qmath.h File Reference

#include <QtCore/qglobal.h>
#include <QtCore/qalgorithms.h>
#include <cmath>

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Go to the source code of this file.

Classes
struct	QtPrivate::QHypotType< R, F >
class	QtPrivate::QHypotHelper< T >

Namespaces
namespace	QtPrivate
	\macro QT_NAMESPACE

Macros
#define	_USE_MATH_DEFINES
#define	undef_USE_MATH_DEFINES
#define	QT_SINE_TABLE_SIZE   256
#define	M_E   (2.7182818284590452354)
#define	M_LOG2E   (1.4426950408889634074)
#define	M_LOG10E   (0.43429448190325182765)
#define	M_LN2   (0.69314718055994530942)
#define	M_LN10   (2.30258509299404568402)
#define	M_PI   (3.14159265358979323846)
#define	M_PI_2   (1.57079632679489661923)
#define	M_PI_4   (0.78539816339744830962)
#define	M_1_PI   (0.31830988618379067154)
#define	M_2_PI   (0.63661977236758134308)
#define	M_2_SQRTPI   (1.12837916709551257390)
#define	M_SQRT2   (1.41421356237309504880)
#define	M_SQRT1_2   (0.70710678118654752440)

Functions
template<typename T >
int	qCeil (T v)
template<typename T >
int	qFloor (T v)
template<typename T >
auto	qFabs (T v)
template<typename T >
auto	qSin (T v)
template<typename T >
auto	qCos (T v)
template<typename T >
auto	qTan (T v)
template<typename T >
auto	qAcos (T v)
template<typename T >
auto	qAsin (T v)
template<typename T >
auto	qAtan (T v)
template<typename T1 , typename T2 >
auto	qAtan2 (T1 y, T2 x)
template<typename T >
auto	qSqrt (T v)
template<typename F , typename ... Fs>
auto	qHypot (F first, Fs... rest)
template<typename Tx , typename Ty >
auto	qHypot (Tx x, Ty y)
template<typename T >
auto	qLn (T v)
template<typename T >
auto	qExp (T v)
template<typename T1 , typename T2 >
auto	qPow (T1 x, T2 y)
qreal	qFastSin (qreal x)
qreal	qFastCos (qreal x)
constexpr float	qDegreesToRadians (float degrees)
constexpr double	qDegreesToRadians (double degrees)
constexpr long double	qDegreesToRadians (long double degrees)
template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>
constexpr double	qDegreesToRadians (T degrees)
constexpr float	qRadiansToDegrees (float radians)
constexpr double	qRadiansToDegrees (double radians)
constexpr long double	qRadiansToDegrees (long double radians)
constexpr quint32	QtPrivate::qConstexprNextPowerOfTwo (quint32 v)
constexpr quint64	QtPrivate::qConstexprNextPowerOfTwo (quint64 v)
constexpr quint32	QtPrivate::qConstexprNextPowerOfTwo (qint32 v)
constexpr quint64	QtPrivate::qConstexprNextPowerOfTwo (qint64 v)
constexpr quint32	qNextPowerOfTwo (quint32 v)
constexpr quint64	qNextPowerOfTwo (quint64 v)
constexpr quint32	qNextPowerOfTwo (qint32 v)
constexpr quint64	qNextPowerOfTwo (qint64 v)
constexpr unsigned long	qNextPowerOfTwo (unsigned long v)
constexpr unsigned long	qNextPowerOfTwo (long v)

Variables
Q_CORE_EXPORT const qreal	qt_sine_table [QT_SINE_TABLE_SIZE]

Macro Definition Documentation

_USE_MATH_DEFINES

#define _USE_MATH_DEFINES

Definition at line 19 of file qmath.h.

M_1_PI

#define M_1_PI   (0.31830988618379067154)

Definition at line 221 of file qmath.h.

M_2_PI

#define M_2_PI   (0.63661977236758134308)

Definition at line 225 of file qmath.h.

M_2_SQRTPI

#define M_2_SQRTPI   (1.12837916709551257390)

Definition at line 229 of file qmath.h.

