diff --git a/include/jemalloc/internal/arena.h b/include/jemalloc/internal/arena.h
index ce9d8b5e..dbd334e6 100644
--- a/include/jemalloc/internal/arena.h
+++ b/include/jemalloc/internal/arena.h
@@ -182,7 +182,7 @@ struct arena_s {
 	 * PRNG state for cache index randomization of large allocation base
 	 * pointers.
 	 */
-	uint64_t		offset_state;
+	size_t			offset_state;
 
 	dss_prec_t		dss_prec;
 
diff --git a/include/jemalloc/internal/extent.h b/include/jemalloc/internal/extent.h
index 673cac2f..531d853c 100644
--- a/include/jemalloc/internal/extent.h
+++ b/include/jemalloc/internal/extent.h
@@ -325,8 +325,8 @@ extent_addr_randomize(tsdn_t *tsdn, extent_t *extent, size_t alignment)
 	if (alignment < PAGE) {
 		unsigned lg_range = LG_PAGE -
 		    lg_floor(CACHELINE_CEILING(alignment));
-		uint64_t r =
-		    prng_lg_range(&extent_arena_get(extent)->offset_state,
+		size_t r =
+		    prng_lg_range_zu(&extent_arena_get(extent)->offset_state,
 		    lg_range, true);
 		uintptr_t random_offset = ((uintptr_t)r) << (LG_PAGE -
 		    lg_range);
diff --git a/include/jemalloc/internal/private_symbols.txt b/include/jemalloc/internal/private_symbols.txt
index 2949de10..f178daf7 100644
--- a/include/jemalloc/internal/private_symbols.txt
+++ b/include/jemalloc/internal/private_symbols.txt
@@ -328,9 +328,15 @@ pind2sz_tab
 pow2_ceil_u32
 pow2_ceil_u64
 pow2_ceil_zu
-prng_lg_range
-prng_range
-prng_state_next
+prng_lg_range_u32
+prng_lg_range_u64
+prng_lg_range_zu
+prng_range_u32
+prng_range_u64
+prng_range_zu
+prng_state_next_u32
+prng_state_next_u64
+prng_state_next_zu
 prof_active
 prof_active_get
 prof_active_get_unlocked
diff --git a/include/jemalloc/internal/prng.h b/include/jemalloc/internal/prng.h
index ebe916f8..c2bda19c 100644
--- a/include/jemalloc/internal/prng.h
+++ b/include/jemalloc/internal/prng.h
@@ -19,8 +19,12 @@
  * the next has a cycle of 4, etc.  For this reason, we prefer to use the upper
  * bits.
  */
-#define	PRNG_A	UINT64_C(6364136223846793005)
-#define	PRNG_C	UINT64_C(1442695040888963407)
+
+#define	PRNG_A_32	UINT32_C(1103515241)
+#define	PRNG_C_32	UINT32_C(12347)
+
+#define	PRNG_A_64	UINT64_C(6364136223846793005)
+#define	PRNG_C_64	UINT64_C(1442695040888963407)
 
 #endif /* JEMALLOC_H_TYPES */
 /******************************************************************************/
@@ -35,45 +39,133 @@
 #ifdef JEMALLOC_H_INLINES
 
 #ifndef JEMALLOC_ENABLE_INLINE
-uint64_t	prng_state_next(uint64_t state);
-uint64_t	prng_lg_range(uint64_t *state, unsigned lg_range, bool atomic);
-uint64_t	prng_range(uint64_t *state, uint64_t range, bool atomic);
+uint32_t	prng_state_next_u32(uint32_t state);
+uint64_t	prng_state_next_u64(uint64_t state);
+size_t	prng_state_next_zu(size_t state);
+
+uint32_t	prng_lg_range_u32(uint32_t *state, unsigned lg_range,
+    bool atomic);
+uint64_t	prng_lg_range_u64(uint64_t *state, unsigned lg_range);
+size_t	prng_lg_range_zu(size_t *state, unsigned lg_range, bool atomic);
+
+uint32_t	prng_range_u32(uint32_t *state, uint32_t range, bool atomic);
+uint64_t	prng_range_u64(uint64_t *state, uint64_t range);
+size_t	prng_range_zu(size_t *state, size_t range, bool atomic);
 #endif
 
 #if (defined(JEMALLOC_ENABLE_INLINE) || defined(JEMALLOC_PRNG_C_))
-JEMALLOC_ALWAYS_INLINE uint64_t
-prng_state_next(uint64_t state)
+JEMALLOC_ALWAYS_INLINE uint32_t
+prng_state_next_u32(uint32_t state)
 {
 
