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AuxMath.pas
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{-------------------------------------------------------------------------------
This Source Code Form is subject to the terms of the Mozilla Public
License, v. 2.0. If a copy of the MPL was not distributed with this
file, You can obtain one at http://mozilla.org/MPL/2.0/.
-------------------------------------------------------------------------------}
{===============================================================================
AuxMath
This library provides small set of auxiliary mathematical functions
implemented explicitly for more types than what is common (in RTL).
It was, at first, developed only to provide combined DivCeil, DivFloor and
Min and Max for mixed types, but more functionality was added during later
development.
Given nature of this library, there are many overloads for each function
that differ only by argument type. Unfortunately, some type overloads
cannot be properly processed (recognized) by older compilers. As a
workaround, almost all functions are provided in two forms/names.
First form is with one- or two-letter prefix in name that marks which
type group the function accepts. These functions are always implemented
for all supported types - the prefixes are here to better distinguish
types, so that the compiler does not have problem recognizing them and
selecting proper overload. Following prefixes are currently used:
i - signed integers
u - unsigned integers
f - floating point (real) numbers
c - characters
s - strings
p - pointers
o - objects/classes
v - variants
g - TGUID
b - general untyped buffer
Second form is without prefix - the function has normal expected name
(eg. Max, DivMod, ...). Given the abovementioned problems, these do not
provide overloads for all supported types in all compilers. For details
about which types and what functions are affected, refer to "Overloading
information symbols" further down.
Version 1.3 (2025-01-24)
Last change (2025-01-24)
©2024-2025 František Milt
Contacts:
František Milt: [email protected]
Support:
If you find this code useful, please consider supporting its author(s) by
making a small donation using the following link(s):
https://www.paypal.me/FMilt
Changelog:
For detailed changelog and history please refer to this git repository:
github.com/TheLazyTomcat/Lib.AuxMath
Dependencies:
* AuxExceptions - github.com/TheLazyTomcat/Lib.AuxExceptions
AuxTypes - github.com/TheLazyTomcat/Lib.AuxTypes
Library AuxExceptions is required only when rebasing local exception classes
(see symbol AuxMath_UseAuxExceptions for details).
Indirect dependencies:
SimpleCPUID - github.com/TheLazyTomcat/Lib.SimpleCPUID
StrRect - github.com/TheLazyTomcat/Lib.StrRect
UInt64Utils - github.com/TheLazyTomcat/Lib.UInt64Utils
WinFileInfo - github.com/TheLazyTomcat/Lib.WinFileInfo
===============================================================================}
unit AuxMath;
{
AuxMath_PurePascal
If you want to compile this unit without ASM, don't want to or cannot define
PurePascal for the entire project and at the same time you don't want to or
cannot make changes to this unit, define this symbol for the entire project
and only this unit will be compiled in PurePascal mode.
}
{$IFDEF AuxMath_PurePascal}
{$DEFINE PurePascal}
{$ENDIF}
{
AuxMath_UseAuxExceptions
If you want library-specific exceptions to be based on more advanced classes
provided by AuxExceptions library instead of basic Exception class, and don't
want to or cannot change code in this unit, you can define global symbol
AuxMath_UseAuxExceptions to achieve this.
}
{$IF Defined(AuxMath_UseAuxExceptions)}
{$DEFINE UseAuxExceptions}
{$IFEND}
//------------------------------------------------------------------------------
{$IFDEF ENDIAN_BIG}
{$MESSAGE FATAL 'Big-endian system not supported'} // because of memory overlays
{$ENDIF}
{$IF Defined(CPU64) or Defined(CPU64BITS)}
{$DEFINE CPU64bit}
{$ELSEIF Defined(CPU16)}
{$MESSAGE FATAL '16bit CPU not supported'}
{$ELSE}
{$DEFINE CPU32bit}
{$IFEND}
{$IF Defined(CPUX86_64) or Defined(CPUX64)}
{$DEFINE x64}
{$ELSEIF Defined(CPU386)}
{$DEFINE x86}
{$ELSE}
{$DEFINE PurePascal}
{$IFEND}
{$IF Defined(WINDOWS) or Defined(MSWINDOWS)}
{$DEFINE Windows}
{$IFEND}
{$IFDEF FPC}
{$MODE ObjFPC}
{$INLINE ON}
{$DEFINE CanInline}
{$IFNDEF PurePascal}
{$ASMMODE Intel}
{$ENDIF}
{$ELSE}
{$IF (CompilerVersion >= 17)} // Delphi 2005+
{$DEFINE CanInline}
{$ELSE}
{$UNDEF CanInline}
{$IFEND}
{$ENDIF}
{$H+}
{$J-} // typed constants are not writeable
//------------------------------------------------------------------------------
// do not touch following defines!
