fix problem with rotation on images such as bitmaps

and replace internal `bring-between' with an efficient version
 Closes PR 11124

collects/2htdp/private/image-more.rkt

@@ -616,8 +616,8 @@
                   (make-bitmap (bitmap-raw-bitmap bitmap)
                                (bitmap-raw-mask bitmap)
                                (bring-between (if flipped? 
-                                                  (+ θ (bitmap-angle bitmap))
+                                                  (- (bitmap-angle bitmap) θ)
-                                                  (- (+ θ (bitmap-angle bitmap))))
+                                                  (+ (bitmap-angle bitmap) θ))
                                               360)
                                (bitmap-x-scale bitmap)
                                (bitmap-y-scale bitmap)
@@ -647,19 +647,14 @@
     (make-point x y)))
 
 
-;; bring-between : number number -> number
+;; bring-between : rational integer -> rational
-;; returns a number that is much like the modulo of 'x' and 'upper-bound'
+;; returns a number that is much like the modulo of 'x' and 'upper-bound',
-;; but does this by repeated subtraction (or addition if it is negative), 
 ;; since modulo only works on integers
 (define (bring-between x upper-bound)
-  (let loop ([x x])
+  (let* ([x-floor (floor x)]
-    (cond
+         [fraction (- x x-floor)])
-      [(< x 0)
+    (+ (modulo x-floor upper-bound) 
-       (loop (+ x upper-bound))]
+       fraction)))
-      [(< x upper-bound)
-       x]
-      [else
-       (loop (- x upper-bound))])))
 
 (define/chk (flip-horizontal image)
   (rotate 90 (flip-vertical (rotate -90 image))))

collects/2htdp/tests/test-image.rkt

@@ -1262,15 +1262,28 @@
       =>
       (image-snip->image (make-object image-snip% blue-20x10-bitmap)))
 
-(test (rotate 90 (make-object image-snip% green-blue-20x10-bitmap))
+(test (rotate -90 (make-object image-snip% green-blue-20x10-bitmap))
       =>
       (image-snip->image (make-object image-snip% green-blue-10x20-bitmap)))
 
+(test (rotate 90 (rotate 90 (make-object image-snip% green-blue-20x10-bitmap)))
+      =>
+      (rotate 180 (make-object image-snip% green-blue-20x10-bitmap)))
+
+(test (rotate 90 (flip-vertical (rotate 90 (make-object image-snip% green-blue-20x10-bitmap))))
+      =>
+      (rotate 0 (make-object image-snip% green-blue-20x10-bitmap)))
+
 ;; there was a bug in the bounding box computation for scaled bitmaps that this test exposes
 (test (image-width (frame (rotate 90 (scale 1/2 (bitmap icons/plt-logo-red-diffuse.png)))))
       =>
       128)
 
+;; Rotation by 0 should produce an equivalent object
+(test (rotate 0 (make-object image-snip% green-blue-20x10-bitmap))
+      =>
+      (to-img (make-object image-snip% green-blue-20x10-bitmap)))
+
 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
 ;;
 ;; cropping (and place-image)