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gb_math.h
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gb_math.h
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/* gb_math.h - v0.07c - public domain C math library - no warranty implied; use at your own risk
A C math library geared towards game development
use '#define GB_MATH_IMPLEMENTATION' before including to create the implementation in _ONE_ file
Version History:
0.07f - Fix constants
0.07e - Fixed a warning
0.07d - Fix mat4_inverse
0.07c - Add gb_random01
0.07b - Fix mat4_inverse
0.07a - Fix Mat2
0.07 - Better Mat4 procedures
0.06h - Ignore silly warnings
0.06g - Remove memzero
0.06f - Remove warning on MSVC
0.06e - Change brace style and fix some warnings
0.06d - Bug fix
0.06c - Remove extra needed define for C++ and inline all operators
0.06b - Just formatting
0.06a - Implement rough versions of mod, remainder, copy_sign
0.06 - Windows GCC Support and C90-ish Support
0.05 - Less/no dependencies or CRT
0.04d - License Update
0.04c - Use 64-bit murmur64 version on WIN64
0.04b - Fix strict aliasing in gb_quake_rsqrt
0.04a - Minor bug fixes
0.04 - Namespace everything with gb
0.03 - Complete Replacement
0.01 - Initial Version
LICENSE
This software is dual-licensed to the public domain and under the following
license: you are granted a perpetual, irrevocable license to copy, modify,
publish, and distribute this file as you see fit.
WARNING
- This library is _slightly_ experimental and features may not work as expected.
- This also means that many functions are not documented.
CONTENTS
- Common Macros
- Types
- gbVec(2,3,4)
- gbMat(2,3,4)
- gbFloat(2,3,4)
- gbQuat
- gbRect(2,3)
- gbAabb(2,3)
- gbHalf (16-bit floating point) (storage only)
- Operations
- Functions
- Type Functions
- Random
- Hash
*/
#ifndef GB_MATH_INCLUDE_GB_MATH_H
#define GB_MATH_INCLUDE_GB_MATH_H
#include <stddef.h>
#if !defined(GB_MATH_NO_MATH_H)
#include <math.h>
#else
#include <intrin.h>
#endif
#ifndef GB_MATH_DEF
#ifdef GB_MATH_STATIC
#define GB_MATH_DEF static
#else
#define GB_MATH_DEF extern
#endif
#endif
#if defined(_MSC_VER)
#pragma warning(push)
#pragma warning(disable:4201)
#endif
typedef union gbVec2 {
struct { float x, y; };
float e[2];
} gbVec2;
typedef union gbVec3 {
struct { float x, y, z; };
struct { float r, g, b; };
gbVec2 xy;
float e[3];
} gbVec3;
typedef union gbVec4 {
struct { float x, y, z, w; };
struct { float r, g, b, a; };
struct { gbVec2 xy, zw; };
gbVec3 xyz;
gbVec3 rgb;
float e[4];
} gbVec4;
typedef union gbMat2 {
struct { gbVec2 x, y; };
gbVec2 col[2];
float e[4];
} gbMat2;
typedef union gbMat3 {
struct { gbVec3 x, y, z; };
gbVec3 col[3];
float e[9];
} gbMat3;
typedef union gbMat4 {
struct { gbVec4 x, y, z, w; };
gbVec4 col[4];
float e[16];
} gbMat4;
typedef union gbQuat {
struct { float x, y, z, w; };
gbVec4 xyzw;
gbVec3 xyz;
float e[4];
} gbQuat;
#if defined(_MSC_VER)
#pragma warning(pop)
#endif
typedef float gbFloat2[2];
typedef float gbFloat3[3];
typedef float gbFloat4[4];
typedef struct gbRect2 { gbVec2 pos, dim; } gbRect2;
typedef struct gbRect3 { gbVec3 pos, dim; } gbRect3;
typedef struct gbAabb2 { gbVec2 centre, half_size; } gbAabb2;
typedef struct gbAabb3 { gbVec3 centre, half_size; } gbAabb3;
#if defined(_MSC_VER)
typedef unsigned __int32 gb_math_u32;
typedef unsigned __int64 gb_math_u64;
#else
#if defined(GB_USE_STDINT)
#include <stdint.h>
typedef uint32_t gb_math_u32;
typedef uint64_t gb_math_u64;
#else
typedef unsigned int gb_math_u32;
typedef unsigned long long gb_math_u64;
#endif
#endif
typedef short gbHalf;
#ifndef GB_MATH_CONSTANTS
#define GB_MATH_CONSTANTS
#define GB_MATH_EPSILON 1.19209290e-7f
#define GB_MATH_ZERO 0.0f
#define GB_MATH_ONE 1.0f
#define GB_MATH_TWO_THIRDS 0.666666666666666666666666666666666666667f
#define GB_MATH_TAU 6.28318530717958647692528676655900576f
#define GB_MATH_PI 3.14159265358979323846264338327950288f
#define GB_MATH_ONE_OVER_TAU 0.159154943091895335768883763372514362f
