Added fpumath.h

include/bx/fpumath.h

@@ -0,0 +1,572 @@
+/*
+ * Copyright 2011-2014 Branimir Karadzic. All rights reserved.
+ * License: http://www.opensource.org/licenses/BSD-2-Clause
+ */
+
+// FPU math lib
+
+#ifndef BX_FPU_MATH_H_HEADER_GUARD
+#define BX_FPU_MATH_H_HEADER_GUARD
+
+#define _USE_MATH_DEFINES
+#include <math.h>
+#include <string.h>
+
+namespace bx
+{
+	inline float toRad(float _deg)
+	{
+		return _deg * float(M_PI / 180.0);
+	}
+
+	inline float toDeg(float _rad)
+	{
+		return _rad * float(180.0 / M_PI);
+	}
+
+	inline float fmin(float _a, float _b)
+	{
+		return _a < _b ? _a : _b;
+	}
+
+	inline float fmax(float _a, float _b)
+	{
+		return _a > _b ? _a : _b;
+	}
+
+	inline float fclamp(float _a, float _min, float _max)
+	{
+		return fmin(fmax(_a, _min), _max);
+	}
+
+	inline float fsaturate(float _a)
+	{
+		return fclamp(_a, 0.0f, 1.0f);
+	}
+
+	inline float flerp(float _a, float _b, float _t)
+	{
+		return _a + (_b - _a) * _t;
+	}
+
+	inline float fsign(float _a)
+	{
+		return _a < 0.0f ? -1.0f : 1.0f;
+	}
+
+	inline void vec3Move(float* __restrict _result, const float* __restrict _a)
+	{
+		_result[0] = _a[0];
+		_result[1] = _a[1];
+		_result[2] = _a[2];
+	}
+
+	inline void vec3Abs(float* __restrict _result, const float* __restrict _a)
+	{
+		_result[0] = fabsf(_a[0]);
+		_result[1] = fabsf(_a[1]);
+		_result[2] = fabsf(_a[2]);
+	}
+
+	inline void vec3Neg(float* __restrict _result, const float* __restrict _a)
+	{
+		_result[0] = -_a[0];
+		_result[1] = -_a[1];
+		_result[2] = -_a[2];
+	}
+
+	inline void vec3Add(float* __restrict _result, const float* __restrict _a, const float* __restrict _b)
+	{
+		_result[0] = _a[0] + _b[0];
+		_result[1] = _a[1] + _b[1];
+		_result[2] = _a[2] + _b[2];
+	}
+
+	inline void vec3Sub(float* __restrict _result, const float* __restrict _a, const float* __restrict _b)
+	{
+		_result[0] = _a[0] - _b[0];
+		_result[1] = _a[1] - _b[1];
+		_result[2] = _a[2] - _b[2];
+	}
+
+	inline void vec3Mul(float* __restrict _result, const float* __restrict _a, const float* __restrict _b)
+	{
+		_result[0] = _a[0] * _b[0];
+		_result[1] = _a[1] * _b[1];
+		_result[2] = _a[2] * _b[2];
+	}
+
+	inline void vec3Mul(float* __restrict _result, const float* __restrict _a, float _b)
+	{
+		_result[0] = _a[0] * _b;
+		_result[1] = _a[1] * _b;
+		_result[2] = _a[2] * _b;
+	}
+
+	inline float vec3Dot(const float* __restrict _a, const float* __restrict _b)
+	{
+		return _a[0]*_b[0] + _a[1]*_b[1] + _a[2]*_b[2];
+	}
+
+	inline void vec3Cross(float* __restrict _result, const float* __restrict _a, const float* __restrict _b)
+	{
+		_result[0] = _a[1]*_b[2] - _a[2]*_b[1];
+		_result[1] = _a[2]*_b[0] - _a[0]*_b[2];
