/*M/////////////////////////////////////////////////////////////////////////////////////// // // IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING. // // By downloading, copying, installing or using the software you agree to this license. // If you do not agree to this license, do not download, install, // copy or use the software. // // // License Agreement // For Open Source Computer Vision Library // // Copyright (C) 2000-2008, Intel Corporation, all rights reserved. // Copyright (C) 2009, Willow Garage Inc., all rights reserved. // Third party copyrights are property of their respective owners. // // Redistribution and use in source and binary forms, with or without modification, // are permitted provided that the following conditions are met: // // * Redistribution's of source code must retain the above copyright notice, // this list of conditions and the following disclaimer. // // * Redistribution's in binary form must reproduce the above copyright notice, // this list of conditions and the following disclaimer in the documentation // and/or other materials provided with the distribution. // // * The name of the copyright holders may not be used to endorse or promote products // derived from this software without specific prior written permission. // // This software is provided by the copyright holders and contributors "as is" and // any express or implied warranties, including, but not limited to, the implied // warranties of merchantability and fitness for a particular purpose are disclaimed. // In no event shall the Intel Corporation or contributors be liable for any direct, // indirect, incidental, special, exemplary, or consequential damages // (including, but not limited to, procurement of substitute goods or services; // loss of use, data, or profits; or business interruption) however caused // and on any theory of liability, whether in contract, strict liability, // or tort (including negligence or otherwise) arising in any way out of // the use of this software, even if advised of the possibility of such damage. // //M*/ #include "precomp.hpp" namespace cv { static const int MAX_BLOCK_SIZE = 1024; typedef CvStatus (CV_STDCALL * MathFunc)(const void* src, void* dst, int len); #define ICV_MATH_BLOCK_SIZE 256 #define _CV_SQRT_MAGIC 0xbe6f0000 #define _CV_SQRT_MAGIC_DBL CV_BIG_UINT(0xbfcd460000000000) #define _CV_ATAN_CF0 (-15.8131890796f) #define _CV_ATAN_CF1 (61.0941945596f) #define _CV_ATAN_CF2 0.f /*(-0.140500406322f)*/ static const float icvAtanTab[8] = { 0.f + _CV_ATAN_CF2, 90.f - _CV_ATAN_CF2, 180.f - _CV_ATAN_CF2, 90.f + _CV_ATAN_CF2, 360.f - _CV_ATAN_CF2, 270.f + _CV_ATAN_CF2, 180.f + _CV_ATAN_CF2, 270.f - _CV_ATAN_CF2 }; static const int icvAtanSign[8] = { 0, 0x80000000, 0x80000000, 0, 0x80000000, 0, 0, 0x80000000 }; float fastAtan2( float y, float x ) { double a, x2 = (double)x*x, y2 = (double)y*y; if( y2 <= x2 ) { a = (180./CV_PI)*x*y/(x2 + 0.28*y2 + DBL_EPSILON); return (float)(x < 0 ? a + 180 : y >= 0 ? a : 360+a); } a = (180./CV_PI)*x*y/(y2 + 0.28*x2 + DBL_EPSILON); return (float)(y >= 0 ? 