#define GB_MATH_ONE_OVER_PI 0.318309886183790671537767526745028724f
#define GB_MATH_TAU_OVER_2 3.14159265358979323846264338327950288f
#define GB_MATH_TAU_OVER_4 1.570796326794896619231321691639751442f
#define GB_MATH_TAU_OVER_8 0.785398163397448309615660845819875721f
#define GB_MATH_E 2.7182818284590452353602874713526625f
#define GB_MATH_SQRT_TWO 1.41421356237309504880168872420969808f
#define GB_MATH_SQRT_THREE 1.73205080756887729352744634150587236f
#define GB_MATH_SQRT_FIVE 2.23606797749978969640917366873127623f
#define GB_MATH_LOG_TWO 0.693147180559945309417232121458176568f
#define GB_MATH_LOG_TEN 2.30258509299404568401799145468436421f
#endif
#if defined(__cplusplus)
extern "C" {
#endif
#ifndef gb_clamp
#define gb_clamp(x, lower, upper) (gb_min(gb_max(x, (lower)), (upper)))
#endif
#ifndef gb_clamp01
#define gb_clamp01(x) gb_clamp(x, 0, 1)
#endif
#ifndef gb_square
#define gb_square(x) ((x)*(x))
#endif
#ifndef gb_cube
#define gb_cube(x) ((x)*(x)*(x))
#endif
#ifndef gb_abs
#define gb_abs(x) ((x) > 0 ? (x) : -(x))
#endif
#ifndef gb_sign
#define gb_sign(x) ((x) >= 0 ? 1 : -1)
#endif
GB_MATH_DEF float gb_to_radians(float degrees);
GB_MATH_DEF float gb_to_degrees(float radians);
/* NOTE(bill): Because to interpolate angles */
GB_MATH_DEF float gb_angle_diff(float radians_a, float radians_b);
#ifndef gb_min
#define gb_min(a, b) ((a) < (b) ? (a) : (b))
#endif
#ifndef gb_max
#define gb_max(a, b) ((a) > (b) ? (a) : (b))
#endif
#ifndef gb_min3
#define gb_min3(a, b, c) gb_min(gb_min(a, b), c)
#endif
#ifndef gb_max3
#define gb_max3(a, b, c) gb_max(gb_max(a, b), c)
#endif
GB_MATH_DEF float gb_copy_sign (float x, float y);
GB_MATH_DEF float gb_remainder (float x, float y);
GB_MATH_DEF float gb_mod (float x, float y);
GB_MATH_DEF float gb_sqrt (float a);
GB_MATH_DEF float gb_rsqrt (float a);
GB_MATH_DEF float gb_quake_rsqrt(float a); /* NOTE(bill): It's probably better to use 1.0f/gb_sqrt(a)
* And for simd, there is usually isqrt functions too!
*/
GB_MATH_DEF float gb_sin (float radians);
GB_MATH_DEF float gb_cos (float radians);
GB_MATH_DEF float gb_tan (float radians);
GB_MATH_DEF float gb_arcsin (float a);
GB_MATH_DEF float gb_arccos (float a);
GB_MATH_DEF float gb_arctan (float a);
GB_MATH_DEF float gb_arctan2(float y, float x);
GB_MATH_DEF float gb_exp (float x);
GB_MATH_DEF float gb_exp2 (float x);
GB_MATH_DEF float gb_log (float x);
GB_MATH_DEF float gb_log2 (float x);
GB_MATH_DEF float gb_fast_exp (float x); /* NOTE(bill): Only valid from -1 <= x <= +1 */
GB_MATH_DEF float gb_fast_exp2(float x); /* NOTE(bill): Only valid from -1 <= x <= +1 */
GB_MATH_DEF float gb_pow (float x, float y); /* x^y */
GB_MATH_DEF float gb_round(float x);
GB_MATH_DEF float gb_floor(float x);
GB_MATH_DEF float gb_ceil (float x);
GB_MATH_DEF float gb_half_to_float(gbHalf value);
GB_MATH_DEF gbHalf gb_float_to_half(float value);
GB_MATH_DEF gbVec2 gb_vec2_zero(void);
GB_MATH_DEF gbVec2 gb_vec2 (float x, float y);
GB_MATH_DEF gbVec2 gb_vec2v (float x[2]);
GB_MATH_DEF gbVec3 gb_vec3_zero(void);
GB_MATH_DEF gbVec3 gb_vec3 (float x, float y, float z);
GB_MATH_DEF gbVec3 gb_vec3v (float x[3]);
GB_MATH_DEF gbVec4 gb_vec4_zero(void);
GB_MATH_DEF gbVec4 gb_vec4 (float x, float y, float z, float w);
GB_MATH_DEF gbVec4 gb_vec4v (float x[4]);
GB_MATH_DEF void gb_vec2_add(gbVec2 *d, gbVec2 v0, gbVec2 v1);
GB_MATH_DEF void gb_vec2_sub(gbVec2 *d, gbVec2 v0, gbVec2 v1);
GB_MATH_DEF void gb_vec2_mul(gbVec2 *d, gbVec2 v, float s);
GB_MATH_DEF void gb_vec2_div(gbVec2 *d, gbVec2 v, float s);
GB_MATH_DEF void gb_vec3_add(gbVec3 *d, gbVec3 v0, gbVec3 v1);
GB_MATH_DEF void gb_vec3_sub(gbVec3 *d, gbVec3 v0, gbVec3 v1);
GB_MATH_DEF void gb_vec3_mul(gbVec3 *d, gbVec3 v, float s);
GB_MATH_DEF void gb_vec3_div(gbVec3 *d, gbVec3 v, float s);
GB_MATH_DEF void gb_vec4_add(gbVec4 *d, gbVec4 v0, gbVec4 v1);
GB_MATH_DEF void gb_vec4_sub(gbVec4 *d, gbVec4 v0, gbVec4 v1);
GB_MATH_DEF void gb_vec4_mul(gbVec4 *d, gbVec4 v, float s);
