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Josh Reuben
<< Extreme Optimization Numerical Libraries for .NET – Part 1 of n

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Extreme Optimization – Numerical Algorithm Support >>
Extreme Optimization –Mathematical Constants and Basic Functions
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Machine constants
The
MachineConstants
class  contains constants for floatingpoint arithmetic because the CLS
System.Single
and
Double
floatingpoint types do not follow the standard conventions and are useless. machine constants for the
Double
type:
machine precision
: Epsilon
,
SqrtEpsilon
CubeRootEpsilon
largest possible value:
MaxDouble
,
SqrtMaxDouble
,
LogMaxDouble
smallest Doubleprecision floating point number that is greater than zero:
MinDouble
,
SqrtMinDouble
,
LogMinDouble
A similar set of constants is available for the
Single
Datatype
Mathematical Constants
The
Constants
class contains static fields for many mathematical constants and
common
expressions involving small integers – if you are doing thousands of iterations, you wouldn't want to calculate
OneOverSqrtTwoPi
,
Sqrt17
or
Log17
!!!
Fundamental constants
E
 The base for the natural logarithm,
e
(2.718...).
EulersConstant
 (0.577...).
GoldenRatio
 (1.618...).
Pi
 the ratio between the circumference and the diameter of a circle (3.1415...).
Expressions involving fundamental constants:
TwoPi, PiOverTwo, PiOverFour, LogTwoPi, PiSquared, SqrPi, SqrtTwoPi, OneOverSqrtPi, OneOverSqrtTwoPi
Square roots of small integers
:
Sqrt2, Sqrt3, Sqrt5, Sqrt7, Sqrt17
Logarithms of small integers
:
Log2, Log3, Log10, Log17, InvLog10
Elementary Functions
The
IterativeAlgorithm<T>
class in the
Extreme.Mathematics
namespace
defines many elementary functions that are missing from
System.Math
.
Hyperbolic Trig Functions:
Cosh, Coth, Csch, Sinh, Sech, Tanh
Inverse Hyperbolic Trig Functions
:
Acosh, Acoth, Acsch, Asinh, Asech, Atanh
Exponential, Logarithmic and Miscellaneous Functions
:
ExpMinus1
 The exponential function minus one,
e
^{x}
1.
Hypot
 The hypotenuse of a
rightangled
triangle with specified sides.
LambertW
 Lambert's W function, the (real) solution
W
of
x
=
We
^{W}
.
Log1PlusX
 The natural logarithm of 1+
x
.
Pow
 A number raised to an integer power.
Posted on Thursday, January 6, 2011 7:57 PM
Numerical Computing

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Comments on this post: Extreme Optimization –Mathematical Constants and Basic Functions
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re: Extreme Optimization –Mathematical Constants and Basic Functions
New information provides useful idea that we can use in most of our projects. 
Antiquities of California
Left by
Williams George
on Dec 29, 2016 5:08 AM
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