+		_result[2] = _a[0]*_b[1] - _a[1]*_b[0];
+	}
+
+	inline float vec3Length(const float* _a)
+	{
+		return sqrtf(vec3Dot(_a, _a) );
+	}
+
+	inline float vec3Norm(float* __restrict _result, const float* __restrict _a)
+	{
+		const float len = vec3Length(_a);
+		const float invLen = 1.0f/len;
+		_result[0] = _a[0] * invLen;
+		_result[1] = _a[1] * invLen;
+		_result[2] = _a[2] * invLen;
+		return len;
+	}
+
+	inline void mtxIdentity(float* _result)
+	{
+		memset(_result, 0, sizeof(float)*16);
+		_result[0] = _result[5] = _result[10] = _result[15] = 1.0f;
+	}
+
+	inline void mtxTranslate(float* _result, float _tx, float _ty, float _tz)
+	{
+		mtxIdentity(_result);
+		_result[12] = _tx;
+		_result[13] = _ty;
+		_result[14] = _tz;
+	}
+
+	inline void mtxScale(float* _result, float _sx, float _sy, float _sz)
+	{
+		memset(_result, 0, sizeof(float) * 16);
+		_result[0]  = _sx;
+		_result[5]  = _sy;
+		_result[10] = _sz;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxLookAt(float* __restrict _result, const float* __restrict _eye, const float* __restrict _at, const float* __restrict _up = NULL)
+	{
+		float tmp[4];
+		vec3Sub(tmp, _at, _eye);
+
+		float view[4];
+		vec3Norm(view, tmp);
+
+		float up[3] = { 0.0f, 1.0f, 0.0f };
+		if (NULL != _up)
+		{
+			up[0] = _up[0];
+			up[1] = _up[1];
+			up[2] = _up[2];
+		}
+		vec3Cross(tmp, up, view);
+
+		float right[4];
+		vec3Norm(right, tmp);
+
+		vec3Cross(up, view, right);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = right[0];
+		_result[ 1] = up[0];
+		_result[ 2] = view[0];
+
+		_result[ 4] = right[1];
+		_result[ 5] = up[1];
+		_result[ 6] = view[1];
+
+		_result[ 8] = right[2];
+		_result[ 9] = up[2];
+		_result[10] = view[2];
+
+		_result[12] = -vec3Dot(right, _eye);
+		_result[13] = -vec3Dot(up, _eye);
+		_result[14] = -vec3Dot(view, _eye);
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxProj(float* _result, float _fovy, float _aspect, float _near, float _far)
+	{
+		const float height = 1.0f/tanf(_fovy*( (float)M_PI/180.0f)*0.5f);
+		const float width = height * 1.0f/_aspect;
+		const float aa = _far/(_far-_near);
+		const float bb = -_near * aa;
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[0] = width;
+		_result[5] = height;
+		_result[10] = aa;
+		_result[11] = 1.0f;
+		_result[14] = bb;
+	}
+
+	inline void mtxOrtho(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far)
+	{
+		const float aa = 2.0f/(_right - _left);
+		const float bb = 2.0f/(_top - _bottom);
+		const float cc = 1.0f/(_far - _near);
+		const float dd = (_left + _right)/(_left - _right);
+		const float ee = (_top + _bottom)/(_bottom - _top);
