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grad_all.glsl
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#ifndef GRAD_H_
#define GRAD_H_
// This file contains methods to compute the gradient of a scalar valued
// function (2-4 variables) using automatic forward differentiation
//--------------------------------
// Types
//--------------------------------
// Data type to hold information about a scalar valued 2 dimensional function
// These should be created by the constG2 (for constants) and varG2 (for variables) helpers
struct GNum2
{
// The current value
float val;
// The current gradient
vec2 g;
};
//--------------------------------
// Data type to hold information about a scalar valued 3 dimensional function
// These should be created by the constG3 (for constants) and varG3 (for variables) helpers
struct GNum3
{
// The current value
float val;
// The current gradient
vec3 g;
};
//--------------------------------
// Data type to hold information about a scalar valued 4 dimensional function
// These should be created by the constG4 (for constants) and varG4 (for variables) helpers
struct GNum4
{
// The current value
float val;
// The current gradient
vec4 g;
};
//--------------------------------
// Prototypes
//--------------------------------
/**
* Creates a constant GNum2
* @param val The current value of the constant
*/
GNum2 constG2(in float val);
GNum2 varG2(in float val, in int index);
GNum2 varG2x(in float val);
GNum2 varG2y(in float val);
GNum2 add(in GNum2 a, in GNum2 b);
GNum2 add(in GNum2 a, in float b);
GNum2 add(in float a, in GNum2 b);
GNum2 sub(in GNum2 a, in GNum2 b);
GNum2 sub(in GNum2 a, in float b);
GNum2 sub(in float a, in GNum2 b);
GNum2 mult(in GNum2 a, in GNum2 b);
GNum2 mult(in GNum2 a, in float b);
GNum2 mult(in float a, in GNum2 b);
GNum2 neg(in GNum2 a);
GNum2 div(in GNum2 a, in GNum2 b);
GNum2 div(in GNum2 a, in float b);
GNum2 div(in float a, in GNum2 b);
GNum2 inv(in GNum2 a);
GNum2 a_pow(in GNum2 a, in GNum2 b);
GNum2 a_pow(in GNum2 a, in float b);
GNum2 a_pow(in float a, in GNum2 b);
GNum2 a_ipow(in GNum2 x, in int n);
GNum2 a_min(in GNum2 a, in GNum2 b);
GNum2 a_max(in GNum2 a, in GNum2 b);
GNum2 a_exp2(in GNum2 a);
GNum2 a_inversesqrt(in GNum2 a);
GNum2 a_atan(in GNum2 a);
GNum2 a_sqrt(in GNum2 a);
GNum2 a_sinh(in GNum2 a);
GNum2 a_ceil(in GNum2 a);
GNum2 a_tan(in GNum2 a);
GNum2 a_asinh(in GNum2 a);
GNum2 a_asin(in GNum2 a);
GNum2 a_acosh(in GNum2 a);
GNum2 a_abs(in GNum2 a);
GNum2 a_exp(in GNum2 a);
GNum2 a_cosh(in GNum2 a);
GNum2 a_floor(in GNum2 a);
GNum2 a_log(in GNum2 a);
GNum2 a_atanh(in GNum2 a);
GNum2 a_log2(in GNum2 a);
GNum2 a_acos(in GNum2 a);
GNum2 a_tanh(in GNum2 a);
GNum2 a_cos(in GNum2 a);
GNum2 a_sin(in GNum2 a);
GNum2 a_atan2(in GNum2 y, in GNum2 x);
GNum2 a_atan2(in GNum2 y, in float x);
GNum2 a_atan2(in float y, in GNum2 x);
GNum2 a_mix(in GNum2 a, in GNum2 b, in GNum2 t);
GNum2 a_mix(in GNum2 a, in GNum2 b, in float t);
GNum2 a_mix(in GNum2 a, in float b, in GNum2 t);
GNum2 a_mix(in GNum2 a, in float b, in float t);
GNum2 a_mix(in float a, in GNum2 b, in GNum2 t);
GNum2 a_mix(in float a, in GNum2 b, in float t);
GNum2 a_mix(in float a, in float b, in GNum2 t);
/**
* Creates a constant GNum3
* @param val The current value of the constant
*/
GNum3 constG3(in float val);
GNum3 varG3(in float val, in int index);
GNum3 varG3x(in float val);
GNum3 varG3y(in float val);
GNum3 varG3z(in float val);
GNum3 add(in GNum3 a, in GNum3 b);
GNum3 add(in GNum3 a, in float b);
GNum3 add(in float a, in GNum3 b);
