
|
|
buf[3].i.lo = h3;
|
|
|
|
|
|
|
|
h0 = (h0 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
h1 = (h1 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
|
|
|
|
y0 += icvLogTab[h0];
|
|
|
|
y1 += icvLogTab[h1];
|
|
|
|
|
|
|
|
h2 = X[i + 2].i.hi;
|
|
|
|
h3 = X[i + 3].i.hi;
|
|
|
|
|
|
|
|
x0 = LOGTAB_TRANSLATE( buf[0].d, h0 );
|
|
|
|
x1 = LOGTAB_TRANSLATE( buf[1].d, h1 );
|
|
|
|
|
|
|
|
buf[2].i.hi = (h2 & LOGTAB_MASK2) | (1023 << 20);
|
|
|
|
buf[3].i.hi = (h3 & LOGTAB_MASK2) | (1023 << 20);
|
|
|
|
|
|
|
|
y2 = (((h2 >> 20) & 0x7ff) - 1023) * ln_2;
|
|
|
|
y3 = (((h3 >> 20) & 0x7ff) - 1023) * ln_2;
|
|
|
|
|
|
|
|
h2 = (h2 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
h3 = (h3 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
|
|
|
|
y2 += icvLogTab[h2];
|
|
|
|
y3 += icvLogTab[h3];
|
|
|
|
|
|
|
|
x2 = LOGTAB_TRANSLATE( buf[2].d, h2 );
|
|
|
|
x3 = LOGTAB_TRANSLATE( buf[3].d, h3 );
|
|
|
|
|
|
|
|
y0 += LOGPOLY( x0, h0 == 510 );
|
|
|
|
y1 += LOGPOLY( x1, h1 == 510 );
|
|
|
|
|
|
|
|
y[i] = y0;
|
|
|
|
y[i + 1] = y1;
|
|
|
|
|
|
|
|
y2 += LOGPOLY( x2, h2 == 510 );
|
|
|
|
y3 += LOGPOLY( x3, h3 == 510 );
|
|
|
|
|
|
|
|
y[i + 2] = y2;
|
|
|
|
y[i + 3] = y3;
|
|
|
|
}
|
2010-10-04 06:45:04 +08:00
|
|
|
|
2010-05-12 01:44:00 +08:00
|
|
|
for( ; i < n; i++ )
|
|
|
|
{
|
|
|
|
int h0 = X[i].i.hi;
|
|
|
|
double xq;
|
|
|
|
double x0, y0 = (((h0 >> 20) & 0x7ff) - 1023) * ln_2;
|
|
|
|
|
|
|
|
buf[0].i.hi = (h0 & LOGTAB_MASK2) | (1023 << 20);
|
|
|
|
buf[0].i.lo = X[i].i.lo;
|
|
|
|
h0 = (h0 >> (20 - LOGTAB_SCALE - 1)) & LOGTAB_MASK * 2;
|
|
|
|
|
|
|
|
y0 += icvLogTab[h0];
|
|
|
|
x0 = LOGTAB_TRANSLATE( buf[0].d, h0 );
|
|
|
|
y0 += LOGPOLY( x0, h0 == 510 );
|
|
|
|
y[i] = y0;
|
|
|
|
}
|
|
|
|
|
|
|
|
return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
#else
|
|
|
|
|
|
|
|
#define Log_32f ippsLn_32f_A21
|
|
|
|
#define Log_64f ippsLn_64f_A50
|
|
|
|
|
|
|
|
#endif
|
|
|
|
|
|
|
|
void log( const Mat& src, Mat& dst )
|
|
|
|
{
|
|
|
|
int depth = src.depth();
|
|
|
|
dst.create( src.size(), src.type() );
|
|
|
|
Size size = getContinuousSize( src, dst, src.channels() );
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
for( int y = 0; y < size.height; y++ )
|
|
|
|
Log_32f( src.ptr<float>(y), dst.ptr<float>(y), size.width );
|
|
|
|
else if( depth == CV_64F )
|
|
|
|
for( int y = 0; y < size.height; y++ )
|
|
|
|
Log_64f( src.ptr<double>(y), dst.ptr<double>(y), size.width );
|
|
|
|
else
|
|
|