{$UNDEF AM_OverflowChecks}
{$UNDEF AM_DistinctUCS4Str}
{$UNDEF AM_DistinctUTF8Str}
{$IFOPT Q+}
{$DEFINE AM_OverflowChecks}
{$ENDIF}
{$IFDEF FPC}
{$DEFINE AM_DistinctUCS4Str}
{$DEFINE AM_DistinctUTF8Str}
{$ELSE}
{$IF (CompilerVersion > 15)} // newer than Delphi 7
{$DEFINE AM_DistinctUCS4Str}
{$IF (CompilerVersion >= 17)} // Delphi 2005+
{$DEFINE AM_DistinctUTF8Str}
{$IFEND}
{$IFEND}
{$ENDIF}
interface
uses
SysUtils,
AuxTypes{$IFDEF UseAuxExceptions}, AuxExceptions{$ENDIF};
{===============================================================================
Overloading information symbols
===============================================================================}
{
This unit provides many overloaded variants for the same function, where
these differ only by arguments type. But in older compilers, some of these
types are either declared only as an alias for exiting type, or the compiler
might not be able to distinguish between some types when overloading based
only on input parameters (ie. no "var" or "out" modifier).
In such cases, it is not possible to provide all overloads, or those
overloads can be implemented but cannot be called (it will generate
"ambiguous overloaded call" compilation error) - therefore, these overloads
are not provided (they are removed from the compilation) in affected
compilers.
Following constants are here to provide a way of knowing whether such
overloads are present or not. Since these are true constants, they can be
used in conditional compilation, so there is no need for runtime binding -
all can be done statically at compilation.
There are always three constants for each problematic type. First is a
boolean (when true, overloads are present), second is numerical (N suffix,
integer, overloads are there when non-zero) and last (suffixed E) is only
declared when the overloads are provided (it can be used in Declared()
conditional).
For more details, refer to description of individual constants.
}
//------------------------------------------------------------------------------
{
Following constants are informing whether overloads accepting type UInt64
are available.
In old compilers, type UInt64 is not (fully) supported, therefore it is
declared only as an alias for type Int64 (to be more precise, Int64 is
retyped to UInt64). This means, among others, that overloads for types Int64
and UInt64 are basically the same and cannot be distinguished in calls
(although they can be compiled).
Unfortunatelly, this also means that, when UInt64 overloads are not present
but Int64 are, compiler will call Int64 overload when UInt64 values/variables
are passed, giving no warning about that. This can lead to hard-to-find bugs,
where you are getting wrong results because unsigned integers are treated as
signed.
So, given the abovementioned, it has been decided to remove not only UInt64,
but also Int64 overloads in problematic environments. But note that there are
always some prefixed variants that can be used with Int64 and UInt64 (named
so they do no clash).
Following functions are affected:
DivCeil
DivFloor
IsPow2
IntLog2
DivCeilPow2
DivFloorPow2
DivCeilPow2NoCheck
DivCeilPow2NC
DivFloorPow2NoCheck
DivFloorPow2NC
Min (any variant accepting Int64 or UInt64)
Max (any variant accepting Int64 or UInt64)
MinValue
MaxValue
CompareValue (any variant accepting Int64 or UInt64)
CompareValueOp (any variant accepting Int64 or UInt64)
IfThen
InRange
EnsureRange
}
const
DistinctOverloadUInt64 = {$IF Declared(NativeUInt64E)}True{$ELSE}False{$IFEND};
DistinctOverloadUInt64N = {$IF Declared(NativeUInt64E)}1{$ELSE}0{$IFEND};
{$IF Declared(NativeUInt64E)}
DistinctOverloadUInt64E = True;
{$IFEND}
//------------------------------------------------------------------------------
{
In modern compilers, the type UnicodeString is a distinct embedded (base)
type, but for old compilers, it is declared only as an alias for WideString.
There, distinct overloads for this type cannot be provided since they would
be completely the same as overloads for WideString.
That being said, you do not need to worry about whether this is so or not,
proper overload will be called in any way, it is here only to provide the
information.
Affected functions:
sIfThen
IfThen
NOTE - there is a non-overloaded function called IfThenUnicodeString, if
you want to be completely sure what is called.
}
const
DistinctOverloadUnicodeString = {$IF Declared(UnicodeIsWideE)}False{$ELSE}True{$IFEND};
DistinctOverloadUnicodeStringN = {$IF Declared(UnicodeIsWideE)}1{$ELSE}1{$IFEND};
{$IF not Declared(UnicodeIsWideE)}
DistinctOverloadUnicodeStringE = True;
{$IFEND}
//------------------------------------------------------------------------------
{
For some bizzare reason, old Delphi (namely D7) cannot distinguish between
untyped pointers and dynamic array types when overloading. Here, this affects
type UCS4String, because it is declared as a dynamic array of UCS4Char.
As a result, the overloads accepting this string type are removed in Delphi 7
and older (I have decided to remove these instead of overloads for pointers,
as those are used more often). Following constants can be used to discern
whether overloads for UCS4String are present or not during compilation.
Affected functions:
IfThen
NOTE - you can always use function IfThenUCS4String if you do not want to
deal with these details.
}
const
DistinctOverloadUCS4String = {$IFDEF AM_DistinctUCS4Str}True{$ELSE}False{$ENDIF};
DistinctOverloadUCS4StringN = {$IFDEF AM_DistinctUCS4Str}1{$ELSE}0{$ENDIF};
{$IFDEF AM_DistinctUCS4Str}
DistinctOverloadUCS4StringE = True;
{$ENDIF}
//------------------------------------------------------------------------------
{
In old Delphi, the type UTF8String is not distinguishable from AnsiString,
therefore in those compilers (older than D2005) the UTF8String overloads are
removed and AnsiString overloads are called instead (since these compilers do
not support code pages, and there is no conversion done, it should be ok).
