FXP: add fxp_mul_frac.

This can multiply size_ts by a fraction without the risk of overflow.

include/jemalloc/internal/fxp.h

@@ -90,6 +90,31 @@ fxp_round_nearest(fxp_t a) {
 	return (a >> 16) + increment;
 }
 
+/*
+ * Approximately computes x * frac, without the size limitations that would be
+ * imposed by converting u to an fxp_t.
+ */
+static inline size_t
+fxp_mul_frac(size_t x_orig, fxp_t frac) {
+	assert(frac <= (1U << 16));
+	/*
+	 * Work around an over-enthusiastic warning about type limits below (on
+	 * 32-bit platforms, a size_t is always less than 1ULL << 48).
+	 */
+	uint64_t x = (uint64_t)x_orig;
+	/*
+	 * If we can guarantee no overflow, multiply first before shifting, to
+	 * preserve some precision.  Otherwise, shift first and then multiply.
+	 * In the latter case, we only lose the low 16 bits of a 48-bit number,
+	 * so we're still accurate to within 1/2**32.
+	 */
+	if (x < (1ULL << 48)) {
+		return (size_t)((x * frac) >> 16);
+	} else {
+		return (size_t)((x >> 16) * (uint64_t)frac);
+	}
+}
+
 /*
  * Returns true on error.  Otherwise, returns false and updates *ptr to point to
  * the first character not parsed (because it wasn't a digit).

test/unit/fxp.c

@@ -222,6 +222,30 @@ TEST_BEGIN(test_round_simple) {
 }
 TEST_END
 
+static void
+expect_mul_frac(size_t a, const char *fracstr, size_t expected) {
+	fxp_t frac = xparse_fxp(fracstr);
+	size_t result = fxp_mul_frac(a, frac);
+	expect_true(double_close(expected, result),
+	    "Expected %zu * %s == %zu (fracmul); got %zu", a, fracstr,
+	    expected, result);
+}
+
+TEST_BEGIN(test_mul_frac_simple) {
+	expect_mul_frac(SIZE_MAX, "1.0", SIZE_MAX);
+	expect_mul_frac(SIZE_MAX, ".75", SIZE_MAX / 4 * 3);
+	expect_mul_frac(SIZE_MAX, ".5", SIZE_MAX / 2);
+	expect_mul_frac(SIZE_MAX, ".25", SIZE_MAX / 4);
+	expect_mul_frac(1U << 16, "1.0", 1U << 16);
+	expect_mul_frac(1U << 30, "0.5", 1U << 29);
+	expect_mul_frac(1U << 30, "0.25", 1U << 28);
+	expect_mul_frac(1U << 30, "0.125", 1U << 27);
+	expect_mul_frac((1U << 30) + 1, "0.125", 1U << 27);
+	expect_mul_frac(100, "0.25", 25);
+	expect_mul_frac(1000 * 1000, "0.001", 1000);
+}
+TEST_END
+
 static void
 expect_print(const char *str) {
 	fxp_t fxp = xparse_fxp(str);
@@ -339,6 +363,7 @@ main(void) {
 	    test_mul_simple,
 	    test_div_simple,
 	    test_round_simple,
+	    test_mul_frac_simple,
 	    test_print_simple,
 	    test_stress);
 }