New package math and package math/linalg

This commit is contained in:
gingerBill
2019-10-27 10:35:35 +00:00
parent 0977ac111a
commit 5e81fc72b9
3 changed files with 671 additions and 395 deletions

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@@ -0,0 +1,257 @@
package linalg
import "core:math"
// Generic
dot_vector :: proc(a, b: $T/[$N]$E) -> (c: E) {
for i in 0..<N {
c += a[i] * b[i];
}
return;
}
dot_quaternion128 :: proc(a, b: $T/quaternion128) -> (c: f32) {
return real(a)*real(a) + imag(a)*imag(b) + jmag(a)*jmag(b) + kmag(a)*kmag(b);
}
dot_quaternion256 :: proc(a, b: $T/quaternion256) -> (c: f64) {
return real(a)*real(a) + imag(a)*imag(b) + jmag(a)*jmag(b) + kmag(a)*kmag(b);
}
dot :: proc{dot_vector, dot_quaternion128, dot_quaternion256};
cross2 :: proc(a, b: $T/[2]$E) -> E {
return a[0]*b[1] - b[0]*a[1];
}
cross3 :: proc(a, b: $T/[3]$E) -> (c: T) {
c[0] = +(a[1]*b[2] - b[1]*a[2]);
c[1] = -(a[2]*b[3] - b[2]*a[3]);
c[2] = +(a[3]*b[1] - b[3]*a[1]);
return;
}
cross :: proc{cross2, cross3};
normalize_vector :: proc(v: $T/[$N]$E) -> T {
return v / length(v);
}
normalize_quaternion128 :: proc(q: $Q/quaternion128) -> Q {
return q/abs(q);
}
normalize_quaternion256 :: proc(q: $Q/quaternion256) -> Q {
return q/abs(q);
}
normalize :: proc{normalize_vector, normalize_quaternion128, normalize_quaternion256};
normalize0_vector :: proc(v: $T/[$N]$E) -> T {
m := length(v);
return m == 0 ? 0 : v/m;
}
normalize0_quaternion128 :: proc(q: $Q/quaternion128) -> Q {
m := abs(q);
return m == 0 ? 0 : q/m;
}
normalize0_quaternion256 :: proc(q: $Q/quaternion256) -> Q {
m := abs(q);
return m == 0 ? 0 : q/m;
}
normalize0 :: proc{normalize0_vector, normalize0_quaternion128, normalize0_quaternion256};
length :: proc(v: $T/[$N]$E) -> E {
return math.sqrt(dot(v, v));
}
identity :: proc($T: typeid/[$N][N]$E) -> (m: T) {
for i in 0..<N do m[i][i] = E(1);
return m;
}
transpose :: proc(a: $T/[$N][$M]$E) -> (m: ((M == N) ? T : [M][N]E)) {
for j in 0..<M {
for i in 0..<N {
m[j][i] = a[i][j];
}
}
return;
}
mul_matrix :: proc(a: $A/[$I][$J]$E, b: $B/[J][$K]E) -> (c: ((I == J && J == K && A == B) ? A : [I][K]E)) {
for i in 0..<I {
for K in 0..<K {
for j in 0..<J {
c[i][k] += a[i][j] * b[j][k];
}
}
}
return;
}
mul_matrix_vector :: proc(a: $A/[$I][$J]$E, b: $B/[I]E) -> (c: B) {
for i in 0..<I {
for j in 0..<J {
c[i] += a[i][j] * b[i];
}
}
return;
}
mul_quaternion128_vector3 :: proc(q: $Q/quaternion128, v: $V/[3]$F/f32) -> V {
Raw_Quaternion :: struct {xyz: [3]f32, r: f32};
q := transmute(Raw_Quaternion)q;
v := transmute([3]f32)v;
t := cross(2*q.xyz, v);
return V(v + q.r*t + cross(q.xyz, t));
}
mul_quaternion256_vector3 :: proc(q: $Q/quaternion256, v: $V/[3]$F/f64) -> V {
Raw_Quaternion :: struct {xyz: [3]f64, r: f64};
q := transmute(Raw_Quaternion)q;
v := transmute([3]f64)v;
t := cross(2*q.xyz, v);
return V(v + q.r*t + cross(q.xyz, t));
}
mul_quaternion_vector3 :: proc{mul_quaternion128_vector3, mul_quaternion256_vector3};
mul :: proc{mul_matrix, mul_matrix_vector, mul_quaternion128_vector3, mul_quaternion256_vector3};
// Specific
Float :: f32;
Vector2 :: distinct [2]Float;
Vector3 :: distinct [3]Float;
Vector4 :: distinct [4]Float;
Matrix2x1 :: distinct [2][1]Float;