GB_MATH_DEF void gb_vec4_div(gbVec4 *d, gbVec4 v, float s);
GB_MATH_DEF void gb_vec2_addeq(gbVec2 *d, gbVec2 v);
GB_MATH_DEF void gb_vec2_subeq(gbVec2 *d, gbVec2 v);
GB_MATH_DEF void gb_vec2_muleq(gbVec2 *d, float s);
GB_MATH_DEF void gb_vec2_diveq(gbVec2 *d, float s);
GB_MATH_DEF void gb_vec3_addeq(gbVec3 *d, gbVec3 v);
GB_MATH_DEF void gb_vec3_subeq(gbVec3 *d, gbVec3 v);
GB_MATH_DEF void gb_vec3_muleq(gbVec3 *d, float s);
GB_MATH_DEF void gb_vec3_diveq(gbVec3 *d, float s);
GB_MATH_DEF void gb_vec4_addeq(gbVec4 *d, gbVec4 v);
GB_MATH_DEF void gb_vec4_subeq(gbVec4 *d, gbVec4 v);
GB_MATH_DEF void gb_vec4_muleq(gbVec4 *d, float s);
GB_MATH_DEF void gb_vec4_diveq(gbVec4 *d, float s);
GB_MATH_DEF float gb_vec2_dot(gbVec2 v0, gbVec2 v1);
GB_MATH_DEF float gb_vec3_dot(gbVec3 v0, gbVec3 v1);
GB_MATH_DEF float gb_vec4_dot(gbVec4 v0, gbVec4 v1);
GB_MATH_DEF void gb_vec2_cross(float *d, gbVec2 v0, gbVec2 v1);
GB_MATH_DEF void gb_vec3_cross(gbVec3 *d, gbVec3 v0, gbVec3 v1);
GB_MATH_DEF float gb_vec2_mag2(gbVec2 v);
GB_MATH_DEF float gb_vec3_mag2(gbVec3 v);
GB_MATH_DEF float gb_vec4_mag2(gbVec4 v);
GB_MATH_DEF float gb_vec2_mag(gbVec2 v);
GB_MATH_DEF float gb_vec3_mag(gbVec3 v);
GB_MATH_DEF float gb_vec4_mag(gbVec4 v);
GB_MATH_DEF void gb_vec2_norm(gbVec2 *d, gbVec2 v);
GB_MATH_DEF void gb_vec3_norm(gbVec3 *d, gbVec3 v);
GB_MATH_DEF void gb_vec4_norm(gbVec4 *d, gbVec4 v);
GB_MATH_DEF void gb_vec2_norm0(gbVec2 *d, gbVec2 v);
GB_MATH_DEF void gb_vec3_norm0(gbVec3 *d, gbVec3 v);
GB_MATH_DEF void gb_vec4_norm0(gbVec4 *d, gbVec4 v);
GB_MATH_DEF void gb_vec2_reflect(gbVec2 *d, gbVec2 i, gbVec2 n);
GB_MATH_DEF void gb_vec3_reflect(gbVec3 *d, gbVec3 i, gbVec3 n);
GB_MATH_DEF void gb_vec2_refract(gbVec2 *d, gbVec2 i, gbVec2 n, float eta);
GB_MATH_DEF void gb_vec3_refract(gbVec3 *d, gbVec3 i, gbVec3 n, float eta);
GB_MATH_DEF float gb_vec2_aspect_ratio(gbVec2 v);
GB_MATH_DEF void gb_mat2_identity (gbMat2 *m);
GB_MATH_DEF void gb_float22_identity(float m[2][2]);
GB_MATH_DEF void gb_mat2_transpose (gbMat2 *m);
GB_MATH_DEF void gb_mat2_mul (gbMat2 *out, gbMat2 *m1, gbMat2 *m2);
GB_MATH_DEF void gb_mat2_mul_vec2 (gbVec2 *out, gbMat2 *m, gbVec2 in);
GB_MATH_DEF void gb_mat2_inverse (gbMat2 *out, gbMat2 *in);
GB_MATH_DEF float gb_mat2_determinate(gbMat2 *m);
GB_MATH_DEF gbMat2 *gb_mat2_v(gbVec2 m[2]);
GB_MATH_DEF gbMat2 *gb_mat2_f(float m[2][2]);
GB_MATH_DEF gbFloat2 *gb_float22_m(gbMat2 *m);
GB_MATH_DEF gbFloat2 *gb_float22_v(gbVec2 m[2]);
GB_MATH_DEF gbFloat2 *gb_float22_4(float m[4]);
GB_MATH_DEF void gb_float22_transpose(float (*vec)[2]);
GB_MATH_DEF void gb_float22_mul (float (*out)[2], float (*mat1)[2], float (*mat2)[2]);
GB_MATH_DEF void gb_float22_mul_vec2 (gbVec2 *out, float m[2][2], gbVec2 in);
GB_MATH_DEF void gb_mat3_identity (gbMat3 *m);
GB_MATH_DEF void gb_float33_identity(float m[3][3]);
GB_MATH_DEF void gb_mat3_transpose (gbMat3 *m);
GB_MATH_DEF void gb_mat3_mul (gbMat3 *out, gbMat3 *m1, gbMat3 *m2);
GB_MATH_DEF void gb_mat3_mul_vec3 (gbVec3 *out, gbMat3 *m, gbVec3 in);
GB_MATH_DEF void gb_mat3_inverse (gbMat3 *out, gbMat3 *in);
GB_MATH_DEF float gb_mat3_determinate(gbMat3 *m);
GB_MATH_DEF gbMat3 *gb_mat3_v(gbVec3 m[3]);
GB_MATH_DEF gbMat3 *gb_mat3_f(float m[3][3]);
GB_MATH_DEF gbFloat3 *gb_float33_m(gbMat3 *m);
GB_MATH_DEF gbFloat3 *gb_float33_v(gbVec3 m[3]);
GB_MATH_DEF gbFloat3 *gb_float33_9(float m[9]);
GB_MATH_DEF void gb_float33_transpose(float (*vec)[3]);
GB_MATH_DEF void gb_float33_mul (float (*out)[3], float (*mat1)[3], float (*mat2)[3]);
GB_MATH_DEF void gb_float33_mul_vec3 (gbVec3 *out, float m[3][3], gbVec3 in);
GB_MATH_DEF void gb_mat4_identity (gbMat4 *m);
GB_MATH_DEF void gb_float44_identity(float m[4][4]);
GB_MATH_DEF void gb_mat4_transpose (gbMat4 *m);
GB_MATH_DEF void gb_mat4_mul (gbMat4 *out, gbMat4 *m1, gbMat4 *m2);
GB_MATH_DEF void gb_mat4_mul_vec4 (gbVec4 *out, gbMat4 *m, gbVec4 in);
GB_MATH_DEF void gb_mat4_inverse (gbMat4 *out, gbMat4 *in);
GB_MATH_DEF gbMat4 *gb_mat4_v(gbVec4 m[4]);