GNum3 sub(in GNum3 a, in GNum3 b);
GNum3 sub(in GNum3 a, in float b);
GNum3 sub(in float a, in GNum3 b);
GNum3 mult(in GNum3 a, in GNum3 b);
GNum3 mult(in GNum3 a, in float b);
GNum3 mult(in float a, in GNum3 b);
GNum3 neg(in GNum3 a);
GNum3 div(in GNum3 a, in GNum3 b);
GNum3 div(in GNum3 a, in float b);
GNum3 div(in float a, in GNum3 b);
GNum3 inv(in GNum3 a);
GNum3 a_pow(in GNum3 a, in GNum3 b);
GNum3 a_pow(in GNum3 a, in float b);
GNum3 a_pow(in float a, in GNum3 b);
GNum3 a_ipow(in GNum3 x, in int n);
GNum3 a_min(in GNum3 a, in GNum3 b);
GNum3 a_max(in GNum3 a, in GNum3 b);
GNum3 a_exp2(in GNum3 a);
GNum3 a_inversesqrt(in GNum3 a);
GNum3 a_atan(in GNum3 a);
GNum3 a_sqrt(in GNum3 a);
GNum3 a_sinh(in GNum3 a);
GNum3 a_ceil(in GNum3 a);
GNum3 a_tan(in GNum3 a);
GNum3 a_asinh(in GNum3 a);
GNum3 a_asin(in GNum3 a);
GNum3 a_acosh(in GNum3 a);
GNum3 a_abs(in GNum3 a);
GNum3 a_exp(in GNum3 a);
GNum3 a_cosh(in GNum3 a);
GNum3 a_floor(in GNum3 a);
GNum3 a_log(in GNum3 a);
GNum3 a_atanh(in GNum3 a);
GNum3 a_log2(in GNum3 a);
GNum3 a_acos(in GNum3 a);
GNum3 a_tanh(in GNum3 a);
GNum3 a_cos(in GNum3 a);
GNum3 a_sin(in GNum3 a);
GNum3 a_atan2(in GNum3 y, in GNum3 x);
GNum3 a_atan2(in GNum3 y, in float x);
GNum3 a_atan2(in float y, in GNum3 x);
GNum3 a_mix(in GNum3 a, in GNum3 b, in GNum3 t);
GNum3 a_mix(in GNum3 a, in GNum3 b, in float t);
GNum3 a_mix(in GNum3 a, in float b, in GNum3 t);
GNum3 a_mix(in GNum3 a, in float b, in float t);
GNum3 a_mix(in float a, in GNum3 b, in GNum3 t);
GNum3 a_mix(in float a, in GNum3 b, in float t);
GNum3 a_mix(in float a, in float b, in GNum3 t);
/**
* Creates a constant GNum4
* @param val The current value of the constant
*/
GNum4 constG4(in float val);
GNum4 varG4(in float val, in int index);
GNum4 varG4x(in float val);
GNum4 varG4y(in float val);
GNum4 varG4z(in float val);
GNum4 varG4w(in float val);
GNum4 add(in GNum4 a, in GNum4 b);
GNum4 add(in GNum4 a, in float b);
GNum4 add(in float a, in GNum4 b);
GNum4 sub(in GNum4 a, in GNum4 b);
GNum4 sub(in GNum4 a, in float b);
GNum4 sub(in float a, in GNum4 b);
GNum4 mult(in GNum4 a, in GNum4 b);
GNum4 mult(in GNum4 a, in float b);
GNum4 mult(in float a, in GNum4 b);
GNum4 neg(in GNum4 a);
GNum4 div(in GNum4 a, in GNum4 b);
GNum4 div(in GNum4 a, in float b);
GNum4 div(in float a, in GNum4 b);
GNum4 inv(in GNum4 a);
GNum4 a_pow(in GNum4 a, in GNum4 b);
GNum4 a_pow(in GNum4 a, in float b);
GNum4 a_pow(in float a, in GNum4 b);
GNum4 a_ipow(in GNum4 x, in int n);
GNum4 a_min(in GNum4 a, in GNum4 b);
GNum4 a_max(in GNum4 a, in GNum4 b);
GNum4 a_exp2(in GNum4 a);
GNum4 a_inversesqrt(in GNum4 a);
GNum4 a_atan(in GNum4 a);
GNum4 a_sqrt(in GNum4 a);
GNum4 a_sinh(in GNum4 a);
GNum4 a_ceil(in GNum4 a);
GNum4 a_tan(in GNum4 a);
GNum4 a_asinh(in GNum4 a);
GNum4 a_asin(in GNum4 a);
GNum4 a_acosh(in GNum4 a);
GNum4 a_abs(in GNum4 a);
GNum4 a_exp(in GNum4 a);
GNum4 a_cosh(in GNum4 a);
GNum4 a_floor(in GNum4 a);
GNum4 a_log(in GNum4 a);
GNum4 a_atanh(in GNum4 a);
GNum4 a_log2(in GNum4 a);
GNum4 a_acos(in GNum4 a);
GNum4 a_tanh(in GNum4 a);
GNum4 a_cos(in GNum4 a);
GNum4 a_sin(in GNum4 a);
GNum4 a_atan2(in GNum4 y, in GNum4 x);
GNum4 a_atan2(in GNum4 y, in float x);
GNum4 a_atan2(in float y, in GNum4 x);
GNum4 a_mix(in GNum4 a, in GNum4 b, in GNum4 t);
GNum4 a_mix(in GNum4 a, in GNum4 b, in float t);
GNum4 a_mix(in GNum4 a, in float b, in GNum4 t);
GNum4 a_mix(in GNum4 a, in float b, in float t);
GNum4 a_mix(in float a, in GNum4 b, in GNum4 t);
GNum4 a_mix(in float a, in GNum4 b, in float t);