Matrix2x2 :: distinct [2][2]Float;
Matrix2x3 :: distinct [2][3]Float;
Matrix2x4 :: distinct [2][4]Float;
Matrix3x1 :: distinct [3][1]Float;
Matrix3x2 :: distinct [3][2]Float;
Matrix3x3 :: distinct [3][3]Float;
Matrix3x4 :: distinct [3][4]Float;
Matrix4x1 :: distinct [4][1]Float;
Matrix4x2 :: distinct [4][2]Float;
Matrix4x3 :: distinct [4][3]Float;
Matrix4x4 :: distinct [4][4]Float;
Matrix2 :: Matrix2x2;
Matrix3 :: Matrix3x3;
Matrix4 :: Matrix4x4;
Quaternion :: distinct (size_of(Float) == size_of(f32) ? quaternion128 : quaternion256);
translate_matrix4 :: proc(v: Vector3) -> Matrix4 {
m := identity(Matrix4);
m[3][0] = v[0];
m[3][1] = v[1];
m[3][2] = v[2];
return m;
}
rotate_matrix4 :: proc(v: Vector3, angle_radians: Float) -> Matrix4 {
c := math.cos(angle_radians);
s := math.sin(angle_radians);
a := normalize(v);
t := a * (1-c);
rot := identity(Matrix4);
rot[0][0] = c + t[0]*a[0];
rot[0][1] = 0 + t[0]*a[1] + s*a[2];
rot[0][2] = 0 + t[0]*a[2] - s*a[1];
rot[0][3] = 0;
rot[1][0] = 0 + t[1]*a[0] - s*a[2];
rot[1][1] = c + t[1]*a[1];
rot[1][2] = 0 + t[1]*a[2] + s*a[0];
rot[1][3] = 0;
rot[2][0] = 0 + t[2]*a[0] + s*a[1];
rot[2][1] = 0 + t[2]*a[1] - s*a[0];
rot[2][2] = c + t[2]*a[2];
rot[2][3] = 0;
return rot;
}
scale_matrix4 :: proc(m: Matrix4, v: Vector3) -> Matrix4 {
mm := m;
mm[0][0] *= v[0];
mm[1][1] *= v[1];
mm[2][2] *= v[2];
return mm;
}
look_at :: proc(eye, centre, up: Vector3) -> Matrix4 {
f := normalize(centre - eye);
s := normalize(cross(f, up));
u := cross(s, f);
return Matrix4{
{+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: Float) -> (m: Matrix4) {
tan_half_fovy := math.tan(0.5 * fovy);
m[0][0] = 1 / (aspect*tan_half_fovy);
m[1][1] = 1 / (tan_half_fovy);
m[2][2] = -(far + near) / (far - near);
m[2][3] = -1;
m[3][2] = -2*far*near / (far - near);
return;
}
ortho3d :: proc(left, right, bottom, top, near, far: Float) -> (m: Matrix4) {
m[0][0] = +2 / (right - left);
m[1][1] = +2 / (top - bottom);
m[2][2] = -2 / (far - near);
m[3][0] = -(right + left) / (right - left);
m[3][1] = -(top + bottom) / (top - bottom);
m[3][2] = -(far + near) / (far- near);
m[3][3] = 1;
return;
}
axis_angle :: proc(axis: Vector3, angle_radians: Float) -> Quaternion {
t := angle_radians*0.5;
w := math.cos(t);
v := normalize(axis) * math.sin(t);
return quaternion(w, v.x, v.y, v.z);
}
angle_axis :: proc(angle_radians: Float, axis: Vector3) -> Quaternion {
t := angle_radians*0.5;
w := math.cos(t);
v := normalize(axis) * math.sin(t);
return quaternion(w, v.x, v.y, v.z);
}
euler_angles :: proc(pitch, yaw, roll: Float) -> Quaternion {
p := axis_angle({1, 0, 0}, pitch);
y := axis_angle({0, 1, 0}, yaw);
r := axis_angle({0, 0, 1}, roll);
return (y * p) * r;
}

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@@ -1,36 +1,41 @@
package math
import "intrinsics"
Float_Class :: enum {
Normal, // an ordinary nonzero floating point value
Subnormal, // a subnormal floating point value
Zero, // zero
Neg_Zero, // the negative zero
NaN, // Not-A-Number (NaN)
Inf, // positive infinity
Neg_Inf // negative infinity
};
TAU :: 6.28318530717958647692528676655900576;
PI :: 3.14159265358979323846264338327950288;
E :: 2.71828182845904523536;
τ :: TAU;
π :: PI;
e :: E;
SQRT_TWO :: 1.41421356237309504880168872420969808;
