545 lines
18 KiB
C
545 lines
18 KiB
C
#ifndef _BGC_COMPLEX_H_
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#define _BGC_COMPLEX_H_
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#include "utilities.h"
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#include "angle.h"
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#include <math.h>
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typedef struct
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{
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float real, imaginary;
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} BGC_FP32_Complex;
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typedef struct
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{
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double real, imaginary;
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} BGC_FP64_Complex;
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// =================== Reset ==================== //
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inline void bgc_fp32_complex_reset(BGC_FP32_Complex* complex)
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{
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complex->real = 0.0f;
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complex->imaginary = 0.0f;
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}
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inline void bgc_fp64_complex_reset(BGC_FP64_Complex* complex)
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{
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complex->real = 0.0;
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complex->imaginary = 0.0;
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}
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// ==================== Set ===================== //
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inline void bgc_fp32_complex_make(BGC_FP32_Complex* complex, const float real, const float imaginary)
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{
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complex->real = real;
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complex->imaginary = imaginary;
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}
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inline void bgc_fp64_complex_make(BGC_FP64_Complex* complex, const double real, const double imaginary)
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{
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complex->real = real;
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complex->imaginary = imaginary;
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}
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// ================== Modulus =================== //
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inline float bgc_fp32_complex_get_square_modulus(const BGC_FP32_Complex* number)
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{
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return number->real * number->real + number->imaginary * number->imaginary;
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}
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inline double bgc_fp64_complex_get_square_modulus(const BGC_FP64_Complex* number)
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{
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return number->real * number->real + number->imaginary * number->imaginary;
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}
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inline float bgc_fp32_complex_get_modulus(const BGC_FP32_Complex* number)
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{
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return sqrtf(bgc_fp32_complex_get_square_modulus(number));
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}
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inline double bgc_fp64_complex_get_modulus(const BGC_FP64_Complex* number)
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{
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return sqrt(bgc_fp64_complex_get_square_modulus(number));
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}
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// ================= Comparison ================= //
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inline int bgc_fp32_complex_is_zero(const BGC_FP32_Complex* number)
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{
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return bgc_fp32_complex_get_square_modulus(number) <= BGC_FP32_SQUARE_EPSILON;
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}
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inline int bgc_fp64_complex_is_zero(const BGC_FP64_Complex* number)
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{
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return bgc_fp64_complex_get_square_modulus(number) <= BGC_FP64_SQUARE_EPSILON;
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}
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inline int bgc_fp32_complex_is_unit(const BGC_FP32_Complex* number)
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{
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return bgc_fp32_is_square_unit(bgc_fp32_complex_get_square_modulus(number));
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}
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inline int bgc_fp64_complex_is_unit(const BGC_FP64_Complex* number)
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{
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return bgc_fp64_is_square_unit(bgc_fp64_complex_get_square_modulus(number));
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}
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// ==================== Copy ==================== //
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inline void bgc_fp32_complex_copy(BGC_FP32_Complex* destination, const BGC_FP32_Complex* source)
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{
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destination->real = source->real;
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destination->imaginary = source->imaginary;
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}
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inline void bgc_fp64_complex_copy(BGC_FP64_Complex* destination, const BGC_FP64_Complex* source)
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{
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destination->real = source->real;
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destination->imaginary = source->imaginary;
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}
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// ==================== Swap ==================== //
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inline void bgc_fp32_complex_swap(BGC_FP32_Complex* number1, BGC_FP32_Complex* number2)
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{
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const float real = number2->real;
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const float imaginary = number2->imaginary;
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number2->real = number1->real;
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number2->imaginary = number1->imaginary;
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number1->real = real;
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number1->imaginary = imaginary;