GNum4 a_mix(in float a, in float b, in GNum4 t);
//--------------------------------
// Macros
//--------------------------------
#define GRAD2(f,x, y,result) { result = f(varG2x(x), varG2y(y)); }
//--------------------------------
#define JACOBI2(f1, f2, x, y, result) { GNum2 gradResult; GRAD2(f1, x, y, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; GRAD2(f2, x, y, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; }
//--------------------------------
#define JACOBI2_VALUE(f1, f2, x, y, result, value) { GNum2 gradResult; GRAD2(f1, x, y, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; GRAD2(f2, x, y, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; }
//--------------------------------
#define JACOBI32(f1, f2, f3, x, y, result) { GNum2 gradResult; GRAD2(f1, x, y, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; GRAD2(f2, x, y, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; GRAD2(f3, x, y, gradResult); result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; }
//--------------------------------
#define JACOBI32_VALUE(f1, f2, f3, x, y, result, value) { GNum2 gradResult; GRAD2(f1, x, y, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; GRAD2(f2, x, y, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; GRAD2(f3, x, y, gradResult); value[2] = gradResult.val; result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; }
//--------------------------------
#define JACOBI42(f1, f2, f3, f4, x, y, result) { GNum2 gradResult; GRAD2(f1, x, y, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; GRAD2(f2, x, y, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; GRAD2(f3, x, y, gradResult); result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; GRAD2(f4, x, y, gradResult); result[0][3] = gradResult.g[0]; result[1][3] = gradResult.g[1]; }
//--------------------------------
#define JACOBI42_VALUE(f1, f2, f3, f4, x, y, result, value) { GNum2 gradResult; GRAD2(f1, x, y, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; GRAD2(f2, x, y, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; GRAD2(f3, x, y, gradResult); value[2] = gradResult.val; result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; GRAD2(f4, x, y, gradResult); value[3] = gradResult.val; result[0][3] = gradResult.g[0]; result[1][3] = gradResult.g[1]; }
//--------------------------------
#define GRAD3(f,x, y, z,result) { result = f(varG3x(x), varG3y(y), varG3z(z)); }
//--------------------------------
#define JACOBI23(f1, f2, x, y, z, result) { GNum3 gradResult; GRAD3(f1, x, y, z, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; GRAD3(f2, x, y, z, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; }
//--------------------------------
#define JACOBI23_VALUE(f1, f2, x, y, z, result, value) { GNum3 gradResult; GRAD3(f1, x, y, z, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; GRAD3(f2, x, y, z, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; }
//--------------------------------
#define JACOBI3(f1, f2, f3, x, y, z, result) { GNum3 gradResult; GRAD3(f1, x, y, z, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; GRAD3(f2, x, y, z, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; GRAD3(f3, x, y, z, gradResult); result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; }
//--------------------------------
#define JACOBI3_VALUE(f1, f2, f3, x, y, z, result, value) { GNum3 gradResult; GRAD3(f1, x, y, z, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; GRAD3(f2, x, y, z, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; GRAD3(f3, x, y, z, gradResult); value[2] = gradResult.val; result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; }
