Rename adjugate to cofactor to keep existing usages for inverse and determinant correct and add new adjugate procedures

core/math/linalg/general.odin

@@ -417,6 +417,13 @@ adjugate :: proc{
 	matrix4x4_adjugate,
 }
 
+cofactor :: proc{
+	matrix1x1_cofactor,
+	matrix2x2_cofactor,
+	matrix3x3_cofactor,
+	matrix4x4_cofactor,
+}
+
 inverse_transpose :: proc{
 	matrix1x1_inverse_transpose,
 	matrix2x2_inverse_transpose,
@@ -479,9 +486,9 @@ matrix3x3_determinant :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (det: T) #
 }
 @(require_results)
 matrix4x4_determinant :: proc "contextless" (m: $M/matrix[4, 4]$T) -> (det: T) #no_bounds_check {
-	a := adjugate(m)
+	c := cofactor(m)
 	for i in 0..<4 {
-		det += m[0, i] * a[0, i]
+		det += m[0, i] * c[0, i]
 	}
 	return
 }
@@ -497,6 +504,47 @@ matrix1x1_adjugate :: proc "contextless" (x: $M/matrix[1, 1]$T) -> (y: M) #no_bo
 
 @(require_results)
 matrix2x2_adjugate :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) #no_bounds_check {
+	y[0, 0] = +x[1, 1]
+	y[0, 1] = -x[0, 1]
+	y[1, 0] = -x[1, 0]
+	y[1, 1] = +x[0, 0]
+	return
+}
+
+@(require_results)
+matrix3x3_adjugate :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
+	y[0, 0] = +(m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
+	y[1, 0] = -(m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2])
+	y[2, 0] = +(m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1])
+	y[0, 1] = -(m[0, 1] * m[2, 2] - m[2, 1] * m[0, 2])
+	y[1, 1] = +(m[0, 0] * m[2, 2] - m[2, 0] * m[0, 2])
+	y[2, 1] = -(m[0, 0] * m[2, 1] - m[2, 0] * m[0, 1])
+	y[0, 2] = +(m[0, 1] * m[1, 2] - m[1, 1] * m[0, 2])
+	y[1, 2] = -(m[0, 0] * m[1, 2] - m[1, 0] * m[0, 2])
+	y[2, 2] = +(m[0, 0] * m[1, 1] - m[1, 0] * m[0, 1])
+	return
+}
+
+@(require_results)
+matrix4x4_adjugate :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
+	for i in 0..<4 {
+		for j in 0..<4 {
+			sign: T = 1 if (i + j) % 2 == 0 else -1
+			y[i, j] = sign * matrix_minor(x, j, i)
+		}
+	}
+	return
+}
+
+
+@(require_results)
+matrix1x1_cofactor :: proc "contextless" (x: $M/matrix[1, 1]$T) -> (y: M) #no_bounds_check {
+	y = x
+	return
+}
+
+@(require_results)
+matrix2x2_cofactor :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) #no_bounds_check {
 	y[0, 0] = +x[1, 1]
 	y[0, 1] = -x[1, 0]
 	y[1, 0] = -x[0, 1]
@@ -505,7 +553,7 @@ matrix2x2_adjugate :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) #no_bo
 }
 
 @(require_results)
-matrix3x3_adjugate :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
+matrix3x3_cofactor :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
 	y[0, 0] = +(m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
 	y[0, 1] = -(m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2])
 	y[0, 2] = +(m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1])
@@ -520,7 +568,7 @@ matrix3x3_adjugate :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) #no_bo
 
 
 @(require_results)
-matrix4x4_adjugate :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
+matrix4x4_cofactor :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
 	for i in 0..<4 {
 		for j in 0..<4 {
 			sign: T = 1 if (i + j) % 2 == 0 else -1
@@ -556,19 +604,19 @@ matrix2x2_inverse_transpose :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y:
 