Note that you do not need to change your code based on this particular
detail. If you call any function with UTF8String it will just be directed
to AnsiString overload (which, as mentioned above, should be ok).
Affected functions:
sIfThen
IfThen
NOTE - use function IfThenUTF8String if you want to be sure.
}
const
DistinctOverloadUTF8String = {$IFDEF AM_DistinctUTF8Str}True{$ELSE}False{$ENDIF};
DistinctOverloadUTF8StringN = {$IFDEF AM_DistinctUTF8Str}1{$ELSE}0{$ENDIF};
{$IFDEF AM_DistinctUTF8Str}
DistinctOverloadUTF8StringE = True;
{$ENDIF}
{===============================================================================
Library-specific exceptions
===============================================================================}
type
EAMException = class({$IFDEF UseAuxExceptions}EAEGeneralException{$ELSE}Exception{$ENDIF});
EAMInvalidOperation = class(EAMException);
EAMInvalidValue = class(EAMException);
EAMRangeError = class(EAMException);
EAMOverflowError = class(EAMException);
{===============================================================================
Public constants
===============================================================================}
{
Lowest and highest possible values of selected integer types. They can all be
obtained using stndard functions Low() and High(), but if anyone wants them
as constants, there they are...
}
const
MinInt8 = Int8($80); // -128
MaxInt8 = Int8($7F); // 127
MinShortInt = MinInt8;
MaxShortInt = MaxInt8;
MinShort = MinInt8;
MaxShort = MaxInt8;
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinUInt8 = UInt8(0);
MaxUInt8 = UInt8($FF); // 255
MinByte = MinUInt8;
MaxByte = MaxUInt8;
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinInt16 = Int16($8000); // -32768
MaxInt16 = Int16($7FFF); // 32767
MinSmallInt = MinInt16;
MaxSmallInt = MaxInt16;
MinSmall = MinInt16;
MaxSmall = MaxInt16;
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinUInt16 = UInt16(0);
MaxUInt16 = UInt16($FFFF); // 65535
MinWord = MinUInt16;
MaxWord = MaxUInt16;
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinInt32 = Int32($80000000); // -2147483648
MaxInt32 = Int32($7FFFFFFF); // 2147483647
{$IF SizeOf(LongInt) = 4}
MinLongInt = MinInt32;
MaxLongInt = MaxInt32;
MinLong = MinInt32;
MaxLong = MaxInt32;
{$IFEND}
{$IF SizeOf(Integer) = 4}
MinInteger = MinInt32;
MaxInteger = MaxInt32;
MinInt = MinInt32;
MaxInt = MaxInt32;
{$IFEND}
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinUInt32 = UInt32(0);
MaxUInt32 = UInt32($FFFFFFFF); // 4294967295
MinDWord = MinUInt32;
MaxDWord = MaxUInt32;
{$IF SizeOf(LongWord) = 4}
MinLongWord = MinUInt32;
MaxLongWord = MaxUInt32;
{$IFEND}
{$IF SizeOf(Cardinal) = 4}
MinCardinal = MinUInt32;
MaxCardinal = MaxUInt32;
{$IFEND}
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinInt64 = Int64($8000000000000000); // -9223372036854775808
MaxInt64 = Int64($7FFFFFFFFFFFFFFF); // 9223372036854775807
MinQuadInt = MinInt64;
MaxQuadInt = MaxInt64;
{$IF SizeOf(LongInt) = 8}
MinLongInt = MinInt64;
MaxLongInt = MaxInt64;
MinLong = MinInt64;
MaxLong = MaxInt64;
{$IFEND}
{$IF SizeOf(Integer) = 8}
MinInteger = MinInt64;
MaxInteger = MaxInt64;
MinInt = MinInt64;
MaxInt = MaxInt64;
{$IFEND}
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinUInt64 = UInt64(0);
MaxUInt64 = UInt64($FFFFFFFFFFFFFFFF); // 18446744073709551615
MinQuadWord = MinUInt64;
MaxQuadWord = MaxUInt64;
MinQWord = MinUInt64;
MaxQWord = MaxUInt64;
{$IF SizeOf(LongWord) = 8}
MinLongWord = MinUInt64;
MaxLongWord = MaxUInt64;
{$IFEND}
{$IF SizeOf(Cardinal) = 8}
MinCardinal = MinUInt64;
MaxCardinal = MaxUInt64;
{$IFEND}
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
MinPtrInt = {$IF SizeOf(PtrInt) = 8}MinInt64{$ELSE}MinInt32{$IFEND};
MaxPtrInt = {$IF SizeOf(PtrInt) = 8}MaxInt64{$ELSE}MaxInt32{$IFEND};
MinPtrUInt = {$IF SizeOf(PtrUInt) = 8}MinUInt64{$ELSE}MinUInt32{$IFEND};
MaxPtrUInt = {$IF SizeOf(PtrUInt) = 8}MaxUInt64{$ELSE}MaxUInt32{$IFEND};
//==============================================================================
{
Special values for half-precision (16bit) floating point number types.
Since those types are not supported by compiler and mostly not even by
hardware, they are declared only as structured types of the right size.
This means, among others, that they cannot be directly used in arithmetics
or comparisons, and their assignments are not automatically checked for
invalid encodings and SNaN.
