Defer building tables; drops 600ms from (require math) on my machine

pkgs/math-pkgs/math-lib/math/private/flonum/flonum-exp.rkt

@@ -35,8 +35,14 @@
                     (fl* x (fl/ (expm1-poly-numer x) (expm1-poly-denom x))))]))
 
 ;; Integer arguments for flexp2
-(: flexp2s (Vectorof Nonnegative-Flonum))
+(: flexp2s (U #f (Vectorof Nonnegative-Flonum)))
-(define flexp2s (build-vector (- 1024 -1074) (λ: ([n : Index]) (fl (expt 2 (- n 1074))))))
+(define flexp2s #f)
+
+(define (build-flexp2s)
+  (: new-flexp2s (Vectorof Nonnegative-Flonum))
+  (define new-flexp2s (build-vector (- 1024 -1074) (λ: ([n : Index]) (fl (expt 2 (- n 1074))))))
+  (set! flexp2s new-flexp2s)
+  new-flexp2s)
 
 (begin-encourage-inline
   
@@ -89,10 +95,14 @@
                  [else  (fl* (flexp x) (flexp 1.0))])]))
   
   (: flexp2 (Flonum -> Nonnegative-Flonum))
+  ;; Computes 2^x
   (define (flexp2 x)
     (cond [(fl<= x -1075.0)  0.0]
           [(fl>= x 1024.0)  +inf.0]
-          [(fl= x (flround x))  (unsafe-vector-ref flexp2s (fl->exact-integer (fl+ x 1074.0)))]
+          [(fl= x (flround x))
+           (let* ([flexp2s  flexp2s]
+                  [flexp2s  (if flexp2s flexp2s (build-flexp2s))])
+             (unsafe-vector-ref flexp2s (fl->exact-integer (fl+ x 1074.0))))]
           [else  (flexpt 2.0 x)]))
   
   )  ; begin-encourage-inline

pkgs/math-pkgs/math-lib/math/private/functions/incomplete-gamma/gamma-temme.rkt

@@ -15,36 +15,43 @@
 (define temme-iters (make-parameter 32))
 
 (define num-fs 100)
-(define fs
+(define: fs : (U #f FlVector)  #f)
-  (let ()
+
-    (define: start-fs : (Vectorof Real)  (vector 1 -1/3 1/12 -2/135))
+(: build-fs (-> FlVector))
-    (define: fs : (Vectorof Real)  (make-vector num-fs 0))
+(define (build-fs)
-    (vector-copy! fs 0 start-fs)
+  (define: start-fs : (Vectorof Real)  (vector 1 -1/3 1/12 -2/135))
-    ;; DP algorithm to compute f coefficients
+  (define: vec-fs : (Vectorof Real)  (make-vector num-fs 0))
-    (for ([m  (in-range 4 num-fs)])
+  (vector-copy! vec-fs 0 start-fs)
-      (vector-set!
+  ;; DP algorithm to compute f coefficients
-       fs m
+  (for ([m  (in-range 4 num-fs)])
-       (* (- (/ (+ m 1) (+ m 2)))
+    (vector-set!
-          (+ (* (/ (- m 1) (* 3 m)) (vector-ref fs (- m 1)))
+     vec-fs m
-             (for/fold: ([sum : Real  0]) ([j  (in-range 3 m)])
+     (* (- (/ (+ m 1) (+ m 2)))
-               (+ sum (/ (* (vector-ref fs (- j 1)) (vector-ref fs (+ m 1 (- j))))
+        (+ (* (/ (- m 1) (* 3 m)) (vector-ref vec-fs (- m 1)))
-                         (+ m 2 (- j)))))))))
+           (for/fold: ([sum : Real  0]) ([j  (in-range 3 m)])
-    (vector->flvector fs)))
+             (+ sum (/ (* (vector-ref vec-fs (- j 1))
+                          (vector-ref vec-fs (+ m 1 (- j))))
+                       (+ m 2 (- j)))))))))
+  (define new-fs (vector->flvector vec-fs))
+  (set! fs new-fs)
+  new-fs)
 
 (: R-sum (Float Flonum -> Flonum))
 (define (R-sum k n)
   (define num-fs (temme-iters))
-  ;; This originally filled a vector of bs, because imperative programmers don't know how to do
+  (let* ([fs  fs]
-  ;; anything else besides bang an array full of values (sheesh)
+         [fs  (if fs fs (build-fs))])
-  (define-values (sum b2 b1)
+    ;; This originally filled a vector of bs, because imperative programmers don't know how to do
-    (for/fold: ([sum : Flonum  0.0]
+    ;; anything else besides bang an array full of values (sheesh)
-                [b2 : Flonum  (unsafe-flvector-ref fs (- num-fs 1))]
+    (define-values (sum b2 b1)
-                [b1 : Flonum  (unsafe-flvector-ref fs (- num-fs 2))]
+      (for/fold: ([sum : Flonum  0.0]
-                ) ([m  (in-range (- num-fs 3) 0 -1)])
+                  [b2 : Flonum  (unsafe-flvector-ref fs (- num-fs 1))]
-      (define c (unsafe-flvector-ref fs m))
+                  [b1 : Flonum  (unsafe-flvector-ref fs (- num-fs 2))]
-      (define b0 (fl+ c (fl/ (fl* (fl+ (fl m) 1.0) b2) k)))
+                  ) ([m  (in-range (- num-fs 3) 0 -1)])
-      (values (fl+ (fl* n sum) b0) b1 b0)))
+        (define c (unsafe-flvector-ref fs m))
-  sum)
+        (define b0 (fl+ c (fl/ (fl* (fl+ (fl m) 1.0) b2) k)))
+        (values (fl+ (fl* n sum) b0) b1 b0)))
+    sum))
 
 (: R-log (Float Float -> (Values Float Float)))
 ;; Log-space version of `R' above

pkgs/math-pkgs/math-lib/math/private/number-theory/small-primes.rkt

@@ -69,6 +69,8 @@
          (clear-bit! y)
          (loop (cdr ds))]))))
 
+(define: sieve-done? : Boolean  #f)
+
 (define: (sieve) : Void
   (define x 1)
   (let loop ([ds deltas])
@@ -85,9 +87,11 @@
            (mark-composites x))
          (loop (cdr ds))]))))
 
-(sieve)
-
 (define: (small-prime? [x : Integer]) : Boolean
+  (unless sieve-done?
+    (sieve)
+    (set! sieve-done? #t))
+  
   (or (= x 2) (= x 3) (= x 5)
       (and (mod60->bit (modulo x 60))
            (bit x))))