add euclDiv and euclMod to math (#16414)

* add `euclDiv` and `euclMod` to `math`
* use abs
* Update lib/pure/math.nim

Co-authored-by: Clyybber <darkmine956@gmail.com>

changelog.md

@@ -73,6 +73,8 @@
   
 - Added `sequtils` import to `prelude`.
 
+- Added `euclDiv` and `euclMod` to `math`.
+
 ## Language changes
 
 - `nimscript` now handles `except Exception as e`.

lib/pure/math.nim

@@ -882,6 +882,32 @@ func floorMod*[T: SomeNumber](x, y: T): T =
   result = x mod y
   if (result > 0 and y < 0) or (result < 0 and y > 0): result += y
 
+func euclDiv*[T: SomeInteger](x, y: T): T {.since: (1, 5, 1).} =
+  ## Returns euclidean division of `x` by `y`.
+  runnableExamples:
+    assert euclDiv(13, 3) == 4
+    assert euclDiv(-13, 3) == -5
+    assert euclDiv(13, -3) == -4
+    assert euclDiv(-13, -3) == 5
+  result = x div y
+  if x mod y < 0:
+    if y > 0:
+      dec result
+    else:
+      inc result
+
+func euclMod*[T: SomeNumber](x, y: T): T {.since: (1, 5, 1).} =
+  ## Returns euclidean modulo of `x` by `y`.
+  ## `euclMod(x, y)` is non-negative.
+  runnableExamples:
+    assert euclMod(13, 3) == 1
+    assert euclMod(-13, 3) == 2
+    assert euclMod(13, -3) == 1
+    assert euclMod(-13, -3) == 2
+  result = x mod y
+  if result < 0:
+    result += abs(y)
+
 when not defined(js):
   func c_frexp*(x: float32, exponent: var int32): float32 {.
       importc: "frexp", header: "<math.h>".}

tests/stdlib/tmath.nim

@@ -270,6 +270,34 @@ block:
       doAssert floorMod(8.0, -3.0) ==~ -1.0
       doAssert floorMod(-8.5, 3.0) ==~ 0.5
 
+    block: # euclDiv/euclMod
+      doAssert euclDiv(8, 3) == 2
+      doAssert euclMod(8, 3) == 2
+
+      doAssert euclDiv(8, -3) == -2
+      doAssert euclMod(8, -3) == 2
+
+      doAssert euclDiv(-8, 3) == -3
+      doAssert euclMod(-8, 3) == 1
+
+      doAssert euclDiv(-8, -3) == 3
+      doAssert euclMod(-8, -3) == 1
+
+      doAssert euclMod(8.0, -3.0) ==~ 2.0
+      doAssert euclMod(-8.5, 3.0) ==~ 0.5
+
+      doAssert euclDiv(9, 3) == 3
+      doAssert euclMod(9, 3) == 0
+
+      doAssert euclDiv(9, -3) == -3
+      doAssert euclMod(9, -3) == 0
+
+      doAssert euclDiv(-9, 3) == -3
+      doAssert euclMod(-9, 3) == 0
+
+      doAssert euclDiv(-9, -3) == 3
+      doAssert euclMod(-9, -3) == 0
+
     block: # log
       doAssert log(4.0, 3.0) ==~ ln(4.0) / ln(3.0)
       doAssert log2(8.0'f64) == 3.0'f64