bx/include/bx/math.h

/*
 * Copyright 2011-2022 Branimir Karadzic. All rights reserved.
 * License: https://github.com/bkaradzic/bx/blob/master/LICENSE
 */

#ifndef BX_MATH_H_HEADER_GUARD
#define BX_MATH_H_HEADER_GUARD

#include "bx.h"
#include "uint32_t.h"

namespace bx
{
	constexpr float kPi         = 3.1415926535897932384626433832795f;
	constexpr float kPi2        = 6.2831853071795864769252867665590f;
	constexpr float kInvPi      = 1.0f/kPi;
	constexpr float kPiHalf     = 1.5707963267948966192313216916398f;
	constexpr float kPiQuarter  = 0.7853981633974483096156608458199f;
	constexpr float kSqrt2      = 1.4142135623730950488016887242097f;
	constexpr float kLogNat10   = 2.3025850929940456840179914546844f;
	constexpr float kInvLogNat2 = 1.4426950408889634073599246810019f;
	constexpr float kLogNat2Hi  = 0.6931471805599453094172321214582f;
	constexpr float kLogNat2Lo  = 1.90821492927058770002e-10f;
	constexpr float kE          = 2.7182818284590452353602874713527f;
	constexpr float kNearZero   = 1.0f/float(1 << 28);
	constexpr float kFloatMin   = 1.175494e-38f;
	constexpr float kFloatMax   = 3.402823e+38f;
	extern const float kInfinity;

	///
	typedef float (*LerpFn)(float _a, float _b, float _t);

	///
	struct Handedness
	{
		enum Enum
		{
			Left,
			Right,
		};
	};

	///
	struct NearFar
	{
		enum Enum
		{
			Default,
			Reverse,
		};
	};

	/// Structure initializer types.
	namespace init
	{
		/// Fields are left uninitialized.
		///
		struct NoneType {};
		constexpr NoneType None;

		/// Fields are initialized to zero.
		///
		struct ZeroType {};
		constexpr ZeroType Zero;

		/// Fields are initialized to identity value.
		///
		struct IdentityType {};
		constexpr IdentityType Identity;
	}

	///
	struct Vec3
	{
		Vec3() = delete;

		///
		Vec3(init::NoneType);

		///
		constexpr Vec3(init::ZeroType);

		///
		constexpr Vec3(init::IdentityType);

		///
		explicit constexpr Vec3(float _v);

		///
		constexpr Vec3(float _x, float _y, float _z);

		float x, y, z;
	};

	///
	struct Plane
	{
		Plane() = delete;

		///
		Plane(init::NoneType);

		///
		constexpr Plane(init::ZeroType);

		///
		constexpr Plane(init::IdentityType);

		///
		constexpr Plane(Vec3 _normal, float _dist);

		Vec3  normal;
		float dist;
	};

	///
	struct Quaternion
	{
		Quaternion() = delete;

		///
		Quaternion(init::NoneType);

		///
		constexpr Quaternion(init::ZeroType);

		///
		constexpr Quaternion(init::IdentityType);

		///
		constexpr Quaternion(float _x, float _y, float _z, float _w);

		float x, y, z, w;
	};

	/// Returns converted the argument _deg to radians.
	///
	BX_CONST_FUNC float toRad(float _deg);

	/// Returns converted the argument _rad to degrees.
	///
	BX_CONST_FUNC float toDeg(float _rad);

	/// Reinterprets the bit pattern of _a as uint32_t.
	///
	BX_CONST_FUNC uint32_t floatToBits(float _a);

	/// Reinterprets the bit pattern of _a as float.
	///
	BX_CONST_FUNC float bitsToFloat(uint32_t _a);

	/// Reinterprets the bit pattern of _a as uint64_t.
	///
	BX_CONST_FUNC uint64_t doubleToBits(double _a);

	/// Reinterprets the bit pattern of _a as double.
	///
	BX_CONST_FUNC double bitsToDouble(uint64_t _a);

	/// Returns sortable floating point value.
	///
	BX_CONST_FUNC uint32_t floatFlip(uint32_t _value);

	/// Returns true if _f is a number that is NaN.
	///
	BX_CONST_FUNC bool isNan(float _f);