90 - a : 270 - a); } static CvStatus CV_STDCALL FastAtan2_32f(const float *Y, const float *X, float *angle, int len, bool angleInDegrees=true ) { if( !Y || !X || !angle || len < 0 ) return CV_BADFACTOR_ERR; int i = 0; float scale = angleInDegrees ? (float)(180/CV_PI) : 1.f; #if CV_SSE2 if( checkHardwareSupport(CV_CPU_SSE) ) { Cv32suf iabsmask; iabsmask.i = 0x7fffffff; __m128 eps = _mm_set1_ps((float)DBL_EPSILON), absmask = _mm_set1_ps(iabsmask.f); __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)); __m128 zero = _mm_setzero_ps(), _0_28 = _mm_set1_ps(0.28f), scale4 = _mm_set1_ps(scale); for( ; i <= len - 4; i += 4 ) { __m128 x4 = _mm_loadu_ps(X + i), y4 = _mm_loadu_ps(Y + i); __m128 xq4 = _mm_mul_ps(x4, x4), yq4 = _mm_mul_ps(y4, y4); __m128 xly = _mm_cmplt_ps(xq4, yq4); __m128 z4 = _mm_div_ps(_mm_mul_ps(x4, y4), _mm_add_ps(_mm_add_ps(_mm_max_ps(xq4, yq4), _mm_mul_ps(_mm_min_ps(xq4, yq4), _0_28)), eps)); // a4 <- x < y ? 90 : 0; __m128 a4 = _mm_and_ps(xly, _90); // a4 <- (y < 0 ? 360 - a4 : a4) == ((x < y ? y < 0 ? 270 : 90) : (y < 0 ? 360 : 0)) __m128 mask = _mm_cmplt_ps(y4, zero); a4 = _mm_or_ps(_mm_and_ps(_mm_sub_ps(_360, a4), mask), _mm_andnot_ps(mask, a4)); // a4 <- (x < 0 && !(x < y) ? 180 : a4) mask = _mm_andnot_ps(xly, _mm_cmplt_ps(x4, zero)); a4 = _mm_or_ps(_mm_and_ps(_180, mask), _mm_andnot_ps(mask, a4)); // a4 <- (x < y ? a4 - z4 : a4 + z4) a4 = _mm_mul_ps(_mm_add_ps(_mm_xor_ps(z4, _mm_andnot_ps(absmask, xly)), a4), scale4); _mm_storeu_ps(angle + i, a4); } } #endif for( ; i < len; i++ ) { float x = X[i], y = Y[i]; float a, x2 = x*x, y2 = y*y; if( y2 <= x2 ) a = x*y/(x2 + 0.28f*y2 + (float)DBL_EPSILON) + (float)(x < 0 ? CV_PI : y >= 0 ? 0 : CV_PI*2); else a = (float)(y >= 0 ? CV_PI*0.5 : CV_PI*1.5) - x*y/(y2 + 0.28f*x2 + (float)DBL_EPSILON); angle[i] = a*scale; } return CV_OK; } /* ************************************************************************** *\ Fast cube root by Ken Turkowski (http://www.worldserver.com/turk/computergraphics/papers.html) \* ************************************************************************** */ float cubeRoot( float value ) { float fr; Cv32suf v, m; int ix, s; int ex, shx; v.f = value; ix = v.i & 0x7fffffff; s = v.i & 0x80000000; ex = (ix >> 23) - 127; shx = ex % 3; shx -= shx >= 0 ? 3 : 0; ex = (ex - shx) / 3; /* exponent of cube root */ v.i = (ix & ((1<<23)-1)) | ((shx + 127)<<23); fr = v.f; /* 0.125 <= fr < 1.0 */ /* Use quartic rational polynomial with error < 2^(-24) */ fr = (float)(((((45.2548339756803022511987494 * fr + 192.2798368355061050458134625) * fr + 119.1654824285581628956914143) * fr + 13.43250139086239872172837314) * fr + 0.1636161226585754240958355063)/ ((((14.80884093219134573786480845 * fr + 151.9714051044435648658557668) * fr + 168.5254414101568283957668343) * fr + 33.9905941350215598754191872) * fr + 1.0)); /* fr *= 2^ex * sign */ m.f = value; v.f = fr; v.i = (v.i + (ex << 23) + s) & (m.i*2 != 0 ? -1 : 0); return v.f; } static CvStatus CV_STDCALL Magnitude_32f(const float* x, const float* y, float* mag, int len) { int i = 0; #if CV_SSE if( checkHardwareSupport(CV_CPU_SSE) ) { for( ; i <= len - 8; i += 8 ) { __m128 x0 = _mm_loadu_ps(x + i), x1 = _mm_loadu_ps(x + i + 4); __m128 y0 = _mm_loadu_ps(y + i), y1 = _mm_loadu_ps(y + i + 4); x0 = _mm_add_ps(_mm_mul_ps(x0, x0), _mm_mul_ps(y0, y0)); x1 = _mm_add_ps(_mm_mul_ps(x1, x1), _mm_mul_ps(y1, y1)); x0 = _mm_sqrt_ps(x0); x1 = _mm_sqrt_ps(x1); _mm_storeu_ps(mag + i, x0); _mm_storeu_ps(mag + i + 4, x1); } } #endif for( ; i < len; i++ ) { float x0 = x[i], y0 = y[i]; mag[i] = std::sqrt(x0*x0 + y0*y0); } return CV_OK; } static CvStatus CV_STDCALL Magnitude_64f(const double* x, const double* y, double* mag, int len) { int i = 0; #if CV_SSE2 if( checkHardwareSupport(CV_CPU_SSE2) ) { for( ; i <= len - 4; i += 4 ) { __m128d x0 = _mm_loadu_pd(x + i), x1 = _mm_loadu_pd(x + i + 2); __m128d y0 = _mm_loadu_pd(y + i), y1 = _mm_loadu_pd(y + i + 2); x0 = _mm_add_pd(_mm_mul_pd(x0, x0), _mm_mul_pd(y0, y0)); x1 = _mm_add_pd(_mm_mul_pd(x1, x1), _mm_mul_pd(y1, y1)); x0 = _mm_sqrt_pd(x0); x1 = _mm_sqrt_pd(x1); _mm_storeu_pd(mag + i, x0); _mm_storeu_pd(mag + i + 2, x1); } } #endif for( ; i < len; i++ ) { double x0 = x[i], y0 = y[i]; mag[i] = std::sqrt(x0*x0 + y0*y0); } return CV_OK; } static CvStatus CV_STDCALL InvSqrt_32f(const float* src, float* dst, int len) { int i = 0; #if CV_SSE if( checkHardwareSupport(CV_CPU_SSE) ) { __m128 _0_5 = _mm_set1_ps(0.5f), _1_5 = _mm_set1_ps(1.5f); if( (((size_t)src|(size_t)dst) & 15) == 0 ) for( ; i <= len - 8; i += 8 ) { __m128 t0 = _mm_load_ps(src + i), t1 = _mm_load_ps(src + i + 4); __m128 h0 = _mm_mul_ps(t0, _0_5), h1 = _mm_mul_ps(t1, _0_5); t0 = _mm_rsqrt_ps(t0); t1 = _mm_rsqrt_ps(t1); t0 = _mm_mul_ps(t0, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t0,t0),h0))); t1 = _mm_mul_ps(t1, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t1,t1),h1))); _mm_store_ps(dst + i, t0); _mm_store_ps(dst + i + 4, t1); } else for( ; i <= len - 8; i += 8 ) { __m128 t0 = _mm_loadu_ps(src + i), t1 = _mm_loadu_ps(src + i + 4); __m128 h0 = _mm_mul_ps(t0, _0_5), h1 = _mm_mul_ps(t1, _0_5); t0 = _mm_rsqrt_ps(t0); t1 = _mm_rsqrt_ps(t1); t0 = _mm_mul_ps(t0, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t0,t0),h0))); t1 = _mm_mul_ps(t1, _mm_sub_ps(_1_5, _mm_mul_ps(_mm_mul_ps(t1,t1),h1))); _mm_storeu_ps(dst + i, t0); _mm_storeu_ps(dst + i + 4, t1); } } #endif for( ; i < len; i++ ) dst[i] = 1/std::sqrt(src[i]); return CV_OK; } static CvStatus CV_STDCALL InvSqrt_64f(const double* src, double* dst, int len) { for( int i = 0; i < len; i++ ) dst[i] = 1/std::sqrt(src[i]); return CV_OK; } static CvStatus CV_STDCALL Sqrt_32f(const float* src, float* dst, int len) { int i = 0; #if CV_SSE if( checkHardwareSupport(CV_CPU_SSE) ) { if( (((size_t)src|(size_t)dst) & 15) == 0 ) for( ; i <= len - 8; i += 8 ) { __m128 t0 = _mm_load_ps(src + i), t1 = _mm_load_ps(src + i + 4); t0 = _mm_sqrt_ps(t0); t1 = _mm_sqrt_ps(t1); _mm_store_ps(dst + i, t0); _mm_store_ps(dst + i + 4, t1); } else for( ; i <= len - 8; i += 8 ) { __m128 t0 = _mm_loadu_ps(src + i), t1 = _mm_loadu_ps(src + i + 4); t0 = _mm_sqrt_ps(t0); t1 = _mm_sqrt_ps(t1); _mm_storeu_ps(dst + i, t0); _mm_storeu_ps(dst + i + 4, t1); } } #endif for( ; i < len; i++ ) dst[i] = std::sqrt(src[i]); 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; } } } } /****************************************************************************************\ * E X P * \****************************************************************************************/ typedef union { struct { #if ( defined( WORDS_BIGENDIAN ) && !defined( OPENCV_UNIVERSAL_BUILD ) ) || defined( __BIG_ENDIAN__ ) int hi; int lo; #else int lo; int hi; #endif } i; double d; } DBLINT; #ifndef HAVE_IPP #define EXPTAB_SCALE 6 #define EXPTAB_MASK ((1 << EXPTAB_SCALE) - 1) #define EXPPOLY_32F_A0 .9670371139572337719125840413672004409288e-2 static const double expTab[] = { 1.0 * EXPPOLY_32F_A0, 1.0108892860517004600204097905619 * EXPPOLY_32F_A0, 1.0218971486541166782344801347833 * EXPPOLY_32F_A0, 1.0330248790212284225001082839705 * EXPPOLY_32F_A0, 1.0442737824274138403219664787399 * EXPPOLY_32F_A0, 1.0556451783605571588083413251529 * EXPPOLY_32F_A0, 1.0671404006768236181695211209928 * EXPPOLY_32F_A0, 1.0787607977571197937406800374385 * EXPPOLY_32F_A0, 1.0905077326652576592070106557607 * EXPPOLY_32F_A0, 1.1023825833078409435564142094256 * EXPPOLY_32F_A0, 1.1143867425958925363088129569196 * EXPPOLY_32F_A0, 1.126521618608241899794798643787 * EXPPOLY_32F_A0, 1.1387886347566916537038302838415 * EXPPOLY_32F_A0, 1.151189229952982705817759635202 * EXPPOLY_32F_A0, 1.1637248587775775138135735990922 * EXPPOLY_32F_A0, 1.1763969916502812762846457284838 * EXPPOLY_32F_A0, 1.1892071150027210667174999705605 * EXPPOLY_32F_A0, 1.2021567314527031420963969574978 * EXPPOLY_32F_A0, 1.2152473599804688781165202513388 * EXPPOLY_32F_A0, 1.2284805361068700056940089577928 * EXPPOLY_32F_A0, 1.2418578120734840485936774687266 * EXPPOLY_32F_A0, 1.2553807570246910895793906574423 * EXPPOLY_32F_A0, 1.2690509571917332225544190810323 * EXPPOLY_32F_A0, 1.2828700160787782807266697810215 * EXPPOLY_32F_A0, 1.2968395546510096659337541177925 * EXPPOLY_32F_A0, 1.3109612115247643419229917863308 * EXPPOLY_32F_A0, 1.3252366431597412946295370954987 * EXPPOLY_32F_A0, 1.3396675240533030053600306697244 * EXPPOLY_32F_A0, 1.3542555469368927282980147401407 * EXPPOLY_32F_A0, 1.3690024229745906119296011329822 * EXPPOLY_32F_A0, 1.3839098819638319548726595272652 * EXPPOLY_32F_A0, 1.3989796725383111402095281367152 * EXPPOLY_32F_A0, 1.4142135623730950488016887242097 * EXPPOLY_32F_A0, 1.4296133383919700112350657782751 * EXPPOLY_32F_A0, 1.4451808069770466200370062414717 * EXPPOLY_32F_A0, 1.4609177941806469886513028903106 * EXPPOLY_32F_A0, 1.476826145939499311386907480374 * EXPPOLY_32F_A0, 1.4929077282912648492006435314867 * EXPPOLY_32F_A0, 1.5091644275934227397660195510332 * EXPPOLY_32F_A0, 1.5255981507445383068512536895169 * EXPPOLY_32F_A0, 1.5422108254079408236122918620907 * EXPPOLY_32F_A0, 1.5590044002378369670337280894749 * EXPPOLY_32F_A0, 1.5759808451078864864552701601819 * EXPPOLY_32F_A0, 1.5931421513422668979372486431191 * EXPPOLY_32F_A0, 1.6104903319492543081795206673574 * EXPPOLY_32F_A0, 1.628027421857347766848218522014 * EXPPOLY_32F_A0, 1.6457554781539648445187567247258 * EXPPOLY_32F_A0, 1.6636765803267364350463364569764 * EXPPOLY_32F_A0, 1.6817928305074290860622509524664 * EXPPOLY_32F_A0, 1.7001063537185234695013625734975 * EXPPOLY_32F_A0, 1.7186192981224779156293443764563 * EXPPOLY_32F_A0, 1.7373338352737062489942020818722 * EXPPOLY_32F_A0, 1.7562521603732994831121606193753 * EXPPOLY_32F_A0, 1.7753764925265212525505592001993 * EXPPOLY_32F_A0, 1.7947090750031071864277032421278 * EXPPOLY_32F_A0, 1.8142521755003987562498346003623 * EXPPOLY_32F_A0, 1.8340080864093424634870831895883 * EXPPOLY_32F_A0, 