diff --git a/mats/ieee.ms b/mats/ieee.ms
index b31e520401..e08cf66588 100644
--- a/mats/ieee.ms
+++ b/mats/ieee.ms
@@ -379,8 +379,8 @@
    (== (expt -inf.0 +1.0) -inf.0)
    (== (expt +inf.0 +inf.0) +inf.0)
    (== (expt +inf.0 -inf.0) +0.0)
-   (== (expt -inf.0 +inf.0) +inf.0)
-   (== (expt -inf.0 -inf.0) +0.0)
+   (== (expt -inf.0 +inf.0) +nan.0+nan.0i)
+   (== (expt -inf.0 -inf.0) +nan.0+nan.0i)
    (== (expt +inf.0 +.5) +inf.0)
    (== (expt (nan) +.5) (nan))
    (== (expt +.5 (nan)) (nan))
diff --git a/mats/mat.ss b/mats/mat.ss
index f82e406c73..a5c341632e 100644
--- a/mats/mat.ss
+++ b/mats/mat.ss
@@ -333,19 +333,7 @@
       (and (fl~= (cfl-real-part x) (cfl-real-part y))
            (fl~= (cfl-imag-part x) (cfl-imag-part y)))))
 
-; from ieee.ms
-(define ==
-   (lambda (x y)
-      (and (inexact? x)
-           (inexact? y)
-           (if (flonum? x)
-               (and (flonum? y)
-                    (if (fl= x y)
-                        (fl= (fl/ 1.0 x) (fl/ 1.0 y))
-                        (and (not (fl= x x)) (not (fl= y y)))))
-               (and (not (flonum? y))
-                    (== (real-part x) (real-part y))
-                    (== (imag-part x) (imag-part y)))))))
+(define == eqv?)
 
 (define (nan) (/ 0.0 0.0))  ; keeps "pretty-equal?" happy
 (define pi (* (asin 1.0) 2))
diff --git a/s/cpnanopass.ss b/s/cpnanopass.ss
index 06de92ae85..c517ee547c 100644
--- a/s/cpnanopass.ss
+++ b/s/cpnanopass.ss
@@ -6034,13 +6034,35 @@
             (lambda (e1 e2)
               (nanopass-case (L7 Expr) e1
                 [(quote ,d) (and (flonum? d)
-                                 (bind #t (e2)
-                                   (build-and
-                                    (%type-check mask-flonum type-flonum ,e2)
-                                    (if ($nan? d)
-                                        (build-not (%inline fl= ,e2 ,e2))
-                                        (%inline fl= ,e2 ,e1)))))]
-                [else #f])))
+                                 (build-and
+                                  (%type-check mask-flonum type-flonum ,e2)
+                                  (if ($nan? d)
+                                      ;; NaN: invert `fl=` on self
+                                      (bind #t (e2)
+                                        (build-not (%inline fl= ,e2 ,e2)))
+                                      ;; Non-NaN: compare bits
+                                      (constant-case ptr-bits
+                                        [(32)
+                                         (bind #t (e2)
+                                           (let ([d0 (if (eq? (constant-case native-endianness) (native-endianness)) 0 4)])
+                                             (let ([word1 ($object-ref 'iptr d (fx+ (constant flonum-data-disp) d0))]
+                                                   [word2 ($object-ref 'iptr d (fx+ (constant flonum-data-disp) (fx- 4 d0)))])
+                                               (build-and
+                                                (%inline eq?
+                                                         ,(%mref ,e2 ,(constant flonum-data-disp))
+                                                         (immediate ,word1))
+                                                (%inline eq?
+                                                         ,(%mref ,e2 ,(fx+ (constant flonum-data-disp) 4))
+                                                         (immediate ,word2))))))]
+                                        [(64)
+                                         (let ([word ($object-ref 'iptr d (constant flonum-data-disp))])
+                                           (%inline eq?
+                                                    ,(%mref ,e2 ,(constant flonum-data-disp))
+                                                    (immediate ,word)))]
+                                        [else ($oops 'compiler-internal
+                                                     "eqv doesn't handle ptr-bits = ~s"
+                                                     (constant ptr-bits))]))))]
+              [else #f])))
           (define eqok-help?
             (lambda (obj)
               (or (symbol? obj)
@@ -6798,7 +6820,7 @@
         (define-inline 3 $fleqv?
           [(e1 e2)
            (bind #t (e1 e2)
-             `(if ,(%inline fl= ,e1 ,e1) ; check e1 no +nan.0
+             `(if ,(%inline fl= ,e1 ,e1) ; check e1 not +nan.0
                   ,(constant-case ptr-bits
                     [(32) (build-and
                             (%inline eq?