From 9e87e07dc32e2c8acc5d95d2e56babded93fc7ac Mon Sep 17 00:00:00 2001
From: Eduardo Julian
Date: Fri, 27 Jan 2017 06:54:08 -0400
Subject: - Added Number implementation for Complex.

---
 stdlib/source/lux/math/complex.lux | 60 ++++++++++++++++++++++++++------------
 1 file changed, 42 insertions(+), 18 deletions(-)

(limited to 'stdlib/source')

diff --git a/stdlib/source/lux/math/complex.lux b/stdlib/source/lux/math/complex.lux
index 69e9f71f9..252e31d51 100644
--- a/stdlib/source/lux/math/complex.lux
+++ b/stdlib/source/lux/math/complex.lux
@@ -116,6 +116,15 @@
     {#real (r./ param real)
      #imaginary (r./ param imaginary)}))
 
+(def: #export (c.% param input)
+  (-> Complex Complex Complex)
+  (let [scaled (c./ param input)
+        quotient (|> scaled
+                     (update@ #real math;floor)
+                     (update@ #imaginary math;floor))]
+    (c.- (c.* quotient param)
+         input)))
+
 (def: #export (cos subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
@@ -167,21 +176,37 @@
      #imaginary (r./ d (math;sin i2))}))
 
 (def: #export (c.abs subject)
-  (-> Complex Real)
+  (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    (if (r.< (r/abs imaginary)
-             (r/abs real))
-      (if (r.= 0.0 imaginary)
-        (r/abs real)
-        (let [q (r./ imaginary real)]
-          (r.* (math;sqrt (r.+ 1.0 (r.* q q)))
-               (r/abs imaginary))))
-      (if (r.= 0.0 real)
-        (r/abs imaginary)
-        (let [q (r./ real imaginary)]
-          (r.* (math;sqrt (r.+ 1.0 (r.* q q)))
-               (r/abs real))))
-      )))
+    (complex (if (r.< (r/abs imaginary)
+                      (r/abs real))
+               (if (r.= 0.0 imaginary)
+                 (r/abs real)
+                 (let [q (r./ imaginary real)]
+                   (r.* (math;sqrt (r.+ 1.0 (r.* q q)))
+                        (r/abs imaginary))))
+               (if (r.= 0.0 real)
+                 (r/abs imaginary)
+                 (let [q (r./ real imaginary)]
+                   (r.* (math;sqrt (r.+ 1.0 (r.* q q)))
+                        (r/abs real))))
+               ))))
+
+(struct: #export _ (Number Complex)
+  (def: + c.+)
+  (def: - c.-)
+  (def: * c.*)
+  (def: / c./)
+  (def: % c.%)
+  (def: (negate x)
+    (|> x
+        (update@ #real r/negate)
+        (update@ #imaginary r/negate)))
+  (def: abs c.abs)
+  (def: (signum x)
+    (|> x
+        (update@ #real r/signum)
+        (update@ #imaginary r/signum))))
 
 (def: #export (exp subject)
   (-> Complex Complex)
@@ -193,7 +218,7 @@
 (def: #export (log subject)
   (-> Complex Complex)
   (let [(^slots [#real #imaginary]) subject]
-    {#real (math;log (c.abs subject))
+    {#real (|> subject c.abs (get@ #real) math;log)
      #imaginary (math;atan2 real imaginary)}))
 
 (do-template [<name> <type> <op>]
@@ -211,7 +236,7 @@
 
 (def: #export (sqrt (^@ input (^slots [#real #imaginary])))
   (-> Complex Complex)
-  (let [t (|> input c.abs (r.+ (r/abs real)) (r./ 2.0) math;sqrt)]
+  (let [t (|> input c.abs (get@ #real) (r.+ (r/abs real)) (r./ 2.0) math;sqrt)]
     (if (r.>= 0.0 real)
       {#real t
        #imaginary (r./ (r.* 2.0 t)
@@ -271,8 +296,7 @@
   (if (n.= +0 nth)
     (list)
     (let [r-nth (|> nth nat-to-int int-to-real)
-          nth-root-of-abs (math;pow (r./ r-nth 1.0)
-                                    (c.abs input))
+          nth-root-of-abs (|> input c.abs (get@ #real) (math;pow (r./ r-nth 1.0)))
           nth-phi (|> input argument (r./ r-nth))
           slice (|> math;pi (r.* 2.0) (r./ r-nth))]
       (|> (list;n.range +0 (n.dec nth))
-- 
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