1.8539791250833855683924530703377 * EXPPOLY_32F_A0, 1.8741676341102999013299989499544 * EXPPOLY_32F_A0, 1.8945759815869656413402186534269 * EXPPOLY_32F_A0, 1.9152065613971472938726112702958 * EXPPOLY_32F_A0, 1.9360617934922944505980559045667 * EXPPOLY_32F_A0, 1.9571441241754002690183222516269 * EXPPOLY_32F_A0, 1.9784560263879509682582499181312 * EXPPOLY_32F_A0, }; static const double exp_prescale = 1.4426950408889634073599246810019 * (1 << EXPTAB_SCALE); static const double exp_postscale = 1./(1 << EXPTAB_SCALE); static const double exp_max_val = 3000.*(1 << EXPTAB_SCALE); // log10(DBL_MAX) < 3000 static CvStatus CV_STDCALL Exp_32f( const float *_x, float *y, int n ) { static const float A4 = (float)(1.000000000000002438532970795181890933776 / EXPPOLY_32F_A0), A3 = (float)(.6931471805521448196800669615864773144641 / EXPPOLY_32F_A0), A2 = (float)(.2402265109513301490103372422686535526573 / EXPPOLY_32F_A0), A1 = (float)(.5550339366753125211915322047004666939128e-1 / EXPPOLY_32F_A0); #undef EXPPOLY #define EXPPOLY(x) \ (((((x) + A1)*(x) + A2)*(x) + A3)*(x) + A4) int i = 0; const Cv32suf* x = (const Cv32suf*)_x; Cv32suf buf[4]; #if CV_SSE2 if( n >= 8 && checkHardwareSupport(CV_CPU_SSE) ) { static const __m128d prescale2 = _mm_set1_pd(exp_prescale); static const __m128 postscale4 = _mm_set1_ps((float)exp_postscale); static const __m128 maxval4 = _mm_set1_ps((float)(exp_max_val/exp_prescale)); static const __m128 minval4 = _mm_set1_ps((float)(-exp_max_val/exp_prescale)); static const __m128 mA1 = _mm_set1_ps(A1); static const __m128 mA2 = _mm_set1_ps(A2); static const __m128 mA3 = _mm_set1_ps(A3); static const __m128 mA4 = _mm_set1_ps(A4); bool y_aligned = (size_t)(void*)y % 16 == 0; ushort CV_DECL_ALIGNED(16) tab_idx[8]; for( ; i <= n - 8; i += 8 ) { __m128 xf0, xf1; xf0 = _mm_loadu_ps(&x[i].f); xf1 = _mm_loadu_ps(&x[i+4].f); __m128i xi0, xi1, xi2, xi3; xf0 = _mm_min_ps(_mm_max_ps(xf0, minval4), maxval4); xf1 = _mm_min_ps(_mm_max_ps(xf1, minval4), maxval4); __m128d xd0 = _mm_cvtps_pd(xf0); __m128d xd2 = _mm_cvtps_pd(_mm_movehl_ps(xf0, xf0)); __m128d xd1 = _mm_cvtps_pd(xf1); __m128d xd3 = _mm_cvtps_pd(_mm_movehl_ps(xf1, xf1)); xd0 = _mm_mul_pd(xd0, prescale2); xd2 = _mm_mul_pd(xd2, prescale2); xd1 = _mm_mul_pd(xd1, prescale2); xd3 = _mm_mul_pd(xd3, prescale2); xi0 = _mm_cvtpd_epi32(xd0); xi2 = _mm_cvtpd_epi32(xd2); xi1 = _mm_cvtpd_epi32(xd1); xi3 = _mm_cvtpd_epi32(xd3); xd0 = _mm_sub_pd(xd0, _mm_cvtepi32_pd(xi0)); xd2 = _mm_sub_pd(xd2, _mm_cvtepi32_pd(xi2)); xd1 = _mm_sub_pd(xd1, _mm_cvtepi32_pd(xi1)); xd3 = _mm_sub_pd(xd3, _mm_cvtepi32_pd(xi3)); xf0 = _mm_movelh_ps(_mm_cvtpd_ps(xd0), _mm_cvtpd_ps(xd2)); xf1 = _mm_movelh_ps(_mm_cvtpd_ps(xd1), _mm_cvtpd_ps(xd3)); xf0 = _mm_mul_ps(xf0, postscale4); xf1 = _mm_mul_ps(xf1, postscale4); xi0 = _mm_unpacklo_epi64(xi0, xi2); xi1 = _mm_unpacklo_epi64(xi1, xi3); xi0 = _mm_packs_epi32(xi0, xi1); _mm_store_si128((__m128i*)tab_idx, _mm_and_si128(xi0, _mm_set1_epi16(EXPTAB_MASK))); xi0 = _mm_add_epi16(_mm_srai_epi16(xi0, EXPTAB_SCALE), _mm_set1_epi16(127)); xi0 = _mm_max_epi16(xi0, _mm_setzero_si128()); xi0 = _mm_min_epi16(xi0, _mm_set1_epi16(255)); xi1 = _mm_unpackhi_epi16(xi0, _mm_setzero_si128()); xi0 = _mm_unpacklo_epi16(xi0, _mm_setzero_si128()); __m128d