General Purpose library for Freestanding C++ and POSIX systems
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#pragma once
#include "gp/algorithms/repeat.hpp"
#include "gp/math/details/math_definitions.hpp"
#include <limits>
#include <stddef.h>
#include <stdint.h>
namespace gp{
namespace math{
template<>
constexpr float pi<float> = 3.1415926535897932384626433832795028841971693993751058209749445923078164062;
template<>
constexpr double pi<double> = 3.1415926535897932384626433832795028841971693993751058209749445923078164062L;
template<>
float abs<float>(float value) {
static_assert(sizeof(float) == 4, "bad float size");
union {
float fp;
uint32_t ab;
} p;
p.fp = value;
p.ab &= 0x7fFFffFF;
return p.fp;
}
template<>
double abs<double>(double value) {
static_assert(sizeof(double) == 8, "bad double size");
union {
double fp;
uint64_t ab;
} p;
p.fp = value;
p.ab &= 0x7fFFffFFffFFffFF;
return p.fp;
}
template<typename T>
T floor(T);
template<>
float floor<float>(float value) {
static_assert(sizeof(float) == 4, "bad float size");
if(
value >= 16777216
|| value <= std::numeric_limits<int32_t>::min()
|| value != value
) {
return value;
}
int32_t ret = value;
float ret_d = ret;
if(value == ret_d || value >= 0) {
return ret;
} else {
return ret-1;
}
}
template<>
double floor<double>(double value) {
static_assert(sizeof(double) == 8, "bad double size");
if(
value >= 9007199254740992
|| value <= std::numeric_limits<int64_t>::min()
|| value != value
) {
return value;
}
int64_t ret = value;
double ret_d = ret;
if(value == ret_d || value >= 0) {
return ret;
} else {
return ret-1;
}
}
template<>
float sign<float>(float value) {
static_assert(sizeof(float) == 4, "bad float size");
if(!value) return 0;
union {
float fp;
uint32_t ab;
} p;
p.fp = value;
p.ab &= 0x7fFFffFF;
return value/p.fp;
}
template<>
double sign<double>(double value) {
static_assert(sizeof(double) == 8, "bad double size");
if(!value) return 0;
union {
double fp;
uint64_t ab;
} p;
p.fp = value;
p.ab &= 0x7fFFffFFffFFffFF;
return value/p.fp;
}
/**
* @brief Calculate the sin of a value using Taylor's method
*
* @tparam steps The number of steps to do at the maximum
* @tparam T the type of value and the return type expected
* @tparam accuracy the maximum accuracy to shoot for (early stopping)
* @param value The value to calculate the sin of. Works better for values close to 0.
* @return T the sin of the value (the sign may be off idk I don't remember)
*/
template<size_t steps, typename T, size_t accuracy = 1000000>
T sin_taylor(T value) {
const T acc = T{1}/T{accuracy};
T B = value;
T C = 1;
T ret = B/C;
for(size_t i = 1; (i < steps) && (abs<>(B/C) > acc); ++i) {
B *= -1*value*value;
C *= 2*i*(2*i+1);
ret += B/C;
}
return ret;
}
/**
* @brief General purpose sin function
*
* @param v
* @return float
*/
inline float sin(float v) {
// limit the range between -pi and +pi
v += pi<float>;
v = v - 2*pi<float>*floor(v/(2*pi<float>));
v -= pi<float>;
float s = sign(v);
v *= s;
// use taylor's method on the value
return sin_taylor<10>(v)*s;
}
/**
* @brief General purpose sin function
*
* @param v
* @return double
*/
inline double sin(double v) {
v += pi<double>;
v = v - 2*pi<double>*floor(v/(2*pi<double>));
v -= pi<double>;
float s = sign(v);
v *= s;
return sin_taylor<10>(v)*s;
}
// TODO: replace with an actual implementation
inline float cos(float v) {
return sin(v+pi<float>/2);
}
// TODO: replace with an actual implementation
inline double cos(double v) {
return sin(v+pi<double>/2);
}
// TODO: replace with an actual implementation
inline float tan(float v) {
return sin(v)/cos(v);
}
// TODO: replace with an actual implementation
inline double tan(double v) {
return sin(v)/cos(v);
}
/**
* @brief Quake isqrt (x) -> 1/sqrt(x)
*
* @tparam cycles the number of newton method cycles to apply
* @param v the value to apply the function on
* @return float \f$\frac{1}{\sqrt{v}}\f$
*/
template<size_t cycles = 5>
float isqrt(float v) {
int32_t i;
float x2, y;
constexpr float threehalfs = 1.5F;
x2 = v * 0.5F;
y = v;
i = * ( int32_t * ) &y;
i = 0x5F375A86 - ( i >> 1 );
y = * ( float * ) &i;
gp::repeat(cycles, [&](){
y = y * ( threehalfs - ( x2 * y * y ) );
});
return y;
}
/**
* @brief Quake isqrt (x) -> 1/sqrt(x) but for doubles
*
* @tparam cycles the number of newton method cycles to apply
* @param v the value to apply the function on
* @return double \f$\frac{1}{\sqrt{v}}\f$
*/
template<size_t cycles = 5>
double isqrt(double v) {
int64_t i;
double x2, y;
constexpr double threehalfs = 1.5F;
x2 = v * 0.5F;
y = v;
i = * ( int64_t * ) &y;
i = 0x5FE6EB50C7B537A9 - ( i >> 1 );
y = * ( double * ) &i;
gp::repeat(cycles, [&](){
y = y * ( threehalfs - ( x2 * y * y ) );
});
return y;
}
/**
* @brief A faster version of the Quake isqrt (actually the same but with defined cycles)
*
* @param v
* @return float
*/
inline float fast_isqrt(float v) {return isqrt<1>(v);}
/**
* @brief A faster version of the Quake isqrt (actually the same but with defined cycles)
*
* @param v
* @return double
*/
inline double fast_isqrt(double v) {return isqrt<1>(v);}
}
}