SQRT_THREE :: 1.73205080756887729352744634150587236;
SQRT_FIVE :: 2.23606797749978969640917366873127623;
LOG_TWO :: 0.693147180559945309417232121458176568;
LOG_TEN :: 2.30258509299404568401799145468436421;
LN2 :: 0.693147180559945309417232121458176568;
LN10 :: 2.30258509299404568401799145468436421;
EPSILON :: 1.19209290e-7;
MAX_F64_PRECISION :: 16; // Maximum number of meaningful digits after the decimal point for 'f64'
MAX_F32_PRECISION :: 8; // Maximum number of meaningful digits after the decimal point for 'f32'
τ :: TAU;
π :: PI;
Vec2 :: distinct [2]f32;
Vec3 :: distinct [3]f32;
Vec4 :: distinct [4]f32;
// Column major
Mat2 :: distinct [2][2]f32;
Mat3 :: distinct [3][3]f32;
Mat4 :: distinct [4][4]f32;
Quat :: struct {x, y, z, w: f32};
QUAT_IDENTITY := Quat{x = 0, y = 0, z = 0, w = 1};
RAD_PER_DEG :: TAU/360.0;
DEG_PER_RAD :: 360.0/TAU;
@(default_calling_convention="c")
@(default_calling_convention="none")
foreign _ {
@(link_name="llvm.sqrt.f32")
sqrt_f32 :: proc(x: f32) -> f32 ---;
@@ -58,9 +63,9 @@ foreign _ {
fmuladd_f64 :: proc(a, b, c: f64) -> f64 ---;
@(link_name="llvm.log.f32")
log_f32 :: proc(x: f32) -> f32 ---;
ln_f32 :: proc(x: f32) -> f32 ---;
@(link_name="llvm.log.f64")
log_f64 :: proc(x: f64) -> f64 ---;
ln_f64 :: proc(x: f64) -> f64 ---;
@(link_name="llvm.exp.f32")
exp_f32 :: proc(x: f32) -> f32 ---;
@@ -68,20 +73,40 @@ foreign _ {
exp_f64 :: proc(x: f64) -> f64 ---;
}
log :: proc{log_f32, log_f64};
exp :: proc{exp_f32, exp_f64};
sqrt :: proc{sqrt_f32, sqrt_f64};
sin :: proc{sin_f32, sin_f64};
cos :: proc{cos_f32, cos_f64};
pow :: proc{pow_f32, pow_f64};
fmuladd :: proc{fmuladd_f32, fmuladd_f64};
ln :: proc{ln_f32, ln_f64};
exp :: proc{exp_f32, exp_f64};
log_f32 :: proc(x, base: f32) -> f32 { return ln(x) / ln(base); }
log_f64 :: proc(x, base: f64) -> f64 { return ln(x) / ln(base); }
log :: proc{log_f32, log_f64};
log2_f32 :: proc(x: f32) -> f32 { return ln(x)/LN2; }
log2_f64 :: proc(x: f64) -> f64 { return ln(x)/LN2; }
log2 :: proc{log2_f32, log2_f64};
log10_f32 :: proc(x: f32) -> f32 { return ln(x)/LN10; }
log10_f64 :: proc(x: f64) -> f64 { return ln(x)/LN10; }
log10 :: proc{log10_f32, log10_f64};
tan_f32 :: proc "c" (θ: f32) -> f32 { return sin(θ)/cos(θ); }
tan_f64 :: proc "c" (θ: f64) -> f64 { return sin(θ)/cos(θ); }
tan :: proc{tan_f32, tan_f64};
lerp :: proc(a, b: $T, t: $E) -> (x: T) { return a*(1-t) + b*t; }
unlerp_f32 :: proc(a, b, x: f32) -> (t: f32) { return (x-a)/(b-a); }
unlerp_f64 :: proc(a, b, x: f64) -> (t: f64) { return (x-a)/(b-a); }
unlerp :: proc{unlerp_f32, unlerp_f64};
sign_f32 :: proc(x: f32) -> f32 { return x >= 0 ? +1 : -1; }
sign_f64 :: proc(x: f64) -> f64 { return x >= 0 ? +1 : -1; }
sign_f32 :: proc(x: f32) -> f32 { return f32(int(0 < x) - int(x < 0)); }
sign_f64 :: proc(x: f64) -> f64 { return f64(int(0 < x) - int(x < 0)); }
sign :: proc{sign_f32, sign_f64};
copy_sign_f32 :: proc(x, y: f32) -> f32 {
ix := transmute(u32)x;
@@ -90,7 +115,6 @@ copy_sign_f32 :: proc(x, y: f32) -> f32 {
ix |= iy & 0x8000_0000;
return transmute(f32)ix;
}
copy_sign_f64 :: proc(x, y: f64) -> f64 {
ix := transmute(u64)x;
iy := transmute(u64)y;
@@ -98,22 +122,89 @@ copy_sign_f64 :: proc(x, y: f64) -> f64 {