-	return ((state * PRNG_A) + PRNG_C);
+	return ((state * PRNG_A_32) + PRNG_C_32);
 }
 
 JEMALLOC_ALWAYS_INLINE uint64_t
-prng_lg_range(uint64_t *state, unsigned lg_range, bool atomic)
+prng_state_next_u64(uint64_t state)
+{
+
+	return ((state * PRNG_A_64) + PRNG_C_64);
+}
+
+JEMALLOC_ALWAYS_INLINE size_t
+prng_state_next_zu(size_t state)
+{
+
+#if LG_SIZEOF_PTR == 2
+	return ((state * PRNG_A_32) + PRNG_C_32);
+#elif LG_SIZEOF_PTR == 3
+	return ((state * PRNG_A_64) + PRNG_C_64);
+#else
+#error Unsupported pointer size
+#endif
+}
+
+JEMALLOC_ALWAYS_INLINE uint32_t
+prng_lg_range_u32(uint32_t *state, unsigned lg_range, bool atomic)
+{
+	uint32_t ret, state1;
+
+	assert(lg_range > 0);
+	assert(lg_range <= 32);
+
+	if (atomic) {
+		uint32_t state0;
+
+		do {
+			state0 = atomic_read_uint32(state);
+			state1 = prng_state_next_u32(state0);
+		} while (atomic_cas_uint32(state, state0, state1));
+	} else {
+		state1 = prng_state_next_u32(*state);
+		*state = state1;
+	}
+	ret = state1 >> (32 - lg_range);
+
+	return (ret);
+}
+
+/* 64-bit atomic operations cannot be supported on all relevant platforms. */
+JEMALLOC_ALWAYS_INLINE uint64_t
+prng_lg_range_u64(uint64_t *state, unsigned lg_range)
 {
 	uint64_t ret, state1;
 
 	assert(lg_range > 0);
 	assert(lg_range <= 64);
 
-	if (atomic) {
-		uint64_t state0;
-
-		do {
-			state0 = atomic_read_uint64(state);
-			state1 = prng_state_next(state0);
-		} while (atomic_cas_uint64(state, state0, state1));
-	} else {
-		state1 = prng_state_next(*state);
-		*state = state1;
-	}
+	state1 = prng_state_next_u64(*state);
+	*state = state1;
 	ret = state1 >> (64 - lg_range);
 
 	return (ret);
 }
 
+JEMALLOC_ALWAYS_INLINE size_t
+prng_lg_range_zu(size_t *state, unsigned lg_range, bool atomic)
+{
+	size_t ret, state1;
+
+	assert(lg_range > 0);
+	assert(lg_range <= ZU(1) << (3 + LG_SIZEOF_PTR));
+
+	if (atomic) {
+		size_t state0;
+
+		do {
+			state0 = atomic_read_z(state);
+			state1 = prng_state_next_zu(state0);
+		} while (atomic_cas_z(state, state0, state1));
+	} else {
+		state1 = prng_state_next_zu(*state);
+		*state = state1;
+	}
+	ret = state1 >> ((ZU(1) << (3 + LG_SIZEOF_PTR)) - lg_range);
+
+	return (ret);
+}
+
+JEMALLOC_ALWAYS_INLINE uint32_t
+prng_range_u32(uint32_t *state, uint32_t range, bool atomic)
+{
+	uint32_t ret;
+	unsigned lg_range;
+
+	assert(range > 1);
+
+	/* Compute the ceiling of lg(range). */
+	lg_range = ffs_u32(pow2_ceil_u32(range)) - 1;
+
+	/* Generate a result in [0..range) via repeated trial. */
+	do {
+		ret = prng_lg_range_u32(state, lg_range, atomic);
+	} while (ret >= range);
+
+	return (ret);
+}
+
 JEMALLOC_ALWAYS_INLINE uint64_t
-prng_range(uint64_t *state, uint64_t range, bool atomic)
+prng_range_u64(uint64_t *state, uint64_t range)
 {
 	uint64_t ret;
 	unsigned lg_range;
@@ -85,7 +177,26 @@ prng_range(uint64_t *state, uint64_t range, bool atomic)
 