GB_MATH_DEF gbMat4 *gb_mat4_f(float m[4][4]);
GB_MATH_DEF gbFloat4 *gb_float44_m (gbMat4 *m);
GB_MATH_DEF gbFloat4 *gb_float44_v (gbVec4 m[4]);
GB_MATH_DEF gbFloat4 *gb_float44_16(float m[16]);
GB_MATH_DEF void gb_float44_transpose(float (*vec)[4]);
GB_MATH_DEF void gb_float44_mul (float (*out)[4], float (*mat1)[4], float (*mat2)[4]);
GB_MATH_DEF void gb_float44_mul_vec4 (gbVec4 *out, float m[4][4], gbVec4 in);
GB_MATH_DEF void gb_mat4_translate (gbMat4 *out, gbVec3 v);
GB_MATH_DEF void gb_mat4_rotate (gbMat4 *out, gbVec3 v, float angle_radians);
GB_MATH_DEF void gb_mat4_scale (gbMat4 *out, gbVec3 v);
GB_MATH_DEF void gb_mat4_scalef (gbMat4 *out, float s);
GB_MATH_DEF void gb_mat4_ortho2d (gbMat4 *out, float left, float right, float bottom, float top);
GB_MATH_DEF void gb_mat4_ortho3d (gbMat4 *out, float left, float right, float bottom, float top, float z_near, float z_far);
GB_MATH_DEF void gb_mat4_perspective (gbMat4 *out, float fovy, float aspect, float z_near, float z_far);
GB_MATH_DEF void gb_mat4_infinite_perspective(gbMat4 *out, float fovy, float aspect, float z_near);
GB_MATH_DEF void gb_mat4_look_at(gbMat4 *out, gbVec3 eye, gbVec3 centre, gbVec3 up);
GB_MATH_DEF gbQuat gb_quat (float x, float y, float z, float w);
GB_MATH_DEF gbQuat gb_quatv (float e[4]);
GB_MATH_DEF gbQuat gb_quat_axis_angle (gbVec3 axis, float angle_radians);
GB_MATH_DEF gbQuat gb_quat_euler_angles(float pitch, float yaw, float roll);
GB_MATH_DEF gbQuat gb_quat_identity (void);
GB_MATH_DEF void gb_quat_add(gbQuat *d, gbQuat q0, gbQuat q1);
GB_MATH_DEF void gb_quat_sub(gbQuat *d, gbQuat q0, gbQuat q1);
GB_MATH_DEF void gb_quat_mul(gbQuat *d, gbQuat q0, gbQuat q1);
GB_MATH_DEF void gb_quat_div(gbQuat *d, gbQuat q0, gbQuat q1);
GB_MATH_DEF void gb_quat_mulf(gbQuat *d, gbQuat q, float s);
GB_MATH_DEF void gb_quat_divf(gbQuat *d, gbQuat q, float s);
GB_MATH_DEF void gb_quat_addeq(gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_subeq(gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_muleq(gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_diveq(gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_muleqf(gbQuat *d, float s);
GB_MATH_DEF void gb_quat_diveqf(gbQuat *d, float s);
GB_MATH_DEF float gb_quat_dot(gbQuat q0, gbQuat q1);
GB_MATH_DEF float gb_quat_mag(gbQuat q);
GB_MATH_DEF void gb_quat_norm (gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_conj (gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_inverse(gbQuat *d, gbQuat q);
GB_MATH_DEF void gb_quat_axis (gbVec3 *axis, gbQuat q);
GB_MATH_DEF float gb_quat_angle(gbQuat q);
GB_MATH_DEF float gb_quat_pitch(gbQuat q);
GB_MATH_DEF float gb_quat_yaw (gbQuat q);
GB_MATH_DEF float gb_quat_roll (gbQuat q);
/* NOTE(bill): Rotate v by q */
GB_MATH_DEF void gb_quat_rotate_vec3(gbVec3 *d, gbQuat q, gbVec3 v);
GB_MATH_DEF void gb_mat4_from_quat (gbMat4 *out, gbQuat q);
GB_MATH_DEF void gb_quat_from_mat4 (gbQuat *out, gbMat4 *m);
/* Interpolations */
GB_MATH_DEF float gb_lerp (float a, float b, float t);
GB_MATH_DEF float gb_unlerp (float t, float a, float b);
GB_MATH_DEF float gb_smooth_step (float a, float b, float t);
GB_MATH_DEF float gb_smoother_step(float a, float b, float t);
GB_MATH_DEF void gb_vec2_lerp(gbVec2 *d, gbVec2 a, gbVec2 b, float t);
GB_MATH_DEF void gb_vec3_lerp(gbVec3 *d, gbVec3 a, gbVec3 b, float t);
GB_MATH_DEF void gb_vec4_lerp(gbVec4 *d, gbVec4 a, gbVec4 b, float t);
GB_MATH_DEF void gb_quat_lerp (gbQuat *d, gbQuat a, gbQuat b, float t);
GB_MATH_DEF void gb_quat_nlerp(gbQuat *d, gbQuat a, gbQuat b, float t);
GB_MATH_DEF void gb_quat_slerp(gbQuat *d, gbQuat a, gbQuat b, float t);
GB_MATH_DEF void gb_quat_nquad(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t);
GB_MATH_DEF void gb_quat_squad(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t);
GB_MATH_DEF void gb_quat_slerp_approx(gbQuat *d, gbQuat a, gbQuat b, float t);
GB_MATH_DEF void gb_quat_squad_approx(gbQuat *d, gbQuat p, gbQuat a, gbQuat b, gbQuat q, float t);