+		const float ff = _near / (_near - _far);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[0] = aa;
+		_result[5] = bb;
+		_result[10] = cc;
+		_result[12] = dd;
+		_result[13] = ee;
+		_result[14] = ff;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxRotateX(float* _result, float _ax)
+	{
+		const float sx = sinf(_ax);
+		const float cx = cosf(_ax);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = 1.0f;
+		_result[ 5] = cx;
+		_result[ 6] = -sx;
+		_result[ 9] = sx;
+		_result[10] = cx;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxRotateY(float* _result, float _ay)
+	{
+		const float sy = sinf(_ay);
+		const float cy = cosf(_ay);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = cy;
+		_result[ 2] = sy;
+		_result[ 5] = 1.0f;
+		_result[ 8] = -sy;
+		_result[10] = cy;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxRotateZ(float* _result, float _az)
+	{
+		const float sz = sinf(_az);
+		const float cz = cosf(_az);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = cz;
+		_result[ 1] = -sz;
+		_result[ 4] = sz;
+		_result[ 5] = cz;
+		_result[10] = 1.0f;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxRotateXY(float* _result, float _ax, float _ay)
+	{
+		const float sx = sinf(_ax);
+		const float cx = cosf(_ax);
+		const float sy = sinf(_ay);
+		const float cy = cosf(_ay);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = cy;
+		_result[ 2] = sy;
+		_result[ 4] = sx*sy;
+		_result[ 5] = cx;
+		_result[ 6] = -sx*cy;
+		_result[ 8] = -cx*sy;
+		_result[ 9] = sx;
+		_result[10] = cx*cy;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxRotateXYZ(float* _result, float _ax, float _ay, float _az)
+	{
+		const float sx = sinf(_ax);
+		const float cx = cosf(_ax);
+		const float sy = sinf(_ay);
+		const float cy = cosf(_ay);
+		const float sz = sinf(_az);
+		const float cz = cosf(_az);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = cy*cz;
+		_result[ 1] = -cy*sz;
+		_result[ 2] = sy;
+		_result[ 4] = cz*sx*sy + cx*sz;
+		_result[ 5] = cx*cz - sx*sy*sz;
+		_result[ 6] = -cy*sx;
+		_result[ 8] = -cx*cz*sy + sx*sz;
+		_result[ 9] = cz*sx + cx*sy*sz;
+		_result[10] = cx*cy;
+		_result[15] = 1.0f;
+	}
+
+	inline void mtxRotateZYX(float* _result, float _ax, float _ay, float _az)
+	{
+		const float sx = sinf(_ax);
+		const float cx = cosf(_ax);
+		const float sy = sinf(_ay);
+		const float cy = cosf(_ay);
+		const float sz = sinf(_az);
+		const float cz = cosf(_az);
+
+		memset(_result, 0, sizeof(float)*16);
+		_result[ 0] = cy*cz;
+		_result[ 1] = cz*sx*sy-cx*sz;
+		_result[ 2] = cx*cz*sy+sx*sz;
+		_result[ 4] = cy*sz;
+		_result[ 5] = cx*cz + sx*sy*sz;
+		_result[ 6] = -cz*sx + cx*sy*sz;
+		_result[ 8] = -sy;