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}
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inline void bgc_fp64_complex_swap(BGC_FP64_Complex* number1, BGC_FP64_Complex* number2)
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{
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const double real = number2->real;
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const double imaginary = number2->imaginary;
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number2->real = number1->real;
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number2->imaginary = number1->imaginary;
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number1->real = real;
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number1->imaginary = imaginary;
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}
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// ================== Convert =================== //
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inline void bgc_fp64_complex_convert_to_fp32(BGC_FP32_Complex* destination, const BGC_FP64_Complex* source)
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{
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destination->real = (float)source->real;
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destination->imaginary = (float)source->imaginary;
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}
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inline void bgc_fp32_complex_convert_to_fp64(BGC_FP64_Complex* destination, const BGC_FP32_Complex* source)
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{
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destination->real = source->real;
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destination->imaginary = source->imaginary;
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}
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// ================== Negative ================== //
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inline void bgc_fp32_complex_revert(BGC_FP32_Complex* number)
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{
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number->real = -number->real;
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number->imaginary = -number->imaginary;
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}
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inline void bgc_fp64_complex_revert(BGC_FP64_Complex* number)
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{
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number->real = -number->real;
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number->imaginary = -number->imaginary;
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}
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inline void bgc_fp32_complex_get_reverse(BGC_FP32_Complex* reverse, const BGC_FP32_Complex* number)
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{
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reverse->real = -number->real;
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reverse->imaginary = -number->imaginary;
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}
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inline void bgc_fp64_complex_get_reverse(BGC_FP64_Complex* reverse, const BGC_FP64_Complex* number)
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{
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reverse->real = -number->real;
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reverse->imaginary = -number->imaginary;
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}
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// ================= Normalize ================== //
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inline int bgc_fp32_complex_normalize(BGC_FP32_Complex* number)
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{
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const float square_modulus = bgc_fp32_complex_get_square_modulus(number);
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if (bgc_fp32_is_square_unit(square_modulus)) {
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return 1;
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}
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
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return 0;
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}
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const float multiplicand = sqrtf(1.0f / square_modulus);
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number->real *= multiplicand;
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number->imaginary *= multiplicand;
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return 1;
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}
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inline int bgc_fp64_complex_normalize(BGC_FP64_Complex* number)
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{
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const double square_modulus = bgc_fp64_complex_get_square_modulus(number);
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if (bgc_fp64_is_square_unit(square_modulus)) {
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return 1;
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}
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
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return 0;
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}
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const double multiplicand = sqrt(1.0 / square_modulus);
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number->real *= multiplicand;
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number->imaginary *= multiplicand;
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return 1;
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}
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inline int bgc_fp32_complex_get_normalized(BGC_FP32_Complex* normalized, const BGC_FP32_Complex* number)
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{
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const float square_modulus = bgc_fp32_complex_get_square_modulus(number);
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if (bgc_fp32_is_square_unit(square_modulus)) {
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normalized->real = number->real;
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normalized->imaginary = number->imaginary;
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return 1;
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}
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
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normalized->real = 0.0f;
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normalized->imaginary = 0.0f;
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return 0;
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}
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const float multiplicand = sqrtf(1.0f / square_modulus);
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normalized->real = number->real * multiplicand;
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normalized->imaginary = number->imaginary * multiplicand;
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return 1;
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}
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inline int bgc_fp64_complex_get_normalized(BGC_FP64_Complex* normalized, const BGC_FP64_Complex* number)
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{
