Integer math functions. More...

#include "strong_typedef_type.hpp"

Functions
template<typename T >
constexpr T	abs (const T a)
	Returns the absolute value of (scalar) variable.

template<typename T >
constexpr T	Align (const T x, uint n)
	Return the smallest multiple of n equal or greater than x.

template<typename T >
constexpr T *	AlignPtr (T *x, uint n)
	Return the smallest multiple of n equal or greater than x Applies to pointers only.

template<typename T >
constexpr T	Clamp (const T a, const T min, const T max)
	Clamp a value between an interval.

template<typename T >
constexpr T	SoftClamp (const T a, const T min, const T max)
	Clamp a value between an interval.

constexpr int	Clamp (const int a, const int min, const int max)
	Clamp an integer between an interval.

constexpr uint	ClampU (const uint a, const uint min, const uint max)
	Clamp an unsigned integer between an interval.

template<typename To , typename From , std::enable_if_t< std::is_integral< From >::value, int > = 0>
constexpr To	ClampTo (From value)
	Clamp the given value down to lie within the requested type.

template<typename T >
constexpr T	Delta (const T a, const T b)
	Returns the (absolute) difference between two (scalar) variables.

template<typename T >
constexpr bool	IsInsideBS (const T x, const size_t base, const size_t size)
	Checks if a value is between a window started at some base point.

template<typename T , std::enable_if_t< std::disjunction_v< std::is_convertible< T, size_t >, std::is_base_of< StrongTypedefBase, T > >, int > = 0>
constexpr bool	IsInsideMM (const T x, const size_t min, const size_t max) noexcept
	Checks if a value is in an interval.

template<typename T >
constexpr void	Swap (T &a, T &b)
	Type safe swap operation.

constexpr uint	ToPercent8 (uint i)
	Converts a "fract" value 0..255 to "percent" value 0..100.

constexpr uint	ToPercent16 (uint i)
	Converts a "fract" value 0..65535 to "percent" value 0..100.

int	DivideApprox (int a, int b)
	Deterministic approximate division.

constexpr uint	CeilDiv (uint a, uint b)
	Computes ceil(a / b) for non-negative a and b.

constexpr uint	Ceil (uint a, uint b)
	Computes ceil(a / b) * b for non-negative a and b.

constexpr int	RoundDivSU (int a, uint b)
	Computes round(a / b) for signed a and unsigned b.

constexpr uint64_t	PowerOfTen (int power)
	Computes ten to the given power.

uint32_t	IntSqrt (uint32_t num)
	Compute the integer square root.

Detailed Description

Integer math functions.

Definition in file math_func.hpp.

Function Documentation

◆ abs()

template<typename T >

constexpr T abs ( const T a )

constexpr

Returns the absolute value of (scalar) variable.

Note: assumes variable to be signed

Parameters

a	The value we want to unsign

Returns: The unsigned value

Definition at line 23 of file math_func.hpp.

Referenced by AircraftController(), AircraftGetEntryPoint(), CalcRaildirsDrawstyle(), ChangeIndustryProduction(), CheckClickOnVehicle(), CheckTrainsLengths(), DeterminePluralForm(), DivideApprox(), LinkGraphOverlay::DrawContent(), BaseGraphWindow::DrawGraph(), TimetableWindow::DrawSummaryPanel(), EnumCheckRoadVehCrashTrain(), Kdtree< T, TxyFunc, CoordT, DistT >::FindNearestRecursive(), FindTrainCollideEnum(), CargoPacket::GetDistance(), GetTunnelBridgeLength(), BaseGraphWindow::GetValuesInterval(), GfxDoDrawLine(), HandleMouseEvents(), HandleWindowDragging(), HeightMapCoastLines(), DiagonalTileIterator::operator++(), CYapfDestinationTileOrStationRailT< Types >::PfCalcEstimate(), CYapfDestinationTileRoadT< Types >::PfCalcEstimate(), CYapfDestinationTileWaterT< Types >::PfCalcEstimate(), PlaceTreeAtSameHeight(), PlaceTreeGroups(), ReportNewsProductionChangeIndustry(), SettingsValueAbsolute(), TerraformTileHeight(), TownHouseChangeInfo(), UpdateViewportPosition(), and VpSelectTilesWithMethod().