 @(require_results)
 matrix3x3_inverse_transpose :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d := determinant(x)
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[i, j] / d
+				y[i, j] = c[i, j] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[i, j] * id
+				y[i, j] = c[i, j] * id
 			}
 		}
 	}
@@ -577,22 +625,22 @@ matrix3x3_inverse_transpose :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y:
 
 @(require_results)
 matrix4x4_inverse_transpose :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d: T
 	for i in 0..<4 {
-		d += x[0, i] * a[0, i]
+		d += x[0, i] * c[0, i]
 	}
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[i, j] / d
+				y[i, j] = c[i, j] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[i, j] * id
+				y[i, j] = c[i, j] * id
 			}
 		}
 	}
@@ -625,19 +673,19 @@ matrix2x2_inverse :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) #no_bou
 
 @(require_results)
 matrix3x3_inverse :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d := determinant(x)
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[j, i] / d
+				y[i, j] = c[j, i] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[j, i] * id
+				y[i, j] = c[j, i] * id
 			}
 		}
 	}
@@ -646,22 +694,22 @@ matrix3x3_inverse :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bou
 
 @(require_results)
 matrix4x4_inverse :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d: T
 	for i in 0..<4 {
-		d += x[0, i] * a[0, i]
+		d += x[0, i] * c[0, i]
 	}
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[j, i] / d
+				y[i, j] = c[j, i] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[j, i] * id
+				y[i, j] = c[j, i] * id
 			}
 		}
 	}

core/math/linalg/glsl/linalg_glsl.odin

@@ -1882,6 +1882,13 @@ adjugate :: proc{
 	adjugate_matrix4x4,
 }
 
+cofactor :: proc{
+	cofactor_matrix1x1,
+	cofactor_matrix2x2,
+	cofactor_matrix3x3,
+	cofactor_matrix4x4,
+}
+
 inverse_transpose :: proc{
 	inverse_transpose_matrix1x1,
 	inverse_transpose_matrix2x2,
@@ -1944,9 +1951,9 @@ determinant_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (det: T) {
 }
 @(require_results)
 determinant_matrix4x4 :: proc "contextless" (m: $M/matrix[4, 4]$T) -> (det: T) {
-	a := adjugate(m)
+	c := cofactor(m)
 	#no_bounds_check for i in 0..<4 {
-		det += m[0, i] * a[0, i]
+		det += m[0, i] * c[0, i]
 	}
 	return
 }
@@ -1962,6 +1969,47 @@ adjugate_matrix1x1 :: proc "contextless" (x: $M/matrix[1, 1]$T) -> (y: M) {
 
 @(require_results)
 adjugate_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
+	y[0, 0] = +x[1, 1]
+	y[0, 1] = -x[0, 1]
+	y[1, 0] = -x[1, 0]
+	y[1, 1] = +x[0, 0]
+	return
+}
+
+@(require_results)
+adjugate_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
+	y[0, 0] = +(m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
+	y[1, 0] = -(m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2])
+	y[2, 0] = +(m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1])
+	y[0, 1] = -(m[0, 1] * m[2, 2] - m[2, 1] * m[0, 2])
+	y[1, 1] = +(m[0, 0] * m[2, 2] - m[2, 0] * m[0, 2])
+	y[2, 1] = -(m[0, 0] * m[2, 1] - m[2, 0] * m[0, 1])
+	y[0, 2] = +(m[0, 1] * m[1, 2] - m[1, 1] * m[0, 2])
+	y[1, 2] = -(m[0, 0] * m[1, 2] - m[1, 0] * m[0, 2])
+	y[2, 2] = +(m[0, 0] * m[1, 1] - m[1, 0] * m[0, 1])
+	return
+}
+
+@(require_results)
+adjugate_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) {
+	for i in 0..<4 {
+		for j in 0..<4 {
+			sign: T = 1 if (i + j) % 2 == 0 else -1
+			y[i, j] = sign * matrix_minor(x, j, i)
+		}
+	}
+	return
+}
+
+
+@(require_results)
+cofactor_matrix1x1 :: proc "contextless" (x: $M/matrix[1, 1]$T) -> (y: M) {
+	y = x
+	return
+}
+
+@(require_results)
+cofactor_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
 	y[0, 0] = +x[1, 1]
 	y[0, 1] = -x[1, 0]
 	y[1, 0] = -x[0, 1]
@@ -1970,7 +2018,7 @@ adjugate_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
 }
 