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const double square_modulus = bgc_fp64_complex_get_square_modulus(number);
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if (bgc_fp64_is_square_unit(square_modulus)) {
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normalized->real = number->real;
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normalized->imaginary = number->imaginary;
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return 1;
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}
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
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normalized->real = 0.0;
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normalized->imaginary = 0.0;
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return 0;
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}
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const double multiplicand = sqrt(1.0 / square_modulus);
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normalized->real = number->real * multiplicand;
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normalized->imaginary = number->imaginary * multiplicand;
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return 1;
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}
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// ================= Conjugate ================== //
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inline void bgc_fp32_complex_conjugate(BGC_FP32_Complex* number)
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{
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number->imaginary = -number->imaginary;
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}
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inline void bgc_fp64_complex_conjugate(BGC_FP64_Complex* number)
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{
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number->imaginary = -number->imaginary;
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}
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inline void bgc_fp32_complex_get_conjugate(BGC_FP32_Complex* conjugate, const BGC_FP32_Complex* number)
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{
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conjugate->real = number->real;
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conjugate->imaginary = -number->imaginary;
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}
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inline void bgc_fp64_complex_get_conjugate(BGC_FP64_Complex* conjugate, const BGC_FP64_Complex* number)
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{
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conjugate->real = number->real;
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conjugate->imaginary = -number->imaginary;
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}
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// =================== Invert =================== //
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inline int bgc_fp32_complex_get_inverse(BGC_FP32_Complex* inverse, const BGC_FP32_Complex* number)
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{
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const float square_modulus = bgc_fp32_complex_get_square_modulus(number);
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON || isnan(square_modulus)) {
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return 0;
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}
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const float multiplicand = 1.0f / square_modulus;
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inverse->real = number->real * multiplicand;
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inverse->imaginary = -number->imaginary * multiplicand;
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return 1;
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}
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inline int bgc_fp64_complex_get_inverse(BGC_FP64_Complex* inverse, const BGC_FP64_Complex* number)
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{
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const double square_modulus = bgc_fp64_complex_get_square_modulus(number);
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON || isnan(square_modulus)) {
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return 0;
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}
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const double multiplicand = 1.0 / square_modulus;
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inverse->real = number->real * multiplicand;
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inverse->imaginary = -number->imaginary * multiplicand;
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return 1;
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}
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inline int bgc_fp32_complex_invert(BGC_FP32_Complex* number)
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{
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return bgc_fp32_complex_get_inverse(number, number);
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}
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inline int bgc_fp64_complex_invert(BGC_FP64_Complex* number)
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{
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return bgc_fp64_complex_get_inverse(number, number);
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}
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// =============== Get Exponation =============== //
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void bgc_fp32_complex_get_exponation(BGC_FP32_Complex* power, const BGC_FP32_Complex* base, const float real_exponent, const float imaginary_exponent);
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void bgc_fp64_complex_get_exponation(BGC_FP64_Complex* power, const BGC_FP64_Complex* base, const double real_exponent, const double imaginary_exponent);
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// ==================== Add ===================== //
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inline void bgc_fp32_complex_add(BGC_FP32_Complex* sum, const BGC_FP32_Complex* number1, const BGC_FP32_Complex* number2)
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{
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sum->real = number1->real + number2->real;
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sum->imaginary = number1->imaginary + number2->imaginary;
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}
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inline void bgc_fp64_complex_add(BGC_FP64_Complex* sum, const BGC_FP64_Complex* number1, const BGC_FP64_Complex* number2)
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{
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sum->real = number1->real + number2->real;
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sum->imaginary = number1->imaginary + number2->imaginary;
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}
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// ================= Add scaled ================= //
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inline void bgc_fp32_complex_add_scaled(BGC_FP32_Complex* sum, const BGC_FP32_Complex* basic_number, const BGC_FP32_Complex* scalable_number, const float scale)
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{
