Fix #30 - modulo failures (#32)

* Add corner cases to test suite

* Add failing div2n1n case

* Fix test and fix #30

* Add to tests

* Fix failing tests due to Nim string change between Apr 27 and Apr 29 (doc: 5237ef4f52)

src/private/uint_div.nim

@@ -137,19 +137,19 @@ func div2n1n[T: SomeunsignedInt](q, r: var T, n_hi, n_lo, d: T) =
     halfSize = size div 2
     halfMask = (1.T shl halfSize) - 1.T
 
-  template halfQR(n_hi, n_lo, d_hi, d_lo: T): tuple[q,r: T] =
+  template halfQR(n_hi, n_lo, d, d_hi, d_lo: T): tuple[q,r: T] =
 
     var (q, r) = divmod(n_hi, d_hi)
     let m = q * d_lo
-    r = (r shl halfSize) or n_lo
+    var r = (r shl halfSize) or n_lo
 
     # Fix the reminder, we're at most 2 iterations off
     if r < m:
       dec q
-      r += d_hi
+      r += d
-      if r >= d_hi and r < m:
+      if r >= d and r < m:
         dec q
-        r += d_hi
+        r += d
     r -= m
     (q, r)
 
@@ -160,10 +160,10 @@ func div2n1n[T: SomeunsignedInt](q, r: var T, n_hi, n_lo, d: T) =
     n_lolo = nlo and halfMask
 
   # First half of the quotient
-  let (q1, r1) = halfQR(n_hi, n_lohi, d_hi, d_lo)
+  let (q1, r1) = halfQR(n_hi, n_lohi, d, d_hi, d_lo)
 
   # Second half
-  let (q2, r2) = halfQR(r1, n_lolo, d_hi, d_lo)
+  let (q2, r2) = halfQR(r1, n_lolo, d, d_hi, d_lo)
 
   q = (q1 shl halfSize) or q2
   r = r2

stint.nimble

@@ -20,6 +20,13 @@ proc test(name: string, lang: string = "c") =
   switch("out", ("./build/" & name))
   setCommand lang, "tests/" & name & ".nim"
 
+task test_internal_debug, "Run tests for internal procs - test implementation (StUint[64] = 2x uint32":
+  switch("define", "mpint_test")
+  test "internal"
+
+task test_internal_release, "Run tests for internal procs - prod implementation (StUint[64] = uint64":
+  test "internal"
+
 task test_debug, "Run all tests - test implementation (StUint[64] = 2x uint32":
   switch("define", "mpint_test")
   test "all_tests"
@@ -52,6 +59,8 @@ task test_property_uint256_release, "Run random tests (release mode) vs TTMath o
   test "property_based", "cpp"
 
 task test, "Run all tests - test and production implementation":
+  exec "nimble test_internal_debug"
+  exec "nimble test_internal_release"
   exec "nimble test_debug"
   exec "nimble test_release"
   exec "nimble test_property_debug"

tests/internal.nim

@@ -0,0 +1,10 @@
+# Stint
+# Copyright 2018 Status Research & Development GmbH
+# Licensed under either of
+#
+#  * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
+#  * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
+#
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
+import internal_uint_div

tests/internal_uint_div.nim

@@ -0,0 +1,60 @@
+# Stint
+# Copyright 2018 Status Research & Development GmbH
+# Licensed under either of
+#
+#  * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE) or http://www.apache.org/licenses/LICENSE-2.0)
+#  * MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
+#
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
+# Test implementation of internal proc:
+
+include ../src/private/uint_div
+import unittest
+
+suite "implementation of internal division procecures":
+  test "Division of 2 words by 1 - specific carry case (issue #30)":
+
+    # // Reference implementation from glibc: udiv.h
+
+    # #include <stdint.h>
+    # typedef uint32_t USItype;
+
+    # #define udiv_qrnnd(q, r, n1, n0, dx) /* d renamed to dx avoiding "=d" */\
+    #   __asm__ ("divl %4"		     /* stringification in K&R C */	\
+    # 	   : "=a" (q), "=d" (r)						\
+    # 	   : "0" ((USItype)(n0)), "1" ((USItype)(n1)), "rm" ((USItype)(dx)))
+
+    ################################
+
+    # #include "udiv.h"
+    # #include <stdio.h>
+    # int main( int argc, const char* argv[] )
+    # {
+    #   UWtype q, r, n1, n0, d;
+
+    #   q = 0;
+    #   r = 0;
+    #   n1 = 233;
+    #   n0 = 1717253765;
+    #   d = 2659025738;
+
+    #   udiv_qrnnd(q, r, n1, n0, d);
+
+    #   printf("q: %u\n", q);
+    #   printf("r: %u\n", r);
+    # }
+
+    ###############################
+
+    var q, r: uint32
+    let
+      n1 = uint32 233
+      n0 = uint32 1717253765
+      d = uint32 2659025738
+
+    div2n1n(q, r, n1, n0, d)
+
+    check:
+      q == 376
+      r == 2650956245'u32

tests/test_uint_muldiv.nim

@@ -68,3 +68,29 @@ suite "Testing unsigned int division and modulo implementation":
 
     check: q == 123456789123456789'u64
     check: r == 0'u64
+
+suite "Testing specific failures highlighted by property-based testing":
+  test "Modulo: 65696211516342324 mod 174261910798982":
+
+    let u = 65696211516342324'u64
+    let v = 174261910798982'u64
+
+    let a = cast[Stuint[64]](u)
+    let b = cast[Stuint[64]](v)
+
+    let z = u mod v
+    let tz = cast[uint64](a mod b)
+
+    check: z == tz
+
+  test "Modulo: 15080397990160655 mod 600432699691":
+    let u = 15080397990160655'u64
+    let v = 600432699691'u64
+
+    let a = cast[Stuint[64]](u)
+    let b = cast[Stuint[64]](v)
+
+    let z = u mod v
+    let tz = cast[uint64](a mod b)
+
+    check: z == tz