/* Rects */
GB_MATH_DEF gbRect2 gb_rect2(gbVec2 pos, gbVec2 dim);
GB_MATH_DEF gbRect2 gb_rect2v(float v[4]);
GB_MATH_DEF gbRect3 gb_rect3(gbVec3 pos, gbVec3 dim);
GB_MATH_DEF gbRect3 gb_rect3v(float v[6]);
GB_MATH_DEF int gb_rect2_contains (gbRect2 a, float x, float y);
GB_MATH_DEF int gb_rect2_contains_vec2 (gbRect2 a, gbVec2 p);
GB_MATH_DEF int gb_rect2_intersects (gbRect2 a, gbRect2 b);
GB_MATH_DEF int gb_rect2_intersection_result(gbRect2 a, gbRect2 b, gbRect2 *intersection);
#ifndef GB_MURMUR64_DEFAULT_SEED
#define GB_MURMUR64_DEFAULT_SEED 0x9747b28c
#endif
/* Hashing */
GB_MATH_DEF gb_math_u64 gb_hash_murmur64(void const *key, size_t num_bytes, gb_math_u64 seed);
/* Random */
/* TODO(bill): Use a generator for the random numbers */
GB_MATH_DEF float gb_random_range_float(float min_inc, float max_inc);
GB_MATH_DEF int gb_random_range_int (int min_inc, int max_inc);
GB_MATH_DEF float gb_random01 (void);
#if defined(__cplusplus)
}
#endif
#if defined(__cplusplus)
/* TODO(bill): How should I apply GB_MATH_DEF to these operator overloads? */
inline bool operator==(gbVec2 a, gbVec2 b) { return (a.x == b.x) && (a.y == b.y); }
inline bool operator!=(gbVec2 a, gbVec2 b) { return !operator==(a, b); }
inline gbVec2 operator+(gbVec2 a) { return a; }
inline gbVec2 operator-(gbVec2 a) { gbVec2 r = {-a.x, -a.y}; return r; }
inline gbVec2 operator+(gbVec2 a, gbVec2 b) { gbVec2 r; gb_vec2_add(&r, a, b); return r; }
inline gbVec2 operator-(gbVec2 a, gbVec2 b) { gbVec2 r; gb_vec2_sub(&r, a, b); return r; }
inline gbVec2 operator*(gbVec2 a, float scalar) { gbVec2 r; gb_vec2_mul(&r, a, scalar); return r; }
inline gbVec2 operator*(float scalar, gbVec2 a) { return operator*(a, scalar); }
inline gbVec2 operator/(gbVec2 a, float scalar) { return operator*(a, 1.0f/scalar); }
/* Hadamard Product */
inline gbVec2 operator*(gbVec2 a, gbVec2 b) { gbVec2 r = {a.x*b.x, a.y*b.y}; return r; }
inline gbVec2 operator/(gbVec2 a, gbVec2 b) { gbVec2 r = {a.x/b.x, a.y/b.y}; return r; }
inline gbVec2 &operator+=(gbVec2 &a, gbVec2 b) { return (a = a + b); }
inline gbVec2 &operator-=(gbVec2 &a, gbVec2 b) { return (a = a - b); }
inline gbVec2 &operator*=(gbVec2 &a, float scalar) { return (a = a * scalar); }
inline gbVec2 &operator/=(gbVec2 &a, float scalar) { return (a = a / scalar); }
inline bool operator==(gbVec3 a, gbVec3 b) { return (a.x == b.x) && (a.y == b.y) && (a.z == b.z); }
inline bool operator!=(gbVec3 a, gbVec3 b) { return !operator==(a, b); }
inline gbVec3 operator+(gbVec3 a) { return a; }
inline gbVec3 operator-(gbVec3 a) { gbVec3 r = {-a.x, -a.y, -a.z}; return r; }
inline gbVec3 operator+(gbVec3 a, gbVec3 b) { gbVec3 r; gb_vec3_add(&r, a, b); return r; }
inline gbVec3 operator-(gbVec3 a, gbVec3 b) { gbVec3 r; gb_vec3_sub(&r, a, b); return r; }
inline gbVec3 operator*(gbVec3 a, float scalar) { gbVec3 r; gb_vec3_mul(&r, a, scalar); return r; }
inline gbVec3 operator*(float scalar, gbVec3 a) { return operator*(a, scalar); }
inline gbVec3 operator/(gbVec3 a, float scalar) { return operator*(a, 1.0f/scalar); }
/* Hadamard Product */
inline gbVec3 operator*(gbVec3 a, gbVec3 b) { gbVec3 r = {a.x*b.x, a.y*b.y, a.z*b.z}; return r; }
inline gbVec3 operator/(gbVec3 a, gbVec3 b) { gbVec3 r = {a.x/b.x, a.y/b.y, a.z/b.z}; return r; }
inline gbVec3 &operator+=(gbVec3 &a, gbVec3 b) { return (a = a + b); }
inline gbVec3 &operator-=(gbVec3 &a, gbVec3 b) { return (a = a - b); }
inline gbVec3 &operator*=(gbVec3 &a, float scalar) { return (a = a * scalar); }
inline gbVec3 &operator/=(gbVec3 &a, float scalar) { return (a = a / scalar); }
inline bool operator==(gbVec4 a, gbVec4 b) { return (a.x == b.x) && (a.y == b.y) && (a.z == b.z) && (a.w == b.w); }
inline bool operator!=(gbVec4 a, gbVec4 b) { return !operator==(a, b); }
inline gbVec4 operator+(gbVec4 a) { return a; }
inline gbVec4 operator-(gbVec4 a) { gbVec4 r = {-a.x, -a.y, -a.z, -a.w}; return r; }