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sum->real = basic_number->real + scalable_number->real * scale;
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sum->imaginary = basic_number->imaginary + scalable_number->imaginary * scale;
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}
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inline void bgc_fp64_complex_add_scaled(BGC_FP64_Complex* sum, const BGC_FP64_Complex* basic_number, const BGC_FP64_Complex* scalable_number, const double scale)
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{
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sum->real = basic_number->real + scalable_number->real * scale;
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sum->imaginary = basic_number->imaginary + scalable_number->imaginary * scale;
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}
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// ================== Subtract ================== //
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inline void bgc_fp32_complex_subtract(BGC_FP32_Complex* difference, const BGC_FP32_Complex* minuend, const BGC_FP32_Complex* subtrahend)
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{
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difference->real = minuend->real - subtrahend->real;
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difference->imaginary = minuend->imaginary - subtrahend->imaginary;
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}
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inline void bgc_fp64_complex_subtract(BGC_FP64_Complex* difference, const BGC_FP64_Complex* minuend, const BGC_FP64_Complex* subtrahend)
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{
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difference->real = minuend->real - subtrahend->real;
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difference->imaginary = minuend->imaginary - subtrahend->imaginary;
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}
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// ================== Multiply ================== //
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inline void bgc_fp32_complex_get_product(BGC_FP32_Complex* product, const BGC_FP32_Complex* number1, const BGC_FP32_Complex* number2)
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{
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const float real = number1->real * number2->real - number1->imaginary * number2->imaginary;
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const float imaginary = number1->real * number2->imaginary + number1->imaginary * number2->real;
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product->real = real;
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product->imaginary = imaginary;
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}
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inline void bgc_fp64_complex_get_product(BGC_FP64_Complex* product, const BGC_FP64_Complex* number1, const BGC_FP64_Complex* number2)
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{
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const double real = number1->real * number2->real - number1->imaginary * number2->imaginary;
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const double imaginary = number1->real * number2->imaginary + number1->imaginary * number2->real;
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product->real = real;
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product->imaginary = imaginary;
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}
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// ============= Multiply By Number ============= //
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inline void bgc_fp32_complex_multiply(BGC_FP32_Complex* product, const BGC_FP32_Complex* multiplicand, const float multiplier)
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{
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product->real = multiplicand->real * multiplier;
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product->imaginary = multiplicand->imaginary * multiplier;
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}
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inline void bgc_fp64_complex_multiply(BGC_FP64_Complex* product, const BGC_FP64_Complex* multiplicand, const double multiplier)
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{
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product->real = multiplicand->real * multiplier;
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product->imaginary = multiplicand->imaginary * multiplier;
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}
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// =================== Divide =================== //
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inline int bgc_fp32_complex_get_ratio(BGC_FP32_Complex* quotient, const BGC_FP32_Complex* divident, const BGC_FP32_Complex* divisor)
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{
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const float square_modulus = bgc_fp32_complex_get_square_modulus(divisor);
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if (square_modulus <= BGC_FP32_SQUARE_EPSILON) {
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return 0;
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}
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const float real = divident->real * divisor->real + divident->imaginary * divisor->imaginary;
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const float imaginary = divident->imaginary * divisor->real - divident->real * divisor->imaginary;
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const float multiplier = 1.0f / square_modulus;
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quotient->real = real * multiplier;
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quotient->imaginary = imaginary * multiplier;
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return 1;
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}
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inline int bgc_fp64_complex_get_ratio(BGC_FP64_Complex* quotient, const BGC_FP64_Complex* divident, const BGC_FP64_Complex* divisor)
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{
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const double square_modulus = bgc_fp64_complex_get_square_modulus(divisor);
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if (square_modulus <= BGC_FP64_SQUARE_EPSILON) {
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return 0;
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}
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const double real = divident->real * divisor->real + divident->imaginary * divisor->imaginary;
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const double imaginary = divident->imaginary * divisor->real - divident->real * divisor->imaginary;
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const double multiplier = 1.0 / square_modulus;
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quotient->real = real * multiplier;
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quotient->imaginary = imaginary * multiplier;
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return 1;
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}
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// ============== Divide By Number ============== //
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inline void bgc_fp32_complex_divide(BGC_FP32_Complex* quotient, const BGC_FP32_Complex* dividend, const float divisor)