}
const
Float16Min: Float16 = ($01,$00); // 5.96046e-8
Float16Max: Float16 = ($FF,$7B); // 65504
Float16MinNormal: Float16 = ($00,$04); // 6.10351562500000e-5 (lowest possible normalized value)
Float16MaxDenormal: Float16 = ($FF,$03); // 6.09755516052246e-5 (highest possible denormalized value)
Float16QNaN: Float16 = ($FF,$7F); // quiet NaN
Float16SNaN: Float16 = ($FF,$7D); // signaled NaN
Float16NaN: Float16 = ($FF,$7F); // quiet NaN
Float16Infinity: Float16 = ($00,$7C); // positive infinity
Float16Zero: Float16 = ($00,$00); // (+)0
Float16One: Float16 = ($00,$3C); // +1.0
Float16Indefinite: Float16 = ($00,$FE); // indefinite quiet NaN
MinFloat16: Float16 = ($01,$00); // Float16Min
MaxFloat16: Float16 = ($FF,$7B); // Float16Max
HalfMin: Half = ($01,$00); // 5.96046e-8
HalfMax: Half = ($FF,$7B); // 65504
HalfMinNormal: Half = ($00,$04); // 6.10351562500000e-5
HalfMaxDenormal: Half = ($FF,$03); // 6.09755516052246e-5
HalfQNaN: Half = ($FF,$7F); // quiet NaN
HalfSNaN: Half = ($FF,$7D); // signaled NaN
HalfNaN: Half = ($FF,$7F); // quiet NaN
HalfInfinity: Half = ($00,$7C); // positive infinity
HalfZero: Half = ($00,$00); // (+)0
HalfOne: Half = ($00,$3C); // +1.0
HalfIndefinite: Half = ($00,$FE); // indefinite quiet NaN
MinHalf: Half = ($01,$00); // HalfMin
MaxHalf: Half = ($FF,$7B); // HalfMax
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
{
Special values for single-precision (32bit) floating point number types.
Note on the implementation...
It is implemented the way it is (ie. as a disgusting hack misusing the fact
that typed constants are stored in memory) because I know of no other way
how to put arbitrary bit pattern into float constant (or, in this case,
static variable). The only other way I am aware of is declaring the symbols
as functions and returning proper values, but call overhead is no-go for me
here (yeah inlining and such, but still, it does not always work and so on).
So, to be completely clear, the special values are declared as global
variables overlayed on typed constants. The compilers are smart enough
to recognize it and (when writeable constants option is off, which here it
explicitly is) treat the variables in code as constants (ie. they cannot be
assigned to).
}
const
iFloat32Min: UInt32 = $00000001; // 1.40129846432482e-45
iFloat32Max: UInt32 = $7F7FFFFF; // 3.40282346638529e+38
iFloat32MinNormal: UInt32 = $00800000; // 1.17549435082229e-38
iFloat32MaxDenormal: UInt32 = $007FFFFF; // 1.17549421069244e-38
iFloat32QNaN: UInt32 = $7FFFFFFF; // quiet NaN
iFloat32SNaN: UInt32 = $7FBFFFFF; // signaled NaN
iFloat32NaN: UInt32 = $7FFFFFFF; // quiet NaN
iFloat32Infinity: UInt32 = $7F800000; // positive infinity
iFloat32Indefinite: UInt32 = $FFC00000; // indefinite quiet NaN
var
Float32Min: Float32 absolute iFloat32Min;
Float32Max: Float32 absolute iFloat32Max;
Float32MinNormal: Float32 absolute iFloat32MinNormal;
Float32MaxDenormal: Float32 absolute iFloat32MaxDenormal;
Float32QNaN: Float32 absolute iFloat32QNaN;
Float32SNaN: Float32 absolute iFloat32SNaN;
Float32NaN: Float32 absolute iFloat32NaN;
Float32Infinity: Float32 absolute iFloat32Infinity;
Float32Indefinite: Float32 absolute iFloat32Indefinite;
SingleMin: Single absolute iFloat32Min;
SingleMax: Single absolute iFloat32Max;
SingleMinNormal: Single absolute iFloat32MinNormal;
SingleMaxDenormal: Single absolute iFloat32MaxDenormal;
SingleQNaN: Single absolute iFloat32QNaN;
SingleSNaN: Single absolute iFloat32SNaN;
SingleNaN: Single absolute iFloat32NaN;
SingleInfinity: Single absolute iFloat32Infinity;
SingleIndefinite: Single absolute iFloat32Indefinite;
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
{
Special values for double-precision (64bit) floating point number types.