 	/* Generate a result in [0..range) via repeated trial. */
 	do {
-		ret = prng_lg_range(state, lg_range, atomic);
+		ret = prng_lg_range_u64(state, lg_range);
+	} while (ret >= range);
+
+	return (ret);
+}
+
+JEMALLOC_ALWAYS_INLINE size_t
+prng_range_zu(size_t *state, size_t range, bool atomic)
+{
+	size_t ret;
+	unsigned lg_range;
+
+	assert(range > 1);
+
+	/* Compute the ceiling of lg(range). */
+	lg_range = ffs_u64(pow2_ceil_u64(range)) - 1;
+
+	/* Generate a result in [0..range) via repeated trial. */
+	do {
+		ret = prng_lg_range_zu(state, lg_range, atomic);
 	} while (ret >= range);
 
 	return (ret);
diff --git a/src/arena.c b/src/arena.c
index dd8e4d9c..4b104a0e 100644
--- a/src/arena.c
+++ b/src/arena.c
@@ -422,8 +422,8 @@ arena_decay_deadline_init(arena_t *arena)
 	if (arena->decay.time > 0) {
 		nstime_t jitter;
 
-		nstime_init(&jitter, prng_range(&arena->decay.jitter_state,
-		    nstime_ns(&arena->decay.interval), false));
+		nstime_init(&jitter, prng_range_u64(&arena->decay.jitter_state,
+		    nstime_ns(&arena->decay.interval)));
 		nstime_add(&arena->decay.deadline, &jitter);
 	}
 }
@@ -1680,7 +1680,7 @@ arena_new(tsdn_t *tsdn, unsigned ind)
 		 * deterministic seed.
 		 */
 		arena->offset_state = config_debug ? ind :
-		    (uint64_t)(uintptr_t)arena;
+		    (size_t)(uintptr_t)arena;
 	}
 
 	arena->dss_prec = extent_dss_prec_get();
diff --git a/src/ckh.c b/src/ckh.c
index 75376017..6f16565f 100644
--- a/src/ckh.c
+++ b/src/ckh.c
@@ -99,8 +99,8 @@ ckh_try_bucket_insert(ckh_t *ckh, size_t bucket, const void *key,
 	 * Cycle through the cells in the bucket, starting at a random position.
 	 * The randomness avoids worst-case search overhead as buckets fill up.
 	 */
-	offset = (unsigned)prng_lg_range(&ckh->prng_state, LG_CKH_BUCKET_CELLS,
-	    false);
+	offset = (unsigned)prng_lg_range_u64(&ckh->prng_state,
+	    LG_CKH_BUCKET_CELLS);
 	for (i = 0; i < (ZU(1) << LG_CKH_BUCKET_CELLS); i++) {
 		cell = &ckh->tab[(bucket << LG_CKH_BUCKET_CELLS) +
 		    ((i + offset) & ((ZU(1) << LG_CKH_BUCKET_CELLS) - 1))];
@@ -142,8 +142,8 @@ ckh_evict_reloc_insert(ckh_t *ckh, size_t argbucket, void const **argkey,
 		 * were an item for which both hashes indicated the same
 		 * bucket.
 		 */
-		i = (unsigned)prng_lg_range(&ckh->prng_state,
-		    LG_CKH_BUCKET_CELLS, false);
+		i = (unsigned)prng_lg_range_u64(&ckh->prng_state,
+		    LG_CKH_BUCKET_CELLS);
 		cell = &ckh->tab[(bucket << LG_CKH_BUCKET_CELLS) + i];
 		assert(cell->key != NULL);
 
diff --git a/src/prof.c b/src/prof.c
index 4bafb39a..19c8fb71 100644
--- a/src/prof.c
+++ b/src/prof.c
@@ -878,7 +878,7 @@ prof_sample_threshold_update(prof_tdata_t *tdata)
 	 *   pp 500
 	 *   (http://luc.devroye.org/rnbookindex.html)
 	 */
-	r = prng_lg_range(&tdata->prng_state, 53, false);
+	r = prng_lg_range_u64(&tdata->prng_state, 53);
 	u = (double)r * (1.0/9007199254740992.0L);
 	tdata->bytes_until_sample = (uint64_t)(log(u) /
 	    log(1.0 - (1.0 / (double)((uint64_t)1U << lg_prof_sample))))
diff --git a/test/unit/prng.c b/test/unit/prng.c
index f3234455..111fa59f 100644
--- a/test/unit/prng.c
+++ b/test/unit/prng.c
@@ -1,34 +1,71 @@
 #include "test/jemalloc_test.h"
 