//--------------------------------
#define JACOBI43(f1, f2, f3, f4, x, y, z, result) { GNum3 gradResult; GRAD3(f1, x, y, z, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; GRAD3(f2, x, y, z, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; GRAD3(f3, x, y, z, gradResult); result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; GRAD3(f4, x, y, z, gradResult); result[0][3] = gradResult.g[0]; result[1][3] = gradResult.g[1]; result[2][3] = gradResult.g[2]; }
//--------------------------------
#define JACOBI43_VALUE(f1, f2, f3, f4, x, y, z, result, value) { GNum3 gradResult; GRAD3(f1, x, y, z, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; GRAD3(f2, x, y, z, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; GRAD3(f3, x, y, z, gradResult); value[2] = gradResult.val; result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; GRAD3(f4, x, y, z, gradResult); value[3] = gradResult.val; result[0][3] = gradResult.g[0]; result[1][3] = gradResult.g[1]; result[2][3] = gradResult.g[2]; }
//--------------------------------
#define GRAD4(f,x, y, z, w,result) { result = f(varG4x(x), varG4y(y), varG4z(z), varG4w(w)); }
//--------------------------------
#define JACOBI24(f1, f2, x, y, z, w, result) { GNum4 gradResult; GRAD4(f1, x, y, z, w, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; result[3][0] = gradResult.g[3]; GRAD4(f2, x, y, z, w, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; result[3][1] = gradResult.g[3]; }
//--------------------------------
#define JACOBI24_VALUE(f1, f2, x, y, z, w, result, value) { GNum4 gradResult; GRAD4(f1, x, y, z, w, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; result[3][0] = gradResult.g[3]; GRAD4(f2, x, y, z, w, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; result[3][1] = gradResult.g[3]; }
//--------------------------------
#define JACOBI34(f1, f2, f3, x, y, z, w, result) { GNum4 gradResult; GRAD4(f1, x, y, z, w, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; result[3][0] = gradResult.g[3]; GRAD4(f2, x, y, z, w, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; result[3][1] = gradResult.g[3]; GRAD4(f3, x, y, z, w, gradResult); result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; result[3][2] = gradResult.g[3]; }
//--------------------------------
#define JACOBI34_VALUE(f1, f2, f3, x, y, z, w, result, value) { GNum4 gradResult; GRAD4(f1, x, y, z, w, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; result[3][0] = gradResult.g[3]; GRAD4(f2, x, y, z, w, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; result[3][1] = gradResult.g[3]; GRAD4(f3, x, y, z, w, gradResult); value[2] = gradResult.val; result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; result[3][2] = gradResult.g[3]; }
//--------------------------------
#define JACOBI4(f1, f2, f3, f4, x, y, z, w, result) { GNum4 gradResult; GRAD4(f1, x, y, z, w, gradResult); result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; result[3][0] = gradResult.g[3]; GRAD4(f2, x, y, z, w, gradResult); result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; result[3][1] = gradResult.g[3]; GRAD4(f3, x, y, z, w, gradResult); result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; result[3][2] = gradResult.g[3]; GRAD4(f4, x, y, z, w, gradResult); result[0][3] = gradResult.g[0]; result[1][3] = gradResult.g[1]; result[2][3] = gradResult.g[2]; result[3][3] = gradResult.g[3]; }
