Consistency (issue #33): mat4 multiply in wrong order

This is a breaking change.

modules/mat4.lua

@@ -323,24 +323,24 @@ end
 -- @tparam mat4 out Matrix to store the result
 -- @tparam mat4 a Left hand operand
 -- @tparam mat4 b Right hand operand
--- @treturn mat4 out
+-- @treturn mat4 out Matrix equivalent to "apply b, then a"
 function mat4.mul(out, a, b)
-	tm4[1]  = a[1]  * b[1] + a[2]  * b[5] + a[3]  * b[9]  + a[4]  * b[13]
-	tm4[2]  = a[1]  * b[2] + a[2]  * b[6] + a[3]  * b[10] + a[4]  * b[14]
-	tm4[3]  = a[1]  * b[3] + a[2]  * b[7] + a[3]  * b[11] + a[4]  * b[15]
-	tm4[4]  = a[1]  * b[4] + a[2]  * b[8] + a[3]  * b[12] + a[4]  * b[16]
-	tm4[5]  = a[5]  * b[1] + a[6]  * b[5] + a[7]  * b[9]  + a[8]  * b[13]
-	tm4[6]  = a[5]  * b[2] + a[6]  * b[6] + a[7]  * b[10] + a[8]  * b[14]
-	tm4[7]  = a[5]  * b[3] + a[6]  * b[7] + a[7]  * b[11] + a[8]  * b[15]
-	tm4[8]  = a[5]  * b[4] + a[6]  * b[8] + a[7]  * b[12] + a[8]  * b[16]
-	tm4[9]  = a[9]  * b[1] + a[10] * b[5] + a[11] * b[9]  + a[12] * b[13]
-	tm4[10] = a[9]  * b[2] + a[10] * b[6] + a[11] * b[10] + a[12] * b[14]
-	tm4[11] = a[9]  * b[3] + a[10] * b[7] + a[11] * b[11] + a[12] * b[15]
-	tm4[12] = a[9]  * b[4] + a[10] * b[8] + a[11] * b[12] + a[12] * b[16]
-	tm4[13] = a[13] * b[1] + a[14] * b[5] + a[15] * b[9]  + a[16] * b[13]
-	tm4[14] = a[13] * b[2] + a[14] * b[6] + a[15] * b[10] + a[16] * b[14]
-	tm4[15] = a[13] * b[3] + a[14] * b[7] + a[15] * b[11] + a[16] * b[15]
-	tm4[16] = a[13] * b[4] + a[14] * b[8] + a[15] * b[12] + a[16] * b[16]
+	tm4[1]  = b[1]  * a[1] + b[2]  * a[5] + b[3]  * a[9]  + b[4]  * a[13]
+	tm4[2]  = b[1]  * a[2] + b[2]  * a[6] + b[3]  * a[10] + b[4]  * a[14]
+	tm4[3]  = b[1]  * a[3] + b[2]  * a[7] + b[3]  * a[11] + b[4]  * a[15]
+	tm4[4]  = b[1]  * a[4] + b[2]  * a[8] + b[3]  * a[12] + b[4]  * a[16]
+	tm4[5]  = b[5]  * a[1] + b[6]  * a[5] + b[7]  * a[9]  + b[8]  * a[13]
+	tm4[6]  = b[5]  * a[2] + b[6]  * a[6] + b[7]  * a[10] + b[8]  * a[14]
+	tm4[7]  = b[5]  * a[3] + b[6]  * a[7] + b[7]  * a[11] + b[8]  * a[15]
+	tm4[8]  = b[5]  * a[4] + b[6]  * a[8] + b[7]  * a[12] + b[8]  * a[16]
+	tm4[9]  = b[9]  * a[1] + b[10] * a[5] + b[11] * a[9]  + b[12] * a[13]
+	tm4[10] = b[9]  * a[2] + b[10] * a[6] + b[11] * a[10] + b[12] * a[14]
+	tm4[11] = b[9]  * a[3] + b[10] * a[7] + b[11] * a[11] + b[12] * a[15]
+	tm4[12] = b[9]  * a[4] + b[10] * a[8] + b[11] * a[12] + b[12] * a[16]
+	tm4[13] = b[13] * a[1] + b[14] * a[5] + b[15] * a[9]  + b[16] * a[13]
+	tm4[14] = b[13] * a[2] + b[14] * a[6] + b[15] * a[10] + b[16] * a[14]
+	tm4[15] = b[13] * a[3] + b[14] * a[7] + b[15] * a[11] + b[16] * a[15]
+	tm4[16] = b[13] * a[4] + b[14] * a[8] + b[15] * a[12] + b[16] * a[16]
 
 	for i=1, 16 do
 		out[i] = tm4[i]

spec/mat4_spec.lua

@@ -131,17 +131,17 @@ describe("mat4:", function()
 
 	it("multiplies two 4x4 matrices", function()
 		local a = mat4 {
-			1,  2,  3,  4,
-			5,  6,  7,  8,
-			9,  10, 11, 12,
-			13, 14, 15, 16
-		}
-		local b = mat4 {
 			1, 5, 9,  13,
 			2, 6, 10, 14,
 			3, 7, 11, 15,
 			4, 8, 12, 16
 		}
+		local b = mat4 {
+			1,  2,  3,  4,
+			5,  6,  7,  8,
+			9,  10, 11, 12,
+			13, 14, 15, 16
+		}
 		local c = mat4():mul(a, b)
 		local d = a * b
 		assert.is.equal(30,  c[1])