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Math: finally implemented precise signed/unsigned normalization. 

(De)normalization from/to [0, 1] for unsigned types and from/to [-1, 1]
for signed types. -1.0 is always denormalized to min+1.

Also updated some tests for Color, as they depended on previous
imprecise implementation.
pull/7/head
Vladimír Vondruš 14 years ago
parent
7dc0fc4a4c
commit
cade175304
3 changed files with 153 additions and 72 deletions
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  1. 51
      src/Math/Functions.h
  2. 140
      src/Math/Test/FunctionsTest.cpp
  3. 34
      src/Test/ColorTest.cpp

51
src/Math/Functions.h
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@ -75,14 +75,18 @@ std::uint32_t MAGNUM_EXPORT log2(std::uint32_t number);
std::uint32_t MAGNUM_EXPORT log(std::uint32_t base, std::uint32_t number);
/**
@brief Normalize floating-point value
@brief Normalize integral value
Converts integral value from full range of given (signed/unsigned) integral
type to value in range @f$ [0, 1] @f$.
Converts integral value from full range of given *unsigned* integral type to
value in range @f$ [0, 1] @f$ or from *signed* integral to range @f$ [-1, 1] @f$.
@note For best precision, `FloatingPoint` type should be always larger that
resulting `Integral` type (e.g. `double` to `std::int32_t`, `long double`
to `std::int64_t`).
@attention To ensure the integral type is correctly detected when using
literals, this function should be called with both template parameters
explicit, e.g.:
literals, this function should be called with both template parameters
explicit, e.g.:
@code
// Even if this is character literal, integral type is 32bit, thus a != 1.0f
float a = normalize<float>('\127');
@ -91,32 +95,43 @@ float a = normalize<float>('\127');
float b = normalize<float, std::int8_t>('\127');
@endcode
@todo Signed normalization to [-1.0, 1.0] like in OpenGL?
@see denormalize()
*/
template<class FloatingPoint, class Integral> inline constexpr typename std::enable_if<std::is_floating_point<FloatingPoint>::value && std::is_integral<Integral>::value, FloatingPoint>::type normalize(Integral value) {
return (FloatingPoint(value)-FloatingPoint(std::numeric_limits<Integral>::min()))/
(FloatingPoint(std::numeric_limits<Integral>::max()) - FloatingPoint(std::numeric_limits<Integral>::min()));
#ifdef DOXYGEN_GENERATING_OUTPUT
template<class FloatingPoint, class Integral> inline constexpr FloatingPoint normalize(Integral value);
#else
template<class FloatingPoint, class Integral> inline constexpr typename std::enable_if<std::is_floating_point<FloatingPoint>::value && std::is_integral<Integral>::value && std::is_unsigned<Integral>::value, FloatingPoint>::type normalize(Integral value) {
return value/FloatingPoint(std::numeric_limits<Integral>::max());
}
template<class FloatingPoint, class Integral> inline constexpr typename std::enable_if<std::is_floating_point<FloatingPoint>::value && std::is_integral<Integral>::value && std::is_signed<Integral>::value, FloatingPoint>::type normalize(Integral value) {
return std::max(value/FloatingPoint(std::numeric_limits<Integral>::max()), FloatingPoint(-1));
}
#endif
/**
@brief Denormalize floating-point value
Converts floating-point value in range @f$ [0, 1] @f$ to full range of given
unsigned integral type or range @f$ [-1, 1] @f$ to full range of given signed
integral type.
@note For best precision, `FloatingPoint` type should be always larger that
resulting `Integral` type (e.g. `double` to `std::int32_t`, `long double` to
`std::int64_t`).
resulting `Integral` type (e.g. `double` to `std::int32_t`, `long double`
to `std::int64_t`).
@todo Signed normalization to [-1.0, 1.0] like in OpenGL?
