Fix off-by-one copy, pass small bigints modulo tests

constantine/bigints_raw.nim

@@ -418,7 +418,8 @@ func reduce*(r: BigIntViewMut, a: BigIntViewAny, M: BigIntViewConst) =
     # and modular shift-left-add the rest
     let mLen = M.numLimbs()
     let aOffset = aLen - mLen
-    copyMem(r[0].addr, a[aOffset].unsafeAddr, (mLen-1) * sizeof(Word))
+    copyMem(r[0].addr, a[aOffset+1].unsafeAddr, (mLen-1) * sizeof(Word))
     r[^1] = Zero
-    for i in countdown(aOffset-1, 0):
+    # Now shift-left the copied words while adding the new word modulo M
+    for i in countdown(aOffset, 0):
       r.shlAddMod(a[i], M)

tests/test_bigints.nim

@@ -127,13 +127,33 @@ suite "Arithmetic operations - Addition":
 suite "Modular operations - small modulus":
   # Vectors taken from Stint - https://github.com/status-im/nim-stint
   test "100 mod 13":
-    let a = BigInt[32].fromUint(100'u32)
-    let m = BigInt[4].fromUint(13'u8)
+    # Test 1 word and more than 1 word
+    block:
+      let a = BigInt[7].fromUint(100'u32)
+      let m = BigInt[4].fromUint(13'u8)
 
-    var r: BigInt[4]
-    r.reduce(a, m)
-    check:
-      bool(r == BigInt[4].fromUint(100'u8 mod 13))
+      var r: BigInt[4]
+      r.reduce(a, m)
+      check:
+        bool(r == BigInt[4].fromUint(100'u8 mod 13))
+
+    block: #
+      let a = BigInt[32].fromUint(100'u32)
+      let m = BigInt[4].fromUint(13'u8)
+
+      var r: BigInt[4]
+      r.reduce(a, m)
+      check:
+        bool(r == BigInt[4].fromUint(100'u8 mod 13))
+
+    block: #
+      let a = BigInt[64].fromUint(100'u32)
+      let m = BigInt[4].fromUint(13'u8)
+
+      var r: BigInt[4]
+      r.reduce(a, m)
+      check:
+        bool(r == BigInt[4].fromUint(100'u8 mod 13))
 
   test "2^64 mod 3":
     let a = BigInt[65].fromHex("0x1_00000000_00000000")
@@ -159,7 +179,7 @@ suite "Modular operations - small modulus - Stint specific failures highlighted
     let u = 65696211516342324'u64
     let v = 174261910798982'u64
 
-    let a = BigInt[64].fromUint(u)
+    let a = BigInt[56].fromUint(u)
     let m = BigInt[48].fromUint(v)
 
     var r: BigInt[48]
@@ -172,7 +192,7 @@ suite "Modular operations - small modulus - Stint specific failures highlighted
     let u = 15080397990160655'u64
     let v = 600432699691'u64
 
-    let a = BigInt[64].fromUint(u)
+    let a = BigInt[54].fromUint(u)
     let m = BigInt[40].fromUint(v)
 
     var r: BigInt[40]