implement proper atan #299 #34

CHANGELOG.md

@@ -15,7 +15,8 @@
 * add R7RS `char<...>?` and `string<...>?` functions [#298](https://github.com/jcubic/lips/issues/298)
 * improve syntax-rule exception message (appending macro code)
 * update `log` to accept two arguments [#301](https://github.com/jcubic/lips/issues/301)
-* allow to use `data-bootstrap` attribute
+* allow to use `data-bootstrap` attribute on script tags
+* make `atan` work for complex numbers
 ### Bugfix
 * fix `let-values` to allow binding to list [#281](https://github.com/jcubic/lips/issues/281)
 * fix wrong strings in `string-fill!`

lib/R5RS.scm

@@ -467,7 +467,7 @@
 
 ;; -----------------------------------------------------------------------------
 ;; generate Math functions with documentation
-(define _maths (list "sin" "cos" "tan" "asin" "acos" "atan"))
+(define _maths (list "asin" "acos"))
 
 ;; -----------------------------------------------------------------------------
 (define _this_env (current-environment))
@@ -533,6 +533,25 @@
                                          (Math.cosh im2))))))
       (Math.tan n)))
 
+;; -----------------------------------------------------------------------------
+(define (atan z . rest)
+  "(atan z)
+   (atan x y)
+
+   Function calculates arcus tangent of a complex number.
+   If two argumets are passed and they are not complex numbers
+   it calulates Math.atan2 on those arguments."
+  (if (and (null? rest) (complex? z))
+      (let ((iz (* +i z)))
+        (* (/ 1 +2i)
+           (log (/ (+ 1 iz)
+                   (- 1 iz)))))
+      (let ((x z) (y (car rest)))
+        (if (and (zero? (imag-part x))
+                 (zero? (imag-part y)))
+            (Math.atan2 x y)
+            (error "atan: can't call with two complex numbers")))))
+
 ;; -----------------------------------------------------------------------------
 (define (exp n)
   "(exp n)

tests/numbers.scm

@@ -1043,6 +1043,23 @@
                     (1/2+1/2i 0.40389645531602575+0.5640831412674985i)
                     (+1/2i +0.46211715726000974i)))))
 
+(test "numbers: atan"
+      (lambda (t)
+        (t.is (atan 10+10i) 1.5207132443509341+0.04991641756298178i)
+        (t.is (atan -10+10i) -1.5207132443509341+0.04991641756298178i)
+        (t.is (atan -10-10i) -1.5207132443509341-0.0499164175629817i)
+        (t.is (atan 10-10i) 1.5207132443509341-0.0499164175629817i)
+
+        (t.is (atan 1/2) 0.46364760900080615)
+        (t.is (atan 0.5) 0.46364760900080615)
+        (t.is (atan 1/2 3/4) 0.5880026035475675)
+        (t.is (atan 2 3) 0.5880026035475675)
+
+        (t.is (atan 0.5 0.6) 0.6947382761967033)
+        (t.is (atan -0.5 0.6) -0.6947382761967033)
+        (t.is (atan 0.5 -0.6) 2.44685437739309)
+        (t.is (atan -0.5 -0.6) -2.44685437739309)))
+
 (test "numbers: should calculate odd? / even?"
       (lambda (t)
         (t.is (odd? 1) #t)