@todo Stable behavior (working/broken) for long double and long long
(currently fails in Debug builds, but passes in Release on GCC 4.7)
@see normalize()
*/
template<class Integral, class FloatingPoint> inline constexpr typename std::enable_if<std::is_floating_point<FloatingPoint>::value && std::is_integral<Integral>::value, Integral>::type denormalize(FloatingPoint value) {
return std::numeric_limits<Integral>::min() +
round(FloatingPoint(value*std::numeric_limits<Integral>::max()) -
FloatingPoint(value*std::numeric_limits<Integral>::min()));
#ifdef DOXYGEN_GENERATING_OUTPUT
template<class Integral, class FloatingPoint> inline constexpr typename Integral denormalize(FloatingPoint value);
#else
template<class Integral, class FloatingPoint> inline constexpr typename std::enable_if<std::is_floating_point<FloatingPoint>::value && std::is_integral<Integral>::value && std::is_unsigned<Integral>::value, Integral>::type denormalize(FloatingPoint value) {
return value*std::numeric_limits<Integral>::max();
}
template<class Integral, class FloatingPoint> inline constexpr typename std::enable_if<std::is_floating_point<FloatingPoint>::value && std::is_integral<Integral>::value && std::is_signed<Integral>::value, Integral>::type denormalize(FloatingPoint value) {
return value*std::numeric_limits<Integral>::max();
}
#endif
/** @brief Clamp value */
template<class T> inline T clamp(T value, T min, T max) {

140
src/Math/Test/FunctionsTest.cpp
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@ -23,8 +23,12 @@ class FunctionsTest: public Corrade::TestSuite::Tester {
public:
FunctionsTest();
void normalize();
void denormalize();
void normalizeUnsigned();
void normalizeSigned();
void denormalizeUnsigned();
void denormalizeSigned();
void renormalizeUnsinged();
void renormalizeSinged();
void clamp();
void pow();
void log();
@ -32,62 +36,124 @@ class FunctionsTest: public Corrade::TestSuite::Tester {
};
FunctionsTest::FunctionsTest() {
addTests(&FunctionsTest::normalize,
&FunctionsTest::denormalize,
addTests(&FunctionsTest::normalizeUnsigned,
&FunctionsTest::normalizeSigned,
&FunctionsTest::denormalizeUnsigned,
&FunctionsTest::denormalizeSigned,
&FunctionsTest::renormalizeUnsinged,
&FunctionsTest::renormalizeSinged,
&FunctionsTest::clamp,
&FunctionsTest::pow,
&FunctionsTest::log,
&FunctionsTest::log2);
}
void FunctionsTest::normalize() {
/* Range for signed and unsigned */
CORRADE_COMPARE((Math::normalize<float, std::int8_t>(-128)), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::int8_t>(127)), 1.0f);
void FunctionsTest::normalizeUnsigned() {
CORRADE_COMPARE((Math::normalize<float, std::uint8_t>(0)), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::uint8_t>(255)), 1.0f);
/* Between */
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(16384)), 0.750011f);
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(-16384)), 0.250004f);
CORRADE_COMPARE((Math::normalize<double, std::uint32_t>(0)), 0.0);
CORRADE_COMPARE((Math::normalize<double, std::uint32_t>(std::numeric_limits<std::uint32_t>::max())), 1.0);
CORRADE_COMPARE((Math::normalize<long double, std::uint64_t>(0)), 0.0);
CORRADE_COMPARE((Math::normalize<long double, std::uint64_t>(std::numeric_limits<std::uint64_t>::max())), 1.0);
/* Test overflow for large types */
CORRADE_COMPARE((Math::normalize<float, std::int32_t>(std::numeric_limits<std::int32_t>::min())), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::int32_t>(std::numeric_limits<std::int32_t>::max())), 1.0f);
CORRADE_COMPARE((Math::normalize<float, std::uint32_t>(0)), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::uint32_t>(std::numeric_limits<std::uint32_t>::max())), 1.0f);