 static void
-test_prng_lg_range(bool atomic)
+test_prng_lg_range_u32(bool atomic)
+{
+	uint32_t sa, sb, ra, rb;
+	unsigned lg_range;
+
+	sa = 42;
+	ra = prng_lg_range_u32(&sa, 32, atomic);
+	sa = 42;
+	rb = prng_lg_range_u32(&sa, 32, atomic);
+	assert_u32_eq(ra, rb,
+	    "Repeated generation should produce repeated results");
+
+	sb = 42;
+	rb = prng_lg_range_u32(&sb, 32, atomic);
+	assert_u32_eq(ra, rb,
+	    "Equivalent generation should produce equivalent results");
+
+	sa = 42;
+	ra = prng_lg_range_u32(&sa, 32, atomic);
+	rb = prng_lg_range_u32(&sa, 32, atomic);
+	assert_u32_ne(ra, rb,
+	    "Full-width results must not immediately repeat");
+
+	sa = 42;
+	ra = prng_lg_range_u32(&sa, 32, atomic);
+	for (lg_range = 31; lg_range > 0; lg_range--) {
+		sb = 42;
+		rb = prng_lg_range_u32(&sb, lg_range, atomic);
+		assert_u32_eq((rb & (UINT32_C(0xffffffff) << lg_range)),
+		    0, "High order bits should be 0, lg_range=%u", lg_range);
+		assert_u32_eq(rb, (ra >> (32 - lg_range)),
+		    "Expected high order bits of full-width result, "
+		    "lg_range=%u", lg_range);
+	}
+}
+
+static void
+test_prng_lg_range_u64(void)
 {
 	uint64_t sa, sb, ra, rb;
 	unsigned lg_range;
 
 	sa = 42;
-	ra = prng_lg_range(&sa, 64, atomic);
+	ra = prng_lg_range_u64(&sa, 64);
 	sa = 42;
-	rb = prng_lg_range(&sa, 64, atomic);
+	rb = prng_lg_range_u64(&sa, 64);
 	assert_u64_eq(ra, rb,
 	    "Repeated generation should produce repeated results");
 
 	sb = 42;
-	rb = prng_lg_range(&sb, 64, atomic);
+	rb = prng_lg_range_u64(&sb, 64);
 	assert_u64_eq(ra, rb,
 	    "Equivalent generation should produce equivalent results");
 
 	sa = 42;
-	ra = prng_lg_range(&sa, 64, atomic);
-	rb = prng_lg_range(&sa, 64, atomic);
+	ra = prng_lg_range_u64(&sa, 64);
+	rb = prng_lg_range_u64(&sa, 64);
 	assert_u64_ne(ra, rb,
 	    "Full-width results must not immediately repeat");
 
 	sa = 42;
-	ra = prng_lg_range(&sa, 64, atomic);
+	ra = prng_lg_range_u64(&sa, 64);
 	for (lg_range = 63; lg_range > 0; lg_range--) {
 		sb = 42;
-		rb = prng_lg_range(&sb, lg_range, atomic);
+		rb = prng_lg_range_u64(&sb, lg_range);
 		assert_u64_eq((rb & (UINT64_C(0xffffffffffffffff) << lg_range)),
 		    0, "High order bits should be 0, lg_range=%u", lg_range);
 		assert_u64_eq(rb, (ra >> (64 - lg_range)),
@@ -37,22 +74,102 @@ test_prng_lg_range(bool atomic)
 	}
 }
 
-TEST_BEGIN(test_prng_lg_range_nonatomic)
+static void
+test_prng_lg_range_zu(bool atomic)
+{
+	uint64_t sa, sb, ra, rb;
+	unsigned lg_range;
+
+	sa = 42;
+	ra = prng_lg_range_zu(&sa, 64, atomic);
+	sa = 42;
+	rb = prng_lg_range_zu(&sa, 64, atomic);
+	assert_zu_eq(ra, rb,
+	    "Repeated generation should produce repeated results");
+
+	sb = 42;
+	rb = prng_lg_range_zu(&sb, 64, atomic);
+	assert_zu_eq(ra, rb,
+	    "Equivalent generation should produce equivalent results");
+
+	sa = 42;
+	ra = prng_lg_range_zu(&sa, 64, atomic);
+	rb = prng_lg_range_zu(&sa, 64, atomic);
+	assert_zu_ne(ra, rb,
+	    "Full-width results must not immediately repeat");
+
+	sa = 42;
+	ra = prng_lg_range_zu(&sa, 64, atomic);
+	for (lg_range = (ZU(1) << (3 + LG_SIZEOF_PTR)) - 1; lg_range > 0;
+	    lg_range--) {
+		sb = 42;
+		rb = prng_lg_range_zu(&sb, lg_range, atomic);
+		assert_zu_eq((rb & (SIZE_T_MAX << lg_range)),
+		    0, "High order bits should be 0, lg_range=%u", lg_range);
+		assert_zu_eq(rb, (ra >> (64 - lg_range)),
+		    "Expected high order bits of full-width result, "
+		    "lg_range=%u", lg_range);
+	}
+}
+
+TEST_BEGIN(test_prng_lg_range_u32_nonatomic)
 {
 
