mirrors/Odin
1
0
Fork 0
mirror of https://github.com/odin-lang/Odin.git synced 2025-12-30 18:02:02 +00:00
Code Issues Packages Projects Releases Wiki Activity
Files
d936ca1ea003f82e0fda330cbad1f5bcf4387df2
Odin/core/math.odin

377 lines
10 KiB
Odin
Raw Blame History

TAU :: 6.28318530717958647692528676655900576;
PI :: 3.14159265358979323846264338327950288;
ONE_OVER_TAU :: 0.636619772367581343075535053490057448;
ONE_OVER_PI :: 0.159154943091895335768883763372514362;
E :: 2.71828182845904523536;
SQRT_TWO :: 1.41421356237309504880168872420969808;
SQRT_THREE :: 1.73205080756887729352744634150587236;
SQRT_FIVE :: 2.23606797749978969640917366873127623;
LOG_TWO :: 0.693147180559945309417232121458176568;
LOG_TEN :: 2.30258509299404568401799145468436421;
EPSILON :: 1.19209290e-7;
τ :: TAU;
π :: PI;
Vec2 :: [vector 2]f32;
Vec3 :: [vector 3]f32;
Vec4 :: [vector 4]f32;
// Column major
Mat2 :: [2][2]f32;
Mat3 :: [3][3]f32;
Mat4 :: [4][4]f32;
Complex :: complex64;
foreign __llvm_core {
sqrt :: proc(x: f32) -> f32 #link_name "llvm.sqrt.f32" ---;
sqrt :: proc(x: f64) -> f64 #link_name "llvm.sqrt.f64" ---;
sin :: proc(θ: f32) -> f32 #link_name "llvm.sin.f32" ---;
sin :: proc(θ: f64) -> f64 #link_name "llvm.sin.f64" ---;
cos :: proc(θ: f32) -> f32 #link_name "llvm.cos.f32" ---;
cos :: proc(θ: f64) -> f64 #link_name "llvm.cos.f64" ---;
pow :: proc(x, power: f32) -> f32 #link_name "llvm.pow.f32" ---;
pow :: proc(x, power: f64) -> f64 #link_name "llvm.pow.f64" ---;
fmuladd :: proc(a, b, c: f32) -> f32 #link_name "llvm.fmuladd.f32" ---;
fmuladd :: proc(a, b, c: f64) -> f64 #link_name "llvm.fmuladd.f64" ---;
}
tan :: proc(θ: f32) -> f32 #inline do return sin(θ)/cos(θ);
tan :: proc(θ: f64) -> f64 #inline do return sin(θ)/cos(θ);
lerp :: proc(a, b, t: f32) -> (x: f32) do return a*(1-t) + b*t;
lerp :: proc(a, b, t: f64) -> (x: f64) do return a*(1-t) + b*t;
unlerp :: proc(a, b, x: f32) -> (t: f32) do return (x-a)/(b-a);
unlerp :: proc(a, b, x: f64) -> (t: f64) do return (x-a)/(b-a);
sign :: proc(x: f32) -> f32 do return x >= 0 ? +1 : -1;
sign :: proc(x: f64) -> f64 do return x >= 0 ? +1 : -1;
copy_sign :: proc(x, y: f32) -> f32 {
ix := transmute(u32, x);
iy := transmute(u32, y);
ix &= 0x7fff_ffff;
ix |= iy & 0x8000_0000;
return transmute(f32, ix);
}
copy_sign :: proc(x, y: f64) -> f64 {
ix := transmute(u64, x);
iy := transmute(u64, y);
ix &= 0x7fff_ffff_ffff_ff;
ix |= iy & 0x8000_0000_0000_0000;
return transmute(f64, ix);
}
round :: proc(x: f32) -> f32 do return x >= 0 ? floor(x + 0.5) : ceil(x - 0.5);