|
CV_Error( CV_StsUnsupportedFormat, "" );
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/****************************************************************************************\
|
|
|
|
* P O W E R *
|
|
|
|
\****************************************************************************************/
|
|
|
|
|
|
|
|
template<typename T, typename WT>
|
|
|
|
static CvStatus CV_STDCALL
|
|
|
|
IPow( const void* _src, void* _dst, int len, int power )
|
|
|
|
{
|
|
|
|
int i;
|
|
|
|
const T* src = (const T*)_src;
|
|
|
|
T* dst = (T*)_dst;
|
|
|
|
for( i = 0; i < len; i++ )
|
|
|
|
{
|
|
|
|
WT a = 1, b = src[i];
|
|
|
|
int p = power;
|
|
|
|
while( p > 1 )
|
|
|
|
{
|
|
|
|
if( p & 1 )
|
|
|
|
a *= b;
|
|
|
|
b *= b;
|
|
|
|
p >>= 1;
|
|
|
|
}
|
|
|
|
|
|
|
|
a *= b;
|
|
|
|
dst[i] = saturate_cast<T>(a);
|
|
|
|
}
|
|
|
|
return CV_OK;
|
|
|
|
}
|
|
|
|
|
|
|
|
typedef CvStatus (CV_STDCALL * IPowFunc)( const void* src, void* dst, int len, int power );
|
|
|
|
|
|
|
|
void pow( const Mat& _src, double power, Mat& dst )
|
|
|
|
{
|
|
|
|
int ipower = cvRound( power ), i, j;
|
|
|
|
bool is_ipower = 0;
|
|
|
|
int depth = _src.depth();
|
|
|
|
const Mat* src = &_src;
|
|
|
|
|
|
|
|
dst.create( _src.size(), _src.type() );
|
|
|
|
|
|
|
|
if( fabs(ipower - power) < DBL_EPSILON )
|
|
|
|
{
|
|
|
|
if( ipower < 0 )
|
|
|
|
{
|
|
|
|
divide( 1., _src, dst );
|
|
|
|
if( ipower == -1 )
|
|
|
|
return;
|
|
|
|
ipower = -ipower;
|
|
|
|
src = &dst;
|
|
|
|
}
|
|
|
|
|
|
|
|
switch( ipower )
|
|
|
|
{
|
|
|
|
case 0:
|
|
|
|
dst = Scalar::all(1);
|
|
|
|
return;
|
|
|
|
case 1:
|
|
|
|
src->copyTo(dst);
|
|
|
|
return;
|
|
|
|
case 2:
|
|
|
|
multiply(*src, *src, dst);
|
|
|
|
return;
|
|
|
|
default:
|
|
|
|
is_ipower = true;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
CV_Assert( depth == CV_32F || depth == CV_64F );
|
|
|
|
|
|
|
|
Size size = getContinuousSize( *src, dst, src->channels() );
|
|
|
|
|
|
|
|
if( is_ipower )
|
|
|
|
{
|
|
|
|
static IPowFunc tab[] =
|
|
|
|
{
|
|
|
|
IPow<uchar, int>, 0, IPow<ushort, int>, IPow<short, int>, IPow<int, int>,
|
|
|
|
IPow<float, float>, IPow<double, double>, 0
|
|
|
|
};
|
|
|
|
|
|
|
|
IPowFunc func = tab[depth];
|
|
|
|
CV_Assert( func != 0 );
|
|
|
|
for( i = 0; i < size.height; i++ )
|
|
|
|
func( src->data + src->step*i, dst.data + dst.step*i, size.width, ipower );
|
|
|
|
}
|
|
|
|
else if( fabs(fabs(power) - 0.5) < DBL_EPSILON )
|
|
|
|
{
|
|
|
|
MathFunc func = power < 0 ?