ix |= iy & 0x8000_0000_0000_0000;
return transmute(f64)ix;
}
sqrt :: proc{sqrt_f32, sqrt_f64};
sin :: proc{sin_f32, sin_f64};
cos :: proc{cos_f32, cos_f64};
tan :: proc{tan_f32, tan_f64};
pow :: proc{pow_f32, pow_f64};
fmuladd :: proc{fmuladd_f32, fmuladd_f64};
sign :: proc{sign_f32, sign_f64};
copy_sign :: proc{copy_sign_f32, copy_sign_f64};
round_f32 :: proc(x: f32) -> f32 { return x >= 0 ? floor(x + 0.5) : ceil(x - 0.5); }
round_f64 :: proc(x: f64) -> f64 { return x >= 0 ? floor(x + 0.5) : ceil(x - 0.5); }
to_radians_f32 :: proc(degrees: f32) -> f32 { return degrees * RAD_PER_DEG; }
to_radians_f64 :: proc(degrees: f64) -> f64 { return degrees * RAD_PER_DEG; }
to_degrees_f32 :: proc(radians: f32) -> f32 { return radians * DEG_PER_RAD; }
to_degrees_f64 :: proc(radians: f64) -> f64 { return radians * DEG_PER_RAD; }
to_radians :: proc{to_radians_f32, to_radians_f64};
to_degrees :: proc{to_degrees_f32, to_degrees_f64};
trunc_f32 :: proc(x: f32) -> f32 {
trunc_internal :: proc(f: f32) -> f32 {
mask :: 0xff;
shift :: 32 - 9;
bias :: 0x7f;
if f < 1 {
switch {
case f < 0: return -trunc_internal(-f);
case f == 0: return f;
case: return 0;
}
}
x := transmute(u32)f;
e := (x >> shift) & mask - bias;
if e < shift {
x &= ~(1 << (shift-e)) - 1;
}
return transmute(f32)x;
}
switch classify(x) {
case .Zero, .Neg_Zero, .NaN, .Inf, .Neg_Inf:
return x;
}
return trunc_internal(x);
}
trunc_f64 :: proc(x: f64) -> f64 {
trunc_internal :: proc(f: f64) -> f64 {
mask :: 0x7ff;
shift :: 64 - 12;
bias :: 0x3ff;
if f < 1 {
switch {
case f < 0: return -trunc_internal(-f);
case f == 0: return f;
case: return 0;
}
}
x := transmute(u64)f;
e := (x >> shift) & mask - bias;
if e < shift {
x &= ~(1 << (shift-e)) - 1;
}
return transmute(f64)x;
}
switch classify(x) {
case .Zero, .Neg_Zero, .NaN, .Inf, .Neg_Inf:
return x;
}
return trunc_internal(x);
}
trunc :: proc{trunc_f32, trunc_f64};
round_f32 :: proc(x: f32) -> f32 {
return x < 0 ? ceil(x - 0.5) : floor(x + 0.5);
}
round_f64 :: proc(x: f64) -> f64 {
return x < 0 ? ceil(x - 0.5) : floor(x + 0.5);
}
round :: proc{round_f32, round_f64};
ceil_f32 :: proc(x: f32) -> f32 { return -floor(-x); }
ceil_f64 :: proc(x: f64) -> f64 { return -floor(-x); }
ceil :: proc{ceil_f32, ceil_f64};
floor_f32 :: proc(x: f32) -> f32 {
if x == 0 || is_nan(x) || is_inf(x) {
return x;
@@ -144,33 +235,27 @@ floor_f64 :: proc(x: f64) -> f64 {
}
floor :: proc{floor_f32, floor_f64};
ceil_f32 :: proc(x: f32) -> f32 { return -floor_f32(-x); }
ceil_f64 :: proc(x: f64) -> f64 { return -floor_f64(-x); }
ceil :: proc{ceil_f32, ceil_f64};
remainder_f32 :: proc(x, y: f32) -> f32 { return x - round(x/y) * y; }
remainder_f64 :: proc(x, y: f64) -> f64 { return x - round(x/y) * y; }
remainder :: proc{remainder_f32, remainder_f64};
mod_f32 :: proc(x, y: f32) -> (n: f32) {
z := abs(y);
n = remainder(abs(x), z);
if sign(n) < 0 {
n += z;
floor_div :: proc(x, y: $T) -> T
where intrinsics.type_is_integer(T) {
a := x / y;
r := x % y;
if (r > 0 && y < 0) || (r < 0 && y > 0) {
a -= 1;
}
return copy_sign(n, x);
return a;
}
mod_f64 :: proc(x, y: f64) -> (n: f64) {
z := abs(y);
n = remainder(abs(x), z);
if sign(n) < 0 {
n += z;
}
return copy_sign(n, x);
}
mod :: proc{mod_f32, mod_f64};
