Add fxp: A fixed-point math library.

This will be used in the next commit to allow non-integer values for
narenas_ratio.

include/jemalloc/internal/fxp.h

@@ -0,0 +1,100 @@
+#ifndef JEMALLOC_INTERNAL_FXP_H
+#define JEMALLOC_INTERNAL_FXP_H
+
+/*
+ * A simple fixed-point math implementation, supporting only unsigned values
+ * (with overflow being an error).
+ *
+ * It's not in general safe to use floating point in core code, because various
+ * libc implementations we get linked against can assume that malloc won't touch
+ * floating point state and call it with an unusual calling convention.
+ */
+
+/*
+ * High 16 bits are the integer part, low 16 are the fractional part.  Or
+ * equivalently, repr == 2**16 * val, where we use "val" to refer to the
+ * (imaginary) fractional representation of the true value.
+ *
+ * We pick a uint32_t here since it's convenient in some places to
+ * double the representation size (i.e. multiplication and division use
+ * 64-bit integer types), and a uint64_t is the largest type we're
+ * certain is available.
+ */
+typedef uint32_t fxp_t;
+#define FXP_INIT_INT(x) ((x) << 16)
+
+/*
+ * Amount of precision used in parsing and printing numbers.  The integer bound
+ * is simply because the integer part of the number gets 16 bits, and so is
+ * bounded by 65536.
+ *
+ * We use a lot of precision for the fractional part, even though most of it
+ * gets rounded off; this lets us get exact values for the important special
+ * case where the denominator is a small power of 2 (for instance,
+ * 1/512 == 0.001953125 is exactly representable even with only 16 bits of
+ * fractional precision).  We need to left-shift by 16 before dividing by
+ * 10**precision, so we pick precision to be floor(log(2**48)) = 14.
+ */
+#define FXP_INTEGER_PART_DIGITS 5
+#define FXP_FRACTIONAL_PART_DIGITS 14
+
+/*
+ * In addition to the integer and fractional parts of the number, we need to
+ * include a null character and (possibly) a decimal point.
+ */
+#define FXP_BUF_SIZE (FXP_INTEGER_PART_DIGITS + FXP_FRACTIONAL_PART_DIGITS + 2)
+
+static inline fxp_t
+fxp_add(fxp_t a, fxp_t b) {
+	return a + b;
+}
+
+static inline fxp_t
+fxp_sub(fxp_t a, fxp_t b) {
+	assert(a >= b);
+	return a - b;
+}
+
+static inline fxp_t
+fxp_mul(fxp_t a, fxp_t b) {
+	uint64_t unshifted = (uint64_t)a * (uint64_t)b;
+	/*
+	 * Unshifted is (a.val * 2**16) * (b.val * 2**16)
+	 *   == (a.val * b.val) * 2**32, but we want
+	 * (a.val * b.val) * 2 ** 16.
+	 */
+	return (uint32_t)(unshifted >> 16);
+}
+
+static inline fxp_t
+fxp_div(fxp_t a, fxp_t b) {
+	assert(b != 0);
+	uint64_t unshifted = ((uint64_t)a << 32) / (uint64_t)b;
+	/*
+	 * Unshifted is (a.val * 2**16) * (2**32) / (b.val * 2**16)
+	 *   == (a.val / b.val) * (2 ** 32), which again corresponds to a right
+	 *   shift of 16.
+	 */
+	return (uint32_t)(unshifted >> 16);
+}
+
+static inline uint32_t
+fxp_round_down(fxp_t a) {
+	return a >> 16;
+}
+
+static inline uint32_t
+fxp_round_nearest(fxp_t a) {
+	uint32_t fractional_part = (a  & ((1U << 16) - 1));
+	uint32_t increment = (uint32_t)(fractional_part >= (1U << 15));
+	return (a >> 16) + increment;
+}
+
+/*
+ * Returns true on error.  Otherwise, returns false and updates *ptr to point to
+ * the first character not parsed (because it wasn't a digit).
+ */
+bool fxp_parse(fxp_t *a, const char *ptr, char **end);
+void fxp_print(fxp_t a, char buf[FXP_BUF_SIZE]);
+
+#endif /* JEMALLOC_INTERNAL_FXP_H */