round :: proc(x: f64) -> f64 do return x >= 0 ? floor(x + 0.5) : ceil(x - 0.5);
floor :: proc(x: f32) -> f32 do return x >= 0 ? f32(i64(x)) : f32(i64(x-0.5)); // TODO: Get accurate versions
floor :: proc(x: f64) -> f64 do return x >= 0 ? f64(i64(x)) : f64(i64(x-0.5)); // TODO: Get accurate versions
ceil :: proc(x: f32) -> f32 do return x < 0 ? f32(i64(x)) : f32(i64(x+1)); // TODO: Get accurate versions
ceil :: proc(x: f64) -> f64 do return x < 0 ? f64(i64(x)) : f64(i64(x+1)); // TODO: Get accurate versions
remainder :: proc(x, y: f32) -> f32 do return x - round(x/y) * y;
remainder :: proc(x, y: f64) -> f64 do return x - round(x/y) * y;
mod :: proc(x, y: f32) -> f32 {
result: f32;
y = abs(y);
result = remainder(abs(x), y);
if sign(result) < 0 {
result += y;
}
return copy_sign(result, x);
}
mod :: proc(x, y: f64) -> f64 {
result: f64;
y = abs(y);
result = remainder(abs(x), y);
if sign(result) < 0 {
result += y;
}
return copy_sign(result, x);
}
to_radians :: proc(degrees: f32) -> f32 do return degrees * TAU / 360;
to_degrees :: proc(radians: f32) -> f32 do return radians * 360 / TAU;
dot :: proc(a, b: Vec2) -> f32 { c := a*b; return c.x + c.y; }
dot :: proc(a, b: Vec3) -> f32 { c := a*b; return c.x + c.y + c.z; }
dot :: proc(a, b: Vec4) -> f32 { c := a*b; return c.x + c.y + c.z + c.w; }
cross :: proc(x, y: Vec3) -> Vec3 {
a := swizzle(x, 1, 2, 0) * swizzle(y, 2, 0, 1);
b := swizzle(x, 2, 0, 1) * swizzle(y, 1, 2, 0);
return a - b;
}
mag :: proc(v: Vec2) -> f32 do return sqrt(dot(v, v));
mag :: proc(v: Vec3) -> f32 do return sqrt(dot(v, v));
mag :: proc(v: Vec4) -> f32 do return sqrt(dot(v, v));
norm :: proc(v: Vec2) -> Vec2 do return v / mag(v);
norm :: proc(v: Vec3) -> Vec3 do return v / mag(v);
norm :: proc(v: Vec4) -> Vec4 do return v / mag(v);
norm0 :: proc(v: Vec2) -> Vec2 {
m := mag(v);
return m == 0 ? 0 : v/m;
}
norm0 :: proc(v: Vec3) -> Vec3 {
m := mag(v);
return m == 0 ? 0 : v/m;
}
norm0 :: proc(v: Vec4) -> Vec4 {
m := mag(v);
return m == 0 ? 0 : v/m;
}
mat4_identity :: proc() -> Mat4 {
return Mat4{
{1, 0, 0, 0},
{0, 1, 0, 0},
{0, 0, 1, 0},
{0, 0, 0, 1},
};
}
mat4_transpose :: proc(m: Mat4) -> Mat4 {
for j in 0..4 {
for i in 0..4 {
m[i][j], m[j][i] = m[j][i], m[i][j];
}
}
return m;
}
mul :: proc(a, b: Mat4) -> Mat4 {
c: Mat4;
for j in 0..4 {
for i in 0..4 {
c[j][i] = a[0][i]*b[j][0] +
a[1][i]*b[j][1] +
a[2][i]*b[j][2] +
a[3][i]*b[j][3];
}
}
return c;
}
mul :: proc(m: Mat4, v: Vec4) -> Vec4 {
return Vec4{
m[0][0]*v.x + m[1][0]*v.y + m[2][0]*v.z + m[3][0]*v.w,
