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gb_math.h v0.04a - Minor bug fixes

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gingerBill 2016-04-08 22:41:14 +01:00
parent eec27b33ed
commit c58b8e1fe7
1 changed files with 50 additions and 45 deletions
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gb_math.h
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@ -1,9 +1,10 @@
// gb_math.h - v0.04 - public domain C math library - no warranty implied; use at your own risk // gb_math.h - v0.04a - public domain C math library - no warranty implied; use at your own risk
// A C math library geared towards game development // A C math library geared towards game development
// use '#define GB_MATH_IMPLEMENTATION' before including to create the implementation in _ONE_ file // use '#define GB_MATH_IMPLEMENTATION' before including to create the implementation in _ONE_ file
/* /*
Version History: Version History:
0.04a - Minor bug fixes
0.04 - Namespace everything with gb 0.04 - Namespace everything with gb
0.03 - Complete Replacement 0.03 - Complete Replacement
0.01 - Initial Version 0.01 - Initial Version
@ -20,12 +21,12 @@ WARNING
CONTENTS CONTENTS
- Common Macros - Common Macros
- Types - Types
- Vec(2,3,4) - gbVec(2,3,4)
- Mat(2,3,4) - gbMat(2,3,4)
- Float(2,3,4) - gbFloat(2,3,4)
- gbQuat - gbQuat
- Rect(2,3) - Rect(2,3)
- Aabb(2,3) - gbAabb(2,3)
- gb_half (16-bit floating point) (storage only) - gb_half (16-bit floating point) (storage only)
- Operations - Operations
- Functions - Functions
@ -37,6 +38,7 @@ CONTENTS
#ifndef GB_MATH_INCLUDE_GB_MATH_H #ifndef GB_MATH_INCLUDE_GB_MATH_H
#define GB_MATH_INCLUDE_GB_MATH_H #define GB_MATH_INCLUDE_GB_MATH_H
// TODO(bill): What of this do I actually need? And can include elsewhere (e.g. implementation)
#include <stddef.h> #include <stddef.h>
#include <math.h> #include <math.h>
#include <limits.h> #include <limits.h>
@ -148,8 +150,8 @@ typedef short gb_half;
#define GB_MATH_SQRT_THREE 1.73205080756887729352744634150587236f #define GB_MATH_SQRT_THREE 1.73205080756887729352744634150587236f
#define GB_MATH_SQRT_FIVE 2.23606797749978969640917366873127623f #define GB_MATH_SQRT_FIVE 2.23606797749978969640917366873127623f
#define GB_LOG_TWO 0.693147180559945309417232121458176568f #define GB_MATH_LOG_TWO 0.693147180559945309417232121458176568f
#define GB_LOG_TEN 2.30258509299404568401799145468436421f #define GB_MATH_LOG_TEN 2.30258509299404568401799145468436421f
#endif #endif
@ -161,8 +163,8 @@ extern "C" {
GB_MATH_DEF float gb_clamp(float a, float lower, float upper); GB_MATH_DEF float gb_clamp(float a, float lower, float upper);
GB_MATH_DEF float gb_clamp01(float a); GB_MATH_DEF float gb_clamp01(float a);
GB_MATH_DEF float gb_as_radians(float degrees); GB_MATH_DEF float gb_to_radians(float degrees);
GB_MATH_DEF float gb_as_degrees(float radians); GB_MATH_DEF float gb_to_degrees(float radians);
// NOTE(bill): Because to interpolate angles // NOTE(bill): Because to interpolate angles
GB_MATH_DEF float gb_angle_diff(float radians_a, float radians_b); GB_MATH_DEF float gb_angle_diff(float radians_a, float radians_b);