//--------------------------------
#define JACOBI4_VALUE(f1, f2, f3, f4, x, y, z, w, result, value) { GNum4 gradResult; GRAD4(f1, x, y, z, w, gradResult); value[0] = gradResult.val; result[0][0] = gradResult.g[0]; result[1][0] = gradResult.g[1]; result[2][0] = gradResult.g[2]; result[3][0] = gradResult.g[3]; GRAD4(f2, x, y, z, w, gradResult); value[1] = gradResult.val; result[0][1] = gradResult.g[0]; result[1][1] = gradResult.g[1]; result[2][1] = gradResult.g[2]; result[3][1] = gradResult.g[3]; GRAD4(f3, x, y, z, w, gradResult); value[2] = gradResult.val; result[0][2] = gradResult.g[0]; result[1][2] = gradResult.g[1]; result[2][2] = gradResult.g[2]; result[3][2] = gradResult.g[3]; GRAD4(f4, x, y, z, w, gradResult); value[3] = gradResult.val; result[0][3] = gradResult.g[0]; result[1][3] = gradResult.g[1]; result[2][3] = gradResult.g[2]; result[3][3] = gradResult.g[3]; }
//--------------------------------
// Implementation
//--------------------------------
GNum2 constG2(in float val)
{
return GNum2(val, vec2(0.0));
}
//--------------------------------
GNum2 varG2(in float val, in int index)
{
vec2 g = vec2(0.0);
g[index] = 1.0;
return GNum2(val, g);
}
//--------------------------------
GNum2 varG2x(in float val)
{
vec2 g = vec2(0.0);
g[0] = 1.0;
return GNum2(val, g);
}
//--------------------------------
GNum2 varG2y(in float val)
{
vec2 g = vec2(0.0);
g[1] = 1.0;
return GNum2(val, g);
}
//--------------------------------
GNum2 add(in GNum2 a, in GNum2 b)
{
return GNum2(a.val + b.val, a.g + b.g);
}
//--------------------------------
GNum2 add(in GNum2 a, in float b)
{
return GNum2(a.val + b, a.g);
}
//--------------------------------
GNum2 add(in float a, in GNum2 b)
{
return GNum2(a + b.val, b.g);
}
//--------------------------------
GNum2 sub(in GNum2 a, in GNum2 b)
{
return GNum2(a.val - b.val, a.g - b.g);
}
//--------------------------------
GNum2 sub(in GNum2 a, in float b)
{
return GNum2(a.val - b, a.g);
}
//--------------------------------
GNum2 sub(in float a, in GNum2 b)
{
return GNum2(a - b.val, -b.g);
}
//--------------------------------
GNum2 mult(in GNum2 a, in GNum2 b)
{
return GNum2(a.val * b.val,
a.val*b.g + b.val*a.g
);
}
//--------------------------------
GNum2 mult(in GNum2 a, in float b)
{
return GNum2(a.val * b, b*a.g);
}
//--------------------------------
GNum2 mult(in float a, in GNum2 b)
{
return GNum2(a * b.val, a*b.g);
}
//--------------------------------
GNum2 neg(in GNum2 a)
{
return mult(-1.0,a);
}
//--------------------------------
GNum2 div(in GNum2 a, in GNum2 b)
{
float b1 = b.val;
float b2 = b1*b1;
return GNum2(a.val / b.val ,
(b.val*a.g - a.val*b.g)/b2
);
}
//--------------------------------
GNum2 div(in GNum2 a, in float b)
{
return GNum2(a.val / b, a.g/b);
}
//--------------------------------
GNum2 div(in float a, in GNum2 b)
{
float b1 = b.val;
float b2 = b1*b1;
return GNum2(a / b.val,
-a*b.g/b2
);
}
//--------------------------------
GNum2 inv(in GNum2 a)
{
return div(1.0, a);
}
//--------------------------------
GNum2 a_pow(in GNum2 a, in GNum2 b)
{
return a_exp(mult(b,a_log(a)));
}
//--------------------------------
GNum2 a_pow(in GNum2 a, in float b)
{
// constant exponent -> make special case
float v = pow(a.val, b); // value f(a(x))
float da = b*pow(a.val,b-1.0); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_pow(in float a, in GNum2 b)
{
return a_exp(mult(b,log(a)));
}
//--------------------------------
GNum2 a_ipow(in GNum2 x, in int n)
{
// based on https://en.wikipedia.org/wiki/Exponentiation_by_squaring