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{
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bgc_fp32_complex_multiply(quotient, dividend, 1.0f / divisor);
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}
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inline void bgc_fp64_complex_divide(BGC_FP64_Complex* quotient, const BGC_FP64_Complex* dividend, const double divisor)
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{
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bgc_fp64_complex_multiply(quotient, dividend, 1.0 / divisor);
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}
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// ================== Average2 ================== //
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inline void bgc_fp32_complex_get_mean2(BGC_FP32_Complex* mean, const BGC_FP32_Complex* number1, const BGC_FP32_Complex* number2)
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{
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mean->real = (number1->real + number2->real) * 0.5f;
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mean->imaginary = (number1->imaginary + number2->imaginary) * 0.5f;
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}
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inline void bgc_fp64_complex_get_mean2(BGC_FP64_Complex* mean, const BGC_FP64_Complex* number1, const BGC_FP64_Complex* number2)
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{
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mean->real = (number1->real + number2->real) * 0.5;
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mean->imaginary = (number1->imaginary + number2->imaginary) * 0.5;
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}
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// ================== Average3 ================== //
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inline void bgc_fp32_complex_get_mean3(BGC_FP32_Complex* mean, const BGC_FP32_Complex* number1, const BGC_FP32_Complex* number2, const BGC_FP32_Complex* number3)
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{
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mean->real = (number1->real + number2->real + number3->real) * BGC_FP32_ONE_THIRD;
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mean->imaginary = (number1->imaginary + number2->imaginary + number3->imaginary) * BGC_FP32_ONE_THIRD;
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}
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inline void bgc_fp64_complex_get_mean3(BGC_FP64_Complex* mean, const BGC_FP64_Complex* number1, const BGC_FP64_Complex* number2, const BGC_FP64_Complex* number3)
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{
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mean->real = (number1->real + number2->real + number3->real) * BGC_FP64_ONE_THIRD;
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mean->imaginary = (number1->imaginary + number2->imaginary + number3->imaginary) * BGC_FP64_ONE_THIRD;
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}
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// =================== Linear =================== //
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inline void bgc_fp32_complex_interpolate(BGC_FP32_Complex* interpolation, const BGC_FP32_Complex* number1, const BGC_FP32_Complex* number2, const float phase)
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{
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const float counter_phase = 1.0f - phase;
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interpolation->real = number1->real * counter_phase + number2->real * phase;
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interpolation->imaginary = number1->imaginary * counter_phase + number2->imaginary * phase;
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}
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inline void bgc_fp64_complex_interpolate(BGC_FP64_Complex* interpolation, const BGC_FP64_Complex* number1, const BGC_FP64_Complex* number2, const double phase)
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{
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const double counter_phase = 1.0 - phase;
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interpolation->real = number1->real * counter_phase + number2->real * phase;
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interpolation->imaginary = number1->imaginary * counter_phase + number2->imaginary * phase;
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}
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// ================== Are Close ================= //
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inline int bgc_fp32_complex_are_close(const BGC_FP32_Complex* number1, const BGC_FP32_Complex* number2)
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{
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const float square_modulus1 = bgc_fp32_complex_get_square_modulus(number1);
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const float square_modulus2 = bgc_fp32_complex_get_square_modulus(number2);
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const float d_real = number1->real - number2->real;
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const float d_imaginary = number1->imaginary - number2->imaginary;
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const float square_distance = d_real * d_real + d_imaginary * d_imaginary;
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if (square_modulus1 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP32_EPSILON_EFFECTIVENESS_LIMIT) {
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return square_distance <= BGC_FP32_SQUARE_EPSILON;
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}
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return square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP32_SQUARE_EPSILON * square_modulus2;
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}
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inline int bgc_fp64_complex_are_close(const BGC_FP64_Complex* number1, const BGC_FP64_Complex* number2)
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{
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const double square_modulus1 = bgc_fp64_complex_get_square_modulus(number1);
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const double square_modulus2 = bgc_fp64_complex_get_square_modulus(number2);
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const double d_real = number1->real - number2->real;
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const double d_imaginary = number1->imaginary - number2->imaginary;
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const double square_distance = d_real * d_real + d_imaginary * d_imaginary;
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if (square_modulus1 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT || square_modulus2 <= BGC_FP64_EPSILON_EFFECTIVENESS_LIMIT) {
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return square_distance <= BGC_FP64_SQUARE_EPSILON;
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}
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return square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus1 && square_distance <= BGC_FP64_SQUARE_EPSILON * square_modulus2;
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}
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#endif
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