inline gbVec4 operator+(gbVec4 a, gbVec4 b) { gbVec4 r; gb_vec4_add(&r, a, b); return r; }
inline gbVec4 operator-(gbVec4 a, gbVec4 b) { gbVec4 r; gb_vec4_sub(&r, a, b); return r; }
inline gbVec4 operator*(gbVec4 a, float scalar) { gbVec4 r; gb_vec4_mul(&r, a, scalar); return r; }
inline gbVec4 operator*(float scalar, gbVec4 a) { return operator*(a, scalar); }
inline gbVec4 operator/(gbVec4 a, float scalar) { return operator*(a, 1.0f/scalar); }
/* Hadamard Product */
inline gbVec4 operator*(gbVec4 a, gbVec4 b) { gbVec4 r = {a.x*b.x, a.y*b.y, a.z*b.z, a.w*b.w}; return r; }
inline gbVec4 operator/(gbVec4 a, gbVec4 b) { gbVec4 r = {a.x/b.x, a.y/b.y, a.z/b.z, a.w/b.w}; return r; }
inline gbVec4 &operator+=(gbVec4 &a, gbVec4 b) { return (a = a + b); }
inline gbVec4 &operator-=(gbVec4 &a, gbVec4 b) { return (a = a - b); }
inline gbVec4 &operator*=(gbVec4 &a, float scalar) { return (a = a * scalar); }
inline gbVec4 &operator/=(gbVec4 &a, float scalar) { return (a = a / scalar); }
inline gbMat2 operator+(gbMat2 const &a, gbMat2 const &b) {
int i, j;
gbMat2 r = {0};
for (j = 0; j < 2; j++) {
for (i = 0; i < 2; i++)
r.e[2*j+i] = a.e[2*j+i] + b.e[2*j+i];
}
return r;
}
inline gbMat2 operator-(gbMat2 const &a, gbMat2 const &b) {
int i, j;
gbMat2 r = {0};
for (j = 0; j < 2; j++) {
for (i = 0; i < 2; i++)
r.e[2*j+i] = a.e[2*j+i] - b.e[2*j+i];
}
return r;
}
inline gbMat2 operator*(gbMat2 const &a, gbMat2 const &b) { gbMat2 r; gb_mat2_mul(&r, (gbMat2 *)&a, (gbMat2 *)&b); return r; }
inline gbVec2 operator*(gbMat2 const &a, gbVec2 v) { gbVec2 r; gb_mat2_mul_vec2(&r, (gbMat2 *)&a, v); return r; }
inline gbMat2 operator*(gbMat2 const &a, float scalar) {
gbMat2 r = {0};
int i;
for (i = 0; i < 2*2; i++) r.e[i] = a.e[i] * scalar;
return r;
}
inline gbMat2 operator*(float scalar, gbMat2 const &a) { return operator*(a, scalar); }
inline gbMat2 operator/(gbMat2 const &a, float scalar) { return operator*(a, 1.0f/scalar); }
inline gbMat2& operator+=(gbMat2& a, gbMat2 const &b) { return (a = a + b); }
inline gbMat2& operator-=(gbMat2& a, gbMat2 const &b) { return (a = a - b); }
inline gbMat2& operator*=(gbMat2& a, gbMat2 const &b) { return (a = a * b); }
inline gbMat3 operator+(gbMat3 const &a, gbMat3 const &b) {
int i, j;
gbMat3 r = {0};
for (j = 0; j < 3; j++) {
for (i = 0; i < 3; i++)
r.e[3*j+i] = a.e[3*j+i] + b.e[3*j+i];
}
return r;
}
inline gbMat3 operator-(gbMat3 const &a, gbMat3 const &b) {
int i, j;
gbMat3 r = {0};
for (j = 0; j < 3; j++) {
for (i = 0; i < 3; i++)
r.e[3*j+i] = a.e[3*j+i] - b.e[3*j+i];
}
return r;
}
inline gbMat3 operator*(gbMat3 const &a, gbMat3 const &b) { gbMat3 r; gb_mat3_mul(&r, (gbMat3 *)&a, (gbMat3 *)&b); return r; }
inline gbVec3 operator*(gbMat3 const &a, gbVec3 v) { gbVec3 r; gb_mat3_mul_vec3(&r, (gbMat3 *)&a, v); return r; } inline gbMat3 operator*(gbMat3 const &a, float scalar) {
gbMat3 r = {0};
int i;
for (i = 0; i < 3*3; i++) r.e[i] = a.e[i] * scalar;
return r;
}
inline gbMat3 operator*(float scalar, gbMat3 const &a) { return operator*(a, scalar); }
inline gbMat3 operator/(gbMat3 const &a, float scalar) { return operator*(a, 1.0f/scalar); }
inline gbMat3& operator+=(gbMat3& a, gbMat3 const &b) { return (a = a + b); }
inline gbMat3& operator-=(gbMat3& a, gbMat3 const &b) { return (a = a - b); }
inline gbMat3& operator*=(gbMat3& a, gbMat3 const &b) { return (a = a * b); }
inline gbMat4 operator+(gbMat4 const &a, gbMat4 const &b) {
int i, j;
gbMat4 r = {0};
for (j = 0; j < 4; j++) {
for (i = 0; i < 4; i++)
r.e[4*j+i] = a.e[4*j+i] + b.e[4*j+i];
}
return r;
}
inline gbMat4 operator-(gbMat4 const &a, gbMat4 const &b) {
int i, j;
gbMat4 r = {0};
for (j = 0; j < 4; j++) {
for (i = 0; i < 4; i++)
r.e[4*j+i] = a.e[4*j+i] - b.e[4*j+i];
}
return r;
}
inline gbMat4 operator*(gbMat4 const &a, gbMat4 const &b) { gbMat4 r; gb_mat4_mul(&r, (gbMat4 *)&a, (gbMat4 *)&b); return r; }
inline gbVec4 operator*(gbMat4 const &a, gbVec4 v) { gbVec4 r; gb_mat4_mul_vec4(&r, (gbMat4 *)&a, v); return r; }