}
const
iFloat64Min: UInt64 = UInt64($0000000000000001); // 4.94065645841247e-324
iFloat64Max: UInt64 = UInt64($7FEFFFFFFFFFFFFF); // 1.79769313486232e+308
iFloat64MinNormal: UInt64 = UInt64($0010000000000000); // 2.2250738585072014e-308
iFloat64MaxDenormal: UInt64 = UInt64($000FFFFFFFFFFFFF); // 2.2250738585072009e-308
iFloat64QNaN: UInt64 = UInt64($7FFFFFFFFFFFFFFF); // quiet NaN
iFloat64SNaN: UInt64 = UInt64($7FF7FFFFFFFFFFFF); // signaled NaN
iFloat64NaN: UInt64 = UInt64($7FFFFFFFFFFFFFFF); // quiet NaN
iFloat64Infinity: UInt64 = UInt64($7FF0000000000000); // positive infinity
iFloat64Indefinite: UInt64 = UInt64($FFF8000000000000); // indefinite quiet NaN
var
Float64Min: Float64 absolute iFloat64Min;
Float64Max: Float64 absolute iFloat64Max;
Float64MinNormal: Float64 absolute iFloat64MinNormal;
Float64MaxDenormal: Float64 absolute iFloat64MaxDenormal;
Float64QNaN: Float64 absolute iFloat64QNaN;
Float64SNaN: Float64 absolute iFloat64SNaN;
Float64NaN: Float64 absolute iFloat64NaN;
Float64Infinity: Float64 absolute iFloat64Infinity;
Float64Indefinite: Float64 absolute iFloat64Indefinite;
DoubleMin: Double absolute iFloat64Min;
DoubleMax: Double absolute iFloat64Max;
DoubleMinNormal: Double absolute iFloat64MinNormal;
DoubleMaxDenormal: Double absolute iFloat64MaxDenormal;
DoubleQNaN: Double absolute iFloat64QNaN;
DoubleSNaN: Double absolute iFloat64SNaN;
DoubleNaN: Double absolute iFloat64NaN;
DoubleInfinity: Double absolute iFloat64Infinity;
DoubleIndefinite: Double absolute iFloat64Indefinite;
//-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
{
Special values for double-extended-precision (80bit) floating point number
types.
}
type
TAMFloat80Overlay = packed record
Mantissa: UInt64;
SignExponent: UInt16;
end;
const
iFloat80Min: TAMFloat80Overlay = (Mantissa: UInt64($0000000000000001); SignExponent: $0000); // 3.64519953188247460253e-4951
iFloat80Max: TAMFloat80Overlay = (Mantissa: UInt64($FFFFFFFFFFFFFFFF); SignExponent: $7FFE); // 1.18973149535723176502e+4932
iFloat80MinNormal: TAMFloat80Overlay = (Mantissa: UInt64($8000000000000000); SignExponent: $0001); // 3.36210314311209350626e-4932
iFloat80MaxDenormal: TAMFloat80Overlay = (Mantissa: UInt64($7FFFFFFFFFFFFFFF); SignExponent: $0000); // 3.36210314311209350590E-4932
iFloat80QNaN: TAMFloat80Overlay = (Mantissa: UInt64($FFFFFFFFFFFFFFFF); SignExponent: $7FFF); // quiet NaN
iFloat80SNaN: TAMFloat80Overlay = (Mantissa: UInt64($BFFFFFFFFFFFFFFF); SignExponent: $7FFF); // signaled NaN
iFloat80NaN: TAMFloat80Overlay = (Mantissa: UInt64($FFFFFFFFFFFFFFFF); SignExponent: $7FFF); // quiet NaN
iFloat80Infinity: TAMFloat80Overlay = (Mantissa: UInt64($8000000000000000); SignExponent: $7FFF); // positive infinity
iFloat80Indefinite: TAMFloat80Overlay = (Mantissa: UInt64($C000000000000000); SignExponent: $FFFF); // indefinite quiet NaN
{
Some super-special values for 80bit floats.
They are not supported by modern hardware and usually produce an exception
when used (except for pseudo-denormals, they are silently converted to
correct denormals or normalized values where possible).
pseudo-denormals ... denormals with integer bit (bit 63) in mantissa set to 1
unnormals ... seemingly normalized numbers, but with zero integer bit
pseudo-NaN ... values encoded as proper NaN, zero integer bit
pseudo-Infinity ... encoded as proper infinity, zero integer bit
}
iFloat80MinPseudoDenormal: TAMFloat80Overlay = (Mantissa: UInt64($8000000000000000); SignExponent: $0000); // 3.36210314311209350626e-4932 (lowest possible pseudo-denormal)
iFloat80MaxPseudoDenormal: TAMFloat80Overlay = (Mantissa: UInt64($FFFFFFFFFFFFFFFF); SignExponent: $0000); // 6.72420628622418701216e-4932 (highest possible pseudo-denormal)
iFloat80MinUnnormal: TAMFloat80Overlay = (Mantissa: UInt64($0000000000000000); SignExponent: $0001); // lowest possible unnormal
iFloat80MaxUnnormal: TAMFloat80Overlay = (Mantissa: UInt64($7FFFFFFFFFFFFFFF); SignExponent: $7FFE); // highest possible unnormal
iFloat80PseudoQNaN: TAMFloat80Overlay = (Mantissa: UInt64($7FFFFFFFFFFFFFFF); SignExponent: $7FFF); // quiet pseudo-NaN
iFloat80PseudoSNaN: TAMFloat80Overlay = (Mantissa: UInt64($3FFFFFFFFFFFFFFF); SignExponent: $7FFF); // signaled pseudo-NaN
iFloat80PseudoNaN: TAMFloat80Overlay = (Mantissa: UInt64($7FFFFFFFFFFFFFFF); SignExponent: $7FFF); // quiet pseudo-NaN
iFloat80PseudoInfinity: TAMFloat80Overlay = (Mantissa: UInt64($0000000000000000); SignExponent: $7FFF); // pseudo-infinity
var
Float80Min: Float80 absolute iFloat80Min;
Float80Max: Float80 absolute iFloat80Max;
Float80MinNormal: Float80 absolute iFloat80MinNormal;
Float80MaxDenormal: Float80 absolute iFloat80MaxDenormal;