// TODO(bill): These need to implemented with the actual instructions
floor_mod :: proc(x, y: $T) -> T
where intrinsics.type_is_integer(T) {
r := x % y;
if (r > 0 && y < 0) || (r < 0 && y > 0) {
r += y;
}
return r;
}
modf_f32 :: proc(x: f32) -> (int: f32, frac: f32) {
shift :: 32 - 8 - 1;
mask :: 0xff;
@@ -190,8 +275,8 @@ modf_f32 :: proc(x: f32) -> (int: f32, frac: f32) {
i := transmute(u32)x;
e := uint(i>>shift)&mask - bias;
if e < 32-9 {
i &~= 1<<(32-9-e) - 1;
if e < shift {
i &~= 1<<(shift-e) - 1;
}
int = transmute(f32)i;
frac = x - int;
@@ -216,360 +301,274 @@ modf_f64 :: proc(x: f64) -> (int: f64, frac: f64) {
i := transmute(u64)x;
e := uint(i>>shift)&mask - bias;
if e < 64-12 {
i &~= 1<<(64-12-e) - 1;
if e < shift {
i &~= 1<<(shift-e) - 1;
}
int = transmute(f64)i;
frac = x - int;
return;
}
modf :: proc{modf_f32, modf_f64};
split_decimal :: modf;
is_nan_f32 :: inline proc(x: f32) -> bool { return x != x; }
is_nan_f64 :: inline proc(x: f64) -> bool { return x != x; }
mod_f32 :: proc(x, y: f32) -> (n: f32) {
z := abs(y);
n = remainder(abs(x), z);
if sign(n) < 0 {
n += z;
}
return copy_sign(n, x);
}
mod_f64 :: proc(x, y: f64) -> (n: f64) {
z := abs(y);
n = remainder(abs(x), z);
if sign(n) < 0 {
n += z;
}
return copy_sign(n, x);
}
mod :: proc{mod_f32, mod_f64};
remainder_f32 :: proc(x, y: f32) -> f32 { return x - round(x/y) * y; }
remainder_f64 :: proc(x, y: f64) -> f64 { return x - round(x/y) * y; }
remainder :: proc{remainder_f32, remainder_f64};
gcd :: proc(x, y: $T) -> T
where intrinsics.type_is_ordered_numeric(T) {
x, y := x, y;
for y != 0 {
x %= y;
x, y = y, x;
}
return abs(x);
}
lcm :: proc(x, y: $T) -> T
where intrinsics.type_is_ordered_numeric(T) {
return x / gcd(x, y) * y;
}
frexp_f32 :: proc(x: f32) -> (significand: f32, exponent: int) {
switch {
case x == 0:
return 0, 0;
case x < 0:
significand, exponent = frexp(-x);
return -significand, exponent;
}
ex := trunc(log2(x));
exponent = int(ex);
significand = x / pow(2.0, ex);
if abs(significand) >= 1 {
exponent += 1;
significand /= 2;
}
if exponent == 1024 && significand == 0 {
significand = 0.99999999999999988898;
}
return;
}
frexp_f64 :: proc(x: f64) -> (significand: f64, exponent: int) {
switch {
case x == 0:
return 0, 0;
case x < 0:
significand, exponent = frexp(-x);
return -significand, exponent;
}
ex := trunc(log2(x));
exponent = int(ex);
significand = x / pow(2.0, ex);
if abs(significand) >= 1 {
exponent += 1;
significand /= 2;
}
if exponent == 1024 && significand == 0 {
significand = 0.99999999999999988898;
}
return;
}
frexp :: proc{frexp_f32, frexp_f64};
binomial :: proc(n, k: int) -> int {
switch {
case k <= 0: return 1;
case 2*k > n: return binomial(n, n-k);
}
b := n;
for i in 2..<k {
b = (b * (n+1-i))/i;
}
return b;
}
factorial :: proc(n: int) -> int {
when size_of(int) == size_of(i64) {
@static table := [21]int{
1,
1,
2,
6,
24,
120,
720,
5_040,
40_320,
362_880,
3_628_800,
39_916_800,
479_001_600,
6_227_020_800,
87_178_291_200,
1_307_674_368_000,
20_922_789_888_000,
355_687_428_096_000,
6_402_373_705_728_000,
121_645_100_408_832_000,
2_432_902_008_176_640_000,
};
} else {
@static table := [13]int{
1,
1,
2,
6,
24,
120,
720,
5_040,
40_320,
362_880,
3_628_800,
39_916_800,
479_001_600,
};
