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!

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 = -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));
+}

tests/gtests/blenlib/CMakeLists.txt

@@ -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")