|
|
|
|
(depth == CV_32F ? (MathFunc)InvSqrt_32f : (MathFunc)InvSqrt_64f) :
|
|
|
|
(depth == CV_32F ? (MathFunc)Sqrt_32f : (MathFunc)Sqrt_64f);
|
|
|
|
|
|
|
|
for( i = 0; i < size.height; i++ )
|
|
|
|
func( src->data + src->step*i, dst.data + dst.step*i, size.width );
|
|
|
|
}
|
|
|
|
else if( depth == CV_32F )
|
|
|
|
{
|
|
|
|
const float *x = (const float*)src->data;
|
|
|
|
float *y = (float*)dst.data;
|
|
|
|
size_t xstep = src->step/sizeof(x[0]), ystep = dst.step/sizeof(y[0]);
|
|
|
|
float p = (float)power;
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i += MAX_BLOCK_SIZE )
|
|
|
|
{
|
|
|
|
int block_size = std::min(MAX_BLOCK_SIZE, size.width - i);
|
|
|
|
Log_32f(x + i, y + i, block_size);
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
y[i + j] *= p;
|
|
|
|
Exp_32f(y + i, y + i, block_size);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
const double *x = (const double*)src->data;
|
|
|
|
double *y = (double*)dst.data;
|
|
|
|
size_t xstep = src->step/sizeof(x[0]), ystep = dst.step/sizeof(y[0]);
|
|
|
|
|
|
|
|
for( ; size.height--; x += xstep, y += ystep )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i += MAX_BLOCK_SIZE )
|
|
|
|
{
|
|
|
|
int block_size = std::min(MAX_BLOCK_SIZE, size.width - i);
|
|
|
|
Log_64f(x + i, y + i, block_size);
|
|
|
|
for( j = 0; j < block_size; j++ )
|
|
|
|
y[i + j] *= power;
|
|
|
|
Exp_64f(y + i, y + i, block_size);
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
void sqrt(const Mat& a, Mat& b)
|
|
|
|
{
|
|
|
|
pow(a, 0.5, b);
|
|
|
|
}
|
|
|
|
|
|
|
|
/************************** CheckArray for NaN's, Inf's *********************************/
|
|
|
|
|
|
|
|
bool checkRange(const Mat& src, bool quiet, Point* pt,
|
|
|
|
double minVal, double maxVal)
|
|
|
|
{
|
|
|
|
int depth = src.depth();
|
|
|
|
Point badPt(-1, -1);
|
|
|
|
double badValue = 0;
|
|
|
|
|
|
|
|
if( depth < CV_32F )
|
|
|
|
{
|
|
|
|
double m = 0, M = 0, badValue = 0;
|
|
|
|
Point mp, MP, badPt(-1,-1);
|
|
|
|
minMaxLoc(src.reshape(1,0), &m, &M, &mp, &MP);
|
|
|
|
if( M >= maxVal )
|
|
|
|
{
|
|
|
|
badPt = MP;
|
|
|
|
badValue = M;
|
|
|
|
}
|
|
|
|
else if( m < minVal )
|
|
|
|
{
|
|
|
|
badPt = mp;
|
|
|
|
badValue = m;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
int i, loc = 0;
|
|
|
|
Size size = getContinuousSize( src, src.channels() );
|
|
|
|
|
|
|
|
if( depth == CV_32F )
|
|
|
|
{
|
|
|
|
Cv32suf a, b;
|
|
|
|
int ia, ib;
|
|
|
|
const int* isrc = (const int*)src.data;
|
|
|
|
size_t step = src.step/sizeof(isrc[0]);
|
|
|
|
|
|
|
|
a.f = (float)std::max(minVal, (double)-FLT_MAX);
|
|
|
|
b.f = (float)std::min(maxVal, (double)FLT_MAX);
|
|
|
|
|
|
|
|
ia = CV_TOGGLE_FLT(a.i);
|
|