M_E

#define M_E   (2.7182818284590452354)

Definition at line 189 of file qmath.h.

M_LN10

#define M_LN10   (2.30258509299404568402)

Definition at line 205 of file qmath.h.

M_LN2

#define M_LN2   (0.69314718055994530942)

Definition at line 201 of file qmath.h.

M_LOG10E

#define M_LOG10E   (0.43429448190325182765)

Definition at line 197 of file qmath.h.

M_LOG2E

#define M_LOG2E   (1.4426950408889634074)

Definition at line 193 of file qmath.h.

M_PI

#define M_PI   (3.14159265358979323846)

Definition at line 209 of file qmath.h.

M_PI_2

#define M_PI_2   (1.57079632679489661923)

Definition at line 213 of file qmath.h.

M_PI_4

#define M_PI_4   (0.78539816339744830962)

Definition at line 217 of file qmath.h.

M_SQRT1_2

#define M_SQRT1_2   (0.70710678118654752440)

Definition at line 237 of file qmath.h.

M_SQRT2

#define M_SQRT2   (1.41421356237309504880)

Definition at line 233 of file qmath.h.

QT_SINE_TABLE_SIZE

#define QT_SINE_TABLE_SIZE   256

Definition at line 32 of file qmath.h.

undef_USE_MATH_DEFINES

#define undef_USE_MATH_DEFINES

Definition at line 20 of file qmath.h.

Function Documentation

qAcos()

template<typename T >

auto qAcos

(

T

v

)

Definition at line 72 of file qmath.h.

Referenced by addCircle(), QQuick3DQuaternionUtils::lookAt(), and rotationQuaternionForLookAt().

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qAsin()

template<typename T >

auto qAsin

(

T

v

)

Definition at line 78 of file qmath.h.

qAtan()

template<typename T >

auto qAtan

(

T

v

)

Definition at line 84 of file qmath.h.

Referenced by QQC2::QStyleHelper::angle(), EaseOvershoot(), and QSSGRenderCamera::verticalFov().

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qAtan2()

template<typename T1 , typename T2 >

auto qAtan2	(	T1	y,
		T2	x
	)

Definition at line 90 of file qmath.h.

Referenced by QQuickFrictionAffector::affectParticle(), QQuickMaterialRipple::anchorPoint(), QLineF::angle(), computeAngle(), QQuickParentChangePrivate::doChange(), QQuickSvgParser::pathArc(), pathArc(), qt_fetch_conical_gradient_template(), QQuickParentAnimation::transition(), and AVFMediaPlayer::videoOrientationForAssetTrack().

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qCeil()

template<typename T >

int qCeil

(

T

v

)

Definition at line 36 of file qmath.h.