CORRADE_COMPARE((Math::normalize<float, std::uint16_t>(0)), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::uint16_t>(std::numeric_limits<std::uint16_t>::max())), 1.0f);
CORRADE_COMPARE((Math::normalize<double, std::int64_t>(std::numeric_limits<std::int64_t>::min())), 0.0);
CORRADE_COMPARE((Math::normalize<double, std::int64_t>(std::numeric_limits<std::int64_t>::max())), 1.0);
CORRADE_COMPARE((Math::normalize<double, std::uint64_t>(0)), 0.0);
CORRADE_COMPARE((Math::normalize<double, std::uint64_t>(std::numeric_limits<std::uint64_t>::max())), 1.0);
CORRADE_COMPARE((Math::normalize<float, std::uint16_t>(8192)), 0.125002f);
CORRADE_COMPARE((Math::normalize<float, std::uint16_t>(49152)), 0.750011f);
}
void FunctionsTest::denormalize() {
/* Range for signed and unsigned */
CORRADE_COMPARE(Math::denormalize<std::int8_t>(0.0f), -128);
CORRADE_COMPARE(Math::denormalize<std::int8_t>(1.0f), 127);
void FunctionsTest::normalizeSigned() {
CORRADE_COMPARE((Math::normalize<float, std::int8_t>(127)), 1.0f);
CORRADE_COMPARE((Math::normalize<float, std::int8_t>(0)), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::int8_t>(-128)), -1.0f);
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(std::numeric_limits<std::int16_t>::min())), -1.0f);
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(0)), 0.0f);
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(std::numeric_limits<std::int16_t>::max())), 1.0f);
CORRADE_COMPARE((Math::normalize<double, std::int32_t>(std::numeric_limits<std::int32_t>::min())), -1.0);
CORRADE_COMPARE((Math::normalize<double, std::int32_t>(0)), 0.0);
CORRADE_COMPARE((Math::normalize<double, std::int32_t>(std::numeric_limits<std::int32_t>::max())), 1.0);
CORRADE_COMPARE((Math::normalize<long double, std::int64_t>(std::numeric_limits<std::int64_t>::min())), -1.0);
CORRADE_COMPARE((Math::normalize<long double, std::int64_t>(0)), 0.0);
CORRADE_COMPARE((Math::normalize<long double, std::int64_t>(std::numeric_limits<std::int64_t>::max())), 1.0);
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(16384)), 0.500015f);
CORRADE_COMPARE((Math::normalize<float, std::int16_t>(-16384)), -0.500015f);
}
void FunctionsTest::denormalizeUnsigned() {
CORRADE_COMPARE(Math::denormalize<std::uint8_t>(0.0f), 0);
CORRADE_COMPARE(Math::denormalize<std::uint8_t>(1.0f), 255);
/* Between */
CORRADE_COMPARE(Math::denormalize<std::int16_t>(0.33f), -11141);
CORRADE_COMPARE(Math::denormalize<std::int16_t>(0.66f), 10485);
CORRADE_COMPARE(Math::denormalize<std::uint16_t>(0.0f), 0);
CORRADE_COMPARE(Math::denormalize<std::uint16_t>(1.0f), std::numeric_limits<std::uint16_t>::max());
CORRADE_COMPARE(Math::denormalize<std::uint32_t>(0.0), 0);
CORRADE_COMPARE(Math::denormalize<std::uint32_t>(1.0), std::numeric_limits<std::uint32_t>::max());
/* Test overflow for large types */
CORRADE_COMPARE(Math::denormalize<std::int32_t>(0.0f), std::numeric_limits<std::int32_t>::min());
CORRADE_COMPARE(Math::denormalize<std::uint32_t>(0.0f), 0);
CORRADE_COMPARE(Math::denormalize<std::int64_t>(0.0), std::numeric_limits<std::int64_t>::min());
CORRADE_COMPARE(Math::denormalize<std::uint64_t>(0.0), 0);
CORRADE_COMPARE(Math::denormalize<std::uint64_t>(1.0), std::numeric_limits<std::uint64_t>::max());
CORRADE_COMPARE(Math::denormalize<std::uint16_t>(0.33f), 21626);
CORRADE_COMPARE(Math::denormalize<std::uint16_t>(0.66f), 43253);
}
void FunctionsTest::denormalizeSigned() {
CORRADE_COMPARE(Math::denormalize<std::int8_t>(-1.0f), -127);