|
|
ib = CV_TOGGLE_FLT(b.i);
|
|
|
|
|
|
|
|
for( ; badPt.x < 0 && size.height--; loc += size.width, isrc += step )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i++ )
|
|
|
|
{
|
|
|
|
int val = isrc[i];
|
|
|
|
val = CV_TOGGLE_FLT(val);
|
|
|
|
|
|
|
|
if( val < ia || val >= ib )
|
|
|
|
{
|
|
|
|
badPt = Point((loc + i) % src.cols, (loc + i) / src.cols);
|
|
|
|
badValue = ((const float*)isrc)[i];
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
Cv64suf a, b;
|
|
|
|
int64 ia, ib;
|
|
|
|
const int64* isrc = (const int64*)src.data;
|
|
|
|
size_t step = src.step/sizeof(isrc[0]);
|
|
|
|
|
|
|
|
a.f = minVal;
|
|
|
|
b.f = maxVal;
|
|
|
|
|
|
|
|
ia = CV_TOGGLE_DBL(a.i);
|
|
|
|
ib = CV_TOGGLE_DBL(b.i);
|
|
|
|
|
|
|
|
for( ; badPt.x < 0 && size.height--; loc += size.width, isrc += step )
|
|
|
|
{
|
|
|
|
for( i = 0; i < size.width; i++ )
|
|
|
|
{
|
|
|
|
int64 val = isrc[i];
|
|
|
|
val = CV_TOGGLE_DBL(val);
|
|
|
|
|
|
|
|
if( val < ia || val >= ib )
|
|
|
|
{
|
|
|
|
badPt = Point((loc + i) % src.cols, (loc + i) / src.cols);
|
|
|
|
badValue = ((const double*)isrc)[i];
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
if( badPt.x >= 0 )
|
|
|
|
{
|
|
|
|
if( pt )
|
|
|
|
*pt = badPt;
|
|
|
|
if( !quiet )
|
|
|
|
CV_Error_( CV_StsOutOfRange,
|
|
|
|
("the value at (%d, %d)=%g is out of range", badPt.x, badPt.y, badValue));
|
|
|
|
}
|
|
|
|
return badPt.x < 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
CV_IMPL float cvCbrt(float value) { return cv::cubeRoot(value); }
|
|
|
|
CV_IMPL float cvFastArctan(float y, float x) { return cv::fastAtan2(y, x); }
|
|
|
|
|
|
|
|
CV_IMPL void
|
|
|
|
cvCartToPolar( const CvArr* xarr, const CvArr* yarr,
|
|
|
|
CvArr* magarr, CvArr* anglearr,
|
|
|
|
int angle_in_degrees )
|
|
|
|
{
|
|
|
|
cv::Mat X = cv::cvarrToMat(xarr), Y = cv::cvarrToMat(yarr), Mag, Angle;
|
|
|
|
if( magarr )
|
|
|
|
{
|
|
|
|
Mag = cv::cvarrToMat(magarr);
|
|
|
|
CV_Assert( Mag.size() == X.size() && Mag.type() == X.type() );
|
|
|
|
}
|
|
|
|
if( anglearr )
|
|
|
|
{
|
|
|
|
Angle = cv::cvarrToMat(anglearr);
|
|
|
|
CV_Assert( Angle.size() == X.size() && Angle.type() == X.type() );
|
|
|
|
}
|
|
|
|
if( magarr )
|
|
|
|
{
|
|
|
|
if( anglearr )
|
|
|
|
cv::cartToPolar( X, Y, Mag, Angle, angle_in_degrees != 0 );
|
|
|
|
else
|
|
|
|
cv::magnitude( X, Y, Mag );
|
|
|
|
}
|
|
|
|
else
|
|
|
|
cv::phase( X, Y, Angle, angle_in_degrees != 0 );
|
|
|
|
}
|
|
|
|
|
|
|
|
CV_IMPL void
|
|
|
|
cvPolarToCart( const CvArr* magarr, const CvArr* anglearr,
|
|
|
|
CvArr* xarr, CvArr* yarr, int angle_in_degrees )
|
|
|
|
{
|
|
|
|
cv::Mat X, Y, Angle = cv::cvarrToMat(anglearr), Mag;
|
|
|
|
if( magarr )
|
|
|
|
{
|
|
|
|