if (n < 0)
{
x = div(1.0,x);
n = -n;
}
if (n == 0)
{
return constG2(1.0);
}
GNum2 y = constG2(1.0);
while (n > 1)
{
if (n % 2 == 0)
{
x = mult(x,x);
}
else
{
y = mult(x, y);
x = mult(x, x);
}
n = n / 2;
}
return mult(x, y);
}
//--------------------------------
GNum2 a_min(in GNum2 a, in GNum2 b)
{
if(a.val < b.val)
{
return a;
}
return b;
}
//--------------------------------
GNum2 a_max(in GNum2 a, in GNum2 b)
{
if(a.val > b.val)
{
return a;
}
return b;
}
//--------------------------------
GNum2 a_exp2(in GNum2 a)
{
float v = exp2(a.val); // value f(a(x))
float da = log(2.0)*exp2(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_inversesqrt(in GNum2 a)
{
float v = inversesqrt(a.val); // value f(a(x))
float da = -0.5/pow(sqrt(a.val),3.0); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_atan(in GNum2 a)
{
float v = atan(a.val); // value f(a(x))
float da = 1.0/(1.0 + a.val * a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_sqrt(in GNum2 a)
{
float v = sqrt(a.val); // value f(a(x))
float da = 0.5/sqrt(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_sinh(in GNum2 a)
{
float v = sinh(a.val); // value f(a(x))
float da = cosh(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_ceil(in GNum2 a)
{
float v = ceil(a.val); // value f(a(x))
float da = 0.0; // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_tan(in GNum2 a)
{
float v = tan(a.val); // value f(a(x))
float da = 1.0 + pow(tan(a.val),2.0); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_asinh(in GNum2 a)
{
float v = asinh(a.val); // value f(a(x))
float da = 1.0/sqrt(1.0 + a.val * a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_asin(in GNum2 a)
{
float v = asin(a.val); // value f(a(x))
float da = 1.0/sqrt(1.0 - a.val * a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_acosh(in GNum2 a)
{
float v = acosh(a.val); // value f(a(x))
float da = 1.0/sqrt(-1.0 + a.val * a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_abs(in GNum2 a)
{
float v = abs(a.val); // value f(a(x))
float da = a.val < 0.0 ? -1.0 : 1.0; // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_exp(in GNum2 a)
{
float v = exp(a.val); // value f(a(x))
float da = exp(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_cosh(in GNum2 a)
{
float v = cosh(a.val); // value f(a(x))
float da = sinh(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_floor(in GNum2 a)
{
float v = floor(a.val); // value f(a(x))
float da = 0.0; // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_log(in GNum2 a)
{
float v = log(a.val); // value f(a(x))
float da = 1.0/a.val; // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_atanh(in GNum2 a)
{
float v = atanh(a.val); // value f(a(x))
float da = 1.0/(1.0 - a.val * a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_log2(in GNum2 a)
{
float v = log2(a.val); // value f(a(x))
float da = 1.0/(a.val * log(2.0)); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_acos(in GNum2 a)
{
float v = acos(a.val); // value f(a(x))
float da = -1.0/sqrt(1.0 - a.val * a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_tanh(in GNum2 a)
{
float v = tanh(a.val); // value f(a(x))
float da = 1.0 - pow(tanh(a.val),2.0); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_cos(in GNum2 a)
{
float v = cos(a.val); // value f(a(x))
float da = -sin(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_sin(in GNum2 a)
{
float v = sin(a.val); // value f(a(x))
float da = cos(a.val); // first derivative f'(a(x))
return GNum2(v , da * a.g);
}
//--------------------------------