CORRADE_COMPARE(Math::denormalize<std::int8_t>(0.0f), 0);
CORRADE_COMPARE(Math::denormalize<std::int8_t>(1.0f), 127);
CORRADE_COMPARE(Math::denormalize<std::int16_t>(-1.0f), std::numeric_limits<std::int16_t>::min()+1);
CORRADE_COMPARE(Math::denormalize<std::int16_t>(0.0f), 0);
CORRADE_COMPARE(Math::denormalize<std::int16_t>(1.0f), std::numeric_limits<std::int16_t>::max());
CORRADE_COMPARE(Math::denormalize<std::int32_t>(-1.0), std::numeric_limits<std::int32_t>::min()+1);
CORRADE_COMPARE(Math::denormalize<std::int32_t>(0.0), 0);
CORRADE_COMPARE(Math::denormalize<std::int32_t>(1.0), std::numeric_limits<std::int32_t>::max());
CORRADE_COMPARE(Math::denormalize<std::uint32_t>(1.0), std::numeric_limits<std::uint32_t>::max());
// {
// CORRADE_EXPECT_FAIL("Denormalize doesn't work for large types well");
// CORRADE_COMPARE((Math::denormalize<long long, long double>(1.0)), numeric_limits<long long>::max());
// CORRADE_COMPARE((Math::denormalize<unsigned long long, long double>(1.0)), numeric_limits<unsigned long long>::max());
// }
CORRADE_COMPARE(Math::denormalize<std::int64_t>(-1.0l), std::numeric_limits<std::int64_t>::min()+1);
CORRADE_COMPARE(Math::denormalize<std::int64_t>(0.0l), 0);
CORRADE_COMPARE(Math::denormalize<std::int64_t>(1.0l), std::numeric_limits<std::int64_t>::max());
CORRADE_COMPARE(Math::denormalize<std::int16_t>(-0.33f), -10813);
CORRADE_COMPARE(Math::denormalize<std::int16_t>(0.66f), 21626);
}
void FunctionsTest::renormalizeUnsinged() {
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::uint8_t>(0.0f)), 0.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::uint8_t>(1.0f)), 1.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::uint16_t>(0.0f)), 0.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::uint16_t>(1.0f)), 1.0f);
CORRADE_COMPARE(Math::normalize<double>(Math::denormalize<std::uint32_t>(0.0)), 0.0);
CORRADE_COMPARE(Math::normalize<double>(Math::denormalize<std::uint32_t>(1.0)), 1.0);
CORRADE_COMPARE(Math::normalize<long double>(Math::denormalize<std::uint64_t>(0.0l)), 0.0l);
CORRADE_COMPARE(Math::normalize<long double>(Math::denormalize<std::uint64_t>(1.0l)), 1.0l);
}
void FunctionsTest::renormalizeSinged() {
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::int8_t>(-1.0f)), -1.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::int8_t>(0.0f)), 0.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::int8_t>(1.0f)), 1.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::int16_t>(-1.0f)), -1.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::int16_t>(0.0f)), 0.0f);
CORRADE_COMPARE(Math::normalize<float>(Math::denormalize<std::int16_t>(1.0f)), 1.0f);
CORRADE_COMPARE(Math::normalize<double>(Math::denormalize<std::int32_t>(-1.0)), -1.0);
CORRADE_COMPARE(Math::normalize<double>(Math::denormalize<std::int32_t>(0.0)), 0.0);
CORRADE_COMPARE(Math::normalize<double>(Math::denormalize<std::int32_t>(1.0)), 1.0);
CORRADE_COMPARE(Math::normalize<long double>(Math::denormalize<std::int64_t>(-1.0l)), -1.0l);
CORRADE_COMPARE(Math::normalize<long double>(Math::denormalize<std::int64_t>(0.0l)), 0.0l);
CORRADE_COMPARE(Math::normalize<long double>(Math::denormalize<std::int64_t>(1.0l)), 1.0l);
}
void FunctionsTest::clamp() {

34
src/Test/ColorTest.cpp
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@ -104,16 +104,16 @@ void ColorTest::fromDenormalized() {
}
void ColorTest::fromNormalized() {
CORRADE_COMPARE(Color3::fromNormalized(Color3f(0.294118, 0.45098, 0.878431)), Color3(75, 115, 224));
CORRADE_COMPARE(Color3::fromNormalized(Color3f(0.294118, 0.45098, 0.878431)), Color3(75, 114, 223));
}
