Add fxp: A fixed-point math library.
This will be used in the next commit to allow non-integer values for narenas_ratio.
This commit is contained in:
David Goldblatt
David Goldblatt
parent
99c2d6c232
commit
ecd39418ac
@ -118,6 +118,7 @@ C_SRCS := $(srcroot)src/jemalloc.c \
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$(srcroot)src/extent.c \
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$(srcroot)src/extent_dss.c \
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$(srcroot)src/extent_mmap.c \
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$(srcroot)src/fxp.c \
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$(srcroot)src/hook.c \
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$(srcroot)src/hpa.c \
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$(srcroot)src/hpa_central.c \
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@ -212,6 +213,7 @@ TESTS_UNIT := \
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$(srcroot)test/unit/extent_quantize.c \
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${srcroot}test/unit/flat_bitmap.c \
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$(srcroot)test/unit/fork.c \
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${srcroot}test/unit/fxp.c \
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$(srcroot)test/unit/hash.c \
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$(srcroot)test/unit/hook.c \
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$(srcroot)test/unit/hpa.c \
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100
include/jemalloc/internal/fxp.h
Normal file
100
include/jemalloc/internal/fxp.h
Normal file
@ -0,0 +1,100 @@
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#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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/*
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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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* 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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@ -58,6 +58,7 @@
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<ClCompile Include="..\..\..\..\src\extent.c" />
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<ClCompile Include="..\..\..\..\src\extent_dss.c" />
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<ClCompile Include="..\..\..\..\src\extent_mmap.c" />
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<ClCompile Include="..\..\..\..\src\fxp.c" />
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<ClCompile Include="..\..\..\..\src\hook.c" />
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<ClCompile Include="..\..\..\..\src\hpa.c" />
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<ClCompile Include="..\..\..\..\src\hpa_central.c" />
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@ -58,6 +58,9 @@
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<ClCompile Include="..\..\..\..\src\extent_mmap.c">
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<Filter>Source Files</Filter>
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</ClCompile>
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<ClCompile Include="..\..\..\..\src\fxp.c">
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<Filter>Source Files</Filter>
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</ClCompile>
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<ClCompile Include="..\..\..\..\src\hook.c">
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<Filter>Source Files</Filter>
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</ClCompile>
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@ -58,6 +58,7 @@
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<ClCompile Include="..\..\..\..\src\extent.c" />
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<ClCompile Include="..\..\..\..\src\extent_dss.c" />
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<ClCompile Include="..\..\..\..\src\extent_mmap.c" />
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<ClCompile Include="..\..\..\..\src\fxp.c" />
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<ClCompile Include="..\..\..\..\src\hook.c" />
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<ClCompile Include="..\..\..\..\src\hpa.c" />
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<ClCompile Include="..\..\..\..\src\hpa_central.c" />
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@ -58,6 +58,9 @@
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<ClCompile Include="..\..\..\..\src\extent_mmap.c">
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<Filter>Source Files</Filter>
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</ClCompile>
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<ClCompile Include="..\..\..\..\src\fxp.c">
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<Filter>Source Files</Filter>
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</ClCompile>
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<ClCompile Include="..\..\..\..\src\hook.c">
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<Filter>Source Files</Filter>
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</ClCompile>
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124
src/fxp.c
Normal file
124
src/fxp.c
Normal file
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#include "jemalloc/internal/jemalloc_preamble.h"
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#include "jemalloc/internal/jemalloc_internal_includes.h"
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#include "jemalloc/internal/fxp.h"
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static bool
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fxp_isdigit(char c) {
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return '0' <= c && c <= '9';
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}
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bool
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fxp_parse(fxp_t *result, const char *str, char **end) {
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/*
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* Using malloc_strtoumax in this method isn't as handy as you might
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* expect (I tried). In the fractional part, significant leading zeros
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* mean that you still need to do your own parsing, now with trickier
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* math. In the integer part, the casting (uintmax_t to uint32_t)
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* forces more reasoning about bounds than just checking for overflow as
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* we parse.
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*/
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uint32_t integer_part = 0;
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const char *cur = str;
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/* The string must start with a digit or a decimal point. */
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if (*cur != '.' && !fxp_isdigit(*cur)) {
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return true;
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}
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while ('0' <= *cur && *cur <= '9') {
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integer_part *= 10;
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integer_part += *cur - '0';
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if (integer_part >= (1U << 16)) {
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return true;
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}
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cur++;
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}
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/*
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* We've parsed all digits at the beginning of the string, without
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* overflow. Either we're done, or there's a fractional part.
