Added nan?, infinite?, degrees->radians, radians->degrees, exact-round, exact-floor, exact-ceiling, exact-truncate to racket/math

Altered TR's random arithmetic testing to generate single-flonums and very small flonums; fails now because of erroneous types

Fixes to sgn, sinh, cosh, and tanh:
 * preserve single-flonum-ness
 * correct zero sign (-0.0) for negative return values that are smaller than epsilon
 * correct behavior with NaN and infinite inputs

original commit: a713ca8a8b6c7aed987e80d0621484e68bc3c6f5

collects/tests/typed-racket/tr-random-testing.rkt

@@ -3,7 +3,7 @@
 ;; Random testing of type preservation for floats.
 
 (require redex
-         racket/flonum racket/unsafe/ops
+         racket/flonum racket/unsafe/ops unstable/flonum
          racket/sandbox)
 
 (require (except-in typed-racket/utils/utils infer)
@@ -18,6 +18,8 @@
 (b:init) (n:init)
 (define-namespace-anchor anch)
 
+todo: exact numbers
+
 (define-language tr-arith ; to stay within floats, removed some numeric ops
   [n real]
   [E n
@@ -99,10 +101,33 @@
   (define subtype? (subtype type-after type-before))
   subtype?)
 
+(define (random-integer->random-float E)
+  (define r (random))
+  (cond 
+    ;; probability 1/4: noisify and convert to single flonum
+    [(r . < . 0.25)
+     (real->single-flonum (* (random) E))]
+    ;; probability 1/4: noisify and convert to double flonum
+    [(r . < . 0.5)
+     (real->double-flonum (* (random) E))]
+    ;; probability 1/4: convert to very small double flonum
+    [(r . < . 0.75)
+     (define x (ordinal->flonum E))
+     (cond [(= x 0.0)  (if ((random) . < . 0.5) 0.0 -0.0)]
+           [else  x])]
+    ;; probability 1/20: +nan.0
+    [(r . < . 0.8)
+     +nan.0]
+    ;; remaining probability: convert to very large double flonum
+    [else
+     (if ((random) . < . 0.5)
+         (flstep -inf.0 E)
+         (flstep +inf.0 (- E)))]))
+
 ;; Redex can't generate floats, so we convert ints to floats.
 (define (exp->float-exp E) ; numbers or symbols or lists
   (cond [(number? E)
-         (exact->inexact (* (random) E))] ; add noise
+         (random-integer->random-float E)]
         [(list? E)
          (map exp->float-exp E)]
         [else

collects/typed-racket/base-env/base-env-numeric.rkt

@@ -1808,7 +1808,8 @@
             (-NegRat . -> . -NegFixnum) ; -1
             (-NonPosRat . -> . -NonPosFixnum) ; 0 or -1
             (-Rat . -> . -Fixnum)
-            (-InexactReal . -> . -Flonum) ; single-flonums give a flonum result
+            (-Flonum . -> . -Flonum)
+            (-SingleFlonum . -> . -SingleFlonum)
             (-Real . -> . -Real))]
 
 [pi -PosFlonum]