Mag = cv::cvarrToMat(magarr);
|
|
|
|
CV_Assert( Mag.size() == Angle.size() && Mag.type() == Angle.type() );
|
|
|
|
}
|
|
|
|
if( xarr )
|
|
|
|
{
|
|
|
|
X = cv::cvarrToMat(xarr);
|
|
|
|
CV_Assert( X.size() == Angle.size() && X.type() == Angle.type() );
|
|
|
|
}
|
|
|
|
if( yarr )
|
|
|
|
{
|
|
|
|
Y = cv::cvarrToMat(yarr);
|
|
|
|
CV_Assert( Y.size() == Angle.size() && Y.type() == Angle.type() );
|
|
|
|
}
|
|
|
|
|
|
|
|
cv::polarToCart( Mag, Angle, X, Y, angle_in_degrees != 0 );
|
|
|
|
}
|
|
|
|
|
|
|
|
CV_IMPL void cvExp( const CvArr* srcarr, CvArr* dstarr )
|
|
|
|
{
|
|
|
|
cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
|
|
|
|
CV_Assert( src.type() == dst.type() && src.size() == dst.size() );
|
|
|
|
cv::exp( src, dst );
|
|
|
|
}
|
|
|
|
|
|
|
|
CV_IMPL void cvLog( const CvArr* srcarr, CvArr* dstarr )
|
|
|
|
{
|
|
|
|
cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
|
|
|
|
CV_Assert( src.type() == dst.type() && src.size() == dst.size() );
|
|
|
|
cv::log( src, dst );
|
|
|
|
}
|
|
|
|
|
|
|
|
CV_IMPL void cvPow( const CvArr* srcarr, CvArr* dstarr, double power )
|
|
|
|
{
|
|
|
|
cv::Mat src = cv::cvarrToMat(srcarr), dst = cv::cvarrToMat(dstarr);
|
|
|
|
CV_Assert( src.type() == dst.type() && src.size() == dst.size() );
|
|
|
|
cv::pow( src, power, dst );
|
|
|
|
}
|
|
|
|
|
|
|
|
CV_IMPL int cvCheckArr( const CvArr* arr, int flags,
|
|
|
|
double minVal, double maxVal )
|
|
|
|
{
|
|
|
|
if( (flags & CV_CHECK_RANGE) == 0 )
|
|
|
|
minVal = -DBL_MAX, maxVal = DBL_MAX;
|
|
|
|
return cv::checkRange(cv::cvarrToMat(arr), (flags & CV_CHECK_QUIET) != 0, 0, minVal, maxVal );
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/*
|
|
|
|
Finds real roots of cubic, quadratic or linear equation.
|
|
|
|
The original code has been taken from Ken Turkowski web page
|
|
|
|
(http://www.worldserver.com/turk/opensource/) and adopted for OpenCV.
|
|
|
|
Here is the copyright notice.
|
|
|
|
|
|
|
|
-----------------------------------------------------------------------
|
|
|
|
Copyright (C) 1978-1999 Ken Turkowski. <turk@computer.org>
|
|
|
|
|
|
|
|
All rights reserved.
|
|
|
|
|
|
|
|
Warranty Information
|
|
|
|
Even though I have reviewed this software, I make no warranty
|
|
|
|
or representation, either express or implied, with respect to this
|
|
|
|
software, its quality, accuracy, merchantability, or fitness for a
|
|
|
|
particular purpose. As a result, this software is provided "as is,"
|
|
|
|
and you, its user, are assuming the entire risk as to its quality
|
|
|
|
and accuracy.
|
|
|
|
|
|
|
|
This code may be used and freely distributed as long as it includes
|
|
|
|
this copyright notice and the above warranty information.
