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egi_math.h
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egi_math.h
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/*-------------------------------------------------------------------
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License version 2 as
published by the Free Software Foundation.
Journal:
2021-05-22:
1. Add MAT_VECTOR2D macros for 2D Vector operation.
Midas Zhou
-------------------------------------------------------------------*/
#ifndef __EGI_MATH_H__
#define __EGI_MATH_H__
#include "egi.h"
#include "egi_fbgeom.h"
#include <inttypes.h>
#include <unistd.h> /* usleep */
#ifdef __cplusplus
extern "C" {
#endif
#define MATH_E 2.7182818284590452
#define MATH_PI 3.1415926535897932
#define MATH_DIVEXP 11 /* An odd number!! exponent of 2, as for divisor of fixed point number */
#define MATH_EPSILON 1.0*e-8;
/* Min. value for a positive float retaining full precision:FLT_MIN 32bits system = 1*2^(0-127+1) = 2^(-126)= 1.175494e-38 */
extern int fp16_sin[360];
extern int fp16_cos[360];
/* EGI fixed point / complex number */
typedef struct {
int64_t num; /* dividend */
int div; /* divisor, 2 exponent taken 16 */
} EGI_FVAL;
typedef struct {
EGI_FVAL real; /* real part */
EGI_FVAL imag; /* imaginery part */
} EGI_FCOMPLEX;
/* TODO: adjustable exponent value MAT_FVAL(a,exp) */
/* shitf MATH_DIVEXP bitS each time, if 15, 64-15-15-15-15-1 */
/* create a fix value */
/* (a) is float */
#define MAT_FVAL(a) ( (EGI_FVAL){ (a)*(1U<<MATH_DIVEXP), MATH_DIVEXP} ) /* 1U */
/* (a) is INT, suppose left bit_shift is also arithmatic !!! */
#define MAT_FVAL_INT(a) ( (EGI_FVAL){ a<<MATH_DIVEXP, MATH_DIVEXP} )
/* create a complex: r--real, i--imaginery */
/* (r) is float */
#define MAT_FCPVAL(r,i) ( (EGI_FCOMPLEX){ MAT_FVAL(r), MAT_FVAL(i) } )
/* (r) is INT, suppose left bit_shift is also arithmatic !!! */
#define MAT_FCPVAL_INT(r,i) ( (EGI_FCOMPLEX){ MAT_FVAL_INT(r), MAT_FVAL(i) } )
/* complex phase angle factor
@n: n*(2*PI)/N nth phase angle
@N: Total parts of a circle(2*PI).
*/
#define MAT_CPANGLE(n, N) ( MAT_FCPVAL( cos(2.0*n*MATH_PI/N), -sin(2.0*n*MATH_PI/N) ) )
/* fixed point hamming window factor
@n: nth hanmming window factor, also [0 N-1] index of input sample data
@N: Total number of sample data for each FFT session.
*/
#define MAT_FHAMMING(n, N) ( MAT_FVAL(0.54-0.46*cos(2.0*n*MATH_PI/N)) )
/* Right_shift and Right_rotate operation
@x: input variable.
@n: Number of places to be moved.
*/
#define MAT_RTSHIFT(x,n) ( (x)>>(n) )
/* Right_rotate operation
@x: input variable.