+		_result[ 9] = cy*sx;
+		_result[10] = cx*cy;
+		_result[15] = 1.0f;
+	};
+
+	inline void mtxSRT(float* _result, float _sx, float _sy, float _sz, float _ax, float _ay, float _az, float _tx, float _ty, float _tz)
+	{
+		const float sx = sinf(_ax);
+		const float cx = cosf(_ax);
+		const float sy = sinf(_ay);
+		const float cy = cosf(_ay);
+		const float sz = sinf(_az);
+		const float cz = cosf(_az);
+
+		const float sxsz = sx*sz;
+		const float cycz = cy*cz;
+
+		_result[ 0] = _sx * (cycz - sxsz*sy);
+		_result[ 1] = _sx * -cx*sz;
+		_result[ 2] = _sx * (cz*sy + cy*sxsz);
+		_result[ 3] = 0.0f;
+
+		_result[ 4] = _sy * (cz*sx*sy + cy*sz);
+		_result[ 5] = _sy * cx*cz;
+		_result[ 6] = _sy * (sy*sz -cycz*sx);
+		_result[ 7] = 0.0f;
+
+		_result[ 8] = _sz * -cx*sy;
+		_result[ 9] = _sz * sx;
+		_result[10] = _sz * cx*cy;
+		_result[11] = 0.0f;
+
+		_result[12] = _tx;
+		_result[13] = _ty;
+		_result[14] = _tz;
+		_result[15] = 1.0f;
+	}
+
+	inline void vec3MulMtx(float* __restrict _result, const float* __restrict _vec, const float* __restrict _mat)
+	{
+		_result[0] = _vec[0] * _mat[ 0] + _vec[1] * _mat[4] + _vec[2] * _mat[ 8] + _mat[12];
+		_result[1] = _vec[0] * _mat[ 1] + _vec[1] * _mat[5] + _vec[2] * _mat[ 9] + _mat[13];
+		_result[2] = _vec[0] * _mat[ 2] + _vec[1] * _mat[6] + _vec[2] * _mat[10] + _mat[14];
+	}
+
+	inline void vec3MulMtxH(float* __restrict _result, const float* __restrict _vec, const float* __restrict _mat)
+	{
+		float xx = _vec[0] * _mat[ 0] + _vec[1] * _mat[4] + _vec[2] * _mat[ 8] + _mat[12];
+		float yy = _vec[0] * _mat[ 1] + _vec[1] * _mat[5] + _vec[2] * _mat[ 9] + _mat[13];
+		float zz = _vec[0] * _mat[ 2] + _vec[1] * _mat[6] + _vec[2] * _mat[10] + _mat[14];
+		float ww = _vec[0] * _mat[ 3] + _vec[1] * _mat[7] + _vec[2] * _mat[11] + _mat[15];
+		float invW = fsign(ww)/ww;
+		_result[0] = xx*invW;
+		_result[1] = yy*invW;
+		_result[2] = zz*invW;
+	}
+
+	inline void vec4MulMtx(float* __restrict _result, const float* __restrict _vec, const float* __restrict _mat)
+	{
+		_result[0] = _vec[0] * _mat[ 0] + _vec[1] * _mat[4] + _vec[2] * _mat[ 8] + _vec[3] * _mat[12];
+		_result[1] = _vec[0] * _mat[ 1] + _vec[1] * _mat[5] + _vec[2] * _mat[ 9] + _vec[3] * _mat[13];
+		_result[2] = _vec[0] * _mat[ 2] + _vec[1] * _mat[6] + _vec[2] * _mat[10] + _vec[3] * _mat[14];
+		_result[3] = _vec[0] * _mat[ 3] + _vec[1] * _mat[7] + _vec[2] * _mat[11] + _vec[3] * _mat[15];
+	}
+
+	inline void mtxMul(float* __restrict _result, const float* __restrict _a, const float* __restrict _b)
+	{
+		vec4MulMtx(&_result[ 0], &_a[ 0], _b);
+		vec4MulMtx(&_result[ 4], &_a[ 4], _b);
+		vec4MulMtx(&_result[ 8], &_a[ 8], _b);