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*/
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if (*cur != '.') {
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*result = (integer_part << 16);
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if (end != NULL) {
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*end = (char *)cur;
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}
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return false;
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}
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/* There's a fractional part. */
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cur++;
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if (!fxp_isdigit(*cur)) {
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/* Shouldn't end on the decimal point. */
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return true;
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}
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/*
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* We use a lot of precision for the fractional part, even though we'll
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* discard most of it; this lets us get exact values for the important
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* special case where the denominator is a small power of 2 (for
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* instance, 1/512 == 0.001953125 is exactly representable even with
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* only 16 bits of fractional precision). We need to left-shift by 16
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* before dividing so we pick the number of digits to be
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* floor(log(2**48)) = 14.
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*/
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uint64_t fractional_part = 0;
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uint64_t frac_div = 1;
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for (int i = 0; i < FXP_FRACTIONAL_PART_DIGITS; i++) {
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fractional_part *= 10;
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frac_div *= 10;
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if (fxp_isdigit(*cur)) {
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fractional_part += *cur - '0';
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cur++;
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}
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}
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/*
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* We only parse the first maxdigits characters, but we can still ignore
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* any digits after that.
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*/
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while (fxp_isdigit(*cur)) {
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cur++;
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}
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assert(fractional_part < frac_div);
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uint32_t fractional_repr = (uint32_t)(
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(fractional_part << 16) / frac_div);
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/* Success! */
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*result = (integer_part << 16) + fractional_repr;
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if (end != NULL) {
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*end = (char *)cur;
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}
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return false;
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}
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void
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fxp_print(fxp_t a, char buf[FXP_BUF_SIZE]) {
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uint32_t integer_part = fxp_round_down(a);
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uint32_t fractional_part = (a & ((1U << 16) - 1));
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int leading_fraction_zeros = 0;
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uint64_t fraction_digits = fractional_part;
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for (int i = 0; i < FXP_FRACTIONAL_PART_DIGITS; i++) {
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if (fraction_digits < (1U << 16)
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&& fraction_digits * 10 >= (1U << 16)) {
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leading_fraction_zeros = i;
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}
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fraction_digits *= 10;
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}
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fraction_digits >>= 16;
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while (fraction_digits > 0 && fraction_digits % 10 == 0) {
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fraction_digits /= 10;
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}
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size_t printed = malloc_snprintf(buf, FXP_BUF_SIZE, "%"FMTu32".",
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integer_part);
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for (int i = 0; i < leading_fraction_zeros; i++) {
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buf[printed] = '0';
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printed++;
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}
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malloc_snprintf(&buf[printed], FXP_BUF_SIZE - printed, "%"FMTu64,
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fraction_digits);
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}
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344
test/unit/fxp.c
Normal file
344
test/unit/fxp.c
Normal file
@ -0,0 +1,344 @@
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#include "test/jemalloc_test.h"
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#include "jemalloc/internal/fxp.h"
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static double
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fxp2double(fxp_t a) {
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double intpart = (double)(a >> 16);
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double fracpart = (double)(a & ((1U << 16) - 1)) / (1U << 16);
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return intpart + fracpart;
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}
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/* Is a close to b? */
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static bool
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double_close(double a, double b) {
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/*
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* Our implementation doesn't try for precision. Correspondingly, don't
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* enforce it too strenuously here; accept values that are close in
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* either relative or absolute terms.