	/// Returns true if _f is a number that is NaN.
	///
	BX_CONST_FUNC bool isNan(double _f);

	/// Returns true if _f is not infinite and is not a NaN.
	///
	BX_CONST_FUNC bool isFinite(float _f);

	/// Returns true if _f is not infinite and is not a NaN.
	///
	BX_CONST_FUNC bool isFinite(double _f);

	/// Returns true if _f is infinite and is not a NaN.
	///
	BX_CONST_FUNC bool isInfinite(float _f);

	/// Returns true if _f is infinite and is not a NaN.
	///
	BX_CONST_FUNC bool isInfinite(double _f);

	/// Returns the largest integer value not greater than _f.
	///
	BX_CONSTEXPR_FUNC float floor(float _f);

	/// Returns the smallest integer value not less than _f.
	///
	BX_CONSTEXPR_FUNC float ceil(float _f);

	/// Returns the nearest integer value to _f, rounding halfway cases away from zero,
	///
	BX_CONSTEXPR_FUNC float round(float _f);

	/// Returns linear interpolation between two values _a and _b.
	///
	BX_CONSTEXPR_FUNC float lerp(float _a, float _b, float _t);

	/// Returns inverse linear interpolation of _value between two values _a and _b.
	///
	BX_CONSTEXPR_FUNC float invLerp(float _a, float _b, float _value);

	/// Returns the sign of _a.
	///
	BX_CONSTEXPR_FUNC float sign(float _a);

	/// Returns the absolute of _a.
	///
	BX_CONSTEXPR_FUNC float abs(float _a);

	/// Returns the square of _a.
	///
	BX_CONSTEXPR_FUNC float square(float _a);

	/// Returns the cosine of the argument _a.
	///
	BX_CONST_FUNC float sin(float _a);

	/// Returns hyperbolic sine of the argument _a.
	///
	BX_CONST_FUNC float sinh(float _a);

	/// Returns radian angle between -pi/2 and +pi/2 whose sine is _a.
	///
	BX_CONST_FUNC float asin(float _a);

	/// Returns the cosine of the argument _a.
	///
	BX_CONST_FUNC float cos(float _a);

	/// Returns hyperbolic cosine of the argument _a.
	///
	BX_CONST_FUNC float cosh(float _a);

	/// Returns radian angle between 0 and pi whose cosine is _a.
	///
	BX_CONST_FUNC float acos(float _a);

	/// Returns the circular tangent of the radian argument _a.
	///
	BX_CONST_FUNC float tan(float _a);

	/// Returns hyperbolic tangent of the argument _a.
	///
	BX_CONST_FUNC float tanh(float _a);

	/// Returns radian angle between -pi/2 and +pi/2 whose tangent is _a.
	///
	BX_CONST_FUNC float atan(float _a);

	/// Returns the inverse tangent of _y/_x.
	///
	BX_CONST_FUNC float atan2(float _y, float _x);

	/// Computes _a raised to the _b power.
	///
	BX_CONST_FUNC float pow(float _a, float _b);

	/// Returns the result of multiplying _a by 2 raised to the power of the exponent.
	///
	BX_CONST_FUNC float ldexp(float _a, int32_t _b);

	/// Returns decomposed given floating point value _a into a normalized fraction and
	/// an integral power of two.
	///
	float frexp(float _a, int32_t* _outExp);

	/// Returns e (2.71828...) raised to the _a power.
	///
	BX_CONST_FUNC float exp(float _a);

	/// Returns 2 raised to the _a power.
	///
	BX_CONST_FUNC float exp2(float _a);

	/// Returns the base e (2.71828...) logarithm of _a.
	///
	BX_CONST_FUNC float log(float _a);

	/// Returns the base 2 logarithm of _a.
	///
	template<typename Ty>
	BX_CONST_FUNC Ty log2(Ty _a);

	/// Returns the square root of _a.
	///
	BX_CONST_FUNC float sqrt(float _a);

	/// Returns reciprocal square root of _a.
	///
	BX_CONST_FUNC float rsqrt(float _a);

	/// Returns the nearest integer not greater in magnitude than _a.
	///
	BX_CONSTEXPR_FUNC float trunc(float _a);