@ -171,7 +173,7 @@ GB_MATH_DEF float gb_angle_diff(float radians_a, float radians_b);
#define gb_max(a, b) ((a) > (b) ? (a) : (b)) #define gb_max(a, b) ((a) > (b) ? (a) : (b))
GB_MATH_DEF float gb_sqrt(float a); GB_MATH_DEF float gb_sqrt(float a);
GB_MATH_DEF float gb_inv_sqrt(float a); // NOTE(bill): Fast inverse square root GB_MATH_DEF float gb_quake_inv_sqrt(float a); // NOTE(bill): It's probably better to use 1.0f/gb_sqrt(a)
GB_MATH_DEF float gb_sin(float radians); GB_MATH_DEF float gb_sin(float radians);
GB_MATH_DEF float gb_cos(float radians); GB_MATH_DEF float gb_cos(float radians);
@ -506,7 +508,7 @@ gbVec4 &operator/=(gbVec4 &a, float scalar) { return (a = a / scalar); }
gbMat2 operator+(gbMat2 const &a, gbMat2 const &b) gbMat2 operator+(gbMat2 const &a, gbMat2 const &b)
{ {
int i, j; int i, j;
gbMat2 r = {}; gbMat2 r = {0};
for (j = 0; j < 2; j++) { for (j = 0; j < 2; j++) {
for (i = 0; i < 2; i++) for (i = 0; i < 2; i++)
r.e[2*j+i] = a.e[2*j+i] + b.e[2*j+i]; r.e[2*j+i] = a.e[2*j+i] + b.e[2*j+i];
@ -517,7 +519,7 @@ gbMat2 operator+(gbMat2 const &a, gbMat2 const &b)
gbMat2 operator-(gbMat2 const &a, gbMat2 const &b) gbMat2 operator-(gbMat2 const &a, gbMat2 const &b)
{ {
int i, j; int i, j;
gbMat2 r = {}; gbMat2 r = {0};
for (j = 0; j < 2; j++) { for (j = 0; j < 2; j++) {
for (i = 0; i < 2; i++) for (i = 0; i < 2; i++)
r.e[2*j+i] = a.e[2*j+i] - b.e[2*j+i]; r.e[2*j+i] = a.e[2*j+i] - b.e[2*j+i];
@ -529,7 +531,7 @@ gbMat2 operator*(gbMat2 const &a, gbMat2 const &b) { gbMat2 r; gb_mat2_mul(&r, (
gbVec2 operator*(gbMat2 const &a, gbVec2 v) { gbVec2 r; gb_mat2_mul_vec2(&r, (gbMat2 *)&a, v); return r; } gbVec2 operator*(gbMat2 const &a, gbVec2 v) { gbVec2 r; gb_mat2_mul_vec2(&r, (gbMat2 *)&a, v); return r; }
gbMat2 operator*(gbMat2 const &a, float scalar) gbMat2 operator*(gbMat2 const &a, float scalar)
{ {
gbMat2 r = {}; gbMat2 r = {0};
int i; int i;
for (i = 0; i < 2*2; i++) r.e[i] = a.e[i] * scalar; for (i = 0; i < 2*2; i++) r.e[i] = a.e[i] * scalar;
return r; return r;
@ -546,7 +548,7 @@ gbMat2& operator*=(gbMat2& a, gbMat2 const &b) { return (a = a * b); }
gbMat3 operator+(gbMat3 const &a, gbMat3 const &b) gbMat3 operator+(gbMat3 const &a, gbMat3 const &b)
{ {
int i, j; int i, j;
gbMat3 r = {}; gbMat3 r = {0};
for (j = 0; j < 3; j++) { for (j = 0; j < 3; j++) {
for (i = 0; i < 3; i++) for (i = 0; i < 3; i++)
r.e[3*j+i] = a.e[3*j+i] + b.e[3*j+i]; r.e[3*j+i] = a.e[3*j+i] + b.e[3*j+i];
@ -557,7 +559,7 @@ gbMat3 operator+(gbMat3 const &a, gbMat3 const &b)
gbMat3 operator-(gbMat3 const &a, gbMat3 const &b) gbMat3 operator-(gbMat3 const &a, gbMat3 const &b)
{ {
int i, j; int i, j;
gbMat3 r = {}; gbMat3 r = {0};
for (j = 0; j < 3; j++) { for (j = 0; j < 3; j++) {
for (i = 0; i < 3; i++) for (i = 0; i < 3; i++)
r.e[3*j+i] = a.e[3*j+i] - b.e[3*j+i]; r.e[3*j+i] = a.e[3*j+i] - b.e[3*j+i];
@ -569,7 +571,7 @@ gbMat3 operator*(gbMat3 const &a, gbMat3 const &b) { gbMat3 r; gb_mat3_mul(&r, (
gbVec3 operator*(gbMat3 const &a, gbVec3 v) { gbVec3 r; gb_mat3_mul_vec3(&r, (gbMat3 *)&a, v); return r; } gbVec3 operator*(gbMat3 const &a, gbVec3 v) { gbVec3 r; gb_mat3_mul_vec3(&r, (gbMat3 *)&a, v); return r; }