Float80QNaN: Float80 absolute iFloat80QNaN;
Float80SNaN: Float80 absolute iFloat80SNaN;
Float80NaN: Float80 absolute iFloat80NaN;
Float80Infinity: Float80 absolute iFloat80Infinity;
Float80Indefinite: Float80 absolute iFloat80Indefinite;
Float80MinPseudoDenormal: Float80 absolute iFloat80MinPseudoDenormal;
Float80MaxPseudoDenormal: Float80 absolute iFloat80MaxPseudoDenormal;
Float80MinUnnormal: Float80 absolute iFloat80MinUnnormal;
Float80MaxUnnormal: Float80 absolute iFloat80MaxUnnormal;
Float80PseudoQNaN: Float80 absolute iFloat80PseudoQNaN;
Float80PseudoSNaN: Float80 absolute iFloat80PseudoSNaN;
Float80PseudoNaN: Float80 absolute iFloat80PseudoNaN;
Float80PseudoInfinity: Float80 absolute iFloat80PseudoInfinity;
{$IF SizeOf(Extended) = 10}
ExtendedMin: Extended absolute iFloat80Min;
ExtendedMax: Extended absolute iFloat80Max;
ExtendedMinNormal: Extended absolute iFloat80MinNormal;
ExtendedMaxDenormal: Extended absolute iFloat80MaxDenormal;
ExtendedQNaN: Extended absolute iFloat80QNaN;
ExtendedSNaN: Extended absolute iFloat80SNaN;
ExtendedNaN: Extended absolute iFloat80NaN;
ExtendedInfinity: Extended absolute iFloat80Infinity;
ExtendedIndefinite: Extended absolute iFloat80Indefinite;
ExtendedMinPseudoDenormal: Extended absolute iFloat80MinPseudoDenormal;
ExtendedMaxPseudoDenormal: Extended absolute iFloat80MaxPseudoDenormal;
ExtendedMinUnnormal: Extended absolute iFloat80MinUnnormal;
ExtendedMaxUnnormal: Extended absolute iFloat80MaxUnnormal;
ExtendedPseudoQNaN: Extended absolute iFloat80PseudoQNaN;
ExtendedPseudoSNaN: Extended absolute iFloat80PseudoSNaN;
ExtendedPseudoNaN: Extended absolute iFloat80PseudoNaN;
ExtendedPseudoInfinity: Extended absolute iFloat80PseudoInfinity;
{$ELSE}
ExtendedMin: Extended absolute iFloat64Min;
ExtendedMax: Extended absolute iFloat64Max;
ExtendedMinNormal: Extended absolute iFloat64MinNormal;
ExtendedMaxDenormal: Extended absolute iFloat64MaxDenormal;
ExtendedQNaN: Extended absolute iFloat64QNaN;
ExtendedSNaN: Extended absolute iFloat64SNaN;
ExtendedNaN: Extended absolute iFloat64NaN;
ExtendedInfinity: Extended absolute iFloat64Infinity;
ExtendedIndefinite: Extended absolute iFloat64Indefinite;
{$IFEND}
{===============================================================================
Public auxiliary constants
===============================================================================}
const
{
Highest and lowest integral value that can be stored in 64bit floating point
number (Double) without losing any information (the numbers have the same
magnitude, so negated positive limit can be used as low value, but for the
sake of clarity, both are provided).
}
AM_INT_DBL_HI = 9007199254740992; // $0020000000000000
AM_INT_DBL_LO = -9007199254740992; // $FFE0000000000000
// "nicer" alias (to get lower limit, just negate it)
Flt64MaxInt = AM_INT_DBL_HI;
{
Highest and lowest integral values that can be stored in Extended floating
point type, whatever its declaration might be, without losing infromation.
}
AM_INT_EXT_HI = {$IF SizeOf(Extended) = 10}High(Int64){$ELSE}AM_INT_DBL_HI{$IFEND};
AM_INT_EXT_LO = {$IF SizeOf(Extended) = 10}Low(Int64){$ELSE}AM_INT_DBL_LO{$IFEND};
AM_UINT_EXT_HI = {$IF SizeOf(Extended) = 10}MaxUInt64{$ELSE}AM_INT_DBL_HI{$IFEND};
{===============================================================================
Public auxiliary funtions - declaration
===============================================================================}
{
Use following two functions to transfer signed 64bit integer value to and
from floating point number. All compilers supporting type Int64 can do it
implicitly (or using Trunc), this functions are here to do controlled
conversion.
In Int64ToFloat, if the type Extended is declared only as an alias for
Double (Win64), the limits for transfer (AM_INT_DBL_LO,AM_INT_DBL_HI) are
in effect. The number must be within those limits otherwise an exception of
class EAMInvalidOperation is raised.
For FloatToInt64, the floating point number must not have non-zero fraction,
must be greater or equal to -2^63 and at the same time smaller than 2^63.
Also, when type extended is aliased to double, the number must lie within
limits for loss-less conversion to integer (must be within interval
[AM_INT_DBL_LO,AM_INT_DBL_HI]). If any mentioned rule is not observed, then
an exception of class EAMInvalidOperation is raised.
}
Function Int64ToFloat(const N: Int64): Extended;
Function FloatToInt64(const N: Extended): Int64;
{
Following functions transfer unsigned 64bit integer value to and from
floating point number. Newer compilers can do it, but older ones (those
without full support for type UInt64) might not be capable of doing it.