	/// Returns the fractional (or decimal) part of _a, which is greater than or equal to 0
	/// and less than 1.
	///
	BX_CONSTEXPR_FUNC float fract(float _a);

	/// Returns result of negated multiply-sub operation -(_a * _b - _c) -> _c - _a * _b.
	///
	BX_CONSTEXPR_FUNC float nms(float _a, float _b, float _c);

	/// Returns result of addition (_a + _b).
	///
	BX_CONSTEXPR_FUNC float add(float _a, float _b);

	/// Returns result of subtracion (_a - _b).
	///
	BX_CONSTEXPR_FUNC float sub(float _a, float _b);

	/// Returns result of multiply (_a * _b).
	///
	BX_CONSTEXPR_FUNC float mul(float _a, float _b);

	/// Returns result of multiply and add (_a * _b + _c).
	///
	BX_CONSTEXPR_FUNC float mad(float _a, float _b, float _c);

	/// Returns reciprocal of _a.
	///
	BX_CONSTEXPR_FUNC float rcp(float _a);

	/// Returns the floating-point remainder of the division operation _a/_b.
	///
	BX_CONST_FUNC float mod(float _a, float _b);

	///
	BX_CONSTEXPR_FUNC bool isEqual(float _a, float _b, float _epsilon);

	///
	BX_CONST_FUNC bool isEqual(const float* _a, const float* _b, uint32_t _num, float _epsilon);

	///
	BX_CONST_FUNC float wrap(float _a, float _wrap);

	///
	BX_CONSTEXPR_FUNC float step(float _edge, float _a);

	///
	BX_CONSTEXPR_FUNC float pulse(float _a, float _start, float _end);

	///
	BX_CONSTEXPR_FUNC float smoothStep(float _a);

	///
	BX_CONST_FUNC float invSmoothStep(float _a);

	///
	BX_CONSTEXPR_FUNC float bias(float _time, float _bias);

	///
	BX_CONSTEXPR_FUNC float gain(float _time, float _gain);

	///
	BX_CONST_FUNC float angleDiff(float _a, float _b);

	/// Returns shortest distance linear interpolation between two angles.
	///
	BX_CONST_FUNC float angleLerp(float _a, float _b, float _t);

	///
	template<typename Ty>
	Ty load(const void* _ptr);

	///
	template<typename Ty>
	void store(void* _ptr, const Ty& _a);

	///
	BX_CONSTEXPR_FUNC Vec3 round(const Vec3 _a);

	///
	BX_CONSTEXPR_FUNC Vec3 abs(const Vec3 _a);

	///
	BX_CONSTEXPR_FUNC Vec3 neg(const Vec3 _a);

	///
	BX_CONSTEXPR_FUNC Vec3 add(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 add(const Vec3 _a, float _b);

	///
	BX_CONSTEXPR_FUNC Vec3 sub(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 sub(const Vec3 _a, float _b);

	///
	BX_CONSTEXPR_FUNC Vec3 mul(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 mul(const Vec3 _a, float _b);

	///
	BX_CONSTEXPR_FUNC Vec3 div(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 div(const Vec3 _a, float _b);

	/// Returns result of negated multiply-sub operation -(_a * _b - _c) -> _c - _a * _b.
	///
	BX_CONSTEXPR_FUNC Vec3 nms(const Vec3 _a, const float _b, const Vec3 _c);

	/// Returns result of negated multiply-sub operation -(_a * _b - _c) -> _c - _a * _b.
	///
	BX_CONSTEXPR_FUNC Vec3 nms(const Vec3 _a, const Vec3 _b, const Vec3 _c);

	///
	BX_CONSTEXPR_FUNC Vec3 mad(const Vec3 _a, const float _b, const Vec3 _c);

	///
	BX_CONSTEXPR_FUNC Vec3 mad(const Vec3 _a, const Vec3 _b, const Vec3 _c);

	///
	BX_CONSTEXPR_FUNC float dot(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 cross(const Vec3 _a, const Vec3 _b);

	///
	BX_CONST_FUNC float length(const Vec3 _a);

	///
	BX_CONST_FUNC float distanceSq(const Vec3 _a, const Vec3 _b);