 @(require_results)
-adjugate_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
+cofactor_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
 	y[0, 0] = +(m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
 	y[0, 1] = -(m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2])
 	y[0, 2] = +(m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1])
@@ -1985,7 +2033,7 @@ adjugate_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
 
 
 @(require_results)
-adjugate_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) {
+cofactor_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) {
 	for i in 0..<4 {
 		for j in 0..<4 {
 			sign: T = 1 if (i + j) % 2 == 0 else -1
@@ -2021,19 +2069,19 @@ inverse_transpose_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y:
 
 @(require_results)
 inverse_transpose_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d := determinant(x)
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[i, j] / d
+				y[i, j] = c[i, j] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[i, j] * id
+				y[i, j] = c[i, j] * id
 			}
 		}
 	}
@@ -2042,22 +2090,22 @@ inverse_transpose_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y:
 
 @(require_results)
 inverse_transpose_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d: T
 	for i in 0..<4 {
-		d += x[0, i] * a[0, i]
+		d += x[0, i] * c[0, i]
 	}
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[i, j] / d
+				y[i, j] = c[i, j] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[i, j] * id
+				y[i, j] = c[i, j] * id
 			}
 		}
 	}
@@ -2090,19 +2138,19 @@ inverse_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
 
 @(require_results)
 inverse_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d := determinant(x)
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[j, i] / d
+				y[i, j] = c[j, i] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[j, i] * id
+				y[i, j] = c[j, i] * id
 			}
 		}
 	}
@@ -2111,22 +2159,22 @@ inverse_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bou
 
 @(require_results)
 inverse_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d: T
 	for i in 0..<4 {
-		d += x[0, i] * a[0, i]
+		d += x[0, i] * c[0, i]
 	}
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[j, i] / d
+				y[i, j] = c[j, i] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[j, i] * id
+				y[i, j] = c[j, i] * id
 			}
 		}
 	}

core/math/linalg/hlsl/linalg_hlsl.odin

@@ -1514,6 +1514,13 @@ adjugate :: proc{
 	adjugate_matrix4x4,
 }
 
+cofactor :: proc{
+	cofactor_matrix1x1,
+	cofactor_matrix2x2,
+	cofactor_matrix3x3,
+	cofactor_matrix4x4,
+}
+
 inverse_transpose :: proc{
 	inverse_transpose_matrix1x1,
 	inverse_transpose_matrix2x2,
@@ -1568,9 +1575,9 @@ determinant_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (det: T) {
 }
 @(require_results)
 determinant_matrix4x4 :: proc "contextless" (m: $M/matrix[4, 4]$T) -> (det: T) {
-	a := adjugate(m)
+	c := cofactor(m)
 	#no_bounds_check for i in 0..<4 {
-		det += m[0, i] * a[0, i]
+		det += m[0, i] * c[0, i]
 	}
 	return
 }
@@ -1586,6 +1593,47 @@ adjugate_matrix1x1 :: proc "contextless" (x: $M/matrix[1, 1]$T) -> (y: M) {
 