Referenced by QFontEngine::alphaMapForGlyph(), QSvgAnimateColor::apply(), QGridLayoutItem::box(), QQuickStyleItemTextField::calculateGeometry(), QQuickTextInputPrivate::calculateImplicitWidthForText(), QQuickBorderImagePrivate::calculateRects(), QtWaylandClient::QWaylandWindow::commit(), QQuickStyleItem::contentSize(), QDistanceFieldData::create(), QtWaylandClient::QWaylandWindow::damage(), QCommandLinkButtonPrivate::descriptionHeight(), QTextLayout::draw(), drawCellBorder(), QTextLayout::drawCursor(), QPaintEngine::drawImage(), QRasterPaintEngine::drawImage(), drawTextItemDecoration(), QTextDocumentLayout::dynamicPageCount(), QQuickLayout::effectiveSizeHints_helper(), QQuickFlickablePrivate::fixup(), QTimeLine::frameForTime(), QSSGMesh::Mesh::fromAssetData(), QSSGMesh::Mesh::fromRuntimeData(), generateWavyPixmap(), getLineHeightParams(), QRasterPaintEnginePrivate::getPenFunc(), intmaxlog(), QPrintPreviewWidgetPrivate::layoutPages(), QQuickTextPrivate::lineHeightOffset(), QScrollerPrivate::nextSnapPos(), QSGOpenVGPainterNode::paint(), QSGSoftwarePainterNode::paint(), QSGDefaultPainterNode::paint(), QQuickBasicDial::paint(), QStaticTextPrivate::paintText(), QQuickSvgParser::pathArc(), pathArc(), QAccessibleBridgeUtils::performEffectiveAction(), QTextureGlyphCache::populate(), QQC2::qDrawBorderPixmap(), QSGSoftwareHelpers::qDrawBorderPixmap(), qt_findAtNxFile(), qt_scale_image_16bit(), qt_scale_image_32bit(), qt_transform_image(), read_jpeg_image(), QSSGMesh::MeshInternal::readMeshData(), QMdi::RegularTiler::rearrange(), QComboBoxPrivate::recomputeSizeHint(), QSGRhiDistanceFieldGlyphCache::requestGlyphs(), QMdiAreaPrivate::resizeToMinimumTileSize(), QSvgAnimateTransform::resolveMatrix(), QHighDpiScaling::roundScaleFactor(), QSvgPaintEngine::saveGradientStops(), QIconLoaderEngine::scaledPixmap(), segmentCount(), QWindowsIntegration::setApplicationBadge(), QQuickTextPrivate::setupTextLayout(), QLabelPrivate::sizeForWidth(), QWasmAudioSink::start(), QSGRhiDistanceFieldGlyphCache::storeGlyphs(), QQC2_NAMESPACE::QMacStyle::subControlRect(), QMacStyle::subControlRect(), QQC2_NAMESPACE::QMacStyle::subElementRect(), QQC2::QCommonStyle::subElementRect(), QMacStyle::subElementRect(), QCommonStyle::subElementRect(), QItemDelegatePrivate::textLayoutBounds(), QItemDelegate::textRectangle(), QRectF::toAlignedRect(), toRectMin(), QQuickMaterialBusyIndicatorNode::updateCurrentTime(), updateDirtySkeletons(), QSGBasicInternalImageNode::updateGeometry(), QSGBasicInternalRectangleNode::updateGeometry(), QSGBasicInternalImageNode::updateGeometry(), QQuickIconImagePrivate::updateIcon(), QQuickTextInputPrivate::updateLayout(), QQuickImage::updatePaintNode(), QQuickShaderEffectSource::updatePaintNode(), QQuickTextPrivate::updateSize(), QQuick3DSkin::updateSpatialNode(), QQuick3DTexture::updateSpatialNode(), QQC2::QCommonStylePrivate::viewItemSize(), and QSSGQmlUtilities::writeQmlForAnimation().

qCos()

template<typename T >

auto qCos

(

T

v

)

Definition at line 60 of file qmath.h.

Referenced by QQuickFrictionAffector::affectParticle(), QQuickGravityAffector::affectParticle(), QQuickMaterialRipple::anchorPoint(), QQC2::calcArrow(), QQC2::QStyleHelper::calcLines(), QQC2::QStyleHelper::calcRadialPos(), QQuickEllipseExtruder::extrude(), QLineF::fromPolar(), QDebugDrawHelper::generateCapsuleGeometry(), QT_BEGIN_NAMESPACE::generateMeshLevelsOfDetail(), QDebugDrawHelper::generateSphereGeometry(), makeDistanceField(), QQuickSvgParser::pathArc(), pathArc(), pathArcSegment(), pathArcSegment(), qt_normalFromRotation(), qt_t_for_arc_angle(), QTransform::rotate(), QTransform::rotateRadians(), QQuickAngleDirection::sample(), QLineF::setAngle(), QSSGMaterialShaderGenerator::setRhiMaterialProperties(), and transformFromLine().

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qDegreesToRadians() [1/4]

constexpr double qDegreesToRadians ( double  degrees )

inlineconstexpr

Definition at line 265 of file qmath.h.

References M_PI.

qDegreesToRadians() [2/4]

constexpr float qDegreesToRadians ( float  degrees )

inlineconstexpr

Definition at line 260 of file qmath.h.

References M_PI.