yd0 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[0]), _mm_load_sd(expTab + tab_idx[1])); __m128d yd1 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[2]), _mm_load_sd(expTab + tab_idx[3])); __m128d yd2 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[4]), _mm_load_sd(expTab + tab_idx[5])); __m128d yd3 = _mm_unpacklo_pd(_mm_load_sd(expTab + tab_idx[6]), _mm_load_sd(expTab + tab_idx[7])); __m128 yf0 = _mm_movelh_ps(_mm_cvtpd_ps(yd0), _mm_cvtpd_ps(yd1)); __m128 yf1 = _mm_movelh_ps(_mm_cvtpd_ps(yd2), _mm_cvtpd_ps(yd3)); yf0 = _mm_mul_ps(yf0, _mm_castsi128_ps(_mm_slli_epi32(xi0, 23))); yf1 = _mm_mul_ps(yf1, _mm_castsi128_ps(_mm_slli_epi32(xi1, 23))); __m128 zf0 = _mm_add_ps(xf0, mA1); __m128 zf1 = _mm_add_ps(xf1, mA1); zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA2); zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA2); zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA3); zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA3); zf0 = _mm_add_ps(_mm_mul_ps(zf0, xf0), mA4); zf1 = _mm_add_ps(_mm_mul_ps(zf1, xf1), mA4); zf0 = _mm_mul_ps(zf0, yf0); zf1 = _mm_mul_ps(zf1, yf1); if( y_aligned ) { _mm_store_ps(y + i, zf0); _mm_store_ps(y + i + 4, zf1); } else { _mm_storeu_ps(y + i, zf0); _mm_storeu_ps(y + i + 4, zf1); } } } else #endif 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; int val0, val1, val2, val3, t; if( ((x[i].i >> 23) & 255) > 127 + 10 ) x0 = x[i].i < 0 ? -exp_max_val : exp_max_val; if( ((x[i+1].i >> 23) & 255) > 127 + 10 ) x1 = x[i+1].i < 0 ? -exp_max_val : exp_max_val; if( ((x[i+2].i >> 23) & 255) > 127 + 10 ) x2 = x[i+2].i < 0 ? -exp_max_val : exp_max_val; if( ((x[i+3].i >> 23) & 255) > 127 + 10 ) x3 = x[i+3].i < 0 ? -exp_max_val : exp_max_val; val0 = cvRound(x0); val1 = cvRound(x1); val2 = cvRound(x2); val3 = cvRound(x3); x0 = (x0 - val0)*exp_postscale; x1 = (x1 - val1)*exp_postscale; x2 = (x2 - val2)*exp_postscale; x3 = (x3 - val3)*exp_postscale; t = (val0 >> EXPTAB_SCALE) + 127; t = !(t & ~255) ? t : t < 0 ? 0 : 255; 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; } for( ; i < n; i++ ) { double x0 = x[i].f * exp_prescale; int val0, t; if( ((x[i].i >> 23) & 255) > 127 + 10 ) x0 = x[i].i < 0 ? -exp_max_val : exp_max_val; val0 = cvRound(x0); t = (val0 >> EXPTAB_SCALE) + 127; t = !(t & ~255) ? t : t < 0 ? 0 : 255; buf[0].i = t << 23; x0 = (x0 - val0)*exp_postscale; y[i] = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY(x0); } return CV_OK; } static CvStatus CV_STDCALL Exp_64f( const double *_x, double *y, int n ) { static const double 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) int i = 0; Cv64suf buf[4]; const Cv64suf* x = (const Cv64suf*)_x; #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 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; double y0, y1, y2, y3; int val0, val1, val2, val3, t; t = (int)(x[i].i >> 52); if( (t & 2047) > 1023 + 10 ) x0 = t < 0 ? -exp_max_val : exp_max_val; t = (int)(x[i+1].i >> 52); if( (t & 2047) > 1023 + 10 ) x1 = t < 0 ? -exp_max_val : exp_max_val; t = (int)(x[i+2].i >> 52); if( (t & 2047) > 1023 + 10 ) x2 = t < 0 ? -exp_max_val : exp_max_val; t = (int)(x[i+3].i >> 52); if( (t & 2047) > 1023 + 10 ) x3 = t < 0 ? -exp_max_val : exp_max_val; val0 = cvRound(x0); val1 = cvRound(x1); val2 = cvRound(x2); val3 = cvRound(x3); x0 = (x0 - val0)*exp_postscale; x1 = (x1 - val1)*exp_postscale; x2 = (x2 - val2)*exp_postscale; x3 = (x3 - val3)*exp_postscale; t = (val0 >> EXPTAB_SCALE) + 1023; t = !