◆ Align()

template<typename T >

constexpr T Align	(	const T	x,
		uint	n
	)

constexpr

Return the smallest multiple of n equal or greater than x.

Note: n must be a power of 2

Parameters

x	The min value
n	The base of the number we are searching

Returns: The smallest multiple of n equal or greater than x

Definition at line 37 of file math_func.hpp.

Referenced by TarScanner::AddFile(), AlignPtr(), VideoDriver_Win32GDI::AllocateBackingStore(), CacheSpriteAllocator::AllocatePtr(), DEFINE_POOL_METHOD(), DrawDirtyBlocks(), MakeBMPImage(), OpenGLBackend::Resize(), OpenGLSprite::Update(), and ViewportSign::UpdatePosition().

◆ AlignPtr()

template<typename T >

constexpr T * AlignPtr	(	T *	x,
		uint	n
	)

constexpr

Return the smallest multiple of n equal or greater than x Applies to pointers only.

Note: n must be a power of 2

Parameters

x	The min value
n	The base of the number we are searching

Returns: The smallest multiple of n equal or greater than x

See also: Align()

Definition at line 55 of file math_func.hpp.

References Align().

◆ Ceil()

constexpr uint Ceil	(	uint	a,
		uint	b
	)

constexpr

Computes ceil(a / b) * b for non-negative a and b.

Parameters

a	Numerator
b	Denominator

Returns: a rounded up to the nearest multiple of b.

Definition at line 331 of file math_func.hpp.

References CeilDiv().

Referenced by ResizeWindow(), and SurveyMemoryToText().

◆ CeilDiv()

constexpr uint CeilDiv	(	uint	a,
		uint	b
	)

constexpr

Computes ceil(a / b) for non-negative a and b.

Parameters

a	Numerator
b	Denominator

Returns: Quotient, rounded up

Definition at line 320 of file math_func.hpp.

Referenced by AfterLoadGame(), AircraftController(), NWidgetMatrix::AssignSizePosition(), BuildLandLegend(), CalcPercentVehicleFilled(), CalcRaildirsDrawstyle(), Ceil(), CompanyCheckBankrupt(), StationViewWindow::DrawAcceptedCargo(), StationViewWindow::DrawCargoRatings(), DepotWindow::DrawVehicleInDepot(), NWidgetMainToolbarContainer::GetButtonArrangement(), Train::GetCurveSpeedLimit(), GetLoadAmount(), SmallMapWindow::GetNumberRowsLegend(), GfxDoDrawLine(), InverseRemapCoords2(), MakeTreeTypeButtons(), DepotWindow::OnPaint(), Industry::RecomputeProductionMultipliers(), ReplaceChain(), Map::ScaleBySize(), Map::ScaleBySize1D(), ServerNetworkAdminSocketHandler::SendCompanyInfo(), ServerNetworkAdminSocketHandler::SendCompanyUpdate(), NWidgetMatrix::SetCount(), SurveyMemoryToText(), and UpdateVehicleTimetable().

◆ Clamp() [1/2]

constexpr int Clamp	(	const int	a,
		const int	min,
		const int	max
	)

constexpr

Clamp an integer between an interval.

This function returns a value which is between the given interval of min and max. If the given value is in this interval the value itself is returned otherwise the border of the interval is returned, according which side of the interval was 'left'.

Note: The min value must be less or equal of max or you get some unexpected results.

Parameters

a	The value to clamp/truncate.
min	The minimum of the interval.
max	the maximum of the interval.

Returns: A value between min and max which is closest to a.

See also: ClampU(uint, uint, uint)

Definition at line 129 of file math_func.hpp.