Referenced by QQuickGravityAffector::affectParticle(), QGeoCoordinatePrivate::atDistanceAndAzimuth(), QGeoCoordinate::azimuthTo(), degToRad(), QGeoCoordinate::distanceTo(), QOpenGL2PaintEngineExPrivate::drawPixmapFragments(), QQuaternion::fromAxisAndAngle(), QQuaternion::fromAxisAndAngle(), QQuaternion::fromEulerAngles(), QLineF::fromPolar(), QT_BEGIN_NAMESPACE::generateMeshLevelsOfDetail(), QQuickImageParticle::initialize(), makeDistanceField(), BasicOperations::paintEvent(), parseTransformationMatrix(), QQuickSvgParser::pathArc(), pathArcSegment(), QDoubleMatrix4x4::perspective(), QMatrix4x4::perspective(), QMatrix4x4::projectedRotate(), qDegreesToRadians(), qt_fromEulerRotation(), qt_normalFromRotation(), qt_t_for_arc_angle(), QLocationUtils::radians(), AVFMediaEncoder::record(), QSvgAnimateTransform::resolveMatrix(), QDoubleMatrix4x4::rotate(), QMatrix4x4::rotate(), QTransform::rotate(), QLineF::setAngle(), QSSGMaterialShaderGenerator::setRhiMaterialProperties(), QSpanData::setup(), setupCameraForShadowMap(), setupCubeReflectionCameras(), setupCubeShadowCameras(), transformFromLine(), QWindowsTabletSupport::translateTabletPacketEvent(), QOpenGL2PaintEngineExPrivate::updateBrushUniforms(), QQuick3DPerspectiveCamera::updateSpatialNode(), QT_BEGIN_NAMESPACE::QQuickShapeCurveMaterialShader::updateUniformData(), QQuickShapeConicalGradientRhiShader::updateUniformData(), and QSSGParticleRenderer::updateUniformsForParticles().

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qDegreesToRadians() [3/4]

constexpr long double qDegreesToRadians ( long double  degrees )

inlineconstexpr

Definition at line 270 of file qmath.h.

References M_PI.

qDegreesToRadians() [4/4]

template<typename T , std::enable_if_t< std::is_integral_v< T >, bool > = true>

constexpr double qDegreesToRadians ( T  degrees )

inlineconstexpr

Definition at line 276 of file qmath.h.

References qDegreesToRadians().

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qExp()

template<typename T >

auto qExp

(

T

v

)

Definition at line 174 of file qmath.h.

qFabs()

template<typename T >

auto qFabs

(

T

v

)

Definition at line 48 of file qmath.h.

Referenced by EVRCustomPresenter::IsRateSupported(), and Scheduler::processSample().

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qFastCos()

qreal qFastCos ( qreal  x )

inline

Definition at line 250 of file qmath.h.

References d, M_PI, qt_sine_table, and QT_SINE_TABLE_SIZE.

Referenced by QOpenGL2PaintEngineExPrivate::drawPixmapFragments(), QTriangulatingStroker::process(), and QSGBasicInternalRectangleNode::updateGeometry().

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qFastSin()

qreal qFastSin ( qreal  x )

inline

Definition at line 240 of file qmath.h.

References d, M_PI, qt_sine_table, and QT_SINE_TABLE_SIZE.

Referenced by QOpenGL2PaintEngineExPrivate::drawPixmapFragments(), QTriangulatingStroker::process(), and QSGBasicInternalRectangleNode::updateGeometry().

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qFloor()

template<typename T >

int qFloor

(

T

v

)

Definition at line 42 of file qmath.h.