-	test_prng_lg_range(false);
+	test_prng_lg_range_u32(false);
 }
 TEST_END
 
-TEST_BEGIN(test_prng_lg_range_atomic)
+TEST_BEGIN(test_prng_lg_range_u32_atomic)
 {
 
-	test_prng_lg_range(true);
+	test_prng_lg_range_u32(true);
+}
+TEST_END
+
+TEST_BEGIN(test_prng_lg_range_u64_nonatomic)
+{
+
+	test_prng_lg_range_u64();
+}
+TEST_END
+
+TEST_BEGIN(test_prng_lg_range_zu_nonatomic)
+{
+
+	test_prng_lg_range_zu(false);
+}
+TEST_END
+
+TEST_BEGIN(test_prng_lg_range_zu_atomic)
+{
+
+	test_prng_lg_range_zu(true);
 }
 TEST_END
 
 static void
-test_prng_range(bool atomic)
+test_prng_range_u32(bool atomic)
+{
+	uint32_t range;
+#define	MAX_RANGE	10000000
+#define	RANGE_STEP	97
+#define	NREPS		10
+
+	for (range = 2; range < MAX_RANGE; range += RANGE_STEP) {
+		uint32_t s;
+		unsigned rep;
+
+		s = range;
+		for (rep = 0; rep < NREPS; rep++) {
+			uint32_t r = prng_range_u32(&s, range, atomic);
+
+			assert_u32_lt(r, range, "Out of range");
+		}
+	}
+}
+
+static void
+test_prng_range_u64(void)
 {
 	uint64_t range;
 #define	MAX_RANGE	10000000
@@ -65,24 +182,66 @@ test_prng_range(bool atomic)
 
 		s = range;
 		for (rep = 0; rep < NREPS; rep++) {
-			uint64_t r = prng_range(&s, range, atomic);
+			uint64_t r = prng_range_u64(&s, range);
 
 			assert_u64_lt(r, range, "Out of range");
 		}
 	}
 }
 
-TEST_BEGIN(test_prng_range_nonatomic)
+static void
+test_prng_range_zu(bool atomic)
+{
+	size_t range;
+#define	MAX_RANGE	10000000
+#define	RANGE_STEP	97
+#define	NREPS		10
+
+	for (range = 2; range < MAX_RANGE; range += RANGE_STEP) {
+		size_t s;
+		unsigned rep;
+
+		s = range;
+		for (rep = 0; rep < NREPS; rep++) {
+			size_t r = prng_range_zu(&s, range, atomic);
+
+			assert_zu_lt(r, range, "Out of range");
+		}
+	}
+}
+
+TEST_BEGIN(test_prng_range_u32_nonatomic)
 {
 
-	test_prng_range(false);
+	test_prng_range_u32(false);
 }
 TEST_END
 
-TEST_BEGIN(test_prng_range_atomic)
+TEST_BEGIN(test_prng_range_u32_atomic)
 {
 
-	test_prng_range(true);
+	test_prng_range_u32(true);
+}
+TEST_END
+
+TEST_BEGIN(test_prng_range_u64_nonatomic)
+{
+
+	test_prng_range_u64();
+}
+TEST_END
+
+TEST_BEGIN(test_prng_range_zu_nonatomic)
+{
+
+	test_prng_range_zu(false);
+}
+TEST_END
+
+TEST_BEGIN(test_prng_range_zu_atomic)
+{
+
+	test_prng_range_zu(true);
 }
 TEST_END
 
@@ -91,8 +250,14 @@ main(void)
 {
 
 	return (test(
-	    test_prng_lg_range_nonatomic,
-	    test_prng_lg_range_atomic,
-	    test_prng_range_nonatomic,
-	    test_prng_range_atomic));
+	    test_prng_lg_range_u32_nonatomic,
+	    test_prng_lg_range_u32_atomic,
+	    test_prng_lg_range_u64_nonatomic,
+	    test_prng_lg_range_zu_nonatomic,
+	    test_prng_lg_range_zu_atomic,
+	    test_prng_range_u32_nonatomic,
+	    test_prng_range_u32_atomic,
+	    test_prng_range_u64_nonatomic,
+	    test_prng_range_zu_nonatomic,
+	    test_prng_range_zu_atomic));
 }