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BLI_math 'compare' cleanup & enhancements.

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This commit:
* Adds a 'compare_ff' function for absolute 'almost equal' comparison of floats.
* Makes 'compare_vxvx' functions use that new 'compare_ff' one.
* Adds a 'compare_ff_relative' function for secured ulp-based relative comparison of floats.
* Adds matching 'compare_vxvx_relative' functions.
* Adds some basic tests for compare_ff_relative.

See https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/

Note that we could replace our python/mathutils' EXPP_FloatsAreEqual() by BLI's compare_ff_relative
(using a very small absolute max_diff), but these do not have exact same behavior...
Left a comment there for now, we can do it later if/when we are sure it won't break anything!
This commit is contained in:
Bastien Montagne 2015-07-10 14:32:35 +02:00
parent bbcbd2eed9
commit 7837f0e833
7 changed files with 183 additions and 25 deletions
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3
source/blender/blenlib/BLI_math_base.h
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@ -196,6 +196,9 @@ MINLINE int max_iii(int a, int b, int c);
MINLINE int min_iiii(int a, int b, int c, int d);
MINLINE int max_iiii(int a, int b, int c, int d);
MINLINE int compare_ff(float a, float b, const float max_diff);
MINLINE int compare_ff_relative(float a, float b, const float max_diff, const int max_ulps);
MINLINE float signf(float f);
MINLINE int signum_i_ex(float a, float eps);
MINLINE int signum_i(float a);

11
source/blender/blenlib/BLI_math_vector.h
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@ -240,14 +240,19 @@ MINLINE bool is_one_v3(const float a[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v2v2(const float v1[2], const float v2[2]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v3v3(const float a[3], const float b[3]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v4v4(const float a[4], const float b[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v2v2(const float a[2], const float b[2], const float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v3v3(const float a[3], const float b[3], const float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v4v4(const float a[4], const float b[4], const float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v2v2_relative(const float a[2], const float b[2], const float limit, const int max_ulps) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v3v3_relative(const float a[3], const float b[3], const float limit, const int max_ulps) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v4v4_relative(const float a[4], const float b[4], const float limit, const int max_ulps) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_len_v3v3(const float a[3], const float b[3], const float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_len_squared_v3v3(const float a[3], const float b[3], const float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool compare_v4v4(const float a[4], const float b[4], const float limit) ATTR_WARN_UNUSED_RESULT;
MINLINE bool equals_v4v4(const float a[4], const float b[4]) ATTR_WARN_UNUSED_RESULT;
MINLINE float line_point_side_v2(const float l1[2], const float l2[2], const float pt[2]) ATTR_WARN_UNUSED_RESULT;
/********************************** Angles ***********************************/

40
source/blender/blenlib/intern/math_base_inline.c
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@ -252,6 +252,46 @@ MINLINE int max_iiii(int a, int b, int c, int d)
return max_ii(max_iii(a, b, c), d);
}
/**
* Almost-equal for IEEE floats, using absolute difference method.
*
* \param max_diff the maximum absolute difference.
*/
MINLINE int compare_ff(float a, float b, const float max_diff)
{
return fabsf(a - b) <= max_diff;
}
/**
* Almost-equal for IEEE floats, using their integer representation (mixing ULP and absolute difference methods).
*
* \param max_diff is the maximum absolute difference (allows to take care of the near-zero area,
* where relative difference methods cannot really work).
* \param max_ulps is the 'maximum number of floats + 1' allowed between \a a and \a b to consider them equal.
*
* \see https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/
*/
MINLINE int compare_ff_relative(float a, float b, const float max_diff, const int max_ulps)
{
union {float f; int i;} ua, ub;
#if 0 /* No BLI_assert in INLINE :/ */
BLI_assert(sizeof(float) == sizeof(int));
BLI_assert(max_ulps < (1 << 22));
#endif
if (fabsf(a - b) <= max_diff) {
return 1;
}
ua.f = a;
ub.f = b;
/* Important to compare sign from integers, since (-0.0f < 0) is false
* (though this shall not be an issue in common cases)... */
return ((ua.i < 0) != (ub.i < 0)) ? 0 : (abs(ua.i - ub.i) <= max_ulps) ? 1 : 0;
}
MINLINE float signf(float f)
{
return (f < 0.f) ? -1.f : 1.f;