m[0][1]*v.x + m[1][1]*v.y + m[2][1]*v.z + m[3][1]*v.w,
m[0][2]*v.x + m[1][2]*v.y + m[2][2]*v.z + m[3][2]*v.w,
m[0][3]*v.x + m[1][3]*v.y + m[2][3]*v.z + m[3][3]*v.w,
};
}
inverse :: proc(m: Mat4) -> Mat4 {
o: Mat4;
sf00 := m[2][2] * m[3][3] - m[3][2] * m[2][3];
sf01 := m[2][1] * m[3][3] - m[3][1] * m[2][3];
sf02 := m[2][1] * m[3][2] - m[3][1] * m[2][2];
sf03 := m[2][0] * m[3][3] - m[3][0] * m[2][3];
sf04 := m[2][0] * m[3][2] - m[3][0] * m[2][2];
sf05 := m[2][0] * m[3][1] - m[3][0] * m[2][1];
sf06 := m[1][2] * m[3][3] - m[3][2] * m[1][3];
sf07 := m[1][1] * m[3][3] - m[3][1] * m[1][3];
sf08 := m[1][1] * m[3][2] - m[3][1] * m[1][2];
sf09 := m[1][0] * m[3][3] - m[3][0] * m[1][3];
sf10 := m[1][0] * m[3][2] - m[3][0] * m[1][2];
sf11 := m[1][1] * m[3][3] - m[3][1] * m[1][3];
sf12 := m[1][0] * m[3][1] - m[3][0] * m[1][1];
sf13 := m[1][2] * m[2][3] - m[2][2] * m[1][3];
sf14 := m[1][1] * m[2][3] - m[2][1] * m[1][3];
sf15 := m[1][1] * m[2][2] - m[2][1] * m[1][2];
sf16 := m[1][0] * m[2][3] - m[2][0] * m[1][3];
sf17 := m[1][0] * m[2][2] - m[2][0] * m[1][2];
sf18 := m[1][0] * m[2][1] - m[2][0] * m[1][1];
o[0][0] = +(m[1][1] * sf00 - m[1][2] * sf01 + m[1][3] * sf02);
o[0][1] = -(m[1][0] * sf00 - m[1][2] * sf03 + m[1][3] * sf04);
o[0][2] = +(m[1][0] * sf01 - m[1][1] * sf03 + m[1][3] * sf05);
o[0][3] = -(m[1][0] * sf02 - m[1][1] * sf04 + m[1][2] * sf05);
o[1][0] = -(m[0][1] * sf00 - m[0][2] * sf01 + m[0][3] * sf02);
o[1][1] = +(m[0][0] * sf00 - m[0][2] * sf03 + m[0][3] * sf04);
o[1][2] = -(m[0][0] * sf01 - m[0][1] * sf03 + m[0][3] * sf05);
o[1][3] = +(m[0][0] * sf02 - m[0][1] * sf04 + m[0][2] * sf05);
o[2][0] = +(m[0][1] * sf06 - m[0][2] * sf07 + m[0][3] * sf08);
o[2][1] = -(m[0][0] * sf06 - m[0][2] * sf09 + m[0][3] * sf10);
o[2][2] = +(m[0][0] * sf11 - m[0][1] * sf09 + m[0][3] * sf12);
o[2][3] = -(m[0][0] * sf08 - m[0][1] * sf10 + m[0][2] * sf12);
o[3][0] = -(m[0][1] * sf13 - m[0][2] * sf14 + m[0][3] * sf15);
o[3][1] = +(m[0][0] * sf13 - m[0][2] * sf16 + m[0][3] * sf17);
o[3][2] = -(m[0][0] * sf14 - m[0][1] * sf16 + m[0][3] * sf18);
o[3][3] = +(m[0][0] * sf15 - m[0][1] * sf17 + m[0][2] * sf18);
ood := 1.0 / (m[0][0] * o[0][0] +
m[0][1] * o[0][1] +
m[0][2] * o[0][2] +
m[0][3] * o[0][3]);
o[0][0] *= ood;
o[0][1] *= ood;
o[0][2] *= ood;
o[0][3] *= ood;
o[1][0] *= ood;
o[1][1] *= ood;
o[1][2] *= ood;
o[1][3] *= ood;
o[2][0] *= ood;
o[2][1] *= ood;
o[2][2] *= ood;
o[2][3] *= ood;
o[3][0] *= ood;
o[3][1] *= ood;
o[3][2] *= ood;
o[3][3] *= ood;
return o;
}
mat4_translate :: proc(v: Vec3) -> Mat4 {