Note that both functions are doing the same checks as corresponding functions
for signed 64bit integers (of course here tweaked for unsigned).
}
Function UInt64ToFloat(const N: UInt64): Extended;
Function FloatToUInt64(const N: Extended): UInt64;
{===============================================================================
--------------------------------------------------------------------------------
Combined division and modulo
--------------------------------------------------------------------------------
===============================================================================}
{
Performs integer division and modulo as one operation, so there is no need to
call them separately when both quotient and remainder are required.
}
procedure iDivMod(const Dividend,Divisor: Int8; out Quotient,Remainder: Int8); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
procedure iDivMod(const Dividend,Divisor: Int16; out Quotient,Remainder: Int16); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
procedure iDivMod(const Dividend,Divisor: Int32; out Quotient,Remainder: Int32); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
procedure iDivMod(const Dividend,Divisor: Int64; out Quotient,Remainder: Int64); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
//------------------------------------------------------------------------------
procedure uDivMod(const Dividend,Divisor: UInt8; out Quotient,Remainder: UInt8); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
procedure uDivMod(const Dividend,Divisor: UInt16; out Quotient,Remainder: UInt16); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
procedure uDivMod(const Dividend,Divisor: UInt32; out Quotient,Remainder: UInt32); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
procedure uDivMod(const Dividend,Divisor: UInt64; out Quotient,Remainder: UInt64); overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
//------------------------------------------------------------------------------
procedure DivMod(const Dividend,Divisor: Int8; out Quotient,Remainder: Int8); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: Int16; out Quotient,Remainder: Int16); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: Int32; out Quotient,Remainder: Int32); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: Int64; out Quotient,Remainder: Int64); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: UInt8; out Quotient,Remainder: UInt8); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: UInt16; out Quotient,Remainder: UInt16); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: UInt32; out Quotient,Remainder: UInt32); overload;{$IFDEF CanInline} inline;{$ENDIF}
procedure DivMod(const Dividend,Divisor: UInt64; out Quotient,Remainder: UInt64); overload;{$IFDEF CanInline} inline;{$ENDIF}
{===============================================================================
--------------------------------------------------------------------------------
Combined division and ceiling
--------------------------------------------------------------------------------
===============================================================================}
{
Performs division and Ceil as one optimized operation (the calculation does
not use floating point unit/numbers, only integers, which ensures that no
information is lost due to precision problems in large float numbers).
}
Function iDivCeil(const Dividend,Divisor: Int8): Int8; overload;
Function iDivCeil(const Dividend,Divisor: Int16): Int16; overload;
Function iDivCeil(const Dividend,Divisor: Int32): Int32; overload;
Function iDivCeil(const Dividend,Divisor: Int64): Int64; overload;
//------------------------------------------------------------------------------
Function uDivCeil(const Dividend,Divisor: UInt8): UInt8; overload;
Function uDivCeil(const Dividend,Divisor: UInt16): UInt16; overload;
Function uDivCeil(const Dividend,Divisor: UInt32): UInt32; overload;
Function uDivCeil(const Dividend,Divisor: UInt64): UInt64; overload;
//------------------------------------------------------------------------------
Function DivCeil(const Dividend,Divisor: Int8): Int8; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivCeil(const Dividend,Divisor: Int16): Int16; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivCeil(const Dividend,Divisor: Int32): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function DivCeil(const Dividend,Divisor: Int64): Int64; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
Function DivCeil(const Dividend,Divisor: UInt8): UInt8; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivCeil(const Dividend,Divisor: UInt16): UInt16; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivCeil(const Dividend,Divisor: UInt32): UInt32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function DivCeil(const Dividend,Divisor: UInt64): UInt64; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
{===============================================================================
--------------------------------------------------------------------------------
Combined division and floor
--------------------------------------------------------------------------------
===============================================================================}
{
Performs division and Floor as one optimized operation (the calculation does
not utilize floating point unit/numbers).
}
Function iDivFloor(const Dividend,Divisor: Int8): Int8; overload;
Function iDivFloor(const Dividend,Divisor: Int16): Int16; overload;
Function iDivFloor(const Dividend,Divisor: Int32): Int32; overload;
Function iDivFloor(const Dividend,Divisor: Int64): Int64; overload;
//------------------------------------------------------------------------------
Function uDivFloor(const Dividend,Divisor: UInt8): UInt8; overload;
Function uDivFloor(const Dividend,Divisor: UInt16): UInt16; overload;
Function uDivFloor(const Dividend,Divisor: UInt32): UInt32; overload;
Function uDivFloor(const Dividend,Divisor: UInt64): UInt64; overload;
//------------------------------------------------------------------------------
Function DivFloor(const Dividend,Divisor: Int8): Int8; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivFloor(const Dividend,Divisor: Int16): Int16; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivFloor(const Dividend,Divisor: Int32): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function DivFloor(const Dividend,Divisor: Int64): Int64; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
Function DivFloor(const Dividend,Divisor: UInt8): UInt8; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivFloor(const Dividend,Divisor: UInt16): UInt16; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function DivFloor(const Dividend,Divisor: UInt32): UInt32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function DivFloor(const Dividend,Divisor: UInt64): UInt64; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
{===============================================================================
--------------------------------------------------------------------------------
64bit ceil and floor
--------------------------------------------------------------------------------
===============================================================================}
{
Standard Ceil and Floor functions are returning only Integers - that is,
32bit numbers. Following functions are here for situations where 64bit wide
integers are required.