}
assert(n >= 0, "parameter must not be negative");
assert(n < len(table), "parameter is too large to lookup in the table");
return 0;
}
classify_f32 :: proc(x: f32) -> Float_Class {
switch {
case x == 0:
i := transmute(i32)x;
if i < 0 {
return .Neg_Zero;
}
return .Zero;
case x*0.5 == x:
if x < 0 {
return .Neg_Inf;
}
return .Inf;
case x != x:
return .NaN;
}
u := transmute(u32)x;
exp := int(u>>23) & (1<<8 - 1);
if exp == 0 {
return .Subnormal;
}
return .Normal;
}
classify_f64 :: proc(x: f64) -> Float_Class {
switch {
case x == 0:
i := transmute(i64)x;
if i < 0 {
return .Neg_Zero;
}
return .Zero;
case x*0.5 == x:
if x < 0 {
return .Neg_Inf;
}
return .Inf;
case x != x:
return .NaN;
}
u := transmute(u64)x;
exp := int(u>>52) & (1<<11 - 1);
if exp == 0 {
return .Subnormal;
}
return .Normal;
}
classify :: proc{classify_f32, classify_f64};
is_nan_f32 :: proc(x: f32) -> bool { return classify(x) == .NaN; }
is_nan_f64 :: proc(x: f64) -> bool { return classify(x) == .NaN; }
is_nan :: proc{is_nan_f32, is_nan_f64};
is_finite_f32 :: inline proc(x: f32) -> bool { return !is_nan(x-x); }
is_finite_f64 :: inline proc(x: f64) -> bool { return !is_nan(x-x); }
is_finite :: proc{is_finite_f32, is_finite_f64};
is_inf_f32 :: proc(x: f32, sign := 0) -> bool {
return sign >= 0 && x > F32_MAX || sign <= 0 && x < -F32_MAX;
}
is_inf_f64 :: proc(x: f64, sign := 0) -> bool {
return sign >= 0 && x > F64_MAX || sign <= 0 && x < -F64_MAX;
}
// If sign > 0, is_inf reports whether f is positive infinity
// If sign < 0, is_inf reports whether f is negative infinity
// If sign == 0, is_inf reports whether f is either infinity
is_inf_f32 :: proc(x: f32) -> bool { return classify(abs(x)) == .Inf; }
is_inf_f64 :: proc(x: f64) -> bool { return classify(abs(x)) == .Inf; }
is_inf :: proc{is_inf_f32, is_inf_f64};
to_radians :: proc(degrees: f32) -> f32 { return degrees * TAU / 360; }
to_degrees :: proc(radians: f32) -> f32 { return radians * 360 / TAU; }
is_power_of_two :: proc(x: int) -> bool {
return x > 0 && (x & (x-1)) == 0;
}
mul :: proc{
mat3_mul,
mat4_mul, mat4_mul_vec4,
quat_mul, quat_mulf,
};
div :: proc{quat_div, quat_divf};
inverse :: proc{mat4_inverse, quat_inverse};
dot :: proc{vec_dot, quat_dot};
cross :: proc{cross2, cross3};
vec_dot :: proc(a, b: $T/[$N]$E) -> E {
res: E;
for i in 0..<N {
res += a[i] * b[i];
next_power_of_two :: proc(x: int) -> int {
k := x -1;
when size_of(int) == 8 {
k = k | (k >> 32);
}
return res;
k = k | (k >> 16);
k = k | (k >> 8);
k = k | (k >> 4);
k = k | (k >> 2);
k = k | (k >> 1);
k += 1 + int(x <= 0);
return k;
}
cross2 :: proc(a, b: $T/[2]$E) -> E {
return a[0]*b[1] - a[1]*b[0];
sum :: proc(x: $T/[]$E) -> (res: E)
where intrinsics.BuiltinProc_type_is_numeric(E) {
for i in x {
res += i;
}
return;
}
cross3 :: proc(a, b: $T/[3]$E) -> T {
i := swizzle(a, 1, 2, 0) * swizzle(b, 2, 0, 1);
j := swizzle(a, 2, 0, 1) * swizzle(b, 1, 2, 0);
return T(i - j);
prod :: proc(x: $T/[]$E) -> (res: E)
where intrinsics.BuiltinProc_type_is_numeric(E) {
for i in x {
res *= i;
}
return;
}
cumsum_inplace :: proc(x: $T/[]$E) -> T
where intrinsics.BuiltinProc_type_is_numeric(E) {
for i in 1..<len(x) {
x[i] = x[i-1] + x[i];
}
}
length :: proc(v: $T/[$N]$E) -> E { return sqrt(dot(v, v)); }