GNum2 a_atan2(in GNum2 y, in GNum2 x)
{
const float pi = 3.14159265;
// from https://en.wikipedia.org/wiki/Atan2
if(x.val > 0.0)
{
GNum2 n = a_sqrt(add(mult(x,x),mult(y,y)));
GNum2 inner = div(y, add(n,x));
return mult(2.0,a_atan(inner));
}else if(x.val <= 0.0 && abs(y.val) > 1E-6)
{
GNum2 n = a_sqrt(add(mult(x,x),mult(y,y)));
GNum2 inner = div(sub(n,x),y);
return mult(2.0,a_atan(inner));
}else if(x.val < 0.0 && abs(y.val) <= 1E-6)
{
return constG2(pi);
}
// return 0 for undefined
return constG2(0.0);
}
//--------------------------------
GNum2 a_atan2(in GNum2 y, in float x)
{
return a_atan2(y,constG2(x));
}
//--------------------------------
GNum2 a_atan2(in float y, in GNum2 x)
{
return a_atan2(constG2(y),x);
}
//--------------------------------
GNum2 a_mix(in GNum2 a, in GNum2 b, in GNum2 t)
{
return add(mult(a, sub(1.0, t)), mult(b, t));
}
//--------------------------------
GNum2 a_mix(in GNum2 a, in GNum2 b, in float t)
{
return add(mult(a, 1.0 - t), mult(b, t));
}
//--------------------------------
GNum2 a_mix(in GNum2 a, in float b, in GNum2 t)
{
return add(mult(a, sub(1.0, t)), mult(b, t));
}
//--------------------------------
GNum2 a_mix(in GNum2 a, in float b, in float t)
{
return add(mult(a, 1.0 - t), b*t);
}
//--------------------------------
GNum2 a_mix(in float a, in GNum2 b, in GNum2 t)
{
return add(mult(a, sub(1.0, t)), mult(b, t));
}
//--------------------------------
GNum2 a_mix(in float a, in GNum2 b, in float t)
{
return add(a * (1.0 - t), mult(b, t));
}
//--------------------------------
GNum2 a_mix(in float a, in float b, in GNum2 t)
{
return add(mult(a, sub(1.0, t)), mult(b, t));
}
//--------------------------------
GNum3 constG3(in float val)
{
return GNum3(val, vec3(0.0));
}
//--------------------------------
GNum3 varG3(in float val, in int index)
{
vec3 g = vec3(0.0);
g[index] = 1.0;
return GNum3(val, g);
}
//--------------------------------
GNum3 varG3x(in float val)
{
vec3 g = vec3(0.0);
g[0] = 1.0;
return GNum3(val, g);
}
//--------------------------------
GNum3 varG3y(in float val)
{
vec3 g = vec3(0.0);
g[1] = 1.0;
return GNum3(val, g);
}
//--------------------------------
GNum3 varG3z(in float val)
{
vec3 g = vec3(0.0);
g[2] = 1.0;
return GNum3(val, g);
}
//--------------------------------
GNum3 add(in GNum3 a, in GNum3 b)
{
return GNum3(a.val + b.val, a.g + b.g);
}
//--------------------------------
GNum3 add(in GNum3 a, in float b)
{
return GNum3(a.val + b, a.g);
}
//--------------------------------
GNum3 add(in float a, in GNum3 b)
{
return GNum3(a + b.val, b.g);
}
//--------------------------------
GNum3 sub(in GNum3 a, in GNum3 b)
{
return GNum3(a.val - b.val, a.g - b.g);
}
//--------------------------------
GNum3 sub(in GNum3 a, in float b)
{
return GNum3(a.val - b, a.g);
}
//--------------------------------
GNum3 sub(in float a, in GNum3 b)
{
return GNum3(a - b.val, -b.g);
}
//--------------------------------
GNum3 mult(in GNum3 a, in GNum3 b)
{
return GNum3(a.val * b.val,
a.val*b.g + b.val*a.g
);
}
//--------------------------------
GNum3 mult(in GNum3 a, in float b)
{
return GNum3(a.val * b, b*a.g);
}
//--------------------------------
GNum3 mult(in float a, in GNum3 b)
{
return GNum3(a * b.val, a*b.g);
}
//--------------------------------
GNum3 neg(in GNum3 a)
{
return mult(-1.0,a);
}
//--------------------------------
GNum3 div(in GNum3 a, in GNum3 b)
{
float b1 = b.val;
float b2 = b1*b1;
return GNum3(a.val / b.val ,
(b.val*a.g - a.val*b.g)/b2
);
}
//--------------------------------
