diff --git a/lib/srfi/27/rand.c b/lib/srfi/27/rand.c
index 9d0f448f..e7125323 100644
--- a/lib/srfi/27/rand.c
+++ b/lib/srfi/27/rand.c
@@ -55,12 +55,12 @@ typedef unsigned int sexp_random_t;
 
 sexp sexp_rs_random_integer (sexp ctx, sexp self, sexp_sint_t n, sexp rs, sexp bound) {
   sexp_gc_var1(res);
-  int64_t m;
+  int i;
+  sexp_uint_t m;
   sexp_int32_t m2;
 #if SEXP_USE_BIGNUMS
-  /* sexp_uint_t mod; */
-  sexp_uint32_t *data;
-  sexp_int32_t hi, len, i;
+  sexp_uint_t *data;
+  int hi, j;
 #endif
   if (!sexp_random_source_p(self, rs))
     return sexp_type_exception(ctx, self, sexp_unbox_fixnum(sexp_opcode_arg1_type(self)), rs);
@@ -69,7 +69,7 @@ sexp sexp_rs_random_integer (sexp ctx, sexp self, sexp_sint_t n, sexp rs, sexp b
       res = sexp_xtype_exception(ctx, self, "random bound must be positive", bound);
     } else {
       /* ensure we have sufficient bits */
-      for (i=m=0; i <= 1<<(CHAR_BIT*sizeof(m))/RAND_MAX; ++i) {
+      for (i=m=0; i-1 <= 1<<(CHAR_BIT*sizeof(m))/RAND_MAX; ++i) {
         sexp_call_random(rs, m2);
         m = m * RAND_MAX + m2;
       }
@@ -79,12 +79,15 @@ sexp sexp_rs_random_integer (sexp ctx, sexp self, sexp_sint_t n, sexp rs, sexp b
   } else if (sexp_bignump(bound)) {
     sexp_gc_preserve1(ctx, res);
     hi = sexp_bignum_hi(bound);
-    len = hi * (sizeof(sexp_uint_t) / sizeof(sexp_int32_t));
-    res = sexp_make_bignum(ctx, hi + 1);
-    data = (sexp_uint32_t*) sexp_bignum_data(res);
-    for (i=0; i<len; i++) {
-      sexp_call_random(rs, m2);
-      data[i] = m2;
+    res = sexp_make_bignum(ctx, hi);
+    data = sexp_bignum_data(res);
+    for (i=0; i<hi; i++) {
+      for (j=m=0; j-1 <= 1<<(CHAR_BIT*sizeof(m))/RAND_MAX; ++j) {
+        sexp_call_random(rs, m2);
+        m = m * (sexp_uint_t)RAND_MAX + (sexp_uint_t) m2;
+      }
+      data[i] = (sexp_uint_t) m;
+      /* fprintf(stderr, "i: %d j: %d m: %lu (%lx) RAND_MAX: %d\n", i, j, m, (sexp_uint_t)m, RAND_MAX); */
     }
     res = sexp_remainder(ctx, res, bound);
     sexp_gc_release1(ctx);
diff --git a/lib/srfi/27/test.sld b/lib/srfi/27/test.sld
index 459ab0b9..5a7da7eb 100644
--- a/lib/srfi/27/test.sld
+++ b/lib/srfi/27/test.sld
@@ -1,13 +1,64 @@
+
 (define-library (srfi 27 test)
   (export run-tests)
-  (import (chibi)
+  (import (scheme base)
+          (scheme flonum)
+          (scheme inexact)
+          (scheme vector)
           (srfi 27)
           (chibi test))
   (begin
+    (define (random-histogram bound n . o)
+      (let* ((hist (make-vector (if (pair? o) (car o) (min 10 bound)) 0))
+             (rs (make-random-source))
+             (rand (random-source-make-integers rs)))
+        (random-source-pseudo-randomize! rs 23 42)
+        (do ((i 0 (+ i 1)))
+            ((= i n) hist)
+          (let* ((a (rand bound))
+                 (b (quotient (* a (vector-length hist)) bound)))
+            (vector-set! hist b (+ 1 (vector-ref hist b)))))))
+    (define (loggamma x)
+      (call-with-values (lambda () (flloggamma x))
+        (lambda (res sign) res)))
+    ;; continued fraction expansion, borrowed from (chibi math stats)
+    (define (lower-incomplete-gamma s z)
+      (let lp ((k 1) (x 1.0) (sum 1.0))
+        (if (or (= k 1000) (< (/ x sum) 1e-14))
+            (exp (+ (* s (log z))
+                    (log sum)
+                    (- z)
+                    (- (loggamma (+ s 1.)))))
+            (let* ((x2 (* x (/ z (+ s k))))
+                   (sum2 (+ sum x2)))
+              (lp (+ k 1) x2 sum2)))))
+    (define (chi^2-cdf X^2 df)
+      (min 1 (lower-incomplete-gamma (/ df 2) (/ X^2 2))))
+    (define (histogram-uniform? hist . o)
+      ;; ultra-conservative alpha to avoid test failures on false positives
+      (let* ((alpha (if (pair? o) (car o) 1e-5))
+             (n (vector-fold + 0 hist))
+             (len (vector-length hist))
+             (expected (/ n (inexact len)))
+             (X^2 (vector-fold
+                   (lambda (X^2 observed)
+                     (+ X^2 (/ (square (- observed expected)) expected)))
+                   0
+                   hist))
+             (p (- 1.0 (chi^2-cdf X^2 (- len 1)))))
+        ;;(write `(hist: ,hist X^2: ,X^2 p: ,p)) (newline)
+        (> p alpha)))
     (define (run-tests)
       (define (test-random rand n)
         (test-assert (<= 0 (rand n) (- n 1))))
       (test-begin "srfi-27: random")
+
+      ;; sanity checks
+      (test 0 (random-integer 1))
+      (test-assert (<= 0 (random-integer 2) 1))
+      (test-error (random-integer 0))
+      (test-error (random-integer -1))
+
       (let ((rs (make-random-source)))
         ;; chosen by fair dice roll.  guaranteed to be random
         (random-source-pseudo-randomize! rs 4 4)
@@ -22,9 +73,42 @@
             ;; resetting the state
             (test-not (= x (rand 1000000)))
             (random-source-state-set! rs state)
-            ;; (test x (rand 1000000))
-            ))
-        (test 0 (random-integer 1))
-        (test-error (random-integer 0))
-        (test-error (random-integer -1)))
+            ;; (test x (rand 1000000))  ;; actually impl defined
+            )))
+
+      ;; Distribution Checks.
+      ;; Since we fall back on the libc rand, we can't test the exact
+      ;; result even for a given seed, so we run some conservative
+      ;; statistical tests.
+      (test-assert
+          (histogram-uniform? (random-histogram 2 1000)))      ; coin
+      (test-assert
+          (histogram-uniform? (random-histogram 6 10000)))     ; die
+      (test-assert
+          (histogram-uniform? (random-histogram 27 10000 27))) ; small prime
+      ;; boundaries
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 31) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 32) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (- (expt 2 62) 1) 10000)))
+      ;; bignums
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 62) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 63) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 63) 10000 100)))
+      (test-assert
+          (histogram-uniform? (random-histogram (- (expt 2 64) 1) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 64) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (+ (expt 2 64) 1) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 65) 10000)))
+      (test-assert
+          (histogram-uniform? (random-histogram (expt 2 164) 10000)))
+
       (test-end))))