inline gbMat4 operator*(gbMat4 const &a, float scalar) {
gbMat4 r = {0};
int i;
for (i = 0; i < 4*4; i++) r.e[i] = a.e[i] * scalar;
return r;
}
inline gbMat4 operator*(float scalar, gbMat4 const &a) { return operator*(a, scalar); }
inline gbMat4 operator/(gbMat4 const &a, float scalar) { return operator*(a, 1.0f/scalar); }
inline gbMat4& operator+=(gbMat4 &a, gbMat4 const &b) { return (a = a + b); }
inline gbMat4& operator-=(gbMat4 &a, gbMat4 const &b) { return (a = a - b); }
inline gbMat4& operator*=(gbMat4 &a, gbMat4 const &b) { return (a = a * b); }
inline bool operator==(gbQuat a, gbQuat b) { return a.xyzw == b.xyzw; }
inline bool operator!=(gbQuat a, gbQuat b) { return !operator==(a, b); }
inline gbQuat operator+(gbQuat q) { return q; }
inline gbQuat operator-(gbQuat q) { return gb_quat(-q.x, -q.y, -q.z, -q.w); }
inline gbQuat operator+(gbQuat a, gbQuat b) { gbQuat r; gb_quat_add(&r, a, b); return r; }
inline gbQuat operator-(gbQuat a, gbQuat b) { gbQuat r; gb_quat_sub(&r, a, b); return r; }
inline gbQuat operator*(gbQuat a, gbQuat b) { gbQuat r; gb_quat_mul(&r, a, b); return r; }
inline gbQuat operator*(gbQuat q, float s) { gbQuat r; gb_quat_mulf(&r, q, s); return r; }
inline gbQuat operator*(float s, gbQuat q) { return operator*(q, s); }
inline gbQuat operator/(gbQuat q, float s) { gbQuat r; gb_quat_divf(&r, q, s); return r; }
inline gbQuat &operator+=(gbQuat &a, gbQuat b) { gb_quat_addeq(&a, b); return a; }
inline gbQuat &operator-=(gbQuat &a, gbQuat b) { gb_quat_subeq(&a, b); return a; }
inline gbQuat &operator*=(gbQuat &a, gbQuat b) { gb_quat_muleq(&a, b); return a; }
inline gbQuat &operator/=(gbQuat &a, gbQuat b) { gb_quat_diveq(&a, b); return a; }
inline gbQuat &operator*=(gbQuat &a, float b) { gb_quat_muleqf(&a, b); return a; }
inline gbQuat &operator/=(gbQuat &a, float b) { gb_quat_diveqf(&a, b); return a; }
/* Rotate v by a */
inline gbVec3 operator*(gbQuat q, gbVec3 v) { gbVec3 r; gb_quat_rotate_vec3(&r, q, v); return r; }
#endif
#endif /* GB_MATH_INCLUDE_GB_MATH_H */
/****************************************************************
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* Implementation
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
****************************************************************/
#if defined(GB_MATH_IMPLEMENTATION) && !defined(GB_MATH_IMPLEMENTATION_DONE)
#define GB_MATH_IMPLEMENTATION_DONE
#if (defined(__GCC__) || defined(__GNUC__)) && !defined(__clang__)
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wattributes"
#pragma GCC diagnostic ignored "-Wmissing-braces"
#elif __clang__
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wattributes"
#pragma clang diagnostic ignored "-Wmissing-braces"
#endif
/* NOTE(bill): To remove the need for memcpy */
static void gb__memcpy_4byte(void *dest, void const *src, size_t size) {
size_t i;
unsigned int *d, *s;
d = (unsigned int *)dest;
s = (unsigned int *)src;
for (i = 0; i < size/4; i++) {
*d++ = *s++;
}
}
float gb_to_radians(float degrees) { return degrees * GB_MATH_TAU / 360.0f; }
float gb_to_degrees(float radians) { return radians * 360.0f / GB_MATH_TAU; }
float gb_angle_diff(float radians_a, float radians_b) {
float delta = gb_mod(radians_b-radians_a, GB_MATH_TAU);
delta = gb_mod(delta + 1.5f*GB_MATH_TAU, GB_MATH_TAU);
delta -= 0.5f*GB_MATH_TAU;
return delta;
}
float gb_copy_sign(float x, float y) {
int ix, iy;
ix = *(int *)&x;
iy = *(int *)&y;
ix &= 0x7fffffff;
ix |= iy & 0x80000000;
return *(float *)&ix;
}
float gb_remainder(float x, float y) {
return x - (gb_round(x/y)*y);
}
float gb_mod(float x, float y) {
float result;
y = gb_abs(y);
result = gb_remainder(gb_abs(x), y);
if (gb_sign(result)) result += y;
return gb_copy_sign(result, x);
}
float gb_quake_rsqrt(float a) {
union {
int i;
float f;
} t;
float x2;
float const three_halfs = 1.5f;
x2 = a * 0.5f;
t.f = a;
t.i = 0x5f375a86 - (t.i >> 1); /* What the fuck? */
t.f = t.f * (three_halfs - (x2 * t.f * t.f)); /* 1st iteration */