◆ Clamp() [2/2]

template<typename T >

constexpr T Clamp	(	const T	a,
		const T	min,
		const T	max
	)

constexpr

Clamp a value between an interval.

This function returns a value which is between the given interval of min and max. If the given value is in this interval the value itself is returned otherwise the border of the interval is returned, according which side of the interval was 'left'.

Note: The min value must be less or equal of max or you get some unexpected results.

Parameters

a	The value to clamp/truncate.
min	The minimum of the interval.
max	the maximum of the interval.

Returns: A value between min and max which is closest to a.

See also: ClampU(uint, uint, uint); Clamp(int, int, int)

Definition at line 79 of file math_func.hpp.

Referenced by AdjustGUIZoom(), AfterLoadGame(), AirportChangeInfo(), AmbientSoundEffectCallback(), AnimationBase< Tbase, Tspec, Tobj, Textra, GetCallback, Tframehelper >::AnimateTile(), BridgeChangeInfo(), ChangeIndustryProduction(), ClampSmoothScroll(), ClickChangeDateCheat(), ClickChangeMaxHlCheat(), ClickSliderWidget(), CmdTownRating(), Train::ConsistChanged(), CreateEffectVehicleAbove(), DrawRoadVehEngine(), DrawSliderWidget(), RefitWindow::DrawWidget(), EnsureVisibleCaption(), NetworkAskRelayWindow::FindWindowPlacementAndResize(), NetworkAskSurveyWindow::FindWindowPlacementAndResize(), GenerateLandscape(), GenerateTerrainPerlin(), GetAmplitude(), QueryString::GetBoundingRect(), Path::GetCapacityRatio(), Train::GetCurveSpeedLimit(), GetGlobalVariable(), GetPlatformInfo(), GetRoadVehLength(), GetSavegameFormat(), GetServiceIntervalClamped(), VideoDriver::GetSuggestedUIScale(), GetTileHeightBelowAircraft(), VehicleScopeResolver::GetVariable(), HandleCrashedAircraft(), HeightMapCurves(), IndustrytilesChangeInfo(), InitializeWindowViewport(), InverseRemapCoords2(), MakeBMPImage(), MakePCXImage(), MakePNGImage(), IntSettingDesc::MakeValueValid(), GenerateLandscapeWindow::OnClick(), CreateScenarioWindow::OnClick(), NetworkStartServerWindow::OnClick(), CustomCurrencyWindow::OnClick(), BuildBridgeWindow::OnInitialPosition(), SpriteAlignerWindow::OnInvalidateData(), GenerateLandscapeWindow::OnQueryTextFinished(), CreateScenarioWindow::OnQueryTextFinished(), NetworkStartServerWindow::OnQueryTextFinished(), OrdersWindow::OnQueryTextFinished(), CustomCurrencyWindow::OnQueryTextFinished(), MultiCommodityFlow::PushFlow(), RailTypeChangeInfo(), RecomputePrices(), SetAircraftPosition(), SetDateWindow::SetDateWindow(), Scrollbar::SetPosition(), SetPriceBaseMultiplier(), SetSelectionTilesDirty(), ScriptConfig::SetSetting(), SetStartingYear(), GRFConfig::SetValue(), SmallMapWindow::SetZoomLevel(), SoundEffectChangeInfo(), MusicDriver_Win32::Start(), TileHeightOutsideMap(), TileLoop_Town(), TownHouseChangeInfo(), TransmitNotesOff(), Train::UpdateAcceleration(), UpdateGUIZoom(), Scrollbar::UpdateListPositionOnKeyPress(), DisasterVehicle::UpdatePosition(), VehicleEnterDepot(), and VpSelectTilesWithMethod().

◆ ClampTo()

template<typename To , typename From , std::enable_if_t< std::is_integral< From >::value, int > = 0>

constexpr To ClampTo ( From value )

constexpr

Clamp the given value down to lie within the requested type.