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*/
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return fabs(a - b) < 0.01 || fabs(a - b) / a < 0.01;
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}
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static bool
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fxp_close(fxp_t a, fxp_t b) {
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return double_close(fxp2double(a), fxp2double(b));
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}
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static fxp_t
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xparse_fxp(const char *str) {
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fxp_t result;
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bool err = fxp_parse(&result, str, NULL);
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assert_false(err, "Invalid fxp string: %s", str);
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return result;
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}
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static void
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expect_parse_accurate(const char *str, const char *parse_str) {
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double true_val = strtod(str, NULL);
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fxp_t fxp_val;
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char *end;
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bool err = fxp_parse(&fxp_val, parse_str, &end);
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expect_false(err, "Unexpected parse failure");
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expect_ptr_eq(parse_str + strlen(str), end,
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"Didn't parse whole string");
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expect_true(double_close(fxp2double(fxp_val), true_val),
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"Misparsed %s", str);
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}
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static void
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parse_valid_trial(const char *str) {
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/* The value it parses should be correct. */
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expect_parse_accurate(str, str);
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char buf[100];
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snprintf(buf, sizeof(buf), "%swith_some_trailing_text", str);
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expect_parse_accurate(str, buf);
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snprintf(buf, sizeof(buf), "%s with a space", str);
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expect_parse_accurate(str, buf);
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snprintf(buf, sizeof(buf), "%s,in_a_malloc_conf_string:1", str);
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expect_parse_accurate(str, buf);
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}
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TEST_BEGIN(test_parse_valid) {
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parse_valid_trial("0");
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parse_valid_trial("1");
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parse_valid_trial("2");
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parse_valid_trial("100");
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parse_valid_trial("345");
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parse_valid_trial("00000000123");
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parse_valid_trial("00000000987");
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parse_valid_trial("0.0");
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parse_valid_trial("0.00000000000456456456");
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parse_valid_trial("100.00000000000456456456");
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parse_valid_trial("123.1");
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parse_valid_trial("123.01");
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parse_valid_trial("123.001");
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parse_valid_trial("123.0001");
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parse_valid_trial("123.00001");
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parse_valid_trial("123.000001");
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parse_valid_trial("123.0000001");
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parse_valid_trial(".0");
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parse_valid_trial(".1");
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parse_valid_trial(".01");
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parse_valid_trial(".001");
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parse_valid_trial(".0001");
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parse_valid_trial(".00001");
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parse_valid_trial(".000001");
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parse_valid_trial(".1");
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parse_valid_trial(".10");
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parse_valid_trial(".100");
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parse_valid_trial(".1000");
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parse_valid_trial(".100000");
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}
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TEST_END
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static void expect_parse_failure(const char *str) {
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fxp_t result = FXP_INIT_INT(333);
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char *end = (void *)0x123;
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bool err = fxp_parse(&result, str, &end);
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expect_true(err, "Expected a parse error on: %s", str);
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expect_ptr_eq((void *)0x123, end,
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"Parse error shouldn't change results");
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expect_u32_eq(result, FXP_INIT_INT(333),
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"Parse error shouldn't change results");
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}