|
|
|
|
-----------------------------------------------------------------------
|
|
|
|
*/
|
|
|
|
CV_IMPL int
|
|
|
|
cvSolveCubic( const CvMat* coeffs, CvMat* roots )
|
|
|
|
{
|
|
|
|
int n = 0;
|
|
|
|
|
|
|
|
double a0 = 1., a1, a2, a3;
|
|
|
|
double x0 = 0., x1 = 0., x2 = 0.;
|
|
|
|
size_t step = 1;
|
|
|
|
int coeff_count;
|
|
|
|
|
|
|
|
if( !CV_IS_MAT(coeffs) )
|
|
|
|
CV_Error( !coeffs ? CV_StsNullPtr : CV_StsBadArg, "Input parameter is not a valid matrix" );
|
|
|
|
|
|
|
|
if( !CV_IS_MAT(roots) )
|
|
|
|
CV_Error( !roots ? CV_StsNullPtr : CV_StsBadArg, "Output parameter is not a valid matrix" );
|
|
|
|
|
|
|
|
if( (CV_MAT_TYPE(coeffs->type) != CV_32FC1 && CV_MAT_TYPE(coeffs->type) != CV_64FC1) ||
|
|
|
|
(CV_MAT_TYPE(roots->type) != CV_32FC1 && CV_MAT_TYPE(roots->type) != CV_64FC1) )
|
|
|
|
CV_Error( CV_StsUnsupportedFormat,
|
|
|
|
"Both matrices should be floating-point (single or double precision)" );
|
|
|
|
|
|
|
|
coeff_count = coeffs->rows + coeffs->cols - 1;
|
|
|
|
|
|
|
|
if( (coeffs->rows != 1 && coeffs->cols != 1) || (coeff_count != 3 && coeff_count != 4) )
|
|
|
|
CV_Error( CV_StsBadSize,
|
|
|
|
"The matrix of coefficients must be 1-dimensional vector of 3 or 4 elements" );
|
|
|
|
|
|
|
|
if( (roots->rows != 1 && roots->cols != 1) ||
|
|
|
|
roots->rows + roots->cols - 1 != 3 )
|
|
|
|
CV_Error( CV_StsBadSize,
|
|
|
|
"The matrix of roots must be 1-dimensional vector of 3 elements" );
|
|
|
|
|
|
|
|
if( CV_MAT_TYPE(coeffs->type) == CV_32FC1 )
|
|
|
|
{
|
|
|
|
const float* c = coeffs->data.fl;
|
|
|
|
if( coeffs->rows > 1 )
|
|
|
|
step = coeffs->step/sizeof(c[0]);
|
|
|
|
if( coeff_count == 4 )
|
|
|
|
a0 = c[0], c += step;
|
|
|
|
a1 = c[0];
|
|
|
|
a2 = c[step];
|
|
|
|
a3 = c[step*2];
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
const double* c = coeffs->data.db;
|
|
|
|
if( coeffs->rows > 1 )
|
|
|
|
step = coeffs->step/sizeof(c[0]);
|
|
|
|
if( coeff_count == 4 )
|
|
|
|
a0 = c[0], c += step;
|
|
|
|
a1 = c[0];
|
|
|
|
a2 = c[step];
|
|
|
|
a3 = c[step*2];
|
|
|
|
}
|
|
|
|
|
|
|
|
if( a0 == 0 )
|
|
|
|
{
|
|
|
|
if( a1 == 0 )
|
|
|
|
{
|
|
|
|
if( a2 == 0 )
|
|
|
|
n = a3 == 0 ? -1 : 0;
|
|
|
|
else
|
|
|
|
{
|
|
|
|
// linear equation
|
|
|
|
x0 = a3/a2;
|
|
|
|
n = 1;
|
|
|
|
}
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|
|
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}
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|
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else
|
|
|
|
{
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|
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|
// quadratic equation
|
|
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|
double d = a2*a2 - 4*a1*a3;
|
|
|
|
if( d >= 0 )
|
|
|
|
{
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|
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|