Specialization of ClampTo for StrongType::Typedef.

For example ClampTo<uint8_t> will return a value clamped to the range of 0 to 255. Anything smaller will become 0, anything larger will become 255.

Parameters

a	The 64-bit value to clamp.

Returns: The 64-bit value reduced to a value within the given allowed range for the return type.

See also: Clamp(int, int, int)

Definition at line 167 of file math_func.hpp.

◆ ClampU()

constexpr uint ClampU	(	const uint	a,
		const uint	min,
		const uint	max
	)

constexpr

Clamp an unsigned integer between an interval.

This function returns a value which is between the given interval of min and max. If the given value is in this interval the value itself is returned otherwise the border of the interval is returned, according which side of the interval was 'left'.

Note: The min value must be less or equal of max or you get some unexpected results.

Parameters

a	The value to clamp/truncate.
min	The minimum of the interval.
max	the maximum of the interval.

Returns: A value between min and max which is closest to a.

See also: Clamp(int, int, int)

Definition at line 150 of file math_func.hpp.

Referenced by CalcClosestStationTile(), ChangeIndustryProduction(), ConvertFromOldCompanyManagerFace(), IntSettingDesc::MakeValueValid(), IndustryViewWindow::OnQueryTextFinished(), VideoDriver::UpdateAutoResolution(), and SavePresetWindow::UpdateWidgetSize().

◆ Delta()

template<typename T >

constexpr T Delta	(	const T	a,
		const T	b
	)

constexpr

Returns the (absolute) difference between two (scalar) variables.

Parameters

a	The first scalar
b	The second scalar

Returns: The absolute difference between the given scalars

Definition at line 234 of file math_func.hpp.

Referenced by DisasterTick_Big_Ufo(), DisasterTick_Big_Ufo_Destroyer(), DisasterTick_Ufo(), DistanceManhattan(), DistanceMax(), DistanceMaxPlusManhattan(), DrawTileSelection(), PlaceTreeAtSameHeight(), and VpSelectTilesWithMethod().

◆ DivideApprox()

int DivideApprox	(	int	a,
		int	b
	)

Deterministic approximate division.

Cancels out division errors stemming from the integer nature of the division over multiple runs.

Parameters

a	Dividend.
b	Divisor.

Returns: a/b or (a/b)+1.

Definition at line 22 of file math_func.cpp.

References abs().

Referenced by StationViewWindow::BuildCargoList(), and StationViewWindow::EstimateDestinations().

◆ IntSqrt()

uint32_t IntSqrt ( uint32_t num )

Compute the integer square root.

Parameters

num Radicand.

Returns: Rounded integer square root.

Note: Algorithm taken from http://en.wikipedia.org/wiki/Methods_of_computing_square_roots

Definition at line 42 of file math_func.cpp.

Referenced by CanalMaintenanceCost(), RailMaintenanceCost(), RoadMaintenanceCost(), SignalMaintenanceCost(), and StationMaintenanceCost().

◆ IsInsideBS()

template<typename T >

constexpr bool IsInsideBS	(	const T	x,
		const size_t	base,
		const size_t	size
	)

constexpr

Checks if a value is between a window started at some base point.

This function checks if the value x is between the value of base and base+size. If x equals base this returns true. If x equals base+size this returns false.

Parameters

x	The value to check
base	The base value of the interval
size	The size of the interval

Returns: True if the value is in the interval, false else.

Definition at line 252 of file math_func.hpp.