Ceil64 and Floor64 are returning Int64, CeilU64 and FloorU64 are returning
UInt64.
Note that, if the N is beyond limits for UInt64, the CeilU64 and FloorU64
will raise an EAMInvalidOperation exception (in Ceil64 and Floor64, this is
manager by the compiler and the exception would be of class EInvalidOP).
}
Function Ceil64(const N: Extended): Int64;
Function Floor64(const N: Extended): Int64;
Function CeilU64(const N: Extended): UInt64;
Function FloorU64(const N: Extended): UInt64;
{===============================================================================
--------------------------------------------------------------------------------
Is positive integer power of 2
--------------------------------------------------------------------------------
===============================================================================}
{
Returns true when given number is a positive integer power of 2 (2^E, where E
is a positive integer), false otherwise.
Note that zero and negative numbers cannot be positive integer power of any
base, therefore in those cases false is returned.
}
Function iIsPow2(const N: Int8): Boolean; overload;
Function iIsPow2(const N: Int16): Boolean; overload;
Function iIsPow2(const N: Int32): Boolean; overload;
Function iIsPow2(const N: Int64): Boolean; overload;
//------------------------------------------------------------------------------
Function uIsPow2(const N: UInt8): Boolean; overload;
Function uIsPow2(const N: UInt16): Boolean; overload;
Function uIsPow2(const N: UInt32): Boolean; overload;
Function uIsPow2(const N: UInt64): Boolean; overload;
//------------------------------------------------------------------------------
Function IsPow2(const N: Int8): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IsPow2(const N: Int16): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IsPow2(const N: Int32): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function IsPow2(const N: Int64): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
Function IsPow2(const N: UInt8): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IsPow2(const N: UInt16): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IsPow2(const N: UInt32): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function IsPow2(const N: UInt64): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
{===============================================================================
--------------------------------------------------------------------------------
Integer logarithm base 2
--------------------------------------------------------------------------------
===============================================================================}
{
If the given number is a positive integer power of 2, then IntLog2 will
return the exponent (effectively Log2(N)).
If the number is zero, negative (for signed integers), or is generally not an
integer power of 2, then it will return -1.
}
Function iIntLog2(const N: Int8): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function iIntLog2(const N: Int16): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function iIntLog2(const N: Int32): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function iIntLog2(const N: Int64): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
//------------------------------------------------------------------------------
Function uIntLog2(const N: UInt8): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function uIntLog2(const N: UInt16): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function uIntLog2(const N: UInt32): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function uIntLog2(const N: UInt64): Int32; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
//------------------------------------------------------------------------------
Function IntLog2(const N: Int8): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IntLog2(const N: Int16): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IntLog2(const N: Int32): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function IntLog2(const N: Int64): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
Function IntLog2(const N: UInt8): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IntLog2(const N: UInt16): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function IntLog2(const N: UInt32): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IF Declared(DistinctOverloadUInt64E)}
Function IntLog2(const N: UInt64): Int32; overload;{$IFDEF CanInline} inline;{$ENDIF}
{$IFEND}
{===============================================================================
--------------------------------------------------------------------------------
Try combined division and modulo by integer power of 2
--------------------------------------------------------------------------------
===============================================================================}
{
If divisor is a positive integer power of 2, it will perform optimized
integer division and modulo in one operation, and return true.
Otherwise it will return false and both output parameters (quotient and
remainder) are undefined.
}
Function iTryDivModPow2(const Dividend,Divisor: Int8; out Quotient,Remainder: Int8): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function iTryDivModPow2(const Dividend,Divisor: Int16; out Quotient,Remainder: Int16): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function iTryDivModPow2(const Dividend,Divisor: Int32; out Quotient,Remainder: Int32): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function iTryDivModPow2(const Dividend,Divisor: Int64; out Quotient,Remainder: Int64): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
//------------------------------------------------------------------------------
Function uTryDivModPow2(const Dividend,Divisor: UInt8; out Quotient,Remainder: UInt8): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function uTryDivModPow2(const Dividend,Divisor: UInt16; out Quotient,Remainder: UInt16): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function uTryDivModPow2(const Dividend,Divisor: UInt32; out Quotient,Remainder: UInt32): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
Function uTryDivModPow2(const Dividend,Divisor: UInt64; out Quotient,Remainder: UInt64): Boolean; overload;{$IFNDEF PurePascal} register; assembler;{$ENDIF}
//------------------------------------------------------------------------------
Function TryDivModPow2(const Dividend,Divisor: Int8; out Quotient,Remainder: Int8): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: Int16; out Quotient,Remainder: Int16): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: Int32; out Quotient,Remainder: Int32): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: Int64; out Quotient,Remainder: Int64): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: UInt8; out Quotient,Remainder: UInt8): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: UInt16; out Quotient,Remainder: UInt16): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: UInt32; out Quotient,Remainder: UInt32): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}
Function TryDivModPow2(const Dividend,Divisor: UInt64; out Quotient,Remainder: UInt64): Boolean; overload;{$IFDEF CanInline} inline;{$ENDIF}