57
source/blender/blenlib/intern/math_vector_inline.c
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@ -966,23 +966,47 @@ MINLINE bool equals_v4v4(const float v1[4], const float v2[4])
MINLINE bool compare_v2v2(const float v1[2], const float v2[2], const float limit)
{
if (fabsf(v1[0] - v2[0]) <= limit)
if (fabsf(v1[1] - v2[1]) <= limit)
return true;
return false;
return (compare_ff(v1[0], v2[0], limit) &&
compare_ff(v1[1], v2[1], limit));
}
MINLINE bool compare_v3v3(const float v1[3], const float v2[3], const float limit)
{
if (fabsf(v1[0] - v2[0]) <= limit)
if (fabsf(v1[1] - v2[1]) <= limit)
if (fabsf(v1[2] - v2[2]) <= limit)
return true;
return false;
return (compare_ff(v1[0], v2[0], limit) &&
compare_ff(v1[1], v2[1], limit) &&
compare_ff(v1[2], v2[2], limit));
}
MINLINE bool compare_v4v4(const float v1[4], const float v2[4], const float limit)
{
return (compare_ff(v1[0], v2[0], limit) &&
compare_ff(v1[1], v2[1], limit) &&
compare_ff(v1[2], v2[2], limit) &&
compare_ff(v1[3], v2[3], limit));
}
MINLINE bool compare_v2v2_relative(const float v1[2], const float v2[2], const float limit, const int max_ulps)
{
return (compare_ff_relative(v1[0], v2[0], limit, max_ulps) &&
compare_ff_relative(v1[1], v2[1], limit, max_ulps));
}
MINLINE bool compare_v3v3_relative(const float v1[3], const float v2[3], const float limit, const int max_ulps)
{
return (compare_ff_relative(v1[0], v2[0], limit, max_ulps) &&
compare_ff_relative(v1[1], v2[1], limit, max_ulps) &&
compare_ff_relative(v1[2], v2[2], limit, max_ulps));
}
MINLINE bool compare_v4v4_relative(const float v1[4], const float v2[4], const float limit, const int max_ulps)
{
return (compare_ff_relative(v1[0], v2[0], limit, max_ulps) &&
compare_ff_relative(v1[1], v2[1], limit, max_ulps) &&
compare_ff_relative(v1[2], v2[2], limit, max_ulps) &&
compare_ff_relative(v1[3], v2[3], limit, max_ulps));
}
MINLINE bool compare_len_v3v3(const float v1[3], const float v2[3], const float limit)
{
float x, y, z;
@ -1005,17 +1029,6 @@ MINLINE bool compare_len_squared_v3v3(const float v1[3], const float v2[3], cons
return ((x * x + y * y + z * z) <= limit_sq);
}
MINLINE bool compare_v4v4(const float v1[4], const float v2[4], const float limit)
{
if (fabsf(v1[0] - v2[0]) <= limit)
if (fabsf(v1[1] - v2[1]) <= limit)
if (fabsf(v1[2] - v2[2]) <= limit)
if (fabsf(v1[3] - v2[3]) <= limit)
return true;
return false;
}
/**
* <pre>
* + l1

9
source/blender/python/mathutils/mathutils.c
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@ -348,6 +348,15 @@ int mathutils_any_to_rotmat(float rmat[3][3], PyObject *value, const char *error
/* Utility functions */
/* LomontRRDCompare4, Ever Faster Float Comparisons by Randy Dillon */
/* XXX We may want to use 'safer' BLI's compare_ff_relative ultimately?
* LomontRRDCompare4() is an optimized version of Dawson's AlmostEqual2sComplement() (see [1] and [2]).
* Dawson himself now claims this is not a 'safe' thing to do (pushing ULP method beyond its limits),
* an recommands using work from [3] instead, which is done in BLI func...
*
* [1] http://www.randydillon.org/Papers/2007/everfast.htm
* [2] http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
* [3] https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/ instead
*/
#define SIGNMASK(i) (-(int)(((unsigned int)(i)) >> 31))
int EXPP_FloatsAreEqual(float af, float bf, int maxDiff)