 @(require_results)
 adjugate_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
+	y[0, 0] = +x[1, 1]
+	y[0, 1] = -x[0, 1]
+	y[1, 0] = -x[1, 0]
+	y[1, 1] = +x[0, 0]
+	return
+}
+
+@(require_results)
+adjugate_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
+	y[0, 0] = +(m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
+	y[1, 0] = -(m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2])
+	y[2, 0] = +(m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1])
+	y[0, 1] = -(m[0, 1] * m[2, 2] - m[2, 1] * m[0, 2])
+	y[1, 1] = +(m[0, 0] * m[2, 2] - m[2, 0] * m[0, 2])
+	y[2, 1] = -(m[0, 0] * m[2, 1] - m[2, 0] * m[0, 1])
+	y[0, 2] = +(m[0, 1] * m[1, 2] - m[1, 1] * m[0, 2])
+	y[1, 2] = -(m[0, 0] * m[1, 2] - m[1, 0] * m[0, 2])
+	y[2, 2] = +(m[0, 0] * m[1, 1] - m[1, 0] * m[0, 1])
+	return
+}
+
+@(require_results)
+adjugate_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) {
+	for i in 0..<4 {
+		for j in 0..<4 {
+			sign: T = 1 if (i + j) % 2 == 0 else -1
+			y[i, j] = sign * matrix_minor(x, j, i)
+		}
+	}
+	return
+}
+
+
+@(require_results)
+cofactor_matrix1x1 :: proc "contextless" (x: $M/matrix[1, 1]$T) -> (y: M) {
+	y = x
+	return
+}
+
+@(require_results)
+cofactor_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
 	y[0, 0] = +x[1, 1]
 	y[0, 1] = -x[1, 0]
 	y[1, 0] = -x[0, 1]
@@ -1594,7 +1642,7 @@ adjugate_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
 }
 
 @(require_results)
-adjugate_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
+cofactor_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
 	y[0, 0] = +(m[1, 1] * m[2, 2] - m[2, 1] * m[1, 2])
 	y[0, 1] = -(m[1, 0] * m[2, 2] - m[2, 0] * m[1, 2])
 	y[0, 2] = +(m[1, 0] * m[2, 1] - m[2, 0] * m[1, 1])
@@ -1609,7 +1657,7 @@ adjugate_matrix3x3 :: proc "contextless" (m: $M/matrix[3, 3]$T) -> (y: M) {
 
 
 @(require_results)
-adjugate_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) {
+cofactor_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) {
 	for i in 0..<4 {
 		for j in 0..<4 {
 			sign: T = 1 if (i + j) % 2 == 0 else -1
@@ -1645,19 +1693,19 @@ inverse_transpose_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y:
 
 @(require_results)
 inverse_transpose_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d := determinant(x)
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[i, j] / d
+				y[i, j] = c[i, j] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[i, j] * id
+				y[i, j] = c[i, j] * id
 			}
 		}
 	}
@@ -1666,22 +1714,22 @@ inverse_transpose_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y:
 
 @(require_results)
 inverse_transpose_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d: T
 	for i in 0..<4 {
-		d += x[0, i] * a[0, i]
+		d += x[0, i] * c[0, i]
 	}
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[i, j] / d
+				y[i, j] = c[i, j] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[i, j] * id
+				y[i, j] = c[i, j] * id
 			}
 		}
 	}
@@ -1714,19 +1762,19 @@ inverse_matrix2x2 :: proc "contextless" (x: $M/matrix[2, 2]$T) -> (y: M) {
 
 @(require_results)
 inverse_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d := determinant(x)
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[j, i] / d
+				y[i, j] = c[j, i] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<3 {
 			for j in 0..<3 {
-				y[i, j] = a[j, i] * id
+				y[i, j] = c[j, i] * id
 			}
 		}
 	}
@@ -1735,22 +1783,22 @@ inverse_matrix3x3 :: proc "contextless" (x: $M/matrix[3, 3]$T) -> (y: M) #no_bou
 
 @(require_results)
 inverse_matrix4x4 :: proc "contextless" (x: $M/matrix[4, 4]$T) -> (y: M) #no_bounds_check {
-	a := adjugate(x)
+	c := cofactor(x)
 	d: T
 	for i in 0..<4 {
-		d += x[0, i] * a[0, i]
+		d += x[0, i] * c[0, i]
 	}
 	when intrinsics.type_is_integer(T) {
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[j, i] / d
+				y[i, j] = c[j, i] / d
 			}
 		}
 	} else {
 		id := 1/d
 		for i in 0..<4 {
 			for j in 0..<4 {
-				y[i, j] = a[j, i] * id
+				y[i, j] = c[j, i] * id
 			}
 		}
 	}