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TEST_BEGIN(test_parse_invalid) {
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expect_parse_failure("123.");
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expect_parse_failure("3.a");
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expect_parse_failure(".a");
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expect_parse_failure("a.1");
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expect_parse_failure("a");
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/* A valid string, but one that overflows. */
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expect_parse_failure("123456789");
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expect_parse_failure("0000000123456789");
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expect_parse_failure("1000000");
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}
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TEST_END
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static void
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expect_add(const char *astr, const char *bstr, const char* resultstr) {
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fxp_t a = xparse_fxp(astr);
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fxp_t b = xparse_fxp(bstr);
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fxp_t result = xparse_fxp(resultstr);
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expect_true(fxp_close(fxp_add(a, b), result),
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"Expected %s + %s == %s", astr, bstr, resultstr);
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}
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TEST_BEGIN(test_add_simple) {
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expect_add("0", "0", "0");
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expect_add("0", "1", "1");
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expect_add("1", "1", "2");
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expect_add("1.5", "1.5", "3");
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expect_add("0.1", "0.1", "0.2");
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expect_add("123", "456", "579");
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}
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TEST_END
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static void
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expect_sub(const char *astr, const char *bstr, const char* resultstr) {
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fxp_t a = xparse_fxp(astr);
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fxp_t b = xparse_fxp(bstr);
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fxp_t result = xparse_fxp(resultstr);
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expect_true(fxp_close(fxp_sub(a, b), result),
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"Expected %s - %s == %s", astr, bstr, resultstr);
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}
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TEST_BEGIN(test_sub_simple) {
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expect_sub("0", "0", "0");
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expect_sub("1", "0", "1");
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expect_sub("1", "1", "0");
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expect_sub("3.5", "1.5", "2");
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expect_sub("0.3", "0.1", "0.2");
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expect_sub("456", "123", "333");
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}
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TEST_END
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static void
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expect_mul(const char *astr, const char *bstr, const char* resultstr) {
|
||||
fxp_t a = xparse_fxp(astr);
|
||||
fxp_t b = xparse_fxp(bstr);
|
||||
fxp_t result = xparse_fxp(resultstr);
|
||||
expect_true(fxp_close(fxp_mul(a, b), result),
|
||||
"Expected %s * %s == %s", astr, bstr, resultstr);
|
||||
}
|
||||
|
||||
TEST_BEGIN(test_mul_simple) {
|
||||
expect_mul("0", "0", "0");
|
||||
expect_mul("1", "0", "0");
|
||||
expect_mul("1", "1", "1");
|
||||
expect_mul("1.5", "1.5", "2.25");
|
||||
expect_mul("100.0", "10", "1000");
|
||||
expect_mul(".1", "10", "1");
|
||||
}
|
||||
TEST_END
|
||||
|
||||
static void
|
||||
expect_div(const char *astr, const char *bstr, const char* resultstr) {
|
||||
fxp_t a = xparse_fxp(astr);
|
||||
fxp_t b = xparse_fxp(bstr);
|
||||
fxp_t result = xparse_fxp(resultstr);
|
||||
expect_true(fxp_close(fxp_div(a, b), result),
|
||||
"Expected %s / %s == %s", astr, bstr, resultstr);
|
||||
}
|
||||
|
||||
TEST_BEGIN(test_div_simple) {
|
||||
expect_div("1", "1", "1");
|
||||
expect_div("0", "1", "0");
|
||||
expect_div("2", "1", "2");
|
||||
expect_div("3", "2", "1.5");
|
||||
expect_div("3", "1.5", "2");
|
||||
expect_div("10", ".1", "100");
|
||||
expect_div("123", "456", ".2697368421");
|
||||
}
|
||||
TEST_END
|
||||
|
||||
static void
|
||||
expect_round(const char *str, uint32_t rounded_down, uint32_t rounded_nearest) {
|
||||
fxp_t fxp = xparse_fxp(str);
|
||||
uint32_t fxp_rounded_down = fxp_round_down(fxp);
|
||||
uint32_t fxp_rounded_nearest = fxp_round_nearest(fxp);
|
||||
expect_u32_eq(rounded_down, fxp_rounded_down,
|
||||
"Mistake rounding %s down", str);
|
||||
expect_u32_eq(rounded_nearest, fxp_rounded_nearest,
|
||||
"Mistake rounding %s to nearest", str);
|
||||
}
|
||||
|
||||
TEST_BEGIN(test_round_simple) {
|
||||
expect_round("1.5", 1, 2);
|
||||
expect_round("0", 0, 0);
|
||||
expect_round("0.1", 0, 0);
|
||||
expect_round("0.4", 0, 0);
|
||||
expect_round("0.40000", 0, 0);
|
||||
expect_round("0.5", 0, 1);
|
||||
expect_round("0.6", 0, 1);
|
||||
expect_round("123", 123, 123);
|
||||
expect_round("123.4", 123, 123);
|
||||
expect_round("123.5", 123, 124);
|
||||
}
|
||||
TEST_END
|
||||
|
||||
static void
|
||||
expect_print(const char *str) {
|
||||
fxp_t fxp = xparse_fxp(str);
|
||||
char buf[FXP_BUF_SIZE];
|
||||
fxp_print(fxp, buf);
|
||||
expect_d_eq(0, strcmp(str, buf), "Couldn't round-trip print %s", str);
|
||||
}
|
||||
|
||||
TEST_BEGIN(test_print_simple) {
|
||||
expect_print("0.0");
|
||||
expect_print("1.0");
|
||||
expect_print("2.0");
|
||||
expect_print("123.0");
|
||||
/*
|
||||
* We hit the possibility of roundoff errors whenever the fractional
|
||||
* component isn't a round binary number; only check these here (we
|
||||
* round-trip properly in the stress test).