GNum3 div(in GNum3 a, in float b)
{
return GNum3(a.val / b, a.g/b);
}
//--------------------------------
GNum3 div(in float a, in GNum3 b)
{
float b1 = b.val;
float b2 = b1*b1;
return GNum3(a / b.val,
-a*b.g/b2
);
}
//--------------------------------
GNum3 inv(in GNum3 a)
{
return div(1.0, a);
}
//--------------------------------
GNum3 a_pow(in GNum3 a, in GNum3 b)
{
return a_exp(mult(b,a_log(a)));
}
//--------------------------------
GNum3 a_pow(in GNum3 a, in float b)
{
// constant exponent -> make special case
float v = pow(a.val, b); // value f(a(x))
float da = b*pow(a.val,b-1.0); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_pow(in float a, in GNum3 b)
{
return a_exp(mult(b,log(a)));
}
//--------------------------------
GNum3 a_ipow(in GNum3 x, in int n)
{
// based on https://en.wikipedia.org/wiki/Exponentiation_by_squaring
if (n < 0)
{
x = div(1.0,x);
n = -n;
}
if (n == 0)
{
return constG3(1.0);
}
GNum3 y = constG3(1.0);
while (n > 1)
{
if (n % 2 == 0)
{
x = mult(x,x);
}
else
{
y = mult(x, y);
x = mult(x, x);
}
n = n / 2;
}
return mult(x, y);
}
//--------------------------------
GNum3 a_min(in GNum3 a, in GNum3 b)
{
if(a.val < b.val)
{
return a;
}
return b;
}
//--------------------------------
GNum3 a_max(in GNum3 a, in GNum3 b)
{
if(a.val > b.val)
{
return a;
}
return b;
}
//--------------------------------
GNum3 a_exp2(in GNum3 a)
{
float v = exp2(a.val); // value f(a(x))
float da = log(2.0)*exp2(a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_inversesqrt(in GNum3 a)
{
float v = inversesqrt(a.val); // value f(a(x))
float da = -0.5/pow(sqrt(a.val),3.0); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_atan(in GNum3 a)
{
float v = atan(a.val); // value f(a(x))
float da = 1.0/(1.0 + a.val * a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_sqrt(in GNum3 a)
{
float v = sqrt(a.val); // value f(a(x))
float da = 0.5/sqrt(a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_sinh(in GNum3 a)
{
float v = sinh(a.val); // value f(a(x))
float da = cosh(a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_ceil(in GNum3 a)
{
float v = ceil(a.val); // value f(a(x))
float da = 0.0; // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_tan(in GNum3 a)
{
float v = tan(a.val); // value f(a(x))
float da = 1.0 + pow(tan(a.val),2.0); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_asinh(in GNum3 a)
{
float v = asinh(a.val); // value f(a(x))
float da = 1.0/sqrt(1.0 + a.val * a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_asin(in GNum3 a)
{
float v = asin(a.val); // value f(a(x))
float da = 1.0/sqrt(1.0 - a.val * a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_acosh(in GNum3 a)
{
float v = acosh(a.val); // value f(a(x))
float da = 1.0/sqrt(-1.0 + a.val * a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_abs(in GNum3 a)
{
float v = abs(a.val); // value f(a(x))
float da = a.val < 0.0 ? -1.0 : 1.0; // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_exp(in GNum3 a)
{
float v = exp(a.val); // value f(a(x))
float da = exp(a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_cosh(in GNum3 a)
{
float v = cosh(a.val); // value f(a(x))
float da = sinh(a.val); // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_floor(in GNum3 a)
{
float v = floor(a.val); // value f(a(x))
float da = 0.0; // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------
GNum3 a_log(in GNum3 a)
{
float v = log(a.val); // value f(a(x))
float da = 1.0/a.val; // first derivative f'(a(x))
return GNum3(v , da * a.g);
}
//--------------------------------