m := mat4_identity();
m[3][0] = v.x;
m[3][1] = v.y;
m[3][2] = v.z;
m[3][3] = 1;
return m;
}
mat4_rotate :: proc(v: Vec3, angle_radians: f32) -> Mat4 {
c := cos(angle_radians);
s := sin(angle_radians);
a := norm(v);
t := a * (1-c);
rot := mat4_identity();
rot[0][0] = c + t.x*a.x;
rot[0][1] = 0 + t.x*a.y + s*a.z;
rot[0][2] = 0 + t.x*a.z - s*a.y;
rot[0][3] = 0;
rot[1][0] = 0 + t.y*a.x - s*a.z;
rot[1][1] = c + t.y*a.y;
rot[1][2] = 0 + t.y*a.z + s*a.x;
rot[1][3] = 0;
rot[2][0] = 0 + t.z*a.x + s*a.y;
rot[2][1] = 0 + t.z*a.y - s*a.x;
rot[2][2] = c + t.z*a.z;
rot[2][3] = 0;
return rot;
}
scale :: proc(m: Mat4, v: Vec3) -> Mat4 {
m[0][0] *= v.x;
m[1][1] *= v.y;
m[2][2] *= v.z;
return m;
}
scale :: proc(m: Mat4, s: f32) -> Mat4 {
m[0][0] *= s;
m[1][1] *= s;
m[2][2] *= s;
return m;
}
look_at :: proc(eye, centre, up: Vec3) -> Mat4 {
f := norm(centre - eye);
s := norm(cross(f, up));
u := cross(s, f);
return Mat4{
{+s.x, +u.x, -f.x, 0},
{+s.y, +u.y, -f.y, 0},
{+s.z, +u.z, -f.z, 0},
{-dot(s, eye), -dot(u, eye), dot(f, eye), 1},
};
}
perspective :: proc(fovy, aspect, near, far: f32) -> Mat4 {
m: Mat4;
tan_half_fovy := tan(0.5 * fovy);
m[0][0] = 1.0 / (aspect*tan_half_fovy);
m[1][1] = 1.0 / (tan_half_fovy);
m[2][2] = -(far + near) / (far - near);
m[2][3] = -1.0;
m[3][2] = -2.0*far*near / (far - near);
return m;
}
ortho3d :: proc(left, right, bottom, top, near, far: f32) -> Mat4 {
m := mat4_identity();
m[0][0] = +2.0 / (right - left);
m[1][1] = +2.0 / (top - bottom);
m[2][2] = -2.0 / (far - near);
m[3][0] = -(right + left) / (right - left);
m[3][1] = -(top + bottom) / (top - bottom);
m[3][2] = -(far + near) / (far - near);
return m;
}
F32_DIG :: 6;
F32_EPSILON :: 1.192092896e-07;
F32_GUARD :: 0;
F32_MANT_DIG :: 24;
F32_MAX :: 3.402823466e+38;
F32_MAX_10_EXP :: 38;
F32_MAX_EXP :: 128;
F32_MIN :: 1.175494351e-38;
F32_MIN_10_EXP :: -37;
F32_MIN_EXP :: -125;
F32_NORMALIZE :: 0;
F32_RADIX :: 2;
F32_ROUNDS :: 1;
F64_DIG :: 15; // # of decimal digits of precision
F64_EPSILON :: 2.2204460492503131e-016; // smallest such that 1.0+F64_EPSILON != 1.0
F64_MANT_DIG :: 53; // # of bits in mantissa
F64_MAX :: 1.7976931348623158e+308; // max value
F64_MAX_10_EXP :: 308; // max decimal exponent
F64_MAX_EXP :: 1024; // max binary exponent
F64_MIN :: 2.2250738585072014e-308; // min positive value
F64_MIN_10_EXP :: -307; // min decimal exponent
F64_MIN_EXP :: -1021; // min binary exponent
F64_RADIX :: 2; // exponent radix
F64_ROUNDS :: 1; // addition rounding: near
Reference in New Issue View Git Blame Copy Permalink