gbMat3 operator*(gbMat3 const &a, float scalar) gbMat3 operator*(gbMat3 const &a, float scalar)
{ {
gbMat3 r = {}; gbMat3 r = {0};
int i; int i;
for (i = 0; i < 3*3; i++) r.e[i] = a.e[i] * scalar; for (i = 0; i < 3*3; i++) r.e[i] = a.e[i] * scalar;
return r; return r;
@ -586,7 +588,7 @@ gbMat3& operator*=(gbMat3& a, gbMat3 const &b) { return (a = a * b); }
gbMat4 operator+(gbMat4 const &a, gbMat4 const &b) gbMat4 operator+(gbMat4 const &a, gbMat4 const &b)
{ {
int i, j; int i, j;
gbMat4 r = {}; gbMat4 r = {0};
for (j = 0; j < 4; j++) { for (j = 0; j < 4; j++) {
for (i = 0; i < 4; i++) for (i = 0; i < 4; i++)
r.e[4*j+i] = a.e[4*j+i] + b.e[4*j+i]; r.e[4*j+i] = a.e[4*j+i] + b.e[4*j+i];
@ -597,7 +599,7 @@ gbMat4 operator+(gbMat4 const &a, gbMat4 const &b)
gbMat4 operator-(gbMat4 const &a, gbMat4 const &b) gbMat4 operator-(gbMat4 const &a, gbMat4 const &b)
{ {
int i, j; int i, j;
gbMat4 r = {}; gbMat4 r = {0};
for (j = 0; j < 4; j++) { for (j = 0; j < 4; j++) {
for (i = 0; i < 4; i++) for (i = 0; i < 4; i++)
r.e[4*j+i] = a.e[4*j+i] - b.e[4*j+i]; r.e[4*j+i] = a.e[4*j+i] - b.e[4*j+i];
@ -609,7 +611,7 @@ gbMat4 operator*(gbMat4 const &a, gbMat4 const &b) { gbMat4 r; gb_mat4_mul(&r, (
gbVec4 operator*(gbMat4 const &a, gbVec4 v) { gbVec4 r; gb_mat4_mul_vec4(&r, (gbMat4 *)&a, v); return r; } gbVec4 operator*(gbMat4 const &a, gbVec4 v) { gbVec4 r; gb_mat4_mul_vec4(&r, (gbMat4 *)&a, v); return r; }
gbMat4 operator*(gbMat4 const &a, float scalar) gbMat4 operator*(gbMat4 const &a, float scalar)
{ {
gbMat4 r = {}; gbMat4 r = {0};
int i; int i;
for (i = 0; i < 4*4; i++) r.e[i] = a.e[i] * scalar; for (i = 0; i < 4*4; i++) r.e[i] = a.e[i] * scalar;
return r; return r;
@ -688,6 +690,7 @@ gbVec3 operator*(gbQuat q, gbVec3 v) { gbVec3 r; gb_quat_rotate_vec3(&r, q, v);
// // // //
// // // //
// // // //
// //
//////////////////// ////////////////////
#if defined(GB_MATH_IMPLEMENTATION) #if defined(GB_MATH_IMPLEMENTATION)
@ -697,8 +700,8 @@ float gb_clamp(float a, float lower, float upper) { return a < lower ? lower : a
float gb_clamp01(float a) { return gb_clamp(a, 0.0f, 1.0f); } float gb_clamp01(float a) { return gb_clamp(a, 0.0f, 1.0f); }
float gb_as_radians(float degrees) { return degrees * GB_MATH_TAU / 360.0f; } float gb_to_radians(float degrees) { return degrees * GB_MATH_TAU / 360.0f; }
float gb_as_degrees(float radians) { return radians * 360.0f / GB_MATH_TAU; } float gb_to_degrees(float radians) { return radians * 360.0f / GB_MATH_TAU; }
float float
gb_angle_diff(float radians_a, float radians_b) gb_angle_diff(float radians_a, float radians_b)
@ -711,8 +714,9 @@ gb_angle_diff(float radians_a, float radians_b)
float gb_sqrt(float a) { return sqrtf(a); } float gb_sqrt(float a) { return sqrtf(a); }
float float
gb_inv_sqrt(float a) gb_quake_inv_sqrt(float a)
{ {
int i; int i;
float x2, y; float x2, y;
@ -740,18 +744,19 @@ float gb_arctan2(float y, float x) { return atan2f(y, x); }
float gb_exp(float x) { return expf(x); } float gb_exp(float x) { return expf(x); }