norm :: proc(v: $T/[$N]$E) -> T { return v / length(v); }
norm0 :: proc(v: $T/[$N]$E) -> T {
m := length(v);
return m == 0 ? 0 : v/m;
}
identity :: proc($T: typeid/[$N][N]$E) -> T {
m: T;
for i in 0..<N do m[i][i] = E(1);
return m;
}
transpose :: proc(m: $M/[$N][N]f32) -> M {
for j in 0..<N {
for i in 0..<N {
m[i][j], m[j][i] = m[j][i], m[i][j];
cumsum :: proc(dst, src: $T/[]$E) -> T
where intrinsics.BuiltinProc_type_is_numeric(E) {
N := min(len(dst), len(src));
if N > 0 {
dst[0] = src[0];
for i in 1..<N {
dst[i] = dst[i-1] + src[i];
}
}
return m;
return dst[:N];
}
mat3_mul :: proc(a, b: Mat3) -> Mat3 {
c: Mat3;
for j in 0..<3 {
for i in 0..<3 {
c[j][i] = a[0][i]*b[j][0] +
a[1][i]*b[j][1] +
a[2][i]*b[j][2];
}
}
return c;
}
mat4_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;
}
mat4_mul_vec4 :: proc(m: Mat4, v: Vec4) -> Vec4 {
return Vec4{
m[0][0]*v[0] + m[1][0]*v[1] + m[2][0]*v[2] + m[3][0]*v[3],
m[0][1]*v[0] + m[1][1]*v[1] + m[2][1]*v[2] + m[3][1]*v[3],
m[0][2]*v[0] + m[1][2]*v[1] + m[2][2]*v[2] + m[3][2]*v[3],
m[0][3]*v[0] + m[1][3]*v[1] + m[2][3]*v[2] + m[3][3]*v[3],
};
}
mat4_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 := identity(Mat4);
m[3][0] = v[0];
m[3][1] = v[1];
m[3][2] = v[2];
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 := identity(Mat4);
rot[0][0] = c + t[0]*a[0];
rot[0][1] = 0 + t[0]*a[1] + s*a[2];
rot[0][2] = 0 + t[0]*a[2] - s*a[1];
rot[0][3] = 0;
rot[1][0] = 0 + t[1]*a[0] - s*a[2];
rot[1][1] = c + t[1]*a[1];
rot[1][2] = 0 + t[1]*a[2] + s*a[0];
rot[1][3] = 0;
rot[2][0] = 0 + t[2]*a[0] + s*a[1];
rot[2][1] = 0 + t[2]*a[1] - s*a[0];
rot[2][2] = c + t[2]*a[2];
rot[2][3] = 0;
return rot;
}
scale_vec3 :: proc(m: Mat4, v: Vec3) -> Mat4 {
mm := m;
mm[0][0] *= v[0];
mm[1][1] *= v[1];
mm[2][2] *= v[2];
return mm;
}
scale_f32 :: proc(m: Mat4, s: f32) -> Mat4 {
mm := m;
mm[0][0] *= s;
mm[1][1] *= s;
mm[2][2] *= s;
return mm;
}
scale :: proc{scale_vec3, scale_f32};
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 := identity(Mat4);
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;
}
// Quaternion operations
conj :: proc(q: Quat) -> Quat {
return Quat{-q.x, -q.y, -q.z, q.w};
}
quat_mul :: proc(q0, q1: Quat) -> Quat {
d: Quat;
d.x = q0.w * q1.x + q0.x * q1.w + q0.y * q1.z - q0.z * q1.y;
d.y = q0.w * q1.y - q0.x * q1.z + q0.y * q1.w + q0.z * q1.x;
d.z = q0.w * q1.z + q0.x * q1.y - q0.y * q1.x + q0.z * q1.w;
d.w = q0.w * q1.w - q0.x * q1.x - q0.y * q1.y - q0.z * q1.z;
return d;
}
quat_mulf :: proc(q: Quat, f: f32) -> Quat { return Quat{q.x*f, q.y*f, q.z*f, q.w*f}; }
quat_divf :: proc(q: Quat, f: f32) -> Quat { return Quat{q.x/f, q.y/f, q.z/f, q.w/f}; }
quat_div :: proc(q0, q1: Quat) -> Quat { return mul(q0, quat_inverse(q1)); }
quat_inverse :: proc(q: Quat) -> Quat { return div(conj(q), dot(q, q)); }
quat_dot :: proc(q0, q1: Quat) -> f32 { return q0.x*q1.x + q0.y*q1.y + q0.z*q1.z + q0.w*q1.w; }
quat_norm :: proc(q: Quat) -> Quat {
m := sqrt(dot(q, q));
return div(q, m);
}
axis_angle :: proc(axis: Vec3, angle_radians: f32) -> Quat {
v := norm(axis) * sin(0.5*angle_radians);
w := cos(0.5*angle_radians);
return Quat{v.x, v.y, v.z, w};
}
euler_angles :: proc(pitch, yaw, roll: f32) -> Quat {