	///
	BX_CONST_FUNC float distance(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 lerp(const Vec3 _a, const Vec3 _b, float _t);

	///
	BX_CONSTEXPR_FUNC Vec3 lerp(const Vec3 _a, const Vec3 _b, const Vec3 _t);

	///
	BX_CONST_FUNC Vec3 normalize(const Vec3 _a);

	///
	BX_CONSTEXPR_FUNC Vec3 min(const Vec3 _a, const Vec3 _b);

	///
	BX_CONSTEXPR_FUNC Vec3 max(const Vec3 _a, const Vec3 _b);

	/// Returns component wise reciprocal of _a.
	///
	BX_CONSTEXPR_FUNC Vec3 rcp(const Vec3 _a);

	///
	BX_CONSTEXPR_FUNC bool isEqual(const Vec3 _a, const Vec3 _b, float _epsilon);

	///
	void calcTangentFrame(Vec3& _outT, Vec3& _outB, const Vec3 _n);

	///
	void calcTangentFrame(Vec3& _outT, Vec3& _outB, const Vec3 _n, float _angle);

	///
	BX_CONST_FUNC Vec3 fromLatLong(float _u, float _v);

	///
	void toLatLong(float* _outU, float* _outV, const Vec3 _dir);

	///
	BX_CONSTEXPR_FUNC Quaternion invert(const Quaternion _a);

	///
	BX_CONSTEXPR_FUNC Vec3 mulXyz(const Quaternion _a, const Quaternion _b);

	///
	BX_CONSTEXPR_FUNC Quaternion add(const Quaternion _a, const Quaternion _b);

	///
	BX_CONSTEXPR_FUNC Quaternion sub(const Quaternion _a, const Quaternion _b);

	///
	BX_CONSTEXPR_FUNC Quaternion mul(const Quaternion _a, float _b);

	///
	BX_CONSTEXPR_FUNC Quaternion mul(const Quaternion _a, const Quaternion _b);

	///
	BX_CONSTEXPR_FUNC Vec3 mul(const Vec3 _v, const Quaternion _q);

	///
	BX_CONSTEXPR_FUNC float dot(const Quaternion _a, const Quaternion _b);

	///
	BX_CONSTEXPR_FUNC Quaternion normalize(const Quaternion _a);

	///
	BX_CONSTEXPR_FUNC Quaternion lerp(const Quaternion _a, const Quaternion _b, float _t);

	///
	BX_CONST_FUNC Quaternion fromEuler(const Vec3 _euler);

	///
	BX_CONST_FUNC Vec3 toEuler(const Quaternion _a);

	///
	BX_CONST_FUNC Vec3 toXAxis(const Quaternion _a);

	///
	BX_CONST_FUNC Vec3 toYAxis(const Quaternion _a);

	///
	BX_CONST_FUNC Vec3 toZAxis(const Quaternion _a);

	///
	BX_CONST_FUNC Quaternion fromAxisAngle(const Vec3 _axis, float _angle);

	///
	void toAxisAngle(Vec3& _outAxis, float& _outAngle, const Quaternion _a);

	///
	BX_CONST_FUNC Quaternion rotateX(float _ax);

	///
	BX_CONST_FUNC Quaternion rotateY(float _ay);

	///
	BX_CONST_FUNC Quaternion rotateZ(float _az);

	///
	BX_CONSTEXPR_FUNC bool isEqual(const Quaternion _a, const Quaternion _b, float _epsilon);

	///
	void mtxIdentity(float* _result);

	///
	void mtxTranslate(float* _result, float _tx, float _ty, float _tz);

	///
	void mtxScale(float* _result, float _sx, float _sy, float _sz);

	///
	void mtxScale(float* _result, float _scale);

	///
	void mtxFromNormal(
		  float* _result
		, const Vec3& _normal
		, float _scale
		, const Vec3& _pos
		);

	///
	void mtxFromNormal(
		  float* _result
		, const Vec3& _normal
		, float _scale
		, const Vec3& _pos
		, float _angle
		);

	///
	void mtxFromQuaternion(float* _result, const Quaternion& _rotation);

