1#ifndef _DEMATH_H
2#define _DEMATH_H
3/*-------------------------------------------------------------------------
4 * drawElements Base Portability Library
5 * -------------------------------------
6 *
7 * Copyright 2014 The Android Open Source Project
8 *
9 * Licensed under the Apache License, Version 2.0 (the "License");
10 * you may not use this file except in compliance with the License.
11 * You may obtain a copy of the License at
12 *
13 *      http://www.apache.org/licenses/LICENSE-2.0
14 *
15 * Unless required by applicable law or agreed to in writing, software
16 * distributed under the License is distributed on an "AS IS" BASIS,
17 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
18 * See the License for the specific language governing permissions and
19 * limitations under the License.
20 *
21 *//*!
22 * \file
23 * \brief Basic mathematical operations.
24 *//*--------------------------------------------------------------------*/
25
26#include "deDefs.h"
27
28#include <math.h>
29#include <float.h>
30
31DE_BEGIN_EXTERN_C
32
33/* Mathematical constants. */
34
35#define DE_PI			3.14159265358979324f	/*!< Pi.					*/
36#define DE_LOG_2		0.69314718056f			/*!< log_e(2.0)				*/
37#define DE_INV_LOG_2	1.44269504089f			/*!< 1.0 / log_e(2.0)		*/
38#define DE_E			2.71828182845904523536f	/*!< e.						*/
39#define DE_LOG2_E		1.44269504088896340736f	/*!< log_2(e).				*/
40#define DE_INV_LOG2_E	0.69314718055994530942f	/*!< 1.0 / log_2(e).		*/
41
42#define DE_PI_DOUBLE	3.14159265358979323846  /*!< Pi as a double.		*/
43
44/* Rounding mode control. */
45
46typedef enum deRoundingMode_e
47{
48	DE_ROUNDINGMODE_TO_NEAREST = 0,
49	DE_ROUNDINGMODE_TO_ZERO,
50	DE_ROUNDINGMODE_TO_POSITIVE_INF,
51	DE_ROUNDINGMODE_TO_NEGATIVE_INF,
52
53	DE_ROUNDINGMODE_LAST
54} deRoundingMode;
55
56deRoundingMode		deGetRoundingMode	(void);
57deBool				deSetRoundingMode	(deRoundingMode mode);
58
59void				deMath_selfTest		(void);
60
61/* Float properties */
62
63/* \note The NaN test probably won't work with -ffast-math */
64
65DE_INLINE int		deFloatIsInf		(float x)		{ return (x > FLT_MAX) - (x < -FLT_MAX); }
66DE_INLINE deBool	deFloatIsNaN		(float x)		{ return (x != x); }
67
68DE_INLINE int		deIsInf				(double x)		{ return (x > DBL_MAX) - (x < -DBL_MAX); }
69DE_INLINE deBool	deIsNaN				(double x)		{ return (x != x); }
70
71/* Basic utilities. */
72
73DE_INLINE float		deFloatAbs			(float x)						{ return (x >= 0.0f) ? x : -x; }
74DE_INLINE float		deFloatMin			(float a, float b)				{ return (a <= b) ? a : b; }
75DE_INLINE float		deFloatMax			(float a, float b)				{ return (a >= b) ? a : b; }
76DE_INLINE float		deFloatClamp		(float x, float mn, float mx)	{ return (x <= mn) ? mn : ((x >= mx) ? mx : x); }
77
78DE_INLINE double	deAbs				(double x)							{ return (x >= 0.0) ? x : -x; }
79DE_INLINE double	deMin				(double a, double b)				{ return (a <= b) ? a : b; }
80DE_INLINE double	deMax				(double a, double b)				{ return (a >= b) ? a : b; }
81DE_INLINE double	deClamp				(double x, double mn, double mx)	{ return (x <= mn) ? mn : ((x >= mx) ? mx : x); }
82
83/* Utility functions. */
84
85DE_INLINE float		deFloatSign			(float a)					{ return (a == 0.0f) ? 0.0f : ((a > 0.0f) ? +1.0f : -1.0f); }
86DE_INLINE int		deFloatIntSign		(float a)					{ return (a == 0.0f) ? 0 : ((a > 0.0f) ? +1 : -1); }
87DE_INLINE float		deFloatFloor		(float a)					{ return (float)floor(a); }
88DE_INLINE float		deFloatCeil			(float a)					{ return (float)ceil(a); }
89DE_INLINE float		deFloatRound		(float a)					{ return deFloatFloor(a + 0.5f); }
90DE_INLINE float 	deFloatFrac			(float a) 					{ return a - deFloatFloor(a); }
91DE_INLINE float		deFloatMod			(float a, float b)			{ return (float)fmod(a, b); }
92DE_INLINE float		deFloatModf			(float x, float* i)			{ double j = 0; double ret = modf(x, &j); *i = (float)j; return (float)ret; }
93DE_INLINE float		deFloatMadd			(float a, float b, float c)	{ return (a*b) + c; }