void ColorTest::fromHue() {
CORRADE_COMPARE(Color3::fromHSV(27.0f, 1.0f, 1.0f), Color3(255, 115, 0));
CORRADE_COMPARE(Color3::fromHSV(86.0f, 1.0f, 1.0f), Color3(145, 255, 0));
CORRADE_COMPARE(Color3::fromHSV(134.0f, 1.0f, 1.0f), Color3(0, 255, 60));
CORRADE_COMPARE(Color3::fromHSV(27.0f, 1.0f, 1.0f), Color3(255, 114, 0));
CORRADE_COMPARE(Color3::fromHSV(86.0f, 1.0f, 1.0f), Color3(144, 255, 0));
CORRADE_COMPARE(Color3::fromHSV(134.0f, 1.0f, 1.0f), Color3(0, 255, 59));
CORRADE_COMPARE(Color3::fromHSV(191.0f, 1.0f, 1.0f), Color3(0, 208, 255));
CORRADE_COMPARE(Color3::fromHSV(269.0f, 1.0f, 1.0f), Color3(123, 0, 255));
CORRADE_COMPARE(Color3::fromHSV(317.0f, 1.0f, 1.0f), Color3(255, 0, 183));
CORRADE_COMPARE(Color3::fromHSV(317.0f, 1.0f, 1.0f), Color3(255, 0, 182));
}
void ColorTest::hue() {
@ -126,7 +126,7 @@ void ColorTest::hue() {
}
void ColorTest::fromSaturation() {
CORRADE_COMPARE(Color3::fromHSV(0.0f, 0.702f, 1.0f), Color3(255, 76, 76));
CORRADE_COMPARE(Color3::fromHSV(0.0f, 0.702f, 1.0f), Color3(255, 75, 75));
}
void ColorTest::saturation() {
@ -143,7 +143,7 @@ void ColorTest::value() {
}
void ColorTest::hsv() {
CORRADE_COMPARE(Color3::fromHSV(230.0f, 0.749f, 0.427f), Color3(27, 41, 109));
CORRADE_COMPARE(Color3::fromHSV(230.0f, 0.749f, 0.427f), Color3(27, 40, 108));
float hue, saturation, value;
std::tie(hue, saturation, value) = Color3(27, 41, 109).toHSV();
@ -153,24 +153,24 @@ void ColorTest::hsv() {
}
void ColorTest::hsvOverflow() {
CORRADE_COMPARE(Color3::fromHSV(27.0f-360.0f, 1.0f, 1.0f), Color3(255, 115, 0));
CORRADE_COMPARE(Color3::fromHSV(86.0f-360.0f, 1.0f, 1.0f), Color3(145, 255, 0));
CORRADE_COMPARE(Color3::fromHSV(134.0f-360.0f, 1.0f, 1.0f), Color3(0, 255, 60));
CORRADE_COMPARE(Color3::fromHSV(27.0f-360.0f, 1.0f, 1.0f), Color3(255, 114, 0));
CORRADE_COMPARE(Color3::fromHSV(86.0f-360.0f, 1.0f, 1.0f), Color3(144, 255, 0));
CORRADE_COMPARE(Color3::fromHSV(134.0f-360.0f, 1.0f, 1.0f), Color3(0, 255, 59));
CORRADE_COMPARE(Color3::fromHSV(191.0f-360.0f, 1.0f, 1.0f), Color3(0, 208, 255));
CORRADE_COMPARE(Color3::fromHSV(269.0f-360.0f, 1.0f, 1.0f), Color3(123, 0, 255));
CORRADE_COMPARE(Color3::fromHSV(317.0f-360.0f, 1.0f, 1.0f), Color3(255, 0, 183));
CORRADE_COMPARE(Color3::fromHSV(317.0f-360.0f, 1.0f, 1.0f), Color3(255, 0, 182));
CORRADE_COMPARE(Color3::fromHSV(360.0f+27.0f, 1.0f, 1.0f), Color3(255, 115, 0));
CORRADE_COMPARE(Color3::fromHSV(360.0f+86.0f, 1.0f, 1.0f), Color3(145, 255, 0));
CORRADE_COMPARE(Color3::fromHSV(360.0f+134.0f, 1.0f, 1.0f), Color3(0, 255, 60));
CORRADE_COMPARE(Color3::fromHSV(360.0f+27.0f, 1.0f, 1.0f), Color3(255, 114, 0));
CORRADE_COMPARE(Color3::fromHSV(360.0f+86.0f, 1.0f, 1.0f), Color3(144, 255, 0));
CORRADE_COMPARE(Color3::fromHSV(360.0f+134.0f, 1.0f, 1.0f), Color3(0, 255, 59));
CORRADE_COMPARE(Color3::fromHSV(360.0f+191.0f, 1.0f, 1.0f), Color3(0, 208, 255));
CORRADE_COMPARE(Color3::fromHSV(360.0f+269.0f, 1.0f, 1.0f), Color3(123, 0, 255));
CORRADE_COMPARE(Color3::fromHSV(360.0f+317.0f, 1.0f, 1.0f), Color3(255, 0, 183));
CORRADE_COMPARE(Color3::fromHSV(360.0f+317.0f, 1.0f, 1.0f), Color3(255, 0, 182));
}
void ColorTest::hsvAlpha() {
CORRADE_COMPARE(Color4::fromHSV(std::make_tuple(230.0f, 0.749f, 0.427f), 23), Color4(27, 41, 109, 23));
CORRADE_COMPARE(Color4::fromHSV(230.0f, 0.749f, 0.427f, 23), Color4(27, 41, 109, 23));
CORRADE_COMPARE(Color4::fromHSV(std::make_tuple(230.0f, 0.749f, 0.427f), 23), Color4(27, 40, 108, 23));
CORRADE_COMPARE(Color4::fromHSV(230.0f, 0.749f, 0.427f, 23), Color4(27, 40, 108, 23));
}
void ColorTest::debug() {

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