@xsize: size of input variable
@n: Rotate position
*/
#define MAT_RTROT(xsize,x,n) ( ((x)>>(n)) | ( ((x)&((1<<(n+1))-1)) << ( ((xsize)<<3)-(n) )) )
/* complex and FFT functions */
void mat_FixPrint(EGI_FVAL a);
void mat_CompPrint(EGI_FCOMPLEX a);
float mat_floatFix(EGI_FVAL a);
EGI_FVAL mat_FixAdd(EGI_FVAL a, EGI_FVAL b);
EGI_FVAL mat_FixSub(EGI_FVAL a, EGI_FVAL b);
EGI_FVAL mat_FixMult(EGI_FVAL a, EGI_FVAL b);
int mat_FixIntMult(EGI_FVAL a, int b);
EGI_FVAL mat_FixDiv(EGI_FVAL a, EGI_FVAL b);
EGI_FCOMPLEX mat_CompAdd(EGI_FCOMPLEX a, EGI_FCOMPLEX b);
EGI_FCOMPLEX mat_CompSub(EGI_FCOMPLEX a, EGI_FCOMPLEX b);
EGI_FCOMPLEX mat_CompMult(EGI_FCOMPLEX a, EGI_FCOMPLEX b);
EGI_FCOMPLEX mat_CompDiv(EGI_FCOMPLEX a, EGI_FCOMPLEX b);
float mat_floatCompAmp( EGI_FCOMPLEX a );
unsigned int mat_uint32Log2(uint32_t np);
unsigned int mat_uintCompAmp( EGI_FCOMPLEX a );
uint64_t mat_uintCompSAmp( EGI_FCOMPLEX a );
EGI_FCOMPLEX *mat_CompFFTAng(uint16_t np);
int mat_egiFFFT( uint16_t np, const EGI_FCOMPLEX *wang,
const float *x, const int *nx, EGI_FCOMPLEX *ffx);
/* other math functions */
void mat_create_fpTrigonTab(void);
uint64_t mat_fp16_sqrtu32(uint32_t x);
void mat_floatArray_limits(float *data, int num, float *min, float *max);
int mat_random_range(int max);
void mat_insert_sort( int *array, int n );
void mat_quick_sort( int *array, int start, int end, int cutoff );
int mat_max(int a, int b);
int mat_min(int a, int b);
int mat_max3(int a, int b, int c);
int mat_min3(int a, int b, int c);
float mat_maxf(float a, float b); //fmaxf()
float mat_minf(float a, float b); //fminf()
float mat_max3f(float a, float b, float c);
float mat_min3f(float a, float b, float c);
/*
void mat_pointrotate_SQMap(int n, int angle, struct egi_point_coord centxy,
struct egi_point_coord *SQMat_XRYR);
*/
/* float point type */
void mat_pointrotate_SQMap(int n, double angle, struct egi_point_coord centxy,
struct egi_point_coord *SQMat_XRYR);
/* fixed point type */
void mat_pointrotate_fpSQMap(int n, int angle, struct egi_point_coord centxy,
struct egi_point_coord *SQMat_XRYR);
void mat_pointrotate_fpAnnulusMap(int n, int ni, int angle, struct egi_point_coord centxy,
struct egi_point_coord *ANMat_XRYR);
int mat_pseudo_curvature(const EGI_POINT *pt);
float mat_normal_distribute(float x, float u, float dev);
float mat_rayleigh_distribute(float x, float dev);
unsigned int mat_factorial(int n);
double mat_double_factorial(int n);
double mat_bernstein_polynomial(int n, int i, double u);
double *mat_bernstein_polynomials(int n, double u, double *berns);
int mat_bspline_basis(int i, int deg, float u, const float *vu, float *LN);
float mat_FastInvSqrt( float x );
int mat_sha256_digest(const uint8_t *input, uint32_t len, uint32_t *init_hv, uint32_t *init_kv, uint32_t *hv, char *digest);
/* ----- 2D Vector Operation ----- */
typedef struct {
float x;
float y;
} MAT_VECTOR2D;
/* Following: a,b are MAT_VECTOR2 */
#define VECTOR2D_ADD(a, b) ( (MAT_VECTOR2D){a.x+b.x, a.y+b.y} ) /* Add */
#define VECTOR2D_SUB(a, b) ( (MAT_VECTOR2D){a.x-b.x, a.y-b.y} ) /* Subtract */
#define VECTOR2D_MULT(a, k) ( (MAT_VECTOR2D){ k*a.x, k*a.y } ) /* Multiply */
#define VECTOR2D_DIV(a, k) ( (MAT_VECTOR2D){ a.x/k, a.y/k } ) /* Divide, K!=0 */
#define VECTOR2D_MOD(a) ( sqrt(a.x*a.x+a.y*a.y) ) /* Module a!=0 */
#define VECTOR2D_NORM(a) ( VECTOR2D_DIV(a, VECTOR2D_MOD(a) ) ) /* Normal, a!=0 */
#define VECTOR2D_DOTPD(a, b) ( a.x*b.x + a.y*b.y ) /* Dot product */
#define VECTOR2D_CROSSPD(a, b) ( a.x*b.y - b.x*a.y ) /* Cross product */
#ifdef __cplusplus
}
#endif
#endif