[Bf-blender-cvs] [7837f0e] master: BLI_math 'compare' cleanup & enhancements.
Bastien Montagne
noreply at git.blender.org
Fri Jul 10 15:26:40 CEST 2015
Commit: 7837f0e8332f3726e0322b0c48b0da4d7c2d5813
Author: Bastien Montagne
Date: Fri Jul 10 14:32:35 2015 +0200
Branches: master
https://developer.blender.org/rB7837f0e8332f3726e0322b0c48b0da4d7c2d5813
BLI_math 'compare' cleanup & enhancements.
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!
===================================================================
M source/blender/blenlib/BLI_math_base.h
M source/blender/blenlib/BLI_math_vector.h
M source/blender/blenlib/intern/math_base_inline.c
M source/blender/blenlib/intern/math_vector_inline.c
M source/blender/python/mathutils/mathutils.c
A tests/gtests/blenlib/BLI_math_base_test.cc
M tests/gtests/blenlib/CMakeLists.txt
===================================================================
diff --git a/source/blender/blenlib/BLI_math_base.h b/source/blender/blenlib/BLI_math_base.h
index 39c1b22..20b7635 100644
--- a/source/blender/blenlib/BLI_math_base.h
+++ b/source/blender/blenlib/BLI_math_base.h
@@ -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);
diff --git a/source/blender/blenlib/BLI_math_vector.h b/source/blender/blenlib/BLI_math_vector.h
index 9bc1121..493c285 100644
--- a/source/blender/blenlib/BLI_math_vector.h
+++ b/source/blender/blenlib/BLI_math_vector.h
@@ -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 ***********************************/
diff --git a/source/blender/blenlib/intern/math_base_inline.c b/source/blender/blenlib/intern/math_base_inline.c
index facee8b..f70c12b 100644
--- a/source/blender/blenlib/intern/math_base_inline.c
+++ b/source/blender/blenlib/intern/math_base_inline.c
@@ -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;
diff --git a/source/blender/blenlib/intern/math_vector_inline.c b/source/blender/blenlib/intern/math_vector_inline.c
index fb33fed..c21b097 100644
--- a/source/blender/blenlib/intern/math_vector_inline.c
+++ b/source/blender/blenlib/intern/math_vector_inline.c
@@ -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 (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));
+}
- return false;
+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
diff --git a/source/blender/python/mathutils/mathutils.c b/source/blender/python/mathutils/mathutils.c
index 361fbc8..8e14319 100644
--- a/source/blender/python/mathutils/mathutils.c
+++ b/source/blender/python/mathutils/mathutils.c
@@ -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)
diff --git a/tests/gtests/blenlib/BLI_math_base_test.cc b/tests/gtests/blenlib/BLI_math_base_test.cc
new file mode 100644
index 0000000..0059eb5
--- /dev/null
+++ b/tests/gtests/blenlib/BLI_math_base_test.cc
@@ -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
@@ Diff output truncated at 10240 characters. @@
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