float gb_exp2(float x) { return gb_exp(0.69314718055994530941723212145818f * x); } float gb_exp2(float x) { return gb_exp(GB_MATH_LOG_TWO * x); }
float gb_log(float x) { return logf(x); } float gb_log(float x) { return logf(x); }
float gb_log2(float x) { return gb_log(x) / 0.69314718055994530941723212145818f; } float gb_log2(float x) { return gb_log(x) / GB_MATH_LOG_TWO; }
float float
gb_fast_exp(float x) gb_fast_exp(float x)
{ {
// NOTE(bill): Only works in the range -1 <= x <= +1
float e = 1.0f + x*(1.0f + x*0.5f*(1.0f + x*0.3333333333f*(1.0f + x*0.25*(1.0f + x*0.2f)))); float e = 1.0f + x*(1.0f + x*0.5f*(1.0f + x*0.3333333333f*(1.0f + x*0.25*(1.0f + x*0.2f))));
return e; return e;
} }
float gb_fast_exp2(float x) { return gb_fast_exp(0.69314718055994530941723212145818f * x); } float gb_fast_exp2(float x) { return gb_fast_exp(GB_MATH_LOG_TWO * x); }
// TODO(bill): Should this be gb_exp(y * gb_log(x)) ??? // TODO(bill): Should this be gb_exp(y * gb_log(x)) ???
float gb_pow(float x, float y) { return powf(x, y); } float gb_pow(float x, float y) { return powf(x, y); }
@ -773,7 +778,6 @@ gb_half_to_float(gb_half value)
if (e == 0) { if (e == 0) {
if(m == 0) { if(m == 0) {
// Plus or minus zero // Plus or minus zero
gb_uif32 result;
result.i = (unsigned int)(s << 31); result.i = (unsigned int)(s << 31);
return result.f; return result.f;
} else { } else {
@ -789,26 +793,18 @@ gb_half_to_float(gb_half value)
} else if (e == 31) { } else if (e == 31) {
if (m == 0) { if (m == 0) {
// Positive or negative infinity // Positive or negative infinity
gb_uif32 result;
result.i = (unsigned int)((s << 31) | 0x7f800000); result.i = (unsigned int)((s << 31) | 0x7f800000);
return result.f; return result.f;
} else { } else {
// Nan // Nan
gb_uif32 result;
result.i = (unsigned int)((s << 31) | 0x7f800000 | (m << 13)); result.i = (unsigned int)((s << 31) | 0x7f800000 | (m << 13));
return result.f; return result.f;
} }
} }
// Normalized number
e = e + (127 - 15); e = e + (127 - 15);
m = m << 13; m = m << 13;
//
// Assemble s, e and m.
//
result.i = (unsigned int)((s << 31) | (e << 23) | m); result.i = (unsigned int)((s << 31) | (e << 23) | m);
return result.f; return result.f;
} }
@ -828,9 +824,7 @@ gb_float_to_half(float value)
if (e <= 0) { if (e <= 0) {
if (e < -10) { if (e < -10) return (gb_half)s;
return (gb_half)s;
}
m = (m | 0x00800000) >> (1 - e); m = (m | 0x00800000) >> (1 - e);
if (m & 0x00001000) if (m & 0x00001000)
@ -839,10 +833,9 @@ gb_float_to_half(float value)
return (gb_half)(s | (m >> 13)); return (gb_half)(s | (m >> 13));
} else if (e == 0xff - (127 - 15)) { } else if (e == 0xff - (127 - 15)) {
if (m == 0) { if (m == 0) {
// infinity return (gb_half)(s | 0x7c00); // NOTE(bill): infinity
return (gb_half)(s | 0x7c00);
} else { } else {
// NAN // NOTE(bill): NAN
m >>= 13; m >>= 13;
return (gb_half)(s | 0x7c00 | m | (m == 0)); return (gb_half)(s | 0x7c00 | m | (m == 0));
} }
@ -856,7 +849,7 @@ gb_float_to_half(float value)
} }
if (e > 30) { if (e > 30) {
float volatile f = 1e10; float volatile f = 1e12f;
for (unsigned int j = 0; j < 10; j++) for (unsigned int j = 0; j < 10; j++)