Referenced by QQuickGridViewPrivate::addVisibleItems(), QQuick3DParticleScaleAffector::affectParticle(), QFontEngine::alphaMapForGlyph(), QSvgAnimateColor::apply(), QQuickGridViewPrivate::applyInsertionChange(), QQuickTableViewPrivate::calculateTopLeft(), QtWaylandClient::QWaylandWindow::commit(), QtWaylandClient::QWaylandWindow::damage(), QDirectFbBlitter::drawCachedGlyphs(), QRasterPaintEngine::drawCachedGlyphs(), QOpenGL2PaintEngineExPrivate::drawCachedGlyphs(), drawCellBorder(), QPaintEngine::drawImage(), QRasterPaintEngine::drawImage(), QX11PaintEngine::drawPoints(), drawTextItemDecoration(), fetchTransformed_fetcher(), fetchTransformedBilinear_slow_fetcher(), QX11PaintEnginePrivate::fillPolygon_dev(), firstDayOfYear(), QQuickFlickablePrivate::fixup(), generateWavyPixmap(), QWaylandOutputPrivate::handleWindowPixelSizeChanged(), QWaylandOutput::initialize(), QWaylandSurface::inputRegionContains(), QJalaliCalendar::julianDayToDate(), QPrintPreviewWidgetPrivate::layoutPages(), QWindowsFontEngine::minRightBearing(), QRhi::mipLevelsForSize(), QScrollerPrivate::nextSnapPos(), QSGOpenVGPainterNode::paint(), QSGSoftwarePainterNode::paint(), QSGDefaultPainterNode::paint(), QQuickBasicDial::paint(), QQuickStyledTextPrivate::parseImageAttributes(), QSGTextMaskMaterial::populate(), QQuickPathView::positionViewAtIndex(), qDrawEdge(), qt_curves_for_arc(), qt_find_ellipse_coords(), qt_image_convolute_filter(), qt_scale_image_16bit(), qt_scale_image_32bit(), qt_transform_image(), QQuickGridViewPrivate::resetColumns(), QHighDpiScaling::roundScaleFactor(), QBackingStore::scroll(), QRectF::toAlignedRect(), toRectMin(), QSGBasicInternalImageNode::updateGeometry(), QSGBasicInternalImageNode::updateGeometry(), and QDoubleValidatorPrivate::validateWithLocale().

qHypot() [1/2]

template<typename F , typename ... Fs>

auto qHypot	(	F	first,
		Fs...	rest
	)

Definition at line 145 of file qmath.h.

References QtPrivate::QHypotHelper< T >::add().

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qHypot() [2/2]

template<typename Tx , typename Ty >

auto qHypot	(	Tx	x,
		Ty	y
	)

Definition at line 152 of file qmath.h.

qLn()

template<typename T >

auto qLn

(

T

v

)

Definition at line 168 of file qmath.h.

Referenced by intmaxlog().

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qNextPowerOfTwo() [1/6]

constexpr unsigned long qNextPowerOfTwo ( long  v )

inlineconstexpr

Definition at line 378 of file qmath.h.

References qNextPowerOfTwo().

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qNextPowerOfTwo() [2/6]

constexpr quint32 qNextPowerOfTwo ( qint32  v )

inlineconstexpr

Definition at line 363 of file qmath.h.

References qNextPowerOfTwo().

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qNextPowerOfTwo() [3/6]

constexpr quint64 qNextPowerOfTwo ( qint64  v )

inlineconstexpr

Definition at line 368 of file qmath.h.

References qNextPowerOfTwo().

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qNextPowerOfTwo() [4/6]

constexpr quint32 qNextPowerOfTwo ( quint32  v )

inlineconstexpr

Definition at line 335 of file qmath.h.

References Q_ASSERT, and QtPrivate::qConstexprNextPowerOfTwo().

Referenced by QSGRhiAtlasTexture::Manager::Manager(), QSSGRhiContext::checkAndAdjustForNPoT(), QSGPlainTexture::commitTextureOperations(), QTextureGlyphCache::fillInPendingGlyphs(), QTextureGlyphCache::populate(), QV4::MarkStack::push(), qCalculateGrowingBlockSize(), qNextPowerOfTwo(), qNextPowerOfTwo(), qNextPowerOfTwo(), qNextPowerOfTwo(), QOpenGLTextureUploader::textureImage(), and QOpenGL2PaintEngineExPrivate::updateBrushTexture().

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qNextPowerOfTwo() [5/6]

constexpr quint64 qNextPowerOfTwo ( quint64  v )

inlineconstexpr

Definition at line 349 of file qmath.h.