87
tests/gtests/blenlib/BLI_math_base_test.cc Normal file
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@ -0,0 +1,87 @@
/* Apache License, Version 2.0 */
#include "testing/testing.h"
#include "BLI_math.h"
/* In tests below, when we are using -1.0f as max_diff value, we actually turn the function into a pure-ULP one. */
/* Put this here, since we cannot use BLI_assert() in inline math files it seems... */
TEST(math_base, CompareFFRelativeValid)
{
EXPECT_TRUE(sizeof(float) == sizeof(int));
}
TEST(math_base, CompareFFRelativeNormal)
{
float f1 = 1.99999988f; /* *(float *)&(*(int *)&f2 - 1) */
float f2 = 2.00000000f;
float f3 = 2.00000048f; /* *(float *)&(*(int *)&f2 + 2) */
float f4 = 2.10000000f; /* *(float *)&(*(int *)&f2 + 419430) */
const float max_diff = FLT_EPSILON * 0.1f;
EXPECT_TRUE(compare_ff_relative(f1, f2, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(f2, f1, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(f3, f2, max_diff, 2));
EXPECT_TRUE(compare_ff_relative(f2, f3, max_diff, 2));
EXPECT_FALSE(compare_ff_relative(f3, f2, max_diff, 1));
EXPECT_FALSE(compare_ff_relative(f2, f3, max_diff, 1));
EXPECT_FALSE(compare_ff_relative(f3, f2, -1.0f, 1));
EXPECT_FALSE(compare_ff_relative(f2, f3, -1.0f, 1));
EXPECT_TRUE(compare_ff_relative(f3, f2, -1.0f, 2));
EXPECT_TRUE(compare_ff_relative(f2, f3, -1.0f, 2));
EXPECT_FALSE(compare_ff_relative(f4, f2, max_diff, 64));
EXPECT_FALSE(compare_ff_relative(f2, f4, max_diff, 64));
EXPECT_TRUE(compare_ff_relative(f1, f3, max_diff, 64));
EXPECT_TRUE(compare_ff_relative(f3, f1, max_diff, 64));
}
TEST(math_base, CompareFFRelativeZero)
{
float f0 = 0.0f;
float f1 = 4.2038954e-045f; /* *(float *)&(*(int *)&f0 + 3) */
float fn0 = -0.0f;
float fn1 = -2.8025969e-045f; /* *(float *)&(*(int *)&fn0 - 2) */
const float max_diff = FLT_EPSILON * 0.1f;
EXPECT_TRUE(compare_ff_relative(f0, f1, -1.0f, 3));
EXPECT_TRUE(compare_ff_relative(f1, f0, -1.0f, 3));
EXPECT_FALSE(compare_ff_relative(f0, f1, -1.0f, 1));
EXPECT_FALSE(compare_ff_relative(f1, f0, -1.0f, 1));
EXPECT_TRUE(compare_ff_relative(fn0, fn1, -1.0f, 8));
EXPECT_TRUE(compare_ff_relative(fn1, fn0, -1.0f, 8));
EXPECT_TRUE(compare_ff_relative(f0, f1, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(f1, f0, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(fn0, f0, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(f0, fn0, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(f0, fn1, max_diff, 1));
EXPECT_TRUE(compare_ff_relative(fn1, f0, max_diff, 1));
/* Note: in theory, this should return false, since 0.0f and -0.0f have 0x80000000 diff,
* but overflow in substraction seems to break something here
* (abs(*(int *)&fn0 - *(int *)&f0) == 0x80000000 == fn0), probably because int32 cannot hold this abs value.
* this is yet another illustration of why one shall never use (near-)zero floats in pure-ULP comparison. */
// EXPECT_FALSE(compare_ff_relative(fn0, f0, -1.0f, 1024));
// EXPECT_FALSE(compare_ff_relative(f0, fn0, -1.0f, 1024));
EXPECT_FALSE(compare_ff_relative(fn0, f1, -1.0f, 1024));
EXPECT_FALSE(compare_ff_relative(f1, fn0, -1.0f, 1024));
}

1
tests/gtests/blenlib/CMakeLists.txt
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@ -38,6 +38,7 @@ set(CMAKE_EXE_LINKER_FLAGS_DEBUG "${CMAKE_EXE_LINKER_FLAGS_DEBUG} ${PLATFORM_LIN
BLENDER_TEST(BLI_stack "bf_blenlib")
BLENDER_TEST(BLI_math_color "bf_blenlib")
BLENDER_TEST(BLI_math_geom "bf_blenlib")
BLENDER_TEST(BLI_math_base "bf_blenlib")
BLENDER_TEST(BLI_string "bf_blenlib")
BLENDER_TEST(BLI_path_util "bf_blenlib;extern_wcwidth;${ZLIB_LIBRARIES}")
BLENDER_TEST(BLI_polyfill2d "bf_blenlib")