Referenced by AirportGetNearestTown(), CmdPlantTree(), OrthogonalTileArea::Contains(), ConvertSdlKeycodeIntoMy(), DrawTileSelection(), ScriptDebugWindow::DrawWidget(), FindStationsNearby(), FindWindowFromPt(), OrdersWindow::GetOrderFromPt(), GetSlopePixelZOutsideMap(), NWidgetNewGRFDisplay::GetWidgetFromPos(), NWidgetCore::GetWidgetFromPos(), NWidgetContainer::GetWidgetFromPos(), NWidgetStacked::GetWidgetFromPos(), NWidgetMatrix::GetWidgetFromPos(), NWidgetBackground::GetWidgetFromPos(), NewGRFInspectWindow::HasVariableParameter(), Scrollbar::IsVisible(), MoveBuoysToWaypoints(), IndustryViewWindow::OnClick(), NetworkContentListWindow::OnClick(), SpriteAlignerWindow::OnClick(), TransparenciesWindow::OnClick(), TranslateXYToTileCoord(), and ViewportAddLandscape().

◆ IsInsideMM()

template<typename T , std::enable_if_t< std::disjunction_v< std::is_convertible< T, size_t >, std::is_base_of< StrongTypedefBase, T > >, int > = 0>

constexpr bool IsInsideMM	(	const T	x,
		const size_t	min,
		const size_t	max
	)

constexprnoexcept

Checks if a value is in an interval.

Returns true if a value is in the interval of [min, max).

Parameters

x	The value to check
min	The minimum of the interval
max	The maximum of the interval

See also: IsInsideBS()

Definition at line 268 of file math_func.hpp.

Referenced by AddChildSpriteToFoundation(), AddDateIntroducedRailTypes(), AddDateIntroducedRoadTypes(), AfterLoadGame(), Map::Allocate(), CmdPlantTree(), RoadVehicle::Crash(), DeleteLastRoadVeh(), NetworkClientListWindow::DrawCompany(), GoalListWindow::DrawListColumn(), SmallMapWindow::DrawVehicles(), GraphLegendWindow::DrawWidget(), PerformanceRatingDetailWindow::DrawWidget(), LinkGraphLegendWindow::DrawWidget(), BuildSignalWindow::DrawWidget(), BuildRailDepotWindow::DrawWidget(), BuildRoadDepotWindow::DrawWidget(), SubsidyListWindow::DrawWidget(), FileList::FindItem(), MissingGlyphSearcher::FindMissingGlyphs(), FormatString(), GenerateCompanyName(), NetworkClientListWindow::GetButtonAtPoint(), QueryString::GetCharAtPosition(), Layouter::GetCharAtPosition(), GetClosestWaterDistance(), GetHalftileFoundationCorner(), IConsoleWindow::GetTextCharacterAtPosition(), GetTownRoadType(), HasRoadTypeAvail(), IsNonContinuousFoundation(), IsPtInWindowViewport(), IsSpecialRailFoundation(), IsValidCorner(), CITYChunkHandler::Load(), PLYRChunkHandler::LoadCheck(), MapGRFStringID(), ReplaceVehicleWindow::OnClick(), BuildVehicleWindow::OnClick(), CheatWindow::OnClick(), GSConfigWindow::OnClick(), GraphLegendWindow::OnClick(), PerformanceRatingDetailWindow::OnClick(), SelectGameWindow::OnClick(), LinkGraphLegendWindow::OnClick(), NewGRFParametersWindow::OnClick(), ScriptSettingsWindow::OnClick(), ScriptDebugWindow::OnClick(), ScenarioEditorLandscapeGenerationWindow::OnClick(), SmallMapWindow::OnMouseWheel(), LinkGraphLegendWindow::OnTooltip(), NetworkClientListWindow::OnTooltip(), PlaceTreeGroupAroundTile(), Vehicle::PreDestructor(), RemapOldStringID(), SwitchNewGRFBlitter(), TTDPStringIDToOTTDStringIDMapping(), Vehicle::UpdateVisualEffect(), LinkGraphLegendWindow::UpdateWidgetSize(), BuildSignalWindow::UpdateWidgetSize(), BuildRailDepotWindow::UpdateWidgetSize(), and BuildRoadDepotWindow::UpdateWidgetSize().

◆ PowerOfTen()

constexpr uint64_t PowerOfTen ( int power )

constexpr

Computes ten to the given power.

Parameters

power The power of ten to get.

