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https://github.com/odin-lang/Odin.git
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Add builtin procedures for matrix values: determinant, adjugate, inverse, inverse_transpose, hermitian_adjoint
This commit is contained in:
gingerBill
317
core/runtime/core_builtin_matrix.odin
Normal file
317
core/runtime/core_builtin_matrix.odin
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package runtime
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import "core:intrinsics"
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_ :: intrinsics
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@(builtin)
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matrix1x1_determinant :: proc(m: $M/matrix[1, 1]$T) -> (det: T) {
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return m[0, 0]
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}
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@(builtin)
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matrix2x2_determinant :: proc(m: $M/matrix[2, 2]$T) -> (det: T) {
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return m[0, 0]*m[1, 1] - m[0, 1]*m[1, 0]
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}
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@(builtin)
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matrix3x3_determinant :: proc(m: $M/matrix[3, 3]$T) -> (det: T) {
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a := +m[0, 0] * (m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
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b := -m[1, 0] * (m[0, 1] * m[2, 2] - m[2, 1] * m[0, 2])
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c := +m[2, 0] * (m[0, 1] * m[1, 2] - m[1, 1] * m[0, 2])
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return a + b + c
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}
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@(builtin)
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matrix4x4_determinant :: proc(m: $M/matrix[4, 4]$T) -> (det: T) {
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a := adjugate(m)
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#no_bounds_check for i in 0..<4 {
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det += m[0, i] * a[0, i]
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}
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return
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}
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@(builtin)
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matrix_determinant :: proc{
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matrix1x1_determinant,
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matrix2x2_determinant,
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matrix3x3_determinant,
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matrix4x4_determinant,
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}
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@(builtin)
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determinant :: proc{
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matrix1x1_determinant,
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matrix2x2_determinant,
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matrix3x3_determinant,
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matrix4x4_determinant,
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}
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@(builtin)
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matrix1x1_adjugate :: proc(x: $M/matrix[1, 1]$T) -> (y: M) {
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y = x
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return
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}
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@(builtin)
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matrix2x2_adjugate :: proc(x: $M/matrix[2, 2]$T) -> (y: M) {
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y[0, 0] = +x[1, 1]
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y[0, 1] = -x[1, 0]
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y[1, 0] = -x[0, 1]
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y[1, 1] = +x[0, 0]
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return
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}
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@(builtin)
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matrix3x3_adjugate :: proc(x: $M/matrix[3, 3]$T) -> (y: M) {
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y[0, 0] = +(x[1, 1] * x[2, 2] - x[1, 2] * x[2, 1])
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y[0, 1] = -(x[1, 0] * x[2, 2] - x[1, 2] * x[2, 0])
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y[0, 2] = +(x[1, 0] * x[2, 1] - x[1, 1] * x[2, 0])
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y[1, 0] = -(x[0, 1] * x[2, 2] - x[0, 2] * x[2, 1])
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y[1, 1] = +(x[0, 0] * x[2, 2] - x[0, 2] * x[2, 0])
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y[1, 2] = -(x[0, 0] * x[2, 1] - x[0, 1] * x[2, 0])
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y[2, 0] = +(x[0, 1] * x[1, 2] - x[0, 2] * x[1, 1])
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y[2, 1] = -(x[0, 0] * x[1, 2] - x[0, 2] * x[1, 0])
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y[2, 2] = +(x[0, 0] * x[1, 1] - x[0, 1] * x[1, 0])
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return
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}
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@(builtin)
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matrix4x4_adjugate :: proc(x: $M/matrix[4, 4]$T) -> (y: M) {
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minor :: proc(m: $M/matrix[4, 4]$T, row, column: i32) -> (minor: T) {
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cut_down: matrix[3, 3]T
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for col_idx in 0..<3 {
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col := col_idx + int(col_idx >= column)
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for row_idx in 0..<3 {
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row := row_idx + int(row_idx >= row)
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cut_down[row_idx, col_idx] = m[row, col]
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}
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}
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return determinant(cut_down)
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}
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cofactor :: proc(m: $M/matrix[4, 4]$T, row, column: i32) -> (cofactor: T) {
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sign: T = 1 if (row + column) % 2 == 0 else -1
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return sign * matrix4x4_minor(m, row, column)
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}
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for i in 0..<4 {
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for j in 0..<4 {
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y[i, j] = matrix4x4_cofactor(x, i, j)
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}
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}
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return
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}
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@(builtin)
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matrix_adjugate :: proc{
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matrix1x1_adjugate,
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matrix2x2_adjugate,
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matrix3x3_adjugate,
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matrix4x4_adjugate,
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}
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@(builtin)
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adjugate :: proc{
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matrix1x1_adjugate,
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matrix2x2_adjugate,
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matrix3x3_adjugate,
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matrix4x4_adjugate,
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}
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@(builtin)
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matrix1x1_inverse_transpose :: proc(x: $M/matrix[1, 1]$T) -> (y: M) {
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y[0, 0] = 1/x[0, 0]
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return
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}
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@(builtin)
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matrix2x2_inverse_transpose :: proc(x: $M/matrix[2, 2]$T) -> (y: M) {
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d := x[0, 0]*x[1, 1] - x[0, 1]*x[1, 0]
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when intrinsics.type_is_integer(T) {
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y[0, 0] = x[1, 1] / d
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y[0, 1] = x[0, 1] / d
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y[1, 0] = x[1, 0] / d
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y[1, 1] = x[0, 0] / d
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} else {
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id := 1 / d
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y[0, 0] = x[1, 1] * id
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y[0, 1] = x[0, 1] * id
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y[1, 0] = x[1, 0] * id
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y[1, 1] = x[0, 0] * id
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}
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return
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}
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@(builtin)
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matrix3x3_inverse_transpose :: proc(x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
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a := adjugate(x)
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d := determinant(x)
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when intrinsics.type_is_integer(T) {
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for i in 0..<3 {
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for j in 0..<3 {
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inverse_transpose[i, j] = a[i, j] / d
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}
