Implement addition (including proper overflow behaviour)

src/mpint.nim

@@ -2,7 +2,9 @@
 # Distributed under the MIT License (license terms are at http://opensource.org/licenses/MIT).
 
 import  ./uint_type,
-        ./uint_init
+        ./uint_init,
+        ./uint_binary_ops
 
 export  uint_type,
-        uint_init
+        uint_init,
+        uint_binary_ops

src/uint_binary_ops.nim

@@ -0,0 +1,19 @@
+# Copyright (c) 2018 Status Research & Development GmbH
+# Distributed under the MIT License (license terms are at http://opensource.org/licenses/MIT).
+
+import uint_type
+
+proc `+=`*[T: MpUint](a: var T, b: T) {.noSideEffect.}=
+
+  type Base = type a.lo
+  let tmp = a.lo
+
+  a.lo += b.lo
+  a.hi += (a.lo < tmp).Base + b.hi
+  # Optimized assembly should contain adc instruction (add with carry)
+  # Clang on MacOS does with the -d:release switch.
+
+proc `+`*[T: MpUint](a: T, b: T): T {.noSideEffect, noInit.}=
+
+  result = a
+  result += b

tests/all_tests.nim

@@ -1,4 +1,5 @@
 # Copyright (c) 2018 Status Research & Development GmbH
 # Distributed under the MIT License (license terms are at http://opensource.org/licenses/MIT).$
 
-import  test_endianness
+import  test_endianness,
+        test_addition

tests/test_addition.nim

@@ -0,0 +1,46 @@
+# Copyright (c) 2018 Status Research & Development GmbH
+# Distributed under the MIT License (license terms are at http://opensource.org/licenses/MIT).
+
+import ../src/mpint, unittest
+
+suite "Testing addition implementation":
+  test "In-place addition gives expected result":
+
+    var a = initMpUint(20182018, uint32)
+    let b = initMpUint(20172017, uint32)
+
+    a += b
+
+    check: cast[uint64](a) == 20182018'u64 + 20172017'u64
+
+  test "Addition gives expected result":
+
+    let a = initMpUint(20182018, uint32)
+    let b = initMpUint(20172017, uint32)
+
+    check: cast[uint64](a+b) == 20182018'u64 + 20172017'u64
+
+  test "When the low half overflows, it is properly carried":
+    # uint8 (low half) overflow at 255
+    let a = initMpUint(100, uint8)
+    let b = initMpUint(100, uint8)
+
+    check: cast[uint16](a+b) == 200
+
+  test "Full overflow is handled like native unsigned types":
+    # uint16 overflows after 65535
+    let a = initMpUint(100, uint8)
+    var z = initMpUint(0, uint8)
+    let o = initMpUint(36, uint8)
+
+    for _ in 0 ..< 655:
+      z += a
+
+    check: cast[uint16](z) == 65500
+    check: cast[uint16](z + o) == 0
+
+    z += a
+    check: cast[uint16](z) == 64
+
+    z += a
+    check: cast[uint16](z) == 164