References Q_ASSERT, Q_UINT64_C, and QtPrivate::qConstexprNextPowerOfTwo().

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qNextPowerOfTwo() [6/6]

constexpr unsigned long qNextPowerOfTwo ( unsigned long  v )

inlineconstexpr

Definition at line 373 of file qmath.h.

References qNextPowerOfTwo().

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qPow()

template<typename T1 , typename T2 >

auto qPow	(	T1	x,
		T2	y
	)

Definition at line 180 of file qmath.h.

Referenced by QWindowsFontEngineData::QWindowsFontEngineData(), QAudio::convertVolume(), QGeoTiledMappingManagerEngineNokia::evaluateCopyrightsText(), QODBCResult::exec(), expblur(), QColorTrcLut::fromGamma(), growthFactorBelowPreferredSize(), QQuickWheelHandler::handleEventPoint(), and AVFMediaPlayer::videoOrientationForAssetTrack().

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qRadiansToDegrees() [1/3]

constexpr double qRadiansToDegrees ( double  radians )

inlineconstexpr

Definition at line 286 of file qmath.h.

References M_PI.

qRadiansToDegrees() [2/3]

constexpr float qRadiansToDegrees ( float  radians )

inlineconstexpr

Definition at line 281 of file qmath.h.

References M_PI.

Referenced by QLineF::angle(), QQuickContext2D::arc(), QGeoCoordinatePrivate::atDistanceAndAzimuth(), QGeoCoordinate::azimuthTo(), QSSGRenderCamera::computeFrustumPerspective(), QLocationUtils::degrees(), QQuickParentChangePrivate::doChange(), QQuaternion::getAxisAndAngle(), QQuaternion::getEulerAngles(), QQuick3DCamera::lookAt(), QQuick3DQuaternionUtils::lookAt(), QQuickJSContext2DPrototype::method_createConicalGradient(), radToDeg(), QQuickContext2D::rotate(), rotationQuaternionForLookAt(), setCameraProperties(), setLightProperties(), setTextureProperties(), setupCubeReflectionCameras(), setupCubeShadowCameras(), QtAndroidInput::touchAdd(), QQuickParentAnimation::transition(), QWindowsTabletSupport::translateTabletPacketEvent(), and AVFMediaPlayer::videoOrientationForAssetTrack().

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qRadiansToDegrees() [3/3]

constexpr long double qRadiansToDegrees ( long double  radians )

inlineconstexpr

Definition at line 291 of file qmath.h.

References M_PI.

qSin()

template<typename T >

auto qSin

(

T

v

)

Definition at line 54 of file qmath.h.

Referenced by QQuick3DParticleScaleAffector::affectParticle(), QQuickFrictionAffector::affectParticle(), QQuickGravityAffector::affectParticle(), QQuickMaterialRipple::anchorPoint(), QQC2::calcArrow(), QQC2::QStyleHelper::calcLines(), QQC2::QStyleHelper::calcRadialPos(), QQuickEllipseExtruder::extrude(), QLineF::fromPolar(), QDebugDrawHelper::generateCapsuleGeometry(), QDebugDrawHelper::generateSphereGeometry(), makeDistanceField(), QQuickSvgParser::pathArc(), pathArc(), pathArcSegment(), pathArcSegment(), qt_normalFromRotation(), qt_t_for_arc_angle(), QTransform::rotate(), QTransform::rotateRadians(), QQuickAngleDirection::sample(), QLineF::setAngle(), and transformFromLine().

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qSqrt()

template<typename T >

auto qSqrt

(

T

v

)

Definition at line 96 of file qmath.h.

qTan()

template<typename T >

auto qTan

(

T

v

)

Definition at line 66 of file qmath.h.

Referenced by parseTransformationMatrix(), QSvgAnimateTransform::resolveMatrix(), and QSSGRenderCamera::verticalFov().

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Variable Documentation

qt_sine_table

Q_CORE_EXPORT const qreal qt_sine_table[QT_SINE_TABLE_SIZE]

extern

Definition at line 9 of file qmath.cpp.

Referenced by qFastCos(), and qFastSin().