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}
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} else {
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id := 1/d
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for i in 0..<3 {
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for j in 0..<3 {
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inverse_transpose[i, j] = a[i, j] * id
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}
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}
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}
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return
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}
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@(builtin)
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matrix4x4_inverse_transpose :: proc(x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
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a := adjugate(x)
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d: T
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for i in 0..<4 {
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d += x[0, i] * a[0, i]
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}
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when intrinsics.type_is_integer(T) {
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for i in 0..<4 {
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for j in 0..<4 {
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inverse_transpose[i, j] = a[i, j] / d
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}
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}
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} else {
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id := 1/d
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for i in 0..<4 {
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for j in 0..<4 {
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inverse_transpose[i, j] = a[i, j] * id
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}
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}
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}
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return
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}
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@(builtin)
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matrix_inverse_transpose :: proc{
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matrix1x1_inverse_transpose,
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matrix2x2_inverse_transpose,
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matrix3x3_inverse_transpose,
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matrix4x4_inverse_transpose,
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}
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@(builtin)
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inverse_transpose :: proc{
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matrix1x1_inverse_transpose,
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matrix2x2_inverse_transpose,
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matrix3x3_inverse_transpose,
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matrix4x4_inverse_transpose,
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}
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@(builtin)
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matrix1x1_inverse :: proc(x: $M/matrix[1, 1]$T) -> (y: M) {
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y[0, 0] = 1/x[0, 0]
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return
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}
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@(builtin)
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matrix2x2_inverse :: proc(x: $M/matrix[2, 2]$T) -> (y: M) {
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d := x[0, 0]*x[1, 1] - x[0, 1]*x[1, 0]
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when intrinsics.type_is_integer(T) {
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y[0, 0] = x[1, 1] / d
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y[0, 1] = x[1, 0] / d
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y[1, 0] = x[0, 1] / d
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y[1, 1] = x[0, 0] / d
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} else {
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id := 1 / d
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y[0, 0] = x[1, 1] * id
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y[0, 1] = x[1, 0] * id
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y[1, 0] = x[0, 1] * id
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y[1, 1] = x[0, 0] * id
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}
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return
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}
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@(builtin)
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matrix3x3_inverse :: proc(x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
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a := adjugate(x)
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d := determinant(x)
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when intrinsics.type_is_integer(T) {
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for i in 0..<3 {
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for j in 0..<3 {
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inverse_transpose[i, j] = a[j, i] / d
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}
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}
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} else {
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id := 1/d
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for i in 0..<3 {
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for j in 0..<3 {
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inverse_transpose[i, j] = a[j, i] * id
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}
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}
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}
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return
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}
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@(builtin)
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matrix4x4_inverse :: proc(x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
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a := adjugate(x)
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d: T
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for i in 0..<4 {
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d += x[0, i] * a[0, i]
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}
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when intrinsics.type_is_integer(T) {
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for i in 0..<4 {
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for j in 0..<4 {
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inverse_transpose[i, j] = a[j, i] / d
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}
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}
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} else {
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id := 1/d
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for i in 0..<4 {
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for j in 0..<4 {
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inverse_transpose[i, j] = a[j, i] * id
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}
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}
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}
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return
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}
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@(builtin)
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matrix_inverse :: proc{
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matrix1x1_inverse,
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matrix2x2_inverse,
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matrix3x3_inverse,
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matrix4x4_inverse,
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}
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@(builtin)
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inverse :: proc{
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matrix1x1_inverse,
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matrix2x2_inverse,
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matrix3x3_inverse,
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matrix4x4_inverse,
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}
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@(builtin)
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matrix1x1_hermitian_adjoint :: proc(m: $M/matrix[1, 1]$T) -> M where intrinsics.type_is_complex(T) {
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return conj(transpose(m))
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}
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@(builtin)
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matrix2x2_hermitian_adjoint :: proc(m: $M/matrix[2, 2]$T) -> M where intrinsics.type_is_complex(T) {
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return conj(transpose(m))
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}
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@(builtin)
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matrix3x3_hermitian_adjoint :: proc(m: $M/matrix[3, 3]$T) -> M where intrinsics.type_is_complex(T) {
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return conj(transpose(m))
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}
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@(builtin)
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matrix4x4_hermitian_adjoint :: proc(m: $M/matrix[4, 4]$T) -> M where intrinsics.type_is_complex(T) {
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return conj(transpose(m))
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}
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@(builtin)
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hermitian_adjoint :: proc{
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matrix1x1_hermitian_adjoint,
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matrix2x2_hermitian_adjoint,
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matrix3x3_hermitian_adjoint,
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matrix4x4_hermitian_adjoint,
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}
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