t.f = t.f * (three_halfs - (x2 * t.f * t.f)); /* 2nd iteration, this can be removed */
return t.f;
}
#if defined(GB_MATH_NO_MATH_H)
#if defined(_MSC_VER)
float gb_rsqrt(float a) { return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(a))); }
float gb_sqrt(float a) { return _mm_cvtss_f32(_mm_sqrt_ss(_mm_set_ss(a))); };
float
gb_sin(float a)
{
static float const a0 = +1.91059300966915117e-31f;
static float const a1 = +1.00086760103908896f;
static float const a2 = -1.21276126894734565e-2f;
static float const a3 = -1.38078780785773762e-1f;
static float const a4 = -2.67353392911981221e-2f;
static float const a5 = +2.08026600266304389e-2f;
static float const a6 = -3.03996055049204407e-3f;
static float const a7 = +1.38235642404333740e-4f;
return a0 + a*(a1 + a*(a2 + a*(a3 + a*(a4 + a*(a5 + a*(a6 + a*a7))))));
}
float
gb_cos(float a)
{
static float const a0 = +1.00238601909309722f;
static float const a1 = -3.81919947353040024e-2f;
static float const a2 = -3.94382342128062756e-1f;
static float const a3 = -1.18134036025221444e-1f;
static float const a4 = +1.07123798512170878e-1f;
static float const a5 = -1.86637164165180873e-2f;
static float const a6 = +9.90140908664079833e-4f;
static float const a7 = -5.23022132118824778e-14f;
return a0 + a*(a1 + a*(a2 + a*(a3 + a*(a4 + a*(a5 + a*(a6 + a*a7))))));
}
float
gb_tan(float radians)
{
float rr = radians*radians;
float a = 9.5168091e-03f;
a *= rr;
a += 2.900525e-03f;
a *= rr;
a += 2.45650893e-02f;
a *= rr;
a += 5.33740603e-02f;
a *= rr;
a += 1.333923995e-01f;
a *= rr;
a += 3.333314036e-01f;
a *= rr;
a += 1.0f;
a *= radians;
return a;
}
float gb_arcsin(float a) { return gb_arctan2(a, gb_sqrt((1.0f + a) * (1.0f - a))); }
float gb_arccos(float a) { return gb_arctan2(gb_sqrt((1.0f + a) * (1.0 - a)), a); }
float
gb_arctan(float a)
{
float u = a*a;
float u2 = u*u;
float u3 = u2*u;
float u4 = u3*u;
float f = 1.0f+0.33288950512027f*u-0.08467922817644f*u2+0.03252232640125f*u3-0.00749305860992f*u4;
return a/f;
}
float
gb_arctan2(float y, float x)
{
if (gb_abs(x) > gb_abs(y)) {
float a = gb_arctan(y/x);
if (x > 0.0f)
return a;
else
return y > 0.0f ? a+GB_MATH_TAU_OVER_2:a-GB_MATH_TAU_OVER_2;
} else {
float a = gb_arctan(x/y);
if (x > 0.0f)
return y > 0.0f ? GB_MATH_TAU_OVER_4-a:-GB_MATH_TAU_OVER_4-a;
else
return y > 0.0f ? GB_MATH_TAU_OVER_4+a:-GB_MATH_TAU_OVER_4+a;
}
}
float
gb_exp(float a)
{
union { float f; int i; } u, v;
u.i = (int)(6051102 * a + 1056478197);
v.i = (int)(1056478197 - 6051102 * a);
return u.f / v.f;
}
float
gb_log(float a)
{
union { float f; int i; } u = {a};
return (u.i - 1064866805) * 8.262958405176314e-8f; /* 1 / 12102203.0; */
}
float
gb_pow(float a, float b)
{
int flipped = 0, e;
float f, r = 1.0f;
if (b < 0) {
flipped = 1;
b = -b;
}
e = (int)b;
f = gb_exp(b - e);
while (e) {
if (e & 1) r *= a;
a *= a;
e >>= 1;
}
r *= f;
return flipped ? 1.0f/r : r;
}
#else
float gb_rsqrt(float a) { return 1.0f/__builtin_sqrt(a); }
float gb_sqrt(float a) { return __builtin_sqrt(a); }
float gb_sin(float radians) { return __builtin_sinf(radians); }
float gb_cos(float radians) { return __builtin_cosf(radians); }
float gb_tan(float radians) { return __builtin_tanf(radians); }
float gb_arcsin(float a) { return __builtin_asinf(a); }
float gb_arccos(float a) { return __builtin_acosf(a); }
float gb_arctan(float a) { return __builtin_atanf(a); }
float gb_arctan2(float y, float x) { return __builtin_atan2f(y, x); }
float gb_exp(float x) { return __builtin_expf(x); }
float gb_log(float x) { return __builtin_logf(x); }
// TODO(bill): Should this be gb_exp(y * gb_log(x)) ???
float gb_pow(float x, float y) { return __builtin_powf(x, y); }
#endif
#else
float gb_rsqrt(float a) { return 1.0f/sqrtf(a); }
float gb_sqrt(float a) { return sqrtf(a); };
float gb_sin(float radians) { return sinf(radians); };
float gb_cos(float radians) { return cosf(radians); };
float gb_tan(float radians) { return tanf(radians); };
float gb_arcsin(float a) { return asinf(a); };