+		vec4MulMtx(&_result[12], &_a[12], _b);
+	}
+
+	inline void mtxTranspose(float* __restrict _result, const float* __restrict _a)
+	{
+		_result[ 0] = _a[ 0];
+		_result[ 4] = _a[ 1];
+		_result[ 8] = _a[ 2];
+		_result[12] = _a[ 3];
+		_result[ 1] = _a[ 4];
+		_result[ 5] = _a[ 5];
+		_result[ 9] = _a[ 6];
+		_result[13] = _a[ 7];
+		_result[ 2] = _a[ 8];
+		_result[ 6] = _a[ 9];
+		_result[10] = _a[10];
+		_result[14] = _a[11];
+		_result[ 3] = _a[12];
+		_result[ 7] = _a[13];
+		_result[11] = _a[14];
+		_result[15] = _a[15];
+	}
+
+	inline void mtx3Inverse(float* __restrict _result, const float* __restrict _a)
+	{
+		float xx = _a[0];
+		float xy = _a[1];
+		float xz = _a[2];
+		float yx = _a[3];
+		float yy = _a[4];
+		float yz = _a[5];
+		float zx = _a[6];
+		float zy = _a[7];
+		float zz = _a[8];
+
+		float det = 0.0f;
+		det += xx * (yy*zz - yz*zy);
+		det -= xy * (yx*zz - yz*zx);
+		det += xz * (yx*zy - yy*zx);
+
+		float invDet = 1.0f/det;
+
+		_result[0] = +(yy*zz - yz*zy) * invDet;
+		_result[1] = -(xy*zz - xz*zy) * invDet;
+		_result[2] = +(xy*yz - xz*yy) * invDet;
+
+		_result[3] = -(yx*zz - yz*zx) * invDet;
+		_result[4] = +(xx*zz - xz*zx) * invDet;
+		_result[5] = -(xx*yz - xz*yx) * invDet;
+
+		_result[6] = +(yx*zy - yy*zx) * invDet;
+		_result[7] = -(xx*zy - xy*zx) * invDet;
+		_result[8] = +(xx*yy - xy*yx) * invDet;
+	}
+
+	inline void mtxInverse(float* __restrict _result, const float* __restrict _a)
+	{
+		float xx = _a[ 0];
+		float xy = _a[ 1];
+		float xz = _a[ 2];
+		float xw = _a[ 3];
+		float yx = _a[ 4];
+		float yy = _a[ 5];
+		float yz = _a[ 6];
+		float yw = _a[ 7];
+		float zx = _a[ 8];
+		float zy = _a[ 9];
+		float zz = _a[10];
+		float zw = _a[11];
+		float wx = _a[12];
+		float wy = _a[13];
+		float wz = _a[14];
+		float ww = _a[15];
+
+		float det = 0.0f;
+		det += xx * (yy*(zz*ww - zw*wz) - yz*(zy*ww - zw*wy) + yw*(zy*wz - zz*wy) );
+		det -= xy * (yx*(zz*ww - zw*wz) - yz*(zx*ww - zw*wx) + yw*(zx*wz - zz*wx) );
+		det += xz * (yx*(zy*ww - zw*wy) - yy*(zx*ww - zw*wx) + yw*(zx*wy - zy*wx) );
+		det -= xw * (yx*(zy*wz - zz*wy) - yy*(zx*wz - zz*wx) + yz*(zx*wy - zy*wx) );
+
+		float invDet = 1.0f/det;
+
+		_result[ 0] = +(yy*(zz*ww - wz*zw) - yz*(zy*ww - wy*zw) + yw*(zy*wz - wy*zz) ) * invDet;
+		_result[ 1] = -(xy*(zz*ww - wz*zw) - xz*(zy*ww - wy*zw) + xw*(zy*wz - wy*zz) ) * invDet;
+		_result[ 2] = +(xy*(yz*ww - wz*yw) - xz*(yy*ww - wy*yw) + xw*(yy*wz - wy*yz) ) * invDet;
+		_result[ 3] = -(xy*(yz*zw - zz*yw) - xz*(yy*zw - zy*yw) + xw*(yy*zz - zy*yz) ) * invDet;
+
+		_result[ 4] = -(yx*(zz*ww - wz*zw) - yz*(zx*ww - wx*zw) + yw*(zx*wz - wx*zz) ) * invDet;
+		_result[ 5] = +(xx*(zz*ww - wz*zw) - xz*(zx*ww - wx*zw) + xw*(zx*wz - wx*zz) ) * invDet;