p := axis_angle(Vec3{1, 0, 0}, pitch);
y := axis_angle(Vec3{0, 1, 0}, yaw);
r := axis_angle(Vec3{0, 0, 1}, roll);
return mul(mul(y, p), r);
}
quat_to_mat4 :: proc(q: Quat) -> Mat4 {
a := quat_norm(q);
xx := a.x*a.x; yy := a.y*a.y; zz := a.z*a.z;
xy := a.x*a.y; xz := a.x*a.z; yz := a.y*a.z;
wx := a.w*a.x; wy := a.w*a.y; wz := a.w*a.z;
m := identity(Mat4);
m[0][0] = 1 - 2*(yy + zz);
m[0][1] = 2*(xy + wz);
m[0][2] = 2*(xz - wy);
m[1][0] = 2*(xy - wz);
m[1][1] = 1 - 2*(xx + zz);
m[1][2] = 2*(yz + wx);
m[2][0] = 2*(xz + wy);
m[2][1] = 2*(yz - wx);
m[2][2] = 1 - 2*(xx + yy);
return m;
}
F32_DIG :: 6;
F32_EPSILON :: 1.192092896e-07;

View File

@@ -3344,7 +3344,7 @@ BuiltinTypeIsProc *builtin_type_is_procs[BuiltinProc__type_end - BuiltinProc__ty
bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32 id) {
bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32 id, Type *type_hint) {
ast_node(ce, CallExpr, call);
if (ce->inlining != ProcInlining_none) {
error(call, "Inlining operators are not allowed on built-in procedures");
@@ -3882,6 +3882,10 @@ bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32
}
operand->mode = Addressing_Value;
if (type_hint != nullptr && check_is_castable_to(c, operand, type_hint)) {
operand->type = type_hint;
}
break;
}
@@ -3945,6 +3949,10 @@ bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32
default: GB_PANIC("Invalid type"); break;
}
if (type_hint != nullptr && check_is_castable_to(c, operand, type_hint)) {
operand->type = type_hint;
}
break;
}
@@ -4033,6 +4041,10 @@ bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32
default: GB_PANIC("Invalid type"); break;
}
if (type_hint != nullptr && check_is_castable_to(c, operand, type_hint)) {
operand->type = type_hint;
}
break;
}
@@ -4087,6 +4099,10 @@ bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32
default: GB_PANIC("Invalid type"); break;
}
if (type_hint != nullptr && check_is_castable_to(c, operand, type_hint)) {
operand->type = type_hint;
}
break;
}
@@ -4134,6 +4150,10 @@ bool check_builtin_procedure(CheckerContext *c, Operand *operand, Ast *call, i32
default: GB_PANIC("Invalid type"); break;
}
if (type_hint != nullptr && check_is_castable_to(c, operand, type_hint)) {
operand->type = type_hint;
}
break;
}
@@ -6363,7 +6383,7 @@ CallArgumentError check_polymorphic_record_type(CheckerContext *c, Operand *oper
ExprKind check_call_expr(CheckerContext *c, Operand *operand, Ast *call) {
ExprKind check_call_expr(CheckerContext *c, Operand *operand, Ast *call, Type *type_hint) {
ast_node(ce, CallExpr, call);
if (ce->proc != nullptr &&
ce->proc->kind == Ast_BasicDirective) {
@@ -6470,7 +6490,7 @@ ExprKind check_call_expr(CheckerContext *c, Operand *operand, Ast *call) {
if (operand->mode == Addressing_Builtin) {
i32 id = operand->builtin_id;
if (!check_builtin_procedure(c, operand, call, id)) {
if (!check_builtin_procedure(c, operand, call, id, type_hint)) {
operand->mode = Addressing_Invalid;
}
operand->expr = call;
@@ -7930,7 +7950,7 @@ ExprKind check_expr_base_internal(CheckerContext *c, Operand *o, Ast *node, Type
case_ast_node(ce, CallExpr, node);
return check_call_expr(c, o, node);
return check_call_expr(c, o, node, type_hint);
case_end;
case_ast_node(de, DerefExpr, node);