127 lines
3.9 KiB
C
127 lines
3.9 KiB
C
#ifndef JEMALLOC_INTERNAL_FXP_H
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#define JEMALLOC_INTERNAL_FXP_H
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/*
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* A simple fixed-point math implementation, supporting only unsigned values
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* (with overflow being an error).
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*
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* It's not in general safe to use floating point in core code, because various
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* libc implementations we get linked against can assume that malloc won't touch
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* floating point state and call it with an unusual calling convention.
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*/
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/*
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* High 16 bits are the integer part, low 16 are the fractional part. Or
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* equivalently, repr == 2**16 * val, where we use "val" to refer to the
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* (imaginary) fractional representation of the true value.
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*
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* We pick a uint32_t here since it's convenient in some places to
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* double the representation size (i.e. multiplication and division use
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* 64-bit integer types), and a uint64_t is the largest type we're
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* certain is available.
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*/
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typedef uint32_t fxp_t;
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#define FXP_INIT_INT(x) ((x) << 16)
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#define FXP_INIT_PERCENT(pct) (((pct) << 16) / 100)
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/*
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* Amount of precision used in parsing and printing numbers. The integer bound
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* is simply because the integer part of the number gets 16 bits, and so is
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* bounded by 65536.
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*
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* We use a lot of precision for the fractional part, even though most of it
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* gets rounded off; this lets us get exact values for the important special
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* case where the denominator is a small power of 2 (for instance,
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* 1/512 == 0.001953125 is exactly representable even with only 16 bits of
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* fractional precision). We need to left-shift by 16 before dividing by
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* 10**precision, so we pick precision to be floor(log(2**48)) = 14.
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*/
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#define FXP_INTEGER_PART_DIGITS 5
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#define FXP_FRACTIONAL_PART_DIGITS 14
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/*
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* In addition to the integer and fractional parts of the number, we need to
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* include a null character and (possibly) a decimal point.
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*/
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#define FXP_BUF_SIZE (FXP_INTEGER_PART_DIGITS + FXP_FRACTIONAL_PART_DIGITS + 2)
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static inline fxp_t
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fxp_add(fxp_t a, fxp_t b) {
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return a + b;
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}
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static inline fxp_t
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fxp_sub(fxp_t a, fxp_t b) {
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assert(a >= b);
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return a - b;
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}
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static inline fxp_t
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fxp_mul(fxp_t a, fxp_t b) {
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uint64_t unshifted = (uint64_t)a * (uint64_t)b;
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/*
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* Unshifted is (a.val * 2**16) * (b.val * 2**16)
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* == (a.val * b.val) * 2**32, but we want
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* (a.val * b.val) * 2 ** 16.
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*/
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return (uint32_t)(unshifted >> 16);
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}
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static inline fxp_t
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fxp_div(fxp_t a, fxp_t b) {
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assert(b != 0);
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uint64_t unshifted = ((uint64_t)a << 32) / (uint64_t)b;
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/*
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* Unshifted is (a.val * 2**16) * (2**32) / (b.val * 2**16)
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* == (a.val / b.val) * (2 ** 32), which again corresponds to a right
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* shift of 16.
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*/
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return (uint32_t)(unshifted >> 16);
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}
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static inline uint32_t
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fxp_round_down(fxp_t a) {
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return a >> 16;
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}
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static inline uint32_t
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fxp_round_nearest(fxp_t a) {
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uint32_t fractional_part = (a & ((1U << 16) - 1));
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uint32_t increment = (uint32_t)(fractional_part >= (1U << 15));
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return (a >> 16) + increment;
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}
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/*
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* Approximately computes x * frac, without the size limitations that would be
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* imposed by converting u to an fxp_t.
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*/
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static inline size_t
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fxp_mul_frac(size_t x_orig, fxp_t frac) {
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assert(frac <= (1U << 16));
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/*
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* Work around an over-enthusiastic warning about type limits below (on
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* 32-bit platforms, a size_t is always less than 1ULL << 48).
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*/
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uint64_t x = (uint64_t)x_orig;
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/*
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* If we can guarantee no overflow, multiply first before shifting, to
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* preserve some precision. Otherwise, shift first and then multiply.
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* In the latter case, we only lose the low 16 bits of a 48-bit number,
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* so we're still accurate to within 1/2**32.
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*/
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if (x < (1ULL << 48)) {
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return (size_t)((x * frac) >> 16);
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} else {
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return (size_t)((x >> 16) * (uint64_t)frac);
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}
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}
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/*
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* Returns true on error. Otherwise, returns false and updates *ptr to point to
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* the first character not parsed (because it wasn't a digit).
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*/
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bool fxp_parse(fxp_t *a, const char *ptr, char **end);
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void fxp_print(fxp_t a, char buf[FXP_BUF_SIZE]);
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#endif /* JEMALLOC_INTERNAL_FXP_H */
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