+		_result[ 6] = -(xx*(yz*ww - wz*yw) - xz*(yx*ww - wx*yw) + xw*(yx*wz - wx*yz) ) * invDet;
+		_result[ 7] = +(xx*(yz*zw - zz*yw) - xz*(yx*zw - zx*yw) + xw*(yx*zz - zx*yz) ) * invDet;
+
+		_result[ 8] = +(yx*(zy*ww - wy*zw) - yy*(zx*ww - wx*zw) + yw*(zx*wy - wx*zy) ) * invDet;
+		_result[ 9] = -(xx*(zy*ww - wy*zw) - xy*(zx*ww - wx*zw) + xw*(zx*wy - wx*zy) ) * invDet;
+		_result[10] = +(xx*(yy*ww - wy*yw) - xy*(yx*ww - wx*yw) + xw*(yx*wy - wx*yy) ) * invDet;
+		_result[11] = -(xx*(yy*zw - zy*yw) - xy*(yx*zw - zx*yw) + xw*(yx*zy - zx*yy) ) * invDet;
+
+		_result[12] = -(yx*(zy*wz - wy*zz) - yy*(zx*wz - wx*zz) + yz*(zx*wy - wx*zy) ) * invDet;
+		_result[13] = +(xx*(zy*wz - wy*zz) - xy*(zx*wz - wx*zz) + xz*(zx*wy - wx*zy) ) * invDet;
+		_result[14] = -(xx*(yy*wz - wy*yz) - xy*(yx*wz - wx*yz) + xz*(yx*wy - wx*yy) ) * invDet;
+		_result[15] = +(xx*(yy*zz - zy*yz) - xy*(yx*zz - zx*yz) + xz*(yx*zy - zx*yy) ) * invDet;
+	}
+
+	/// Convert LH to RH projection matrix and vice versa.
+	inline void mtxProjFlipHandedness(float* __restrict _dst, const float* __restrict _src)
+	{
+		_dst[ 0] = -_src[ 0];
+		_dst[ 1] = -_src[ 1];
+		_dst[ 2] = -_src[ 2];
+		_dst[ 3] = -_src[ 3];
+		_dst[ 4] =  _src[ 4];
+		_dst[ 5] =  _src[ 5];
+		_dst[ 6] =  _src[ 6];
+		_dst[ 7] =  _src[ 7];
+		_dst[ 8] = -_src[ 8];
+		_dst[ 9] = -_src[ 9];
+		_dst[10] = -_src[10];
+		_dst[11] = -_src[11];
+		_dst[12] =  _src[12];
+		_dst[13] =  _src[13];
+		_dst[14] =  _src[14];
+		_dst[15] =  _src[15];
+	}
+
+	/// Convert LH to RH view matrix and vice versa.
+	inline void mtxViewFlipHandedness(float* __restrict _dst, const float* __restrict _src)
+	{
+		_dst[ 0] = -_src[ 0];
+		_dst[ 1] =  _src[ 1];
+		_dst[ 2] = -_src[ 2];
+		_dst[ 3] =  _src[ 3];
+		_dst[ 4] = -_src[ 4];
+		_dst[ 5] =  _src[ 5];
+		_dst[ 6] = -_src[ 6];
+		_dst[ 7] =  _src[ 7];
+		_dst[ 8] = -_src[ 8];
+		_dst[ 9] =  _src[ 9];
+		_dst[10] = -_src[10];
+		_dst[11] =  _src[11];
+		_dst[12] = -_src[12];
+		_dst[13] =  _src[13];
+		_dst[14] = -_src[14];
+		_dst[15] =  _src[15];
+	}
+
+	inline void calcNormal(float _result[3], float _va[3], float _vb[3], float _vc[3])
+	{
+		float ba[3];
+		vec3Sub(ba, _vb, _va);
+
+		float ca[3];
+		vec3Sub(ca, _vc, _va);
+
+		float baxca[3];
+		vec3Cross(baxca, ba, ca);
+
+		vec3Norm(_result, baxca);
+	}
+
+	inline void calcPlane(float _result[4], float _va[3], float _vb[3], float _vc[3])
+	{
+		float normal[3];
+		calcNormal(normal, _va, _vb, _vc);
+
+		_result[0] = normal[0];
+		_result[1] = normal[1];
+		_result[2] = normal[2];
+		_result[3] = -vec3Dot(normal, _va);
+	}
+} // namespace bx
+
+#endif // BX_FPU_MATH_H_HEADER_GUARD