(t & ~2047) ? t : t < 0 ? 0 : 2047; buf[0].i = (int64)t << 52; t = (val1 >> EXPTAB_SCALE) + 1023; t = !(t & ~2047) ? t : t < 0 ? 0 : 2047; buf[1].i = (int64)t << 52; t = (val2 >> EXPTAB_SCALE) + 1023; t = !(t & ~2047) ? t : t < 0 ? 0 : 2047; buf[2].i = (int64)t << 52; t = (val3 >> EXPTAB_SCALE) + 1023; 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 ); y[i] = y0; y[i + 1] = y1; y2 = buf[2].f * expTab[val2 & EXPTAB_MASK] * EXPPOLY( x2 ); y3 = buf[3].f * expTab[val3 & EXPTAB_MASK] * EXPPOLY( x3 ); y[i + 2] = y2; y[i + 3] = y3; } for( ; i < n; i++ ) { double x0 = x[i].f * exp_prescale; int val0, t; t = (int)(x[i].i >> 52); if( (t & 2047) > 1023 + 10 ) x0 = t < 0 ? -exp_max_val : exp_max_val; val0 = cvRound(x0); t = (val0 >> EXPTAB_SCALE) + 1023; t = !(t & ~2047) ? t : t < 0 ? 0 : 2047; buf[0].i = (int64)t << 52; x0 = (x0 - val0)*exp_postscale; y[i] = buf[0].f * expTab[val0 & EXPTAB_MASK] * EXPPOLY( x0 ); } 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(y), dst.ptr(y), size.width ); else if( depth == CV_64F ) for( int y = 0; y < size.height; y++ ) Exp_64f( src.ptr(y), dst.ptr(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) static const double CV_DECL_ALIGNED(16) icvLogTab[] = { 0.0000000000000000000000000000000000000000, 1.000000000000000000000000000000000000000, .00389864041565732288852075271279318258166, .9961089494163424124513618677042801556420, .00778214044205494809292034119607706088573, .9922480620155038759689922480620155038760, .01165061721997527263705585198749759001657, .9884169884169884169884169884169884169884, .01550418653596525274396267235488267033361, .9846153846153846153846153846153846153846, .01934296284313093139406447562578250654042, .9808429118773946360153256704980842911877, .02316705928153437593630670221500622574241, .9770992366412213740458015267175572519084, .02697658769820207233514075539915211265906, .9733840304182509505703422053231939163498, .03077165866675368732785500469617545604706, .9696969696969696969696969696969696969697, .03455238150665972812758397481047722976656, .9660377358490566037735849056603773584906, .03831886430213659461285757856785494368522, .9624060150375939849624060150375939849624, .04207121392068705056921373852674150839447, .9588014981273408239700374531835205992509, .04580953603129420126371940114040626212953, .9552238805970149253731343283582089552239, .04953393512227662748292900118940451648088, .9516728624535315985130111524163568773234, .05324451451881227759255210685296333394944, .9481481481481481481481481481481481481481, .05694137640013842427411105973078520037234, .9446494464944649446494464944649446494465, .06062462181643483993820353816772694699466, .9411764705882352941176470588235294117647, .06429435070539725460836422143984236754475, .9377289377289377289377289377289377289377, .06795066190850773679699159401934593915938, .9343065693430656934306569343065693430657, .07159365318700880442825962290953611955044, .9309090909090909090909090909090909090909, .07522342123758751775142172846244648098944, 