	///
	void mtxFromQuaternion(float* _result, const Quaternion& _rotation, const Vec3& _translation);

	///
	void mtxLookAt(
		  float* _result
		, const Vec3& _eye
		, const Vec3& _at
		, const Vec3& _up = { 0.0f, 1.0f, 0.0f }
		, Handedness::Enum _handedness = Handedness::Left
		);

	///
	void mtxProj(
		  float* _result
		, float _ut
		, float _dt
		, float _lt
		, float _rt
		, float _near
		, float _far
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		);

	///
	void mtxProj(
		  float* _result
		, const float _fov[4]
		, float _near
		, float _far
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		);

	///
	void mtxProj(
		  float* _result
		, float _fovy
		, float _aspect
		, float _near
		, float _far
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		);

	///
	void mtxProjInf(
		  float* _result
		, const float _fov[4]
		, float _near
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		, NearFar::Enum _nearFar = NearFar::Default
		);

	///
	void mtxProjInf(
		  float* _result
		, float _ut
		, float _dt
		, float _lt
		, float _rt
		, float _near
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		, NearFar::Enum _nearFar = NearFar::Default
		);

	///
	void mtxProjInf(
		  float* _result
		, float _fovy
		, float _aspect
		, float _near
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		, NearFar::Enum _nearFar = NearFar::Default
		);

	///
	void mtxOrtho(
		  float* _result
		, float _left
		, float _right
		, float _bottom
		, float _top
		, float _near
		, float _far
		, float _offset
		, bool _homogeneousNdc
		, Handedness::Enum _handedness = Handedness::Left
		);

	///
	void mtxRotateX(float* _result, float _ax);

	///
	void mtxRotateY(float* _result, float _ay);

	///
	void mtxRotateZ(float* _result, float _az);

	///
	void mtxRotateXY(float* _result, float _ax, float _ay);

	///
	void mtxRotateXYZ(float* _result, float _ax, float _ay, float _az);

	///
	void mtxRotateZYX(float* _result, float _ax, float _ay, float _az);

	///
	void mtxSRT(
		  float* _result
		, float _sx
		, float _sy
		, float _sz
		, float _ax
		, float _ay
		, float _az
		, float _tx
		, float _ty
		, float _tz
		);

	///
	Vec3 mul(const Vec3& _vec, const float* _mat);

	///
	Vec3 mulXyz0(const Vec3& _vec, const float* _mat);

	///
	Vec3 mulH(const Vec3& _vec, const float* _mat);

	///
	void vec4MulMtx(float* _result, const float* _vec, const float* _mat);

	///
	void mtxMul(float* _result, const float* _a, const float* _b);

	///
	void mtxTranspose(float* _result, const float* _a);

	///
	void mtx3Inverse(float* _result, const float* _a);

	///
	void mtxInverse(float* _result, const float* _a);

	///
	void mtx3Cofactor(float* _result, const float* _a);

	///
	void mtxCofactor(float* _result, const float* _a);

	///
	Vec3 calcNormal(const Vec3& _va, const Vec3& _vb, const Vec3& _vc);

	///
	void calcPlane(Plane& _outPlane, const Vec3& _va, const Vec3& _vb, const Vec3& _vc);

	///
	void calcPlane(Plane& _outPlane, const Vec3& _normal, const Vec3& _pos);

	///
	BX_CONSTEXPR_FUNC float distance(const Plane& _plane, const Vec3& _pos);

	///
	BX_CONSTEXPR_FUNC bool isEqual(const Plane& _a, const Plane& _b, float _epsilon);

	///
	void calcLinearFit2D(float _result[2], const void* _points, uint32_t _stride, uint32_t _numPoints);

	///
	void calcLinearFit3D(float _result[3], const void* _points, uint32_t _stride, uint32_t _numPoints);

	///
	void rgbToHsv(float _hsv[3], const float _rgb[3]);

	///
	void hsvToRgb(float _rgb[3], const float _hsv[3]);

	///
	BX_CONST_FUNC float toLinear(float _a);

	///
	BX_CONST_FUNC float toGamma(float _a);

} // namespace bx

#include "inline/math.inl"

#endif // BX_MATH_H_HEADER_GUARD