94DE_INLINE float		deFloatTrunc		(float a)					{ return deFloatSign(a) * deFloatFloor(deFloatAbs(a)); }
95DE_INLINE float		deFloatLdExp		(float a, int exponent)		{ return (float)ldexp(a, exponent); }
96DE_INLINE float		deFloatFrExp		(float x, int* exponent)	{ return (float)frexp(x, exponent); }
97float				deFloatFractExp		(float x, int* exponent);
98
99DE_INLINE double	deSign				(double x)						{ return deIsNaN(x) ? x : (double)((x > 0.0) - (x < 0.0)); }
100DE_INLINE int		deIntSign			(double x)						{ return (x > 0.0) - (x < 0.0); }
101DE_INLINE double	deFloor				(double a)						{ return floor(a); }
102DE_INLINE double	deCeil				(double a)						{ return ceil(a); }
103DE_INLINE double	deRound				(double a)						{ return floor(a + 0.5); }
104DE_INLINE double 	deFrac				(double a) 						{ return a - deFloor(a); }
105DE_INLINE double	deMod				(double a, double b)			{ return fmod(a, b); }
106DE_INLINE double	deModf				(double x, double* i)			{ return modf(x, i); }
107DE_INLINE double	deMadd				(double a, double b, double c)	{ return (a*b) + c; }
108DE_INLINE double	deTrunc				(double a)						{ return deSign(a) * floor(fabs(a)); }
109DE_INLINE double	deLdExp				(double a, int exponent)		{ return ldexp(a, exponent); }
110double				deRoundEven			(double a);
111DE_INLINE double	deFrExp				(double x, int* exponent)		{ return frexp(x, exponent); }
112/* Like frexp, except the returned fraction is in range [1.0, 2.0) */
113double				deFractExp			(double x, int* exponent);
114
115/* Exponential functions. */
116
117DE_INLINE float		deFloatPow			(float a, float b)			{ return (float)pow(a, b); }
118DE_INLINE float		deFloatExp			(float a)					{ return (float)exp(a); }
119DE_INLINE float		deFloatLog			(float a)					{ return (float)log(a); }
120DE_INLINE float		deFloatExp2			(float a)					{ return (float)exp(a * DE_LOG_2); }
121DE_INLINE float		deFloatLog2			(float a)					{ return (float)log(a) * DE_INV_LOG_2; }
122DE_INLINE float		deFloatSqrt			(float a)					{ return (float)sqrt(a); }
123DE_INLINE float		deFloatRcp			(float a)					{ return (1.0f / a); }
124DE_INLINE float		deFloatRsq			(float a)					{ float s = (float)sqrt(a); return (s == 0.0f) ? 0.0f : (1.0f / s); }
125
126DE_INLINE double	dePow				(double a, double b)		{ return pow(a, b); }
127DE_INLINE double	deExp				(double a)					{ return exp(a); }
128DE_INLINE double	deLog				(double a)					{ return log(a); }
129DE_INLINE double	deExp2				(double a)					{ return exp(a * log(2.0)); }
130DE_INLINE double	deLog2				(double a)					{ return log(a) / log(2.0); }
131DE_INLINE double	deSqrt				(double a)					{ return sqrt(a); }
132DE_INLINE double	deCbrt				(double a)					{ return deSign(a) * dePow(deAbs(a), 1.0 / 3.0); }
133
134/* Geometric functions. */
135
136DE_INLINE float		deFloatRadians		(float a)					{ return a * (DE_PI / 180.0f); }
137DE_INLINE float		deFloatDegrees		(float a)					{ return a * (180.0f / DE_PI); }
138DE_INLINE float		deFloatSin			(float a)					{ return (float)sin(a); }
139DE_INLINE float		deFloatCos			(float a)					{ return (float)cos(a); }
140DE_INLINE float		deFloatTan			(float a)					{ return (float)tan(a); }
141DE_INLINE float		deFloatAsin			(float a)					{ return (float)asin(a); }
142DE_INLINE float		deFloatAcos			(float a)					{ return (float)acos(a); }
143DE_INLINE float		deFloatAtan2		(float y, float x)			{ return (float)atan2(y, x); }
144DE_INLINE float		deFloatAtanOver		(float yOverX)				{ return (float)atan(yOverX); }
145DE_INLINE float		deFloatSinh			(float a)					{ return (float)sinh(a); }
146DE_INLINE float		deFloatCosh			(float a)					{ return (float)cosh(a); }
147DE_INLINE float		deFloatTanh			(float a)					{ return (float)tanh(a); }
148DE_INLINE float		deFloatAsinh		(float a)					{ return deFloatLog(a + deFloatSqrt(a*a + 1)); }
149DE_INLINE float		deFloatAcosh		(float a)					{ return deFloatLog(a + deFloatSqrt(a*a - 1)); }
150DE_INLINE float		deFloatAtanh		(float a)					{ return 0.5f*deFloatLog((1.0f+a)/(1.0f-a)); }
151
152DE_INLINE double	deSin			(double a)						{ return sin(a); }
