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211 linhas
3.9 KiB
211 linhas
3.9 KiB
#pragma once
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#include "gp/algorithm/repeat.hpp"
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#include <limits>
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#include <stddef.h>
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#include <stdint.h>
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namespace gp{
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template<typename T>
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constexpr T pi;
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template<>
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constexpr float pi<float> = 3.1415926535897932384626433832795028841971693993751058209749445923078164062;
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template<>
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constexpr double pi<double> = 3.1415926535897932384626433832795028841971693993751058209749445923078164062L;
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template<typename T>
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T abs(T);
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template<>
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float abs<float>(float value) {
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static_assert(sizeof(float) == 4, "bad float size");
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union {
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float fp;
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uint32_t ab;
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} p;
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p.fp = value;
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p.ab &= 0x7fFFffFF;
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return p.fp;
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}
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template<>
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double abs<double>(double value) {
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static_assert(sizeof(double) == 8, "bad double size");
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union {
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double fp;
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uint64_t ab;
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} p;
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p.fp = value;
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p.ab &= 0x7fFFffFFffFFffFF;
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return p.fp;
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}
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template<typename T>
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T floor(T);
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template<>
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float floor<float>(float value) {
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static_assert(sizeof(float) == 4, "bad float size");
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if(
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value >= 16777216
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|| value <= std::numeric_limits<int32_t>::min()
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|| value != value
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) {
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return value;
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}
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int32_t ret = value;
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float ret_d = ret;
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if(value == ret_d || value >= 0) {
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return ret;
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} else {
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return ret-1;
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}
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}
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template<>
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double floor<double>(double value) {
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static_assert(sizeof(double) == 8, "bad double size");
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if(
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value >= 9007199254740992
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|| value <= std::numeric_limits<int64_t>::min()
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|| value != value
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) {
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return value;
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}
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int64_t ret = value;
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double ret_d = ret;
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if(value == ret_d || value >= 0) {
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return ret;
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} else {
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return ret-1;
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}
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}
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template<typename T>
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T sign(T);
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template<>
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float sign<float>(float value) {
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static_assert(sizeof(float) == 4, "bad float size");
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if(!value) return 0;
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union {
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float fp;
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uint32_t ab;
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} p;
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p.fp = value;
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p.ab &= 0x7fFFffFF;
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return value/p.fp;
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}
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template<>
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double sign<double>(double value) {
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static_assert(sizeof(double) == 8, "bad double size");
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if(!value) return 0;
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union {
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double fp;
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uint64_t ab;
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} p;
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p.fp = value;
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p.ab &= 0x7fFFffFFffFFffFF;
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return value/p.fp;
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}
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template<size_t steps, typename T, size_t accuracy = 1000000>
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T sin_taylor(T value) {
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const T acc = T{1}/T{accuracy};
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T B = value;
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T C = 1;
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T ret = B/C;
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for(size_t i = 1; (i < steps) && (abs<>(B/C) > acc); ++i) {
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B *= -1*value*value;
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C *= 2*i*(2*i+1);
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ret += B/C;
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}
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return ret;
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}
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float sin(float v) {
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v += pi<float>;
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v = v - 2*pi<float>*floor(v/(2*pi<float>));
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v -= pi<float>;
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float s = sign(v);
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v *= s;
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return sin_taylor<10>(v)*s;
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}
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double sin(double v) {
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v += pi<double>;
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v = v - 2*pi<double>*floor(v/(2*pi<double>));
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v -= pi<double>;
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float s = sign(v);
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v *= s;
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return sin_taylor<10>(v)*s;
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}
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// TODO: replace with an actual implementation
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float cos(float v) {
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return sin(v+pi<float>/2);
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}
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// TODO: replace with an actual implementation
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double cos(double v) {
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return sin(v+pi<double>/2);
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}
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// TODO: replace with an actual implementation
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float tan(float v) {
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return sin(v)/cos(v);
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}
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// TODO: replace with an actual implementation
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double tan(double v) {
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return sin(v)/cos(v);
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}
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template<size_t cycles = 5>
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float isqrt(float v) {
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int32_t i;
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float x2, y;
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constexpr float threehalfs = 1.5F;
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x2 = v * 0.5F;
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y = v;
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i = * ( int32_t * ) &y;
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i = 0x5F375A86 - ( i >> 1 );
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y = * ( float * ) &i;
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gp::repeat(cycles, [&](){
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y = y * ( threehalfs - ( x2 * y * y ) );
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});
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return y;
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}
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template<size_t cycles = 5>
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double isqrt(double v) {
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int64_t i;
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double x2, y;
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constexpr double threehalfs = 1.5F;
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x2 = v * 0.5F;
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y = v;
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i = * ( int64_t * ) &y;
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i = 0x5FE6EB50C7B537A9 - ( i >> 1 );
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y = * ( double * ) &i;
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gp::repeat(cycles, [&](){
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y = y * ( threehalfs - ( x2 * y * y ) );
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});
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return y;
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}
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float fast_isqrt(float v) {return isqrt<1>(v);}
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double fast_isqrt(double v) {return isqrt<1>(v);}
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}
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