d = sqrt(d);
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|
double q = (-a2 + (a2 < 0 ? -d : d)) * 0.5;
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|
|
|
x0 = q / a1;
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|
x1 = a3 / q;
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|
|
|
n = d > 0 ? 2 : 1;
|
|
|
|
}
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|
|
|
}
|
|
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|
}
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|
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|
else
|
|
|
|
{
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|
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|
a0 = 1./a0;
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|
|
a1 *= a0;
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|
|
a2 *= a0;
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|
a3 *= a0;
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|
|
|
|
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|
double Q = (a1 * a1 - 3 * a2) * (1./9);
|
|
|
|
double R = (2 * a1 * a1 * a1 - 9 * a1 * a2 + 27 * a3) * (1./54);
|
|
|
|
double Qcubed = Q * Q * Q;
|
|
|
|
double d = Qcubed - R * R;
|
|
|
|
|
|
|
|
if( d >= 0 )
|
|
|
|
{
|
|
|
|
double theta = acos(R / sqrt(Qcubed));
|
|
|
|
double sqrtQ = sqrt(Q);
|
|
|
|
double t0 = -2 * sqrtQ;
|
|
|
|
double t1 = theta * (1./3);
|
|
|
|
double t2 = a1 * (1./3);
|
|
|
|
x0 = t0 * cos(t1) - t2;
|
|
|
|
x1 = t0 * cos(t1 + (2.*CV_PI/3)) - t2;
|
|
|
|
x2 = t0 * cos(t1 + (4.*CV_PI/3)) - t2;
|
|
|
|
n = 3;
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
double e;
|
|
|
|
d = sqrt(-d);
|
|
|
|
e = pow(d + fabs(R), 0.333333333333);
|
|
|
|
if( R > 0 )
|
|
|
|
e = -e;
|
|
|
|
x0 = (e + Q / e) - a1 * (1./3);
|
|
|
|
n = 1;
|
|
|
|
}
|
|
|
|
}
|
|
|
|
|
|
|
|
step = 1;
|
|
|
|
|
|
|
|
if( CV_MAT_TYPE(roots->type) == CV_32FC1 )
|
|
|
|
{
|
|
|
|
float* r = roots->data.fl;
|
|
|
|
if( roots->rows > 1 )
|
|
|
|
step = roots->step/sizeof(r[0]);
|
|
|
|
r[0] = (float)x0;
|
|
|
|
r[step] = (float)x1;
|
|
|
|
r[step*2] = (float)x2;
|
|
|
|
}
|
|
|
|
else
|
|
|
|
{
|
|
|
|
double* r = roots->data.db;
|
|
|
|
if( roots->rows > 1 )
|
|
|
|
step = roots->step/sizeof(r[0]);
|
|
|
|
r[0] = x0;
|
|
|
|
r[step] = x1;
|
|
|
|
r[step*2] = x2;
|
|
|
|
}
|
|
|
|
|
|
|
|
return n;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
int cv::solveCubic( const Mat& coeffs, Mat& roots )
|
|
|
|
{
|
|
|
|
const int n = 3;
|
|
|
|
if( ((roots.rows != 1 || roots.cols != n) &&
|
|
|
|
(roots.rows != n || roots.cols != 1)) ||
|
|
|
|
(roots.type() != CV_32F && roots.type() != CV_64F) )
|
|
|
|
roots.create(n, 1, CV_64F);
|
|
|
|
|
|
|
|
CvMat _coeffs = coeffs, _roots = roots;
|
|
|
|
int nroots = cvSolveCubic( &_coeffs, &_roots);
|
|
|
|
if( nroots == 0 )
|
|
|
|
