From d0ff06b8c14e3b505d0c14ca5c9c37e8b667c875 Mon Sep 17 00:00:00 2001
From: Josep Sanjuas <jsanjuas@gmail.com>
Date: Sun, 12 Apr 2015 19:40:30 +0200
Subject: [PATCH 1/4] Generalize mean to other types

---
 lib/pure/math.nim | 7 +++++--
 1 file changed, 5 insertions(+), 2 deletions(-)

diff --git a/lib/pure/math.nim b/lib/pure/math.nim
index aa64933fb..0051c9d88 100644
--- a/lib/pure/math.nim
+++ b/lib/pure/math.nim
@@ -114,10 +114,13 @@ proc sum*[T](x: openArray[T]): T {.noSideEffect.} =
   ## If `x` is empty, 0 is returned.
   for i in items(x): result = result + i
 
-proc mean*(x: openArray[float]): float {.noSideEffect.} = 
+template toFloat(f: float): float = f
+
+proc mean*[T](x: openArray[T]): float {.noSideEffect.} =
   ## computes the mean of the elements in `x`. 
   ## If `x` is empty, NaN is returned.
-  result = sum(x) / toFloat(len(x))
+  ## ``toFloat(x: T): float`` must be defined.
+  result = toFloat(sum(x)) / toFloat(len(x))
 
 proc variance*(x: openArray[float]): float {.noSideEffect.} = 
   ## computes the variance of the elements in `x`. 

From e76f54e059fc89bb2cdab0a61700988c56b609d3 Mon Sep 17 00:00:00 2001
From: Josep Sanjuas <jsanjuas@gmail.com>
Date: Sat, 18 Apr 2015 13:28:48 +0200
Subject: [PATCH 2/4] Generalize variance to other types

---
 lib/pure/math.nim | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/pure/math.nim b/lib/pure/math.nim
index 0051c9d88..ef9c69e3c 100644
--- a/lib/pure/math.nim
+++ b/lib/pure/math.nim
@@ -122,13 +122,13 @@ proc mean*[T](x: openArray[T]): float {.noSideEffect.} =
   ## ``toFloat(x: T): float`` must be defined.
   result = toFloat(sum(x)) / toFloat(len(x))
 
-proc variance*(x: openArray[float]): float {.noSideEffect.} = 
+proc variance*[T](x: openArray[T]): float {.noSideEffect.} =
   ## computes the variance of the elements in `x`. 
   ## If `x` is empty, NaN is returned.
   result = 0.0
   var m = mean(x)
-  for i in 0 .. high(x):
-    var diff = x[i] - m
+  for i in items(x):
+    var diff = toFloat(i) - m
     result = result + diff*diff
   result = result / toFloat(len(x))
 

From 44246b670921aca1d31cb74dcc00139b5ed9a2c2 Mon Sep 17 00:00:00 2001
From: Josep Sanjuas <jsanjuas@gmail.com>
Date: Sat, 18 Apr 2015 13:38:15 +0200
Subject: [PATCH 3/4] Document toFloat is necessary

---
 lib/pure/math.nim | 1 +
 1 file changed, 1 insertion(+)

diff --git a/lib/pure/math.nim b/lib/pure/math.nim
index ef9c69e3c..05c2cf57c 100644
--- a/lib/pure/math.nim
+++ b/lib/pure/math.nim
@@ -125,6 +125,7 @@ proc mean*[T](x: openArray[T]): float {.noSideEffect.} =
 proc variance*[T](x: openArray[T]): float {.noSideEffect.} =
   ## computes the variance of the elements in `x`. 
   ## If `x` is empty, NaN is returned.
+  ## ``toFloat(x: T): float`` must be defined.
   result = 0.0
   var m = mean(x)
   for i in items(x):

From f72bb57fff29609336beae56ae148e20d0dd702e Mon Sep 17 00:00:00 2001
From: Josep Sanjuas <jsanjuas@gmail.com>
Date: Sat, 18 Apr 2015 13:40:20 +0200
Subject: [PATCH 4/4] Convert to float before sum

---
 lib/pure/math.nim | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/lib/pure/math.nim b/lib/pure/math.nim
index 05c2cf57c..9bd594549 100644
--- a/lib/pure/math.nim
+++ b/lib/pure/math.nim
@@ -117,10 +117,11 @@ proc sum*[T](x: openArray[T]): T {.noSideEffect.} =
 template toFloat(f: float): float = f
 
 proc mean*[T](x: openArray[T]): float {.noSideEffect.} =
-  ## computes the mean of the elements in `x`. 
+  ## computes the mean of the elements in `x`, which are first converted to floats.
   ## If `x` is empty, NaN is returned.
   ## ``toFloat(x: T): float`` must be defined.
-  result = toFloat(sum(x)) / toFloat(len(x))
+  for i in items(x): result = result + toFloat(i)
+  result = result / toFloat(len(x))
 
 proc variance*[T](x: openArray[T]): float {.noSideEffect.} =
   ## computes the variance of the elements in `x`.