Direct rounding for mul and div

Author: obround

ops/arith.rkt

@@ -46,7 +46,7 @@
 (define (ival-sub x y)
   (ival-sub! (new-ival) x y))
 
-(define (epmul! out a-endpoint b-endpoint a-class b-class)
+(define (epmul! out a-endpoint b-endpoint a-class b-class rnd)
   (match-define (endpoint a a!) a-endpoint)
   (match-define (endpoint b b!) b-endpoint)
   (define a0 (bfzero? a))
@@ -57,7 +57,7 @@
       [(or a0 b0)
        (mpfr-set! out 0.bf 'nearest)
        #t]
-      [else (= 0 (mpfr-mul! out a b (bf-rounding-mode)))]))
+      [else (= 0 (mpfr-mul! out a b rnd))]))
   (endpoint out
             (or (and a! b! exact?)
                 (and a! a0)
@@ -76,8 +76,8 @@
 
   (define (mkmult out a b c d)
     (match-define (ival (endpoint rlo _) (endpoint rhi _) _ _) out)
-    (ival (rnd 'down epmul! rlo a b x-sign y-sign)
-          (rnd 'up epmul! rhi c d x-sign y-sign)
+    (ival (epmul! rlo a b x-sign y-sign 'down)
+          (epmul! rhi c d x-sign y-sign 'up)
           (or xerr? yerr?)
           (or xerr yerr)))
 
@@ -102,11 +102,11 @@
      (mpfr-set! (ival-hi-val out) hi 'up) ; should be exact
      (ival (endpoint (ival-lo-val out) lo!) (endpoint (ival-hi-val out) hi!) err? err)]))
 
-(define (epdiv! out a-endpoint b-endpoint a-class)
+(define (epdiv! out a-endpoint b-endpoint a-class rnd)
   (match-define (endpoint a a!) a-endpoint)
   (match-define (endpoint b b!) b-endpoint)
   (mpfr-set-prec! out (bf-precision))
-  (define exact? (= 0 (mpfr-div! out a b (bf-rounding-mode))))
+  (define exact? (= 0 (mpfr-div! out a b rnd)))
   (endpoint out
             (or (and a! b! exact?)
                 (and a! (bfzero? a))
@@ -124,7 +124,7 @@
   (define y-class (classify-ival-strict y))
 
   (define (mkdiv a b c d)
-    (ival (rnd 'down epdiv! rlo a b x-class) (rnd 'up epdiv! rhi c d x-class) err? err))
+    (ival (epdiv! rlo a b x-class 'down) (epdiv! rhi c d x-class 'up) err? err))
 
   (match* (x-class y-class)
     [(_ 0) ; In this case, y stradles 0