153DE_INLINE double	deCos			(double a)						{ return cos(a); }
154DE_INLINE double	deTan			(double a)						{ return tan(a); }
155DE_INLINE double	deAsin			(double a)						{ return asin(a); }
156DE_INLINE double	deAcos			(double a)						{ return acos(a); }
157DE_INLINE double	deAtan2			(double y, double x)			{ return atan2(y, x); }
158DE_INLINE double	deAtanOver		(double yOverX)					{ return atan(yOverX); }
159DE_INLINE double	deSinh			(double a)						{ return sinh(a); }
160DE_INLINE double	deCosh			(double a)						{ return cosh(a); }
161DE_INLINE double	deTanh			(double a)						{ return tanh(a); }
162DE_INLINE double	deAsinh			(double a)						{ return deLog(a + deSqrt(a*a + 1)); }
163DE_INLINE double	deAcosh			(double a)						{ return deLog(a + deSqrt(a*a - 1)); }
164DE_INLINE double	deAtanh			(double a)						{ return 0.5*deLog((1.0+a)/(1.0-a)); }
165
166/* Interpolation. */
167
168DE_INLINE float		deFloatMix			(float a, float b, float t)	{ return a*(1.0f-t) + b*t; }
169DE_INLINE float		deFloatStep			(float limit, float val)	{ return (val < limit) ? 0.0f : 1.0f; }
170DE_INLINE float		deFloatSmoothStep	(float e0, float e1, float v)
171{
172	float t;
173	if (v <= e0) return 0.0f;
174	if (v >= e1) return 1.0f;
175	t = (v - e0) / (e1 - e0);
176	return t * t * (3.0f - 2.0f * t);
177}
178
179DE_INLINE double	deMix				(double a, double b, double t)	{ return a*(1.0-t) + b*t; }
180DE_INLINE double	deStep				(double limit, double val)		{ return (val < limit) ? 0.0 : 1.0; }
181
182/* Comparison functions. */
183
184DE_INLINE deBool	deFloatCmpEQ		(float a, float b)			{ return (a == b); }
185DE_INLINE deBool	deFloatCmpNE		(float a, float b)			{ return (a != b); }
186DE_INLINE deBool	deFloatCmpLT		(float a, float b)			{ return (a < b);  }
187DE_INLINE deBool	deFloatCmpLE		(float a, float b)			{ return (a <= b); }
188DE_INLINE deBool	deFloatCmpGT		(float a, float b)			{ return (a > b);  }
189DE_INLINE deBool	deFloatCmpGE		(float a, float b)			{ return (a >= b); }
190
191/* Convert int to float. If the value cannot be represented exactly in native single precision format, return
192 * either the nearest lower or the nearest higher representable value, chosen in an implementation-defined manner.
193 *
194 * \note Choosing either nearest lower or nearest higher means that implementation could for example consistently
195 *       choose the lower value, i.e. this function does not round towards nearest.
196 * \note Value returned is in native single precision format. For example with x86 extended precision, the value
197 *       returned might not be representable in IEEE single precision float.
198 */
199DE_INLINE float		deInt32ToFloat				(deInt32 x)					{ return (float)x; }
200
201/* Convert to float. If the value cannot be represented exactly in IEEE single precision floating point format,
202 * return the nearest lower (round towards negative inf). */
203float				deInt32ToFloatRoundToNegInf	(deInt32 x);
204
205/* Convert to float. If the value cannot be represented exactly IEEE single precision floating point format,
206 * return the nearest higher (round towards positive inf). */
207float				deInt32ToFloatRoundToPosInf	(deInt32 x);
208
209/* Conversion to integer. */
210
211DE_INLINE deInt32	deChopFloatToInt32	(float x)					{ return (deInt32)x; }
212DE_INLINE deInt32	deFloorFloatToInt32	(float x)					{ return (deInt32)(deFloatFloor(x)); }
213DE_INLINE deInt32	deCeilFloatToInt32	(float x)					{ return (deInt32)(deFloatCeil(x)); }
214
215/* Arithmetic round */
216DE_INLINE deInt16 	deRoundFloatToInt16 (float x)				{ if(x >= 0.0f) return (deInt16)(x + 0.5f); else return (deInt16)(x - 0.5f); }
217DE_INLINE deInt32	deRoundFloatToInt32	(float x)				{ if(x >= 0.0f) return (deInt32)(x + 0.5f); else return (deInt32)(x - 0.5f); }
218DE_INLINE deInt64	deRoundFloatToInt64 (float x)				{ if(x >= 0.0f) return (deInt64)(x + 0.5f); else return (deInt64)(x - 0.5f); }
219
220DE_END_EXTERN_C
221
222#endif /* _DEMATH_H */
223