|
||||
*/
|
||||
expect_print("1.5");
|
||||
expect_print("3.375");
|
||||
expect_print("0.25");
|
||||
expect_print("0.125");
|
||||
/* 1 / 2**14 */
|
||||
expect_print("0.00006103515625");
|
||||
}
|
||||
TEST_END
|
||||
|
||||
TEST_BEGIN(test_stress) {
|
||||
const char *numbers[] = {
|
||||
"0.0", "0.1", "0.2", "0.3", "0.4",
|
||||
"0.5", "0.6", "0.7", "0.8", "0.9",
|
||||
|
||||
"1.0", "1.1", "1.2", "1.3", "1.4",
|
||||
"1.5", "1.6", "1.7", "1.8", "1.9",
|
||||
|
||||
"2.0", "2.1", "2.2", "2.3", "2.4",
|
||||
"2.5", "2.6", "2.7", "2.8", "2.9",
|
||||
|
||||
"17.0", "17.1", "17.2", "17.3", "17.4",
|
||||
"17.5", "17.6", "17.7", "17.8", "17.9",
|
||||
|
||||
"18.0", "18.1", "18.2", "18.3", "18.4",
|
||||
"18.5", "18.6", "18.7", "18.8", "18.9",
|
||||
|
||||
"123.0", "123.1", "123.2", "123.3", "123.4",
|
||||
"123.5", "123.6", "123.7", "123.8", "123.9",
|
||||
|
||||
"124.0", "124.1", "124.2", "124.3", "124.4",
|
||||
"124.5", "124.6", "124.7", "124.8", "124.9",
|
||||
|
||||
"125.0", "125.1", "125.2", "125.3", "125.4",
|
||||
"125.5", "125.6", "125.7", "125.8", "125.9"};
|
||||
size_t numbers_len = sizeof(numbers)/sizeof(numbers[0]);
|
||||
for (size_t i = 0; i < numbers_len; i++) {
|
||||
fxp_t fxp_a = xparse_fxp(numbers[i]);
|
||||
double double_a = strtod(numbers[i], NULL);
|
||||
|
||||
uint32_t fxp_rounded_down = fxp_round_down(fxp_a);
|
||||
uint32_t fxp_rounded_nearest = fxp_round_nearest(fxp_a);
|
||||
uint32_t double_rounded_down = (uint32_t)double_a;
|
||||
uint32_t double_rounded_nearest = (uint32_t)round(double_a);
|
||||
|
||||
expect_u32_eq(double_rounded_down, fxp_rounded_down,
|
||||
"Incorrectly rounded down %s", numbers[i]);
|
||||
expect_u32_eq(double_rounded_nearest, fxp_rounded_nearest,
|
||||
"Incorrectly rounded-to-nearest %s", numbers[i]);
|
||||
|
||||
for (size_t j = 0; j < numbers_len; j++) {
|
||||
fxp_t fxp_b = xparse_fxp(numbers[j]);
|
||||
double double_b = strtod(numbers[j], NULL);
|
||||
|
||||
fxp_t fxp_sum = fxp_add(fxp_a, fxp_b);
|
||||
double double_sum = double_a + double_b;
|
||||
expect_true(
|
||||
double_close(fxp2double(fxp_sum), double_sum),
|
||||
"Miscomputed %s + %s", numbers[i], numbers[j]);
|
||||
|
||||
if (double_a > double_b) {
|
||||
fxp_t fxp_diff = fxp_sub(fxp_a, fxp_b);
|
||||
double double_diff = double_a - double_b;
|
||||
expect_true(
|
||||
double_close(fxp2double(fxp_diff),
|
||||
double_diff),
|
||||
"Miscomputed %s - %s", numbers[i],
|
||||
numbers[j]);
|
||||
}
|
||||
|
||||
fxp_t fxp_prod = fxp_mul(fxp_a, fxp_b);
|
||||
double double_prod = double_a * double_b;
|
||||
expect_true(
|
||||
double_close(fxp2double(fxp_prod), double_prod),
|
||||
"Miscomputed %s * %s", numbers[i], numbers[j]);
|
||||
|
||||
if (double_b != 0.0) {
|
||||
fxp_t fxp_quot = fxp_div(fxp_a, fxp_b);
|
||||
double double_quot = double_a / double_b;
|
||||
expect_true(
|
||||
double_close(fxp2double(fxp_quot),
|
||||
double_quot),
|
||||
"Miscomputed %s / %s", numbers[i],
|
||||
numbers[j]);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
TEST_END
|
||||
|
||||
int
|
||||
main(void) {
|
||||
return test_no_reentrancy(
|
||||
test_parse_valid,
|
||||
test_parse_invalid,
|
||||
test_add_simple,
|
||||
test_sub_simple,
|
||||
test_mul_simple,
|
||||
test_div_simple,
|
||||
test_round_simple,
|
||||
test_print_simple,
|
||||
test_stress);
|
||||
}
|
||||
Loading…
Reference in New Issue
Block a user