Returns: The power of ten.

Definition at line 358 of file math_func.hpp.

Referenced by FormatString().

◆ RoundDivSU()

constexpr int RoundDivSU	(	int	a,
		uint	b
	)

constexpr

Computes round(a / b) for signed a and unsigned b.

Parameters

a	Numerator
b	Denominator

Returns: Quotient, rounded to nearest

Definition at line 342 of file math_func.hpp.

Referenced by IndustryViewWindow::DrawInfo(), DrawLayoutLine(), DrawStringMultiLine(), ScenarioEditorLandscapeGenerationWindow::DrawWidget(), TownViewWindow::DrawWidget(), HandleScrollbarScrolling(), IndustryViewWindow::OnClick(), IndustryViewWindow::OnQueryTextFinished(), and UpdateTownGrowCounter().

◆ SoftClamp()

template<typename T >

constexpr T SoftClamp	(	const T	a,
		const T	min,
		const T	max
	)

constexpr

Clamp a value between an interval.

This function returns a value which is between the given interval of min and max. If the given value is in this interval the value itself is returned otherwise the border of the interval is returned, according which side of the interval was 'left'.

Note: If the min value is greater than the max, return value is the average of the min and max.

Parameters

a	The value to clamp/truncate.
min	The minimum of the interval.
max	the maximum of the interval.

Returns: A value between min and max which is closest to a.

Definition at line 102 of file math_func.hpp.

Referenced by QueryWindow::FindWindowPlacementAndResize(), and TooltipsWindow::OnInitialPosition().

◆ Swap()

template<typename T >

constexpr void Swap	(	T &	a,
		T &	b
	)

constexpr

Type safe swap operation.

Parameters

a	variable to swap with b
b	variable to swap with a

Definition at line 283 of file math_func.hpp.

Referenced by AfterLoadGame(), BuildRailClick_Remove(), CalcHeightdiff(), CmdBuildAirport(), CmdBuildBridge(), GenerateCompanyColour(), GetNearbyTile(), GetPlatformInfo(), FlowStat::GetVia(), IsInRangeInclusive(), AirportSpec::IsWithinMapBounds(), AIConfigWindow::OnClick(), BuildRailStationWindow::OnPaint(), OrthogonalTileArea::OrthogonalTileArea(), PlaceRail_Station(), ReverseTrainSwapVeh(), FlowStat::SwapShares(), and UpdateTileSelection().

◆ ToPercent16()

constexpr uint ToPercent16 ( uint i )

constexpr

Converts a "fract" value 0..65535 to "percent" value 0..100.

Parameters

i	value to convert, range 0..65535

Returns: value in range 0..100

Definition at line 306 of file math_func.hpp.

Referenced by DrawVehiclePurchaseInfo(), VehicleDetailsWindow::DrawWidget(), and ProcessConditionalOrder().

◆ ToPercent8()

constexpr uint ToPercent8 ( uint i )

constexpr

Converts a "fract" value 0..255 to "percent" value 0..100.

Parameters

i	value to convert, range 0..255

Returns: value in range 0..100

Definition at line 295 of file math_func.hpp.

Referenced by StationViewWindow::DrawCargoRatings(), IndustryViewWindow::DrawInfo(), IndustryDirectoryWindow::GetCargoTransportedPercentsIfValid(), and IndustryDirectoryWindow::GetIndustryString().

Functions

Detailed Description

Function Documentation

◆ abs()

◆ Align()

◆ AlignPtr()

◆ Ceil()

◆ CeilDiv()

◆ Clamp() [1/2]

◆ Clamp() [2/2]

◆ ClampTo()

◆ ClampU()

◆ Delta()

◆ DivideApprox()

◆ IntSqrt()

◆ IsInsideBS()

◆ IsInsideMM()

◆ PowerOfTen()

◆ RoundDivSU()

◆ SoftClamp()

◆ Swap()

◆ ToPercent16()

◆ ToPercent8()