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.19461546769967164038916962454095482826240, .8231511254019292604501607717041800643087, .19782574332991986754137769821682013571260, .8205128205128205128205128205128205128205, .20102574606059073203390141770796617493040, .8178913738019169329073482428115015974441, .20421554142869088876999228432396193966280, .8152866242038216560509554140127388535032, .20739519434607056602715147164417430758480, .8126984126984126984126984126984126984127, .21056476910734961416338251183333341032260, .8101265822784810126582278481012658227848, .21372432939771812687723695489694364368910, .8075709779179810725552050473186119873817, .21687393830061435506806333251006435602900, .8050314465408805031446540880503144654088, .22001365830528207823135744547471404075630, .8025078369905956112852664576802507836991, .22314355131420973710199007200571941211830, .8000000000000000000000000000000000000000, .22626367865045338145790765338460914790630, .7975077881619937694704049844236760124611, .22937410106484582006380890106811420992010, 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.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 ) { static const float shift[] = { 0, -1.f/512 }; static const float A0 = 0.3333333333333333333333333f, A1 = -0.5f, A2 = 1.f; #undef LOGPOLY #define LOGPOLY(x) (((A0*(x) + A1)*(x) + A2)*(x)) int i = 0; Cv32suf buf[4]; const int* x = (const int*)_x; #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 ) { 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 ); x0 += shift[h0 == 510]; x1 += shift[h1 == 510]; y0 += LOGPOLY( x0 ); y1 += LOGPOLY( x1 ); y[i] = (float) y0; y[i + 1] = (float) y1; x2 += shift[h2 == 510]; x3 += shift[h3 == 510]; y2 += LOGPOLY( x2 ); y3 += LOGPOLY( x3 ); y[i + 2] = (float) y2; y[i + 3] = (float) y3; } for( ; i < n; i++ ) { int h0 = x[i]; double y0; float x0; 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 ); x0 += shift[h0 == 510]; y0 += LOGPOLY( x0 ); 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; #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 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; } 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(y), dst.ptr(y), size.width ); else if( depth == CV_64F ) for( int y = 0; y < size.height; y++ ) Log_64f( src.ptr(y), dst.ptr(y), size.width ); else CV_Error( CV_StsUnsupportedFormat, "" ); } /****************************************************************************************\ * P O W E R * \****************************************************************************************/ template 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(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, 0, IPow, IPow, IPow, IPow, IPow, 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. 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; } } else { // quadratic equation double d = a2*a2 - 4*a1*a3; if( d >= 0 ) { d = sqrt(d); double q = (-a2 + (a2 < 0 ? -d : d)) * 0.5; x0 = q / a1; x1 = a3 / q; n = d > 0 ? 2 : 1; } } } else { a0 = 1./a0; a1 *= a0; a2 *= a0; a3 *= a0; 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 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 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. */