roots = Mat();
|
|
|
|
else if( roots.rows > 1 )
|
|
|
|
roots = roots.rowRange(0, nroots);
|
|
|
|
else
|
|
|
|
roots = roots.colRange(0, nroots);
|
|
|
|
return nroots;
|
|
|
|
}
|
|
|
|
|
|
|
|
/* finds complex roots of a polynomial using Durand-Kerner method:
|
|
|
|
http://en.wikipedia.org/wiki/Durand%E2%80%93Kerner_method */
|
|
|
|
double cv::solvePoly( const Mat& coeffs0, Mat& roots0, int maxIters )
|
|
|
|
{
|
|
|
|
typedef Complex<double> C;
|
|
|
|
|
|
|
|
double maxDiff = 0;
|
|
|
|
int iter, i, j, n;
|
|
|
|
|
|
|
|
CV_Assert( (coeffs0.cols == 1 || coeffs0.rows == 1) &&
|
|
|
|
(coeffs0.depth() == CV_32F || coeffs0.depth() == CV_64F) &&
|
|
|
|
coeffs0.channels() <= 2 );
|
|
|
|
n = coeffs0.cols + coeffs0.rows - 2;
|
|
|
|
|
|
|
|
if( ((roots0.rows != 1 || roots0.cols != n) &&
|
|
|
|
(roots0.rows != n || roots0.cols != 1)) ||
|
|
|
|
(roots0.type() != CV_32FC2 && roots0.type() != CV_64FC2) )
|
|
|
|
roots0.create( n, 1, CV_64FC2 );
|
|
|
|
|
|
|
|
AutoBuffer<C> buf(n*2+2);
|
|
|
|
C *coeffs = buf, *roots = coeffs + n + 1;
|
|
|
|
Mat coeffs1(coeffs0.size(), CV_MAKETYPE(CV_64F, coeffs0.channels()), coeffs0.channels() == 2 ? coeffs : roots);
|
|
|
|
coeffs0.convertTo(coeffs1, coeffs1.type());
|
|
|
|
if( coeffs0.channels() == 1 )
|
|
|
|
{
|
|
|
|
const double* rcoeffs = (const double*)roots;
|
|
|
|
for( i = 0; i <= n; i++ )
|
|
|
|
coeffs[i] = C(rcoeffs[i], 0);
|
|
|
|
}
|
|
|
|
|
|
|
|
C p(1, 0), r(1, 1);
|
|
|
|
|
|
|
|
for( i = 0; i < n; i++ )
|
|
|
|
{
|
|
|
|
roots[i] = p;
|
|
|
|
p = p * r;
|
|
|
|
}
|
|
|
|
|
|
|
|
maxIters = maxIters <= 0 ? 1000 : maxIters;
|
|
|
|
for( iter = 0; iter < maxIters; iter++ )
|
|
|
|
{
|
|
|
|
maxDiff = 0;
|
|
|
|
for( i = 0; i < n; i++ )
|
|
|
|
{
|
|
|
|
p = roots[i];
|
|
|
|
C num = coeffs[n], denom = 1;
|
|
|
|
for( j = 0; j < n; j++ )
|
|
|
|
{
|
|
|
|
num = num*p + coeffs[n-j-1];
|
|
|
|
if( j != i ) denom = denom * (p - roots[j]);
|
|
|
|
}
|
|
|
|
num /= denom;
|
|
|
|
roots[i] = p - num;
|
|
|
|
maxDiff = max(maxDiff, abs(num));
|
|
|
|
}
|
|
|
|
if( maxDiff <= 0 )
|
|
|
|
break;
|
|
|
|
}
|
|
|
|
|
|
|
|
if( coeffs0.channels() == 1 )
|
|
|
|
{
|
|
|
|
const double verySmallEps = 1e-100;
|
|
|
|
for( i = 0; i < n; i++ )
|
|
|
|
if( fabs(roots[i].im) < verySmallEps )
|
|
|
|
roots[i].im = 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
Mat(roots0.size(), CV_64FC2, roots).convertTo(roots0, roots0.type());
|
|
|
|
return maxDiff;
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
void cvSolvePoly(const CvMat* a, CvMat *r, int maxiter, int)
|
|
|
|
{
|
|
|
|
cv::Mat _a = cv::cvarrToMat(a), _r = cv::cvarrToMat(r), _r0 = r;
|
|
|
|
cv::solvePoly(_a, _r, maxiter);
|
|
|
|
CV_Assert( _r.data == _r0.data ); // check that the array of roots was not reallocated
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
|
|
/* End of file. */
|