f *= f; // NOTE(bill): Cause overflow f *= f; // NOTE(bill): Cause overflow
@ -949,6 +942,16 @@ void gb_vec4_muleq(gbVec4 *d, float s) { GB_VEC4_2OP(d,(*d),* s); }
void gb_vec4_diveq(gbVec4 *d, float s) { GB_VEC4_2OP(d,(*d),/ s); } void gb_vec4_diveq(gbVec4 *d, float s) { GB_VEC4_2OP(d,(*d),/ s); }
#undef GB_VEC2_2OP
#undef GB_VEC2_3OP
#undef GB_VEC3_3OP
#undef GB_VEC3_2OP
#undef GB_VEC4_2OP
#undef GB_VEC4_3OP
float gb_vec2_dot(gbVec2 v0, gbVec2 v1) { return v0.x*v1.x + v0.y*v1.y; } float gb_vec2_dot(gbVec2 v0, gbVec2 v1) { return v0.x*v1.x + v0.y*v1.y; }
float gb_vec3_dot(gbVec3 v0, gbVec3 v1) { return v0.x*v1.x + v0.y*v1.y + v0.z*v1.z; } float gb_vec3_dot(gbVec3 v0, gbVec3 v1) { return v0.x*v1.x + v0.y*v1.y + v0.z*v1.z; }
float gb_vec4_dot(gbVec4 v0, gbVec4 v1) { return v0.x*v1.x + v0.y*v1.y + v0.z*v1.z + v0.w*v1.w; } float gb_vec4_dot(gbVec4 v0, gbVec4 v1) { return v0.x*v1.x + v0.y*v1.y + v0.z*v1.z + v0.w*v1.w; }
@ -1660,7 +1663,7 @@ void gb_vec2_lerp(gbVec2 *d, gbVec2 a, gbVec2 b, float t) { GB_VEC_LERPN(2, d, a
void gb_vec3_lerp(gbVec3 *d, gbVec3 a, gbVec3 b, float t) { GB_VEC_LERPN(3, d, a, b, t); } void gb_vec3_lerp(gbVec3 *d, gbVec3 a, gbVec3 b, float t) { GB_VEC_LERPN(3, d, a, b, t); }
void gb_vec4_lerp(gbVec4 *d, gbVec4 a, gbVec4 b, float t) { GB_VEC_LERPN(4, d, a, b, t); } void gb_vec4_lerp(gbVec4 *d, gbVec4 a, gbVec4 b, float t) { GB_VEC_LERPN(4, d, a, b, t); }
#undef GB_VEC_LERPN
void gb_quat_lerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gb_vec4_lerp(&d->xyzw, a.xyzw, b.xyzw, t); } void gb_quat_lerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gb_vec4_lerp(&d->xyzw, a.xyzw, b.xyzw, t); }
void gb_quat_nlerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gb_quat_lerp(d, a, b, t); gb_quat_norm(d, *d); } void gb_quat_nlerp(gbQuat *d, gbQuat a, gbQuat b, float t) { gb_quat_lerp(d, a, b, t); gb_quat_norm(d, *d); }
@ -1700,6 +1703,8 @@ void
gb_quat_slerp_approx(gbQuat *d, gbQuat a, gbQuat b, float t) gb_quat_slerp_approx(gbQuat *d, gbQuat a, gbQuat b, float t)
{ {
// NOTE(bill): Derived by taylor expanding the geometric interpolation equation // NOTE(bill): Derived by taylor expanding the geometric interpolation equation
// Even works okay for nearly anti-parallel versors!!!
// NOTE(bill): Extra interations cannot be used as they require angle^4 which is not worth it to approximate
float tp = t + (1.0f - gb_quat_dot(a, b))/3.0f * t*(-2.0f*t*t + 3.0f*t - 1.0f); float tp = t + (1.0f - gb_quat_dot(a, b))/3.0f * t*(-2.0f*t*t + 3.0f*t - 1.0f);
return gb_quat_nlerp(d, a, b, tp); return gb_quat_nlerp(d, a, b, tp);
} }
@ -1918,8 +1923,8 @@ gb_rect2_intersection_result(gbRect2 a, gbRect2 b, gbRect2 *intersection)
float float
gb_random_range_float(float min_inc, float max_inc) gb_random_range_float(float min_inc, float max_inc)
{ {
int int_result = gb_random_range_int(0, INT_MAX); int int_result = gb_random_range_int(0, INT_MAX-1); // Prevent integer overflow
float result = int_result/(float)INT_MAX; float result = int_result/(float)(INT_MAX-1);
result *= max_inc - min_inc; result *= max_inc - min_inc;
result += min_inc; result += min_inc;
return result; return result;