freepascal.compiler/docs/math.xml

<?xml version="1.0" encoding="ISO8859-1"?>
<fpdoc-descriptions>
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<package name="rtl">
<module name="math">
<short>Additional mathematical routines.</short>
<!-- \FPCexampledir{mathex} -->
<descr>
<p>
This document describes the <file>math</file> unit. The <var>math</var> unit
was initially written by Florian Klaempfl. It provides mathematical
functions which aren't covered by the system unit.
</p>
<p>
This chapter starts out with a definition of all types and constants
that are defined, after which an overview is presented of the available 
functions, grouped by category, and the last part contains a 
complete explanation of each function.
</p>
<p>
The following things must be taken into account when using this unit:
</p>
<ol>
<li>This unit is compiled in Object Pascal mode so all <var>integers</var> are 32 bit.</li>
<li> Some overloaded functions exist for data arrays of integers and
floats. When using the address operator (<var>@</var>) to pass an array of 
data to such a function, make sure the address is typecasted to the 
right type, or turn on the 'typed address operator' feature. failing to
do so, will cause the compiler not be able to decide which function you 
want to call.
</li>
</ol>
</descr>

<topic name="MinMaxRoutines">
<short>Min/max determination</short>
<descr>
<p>
Functions to determine the minimum or maximum of numbers:
</p>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="max"/></td><td>Maximum of 2 values</td></tr>
<tr><td><link id="maxIntValue"/></td><td>Maximum of an array of integer values</td></tr>
<tr><td><link id="maxvalue"/></td><td>Maximum of an array of values</td></tr>
<tr><td><link id="min"/></td><td>Minimum of 2 values</td></tr>
<tr><td><link id="minIntValue"/></td><td>Minimum of an array of integer values</td></tr>
<tr><td><link id="minvalue"/></td><td>Minimum of an array of values</td></tr>
</table>
</descr>
</topic>

<topic name="AngleConversionRoutines">
<short>Angle unit conversion</short>
<descr>
<p>
Routines to convert angles between different angle units.
</p>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="cycletorad"/></td><td>convert cycles to radians</td></tr>
<tr><td><link id="degtograd"/></td><td>convert degrees to grads</td></tr>
<tr><td><link id="degtorad"/></td><td>convert degrees to radians</td></tr>
<tr><td><link id="gradtodeg"/></td><td>convert grads to degrees</td></tr>
<tr><td><link id="gradtorad"/></td><td>convert grads to radians</td></tr>
<tr><td><link id="radtocycle"/></td><td>convert radians to cycles</td></tr>
<tr><td><link id="radtodeg"/></td><td>convert radians to degrees</td></tr>
<tr><td><link id="radtograd"/></td><td>convert radians to grads</td></tr>
</table>
</descr>
</topic>

<topic name="TrigoniometricRoutines">
<short>Trigoniometric functions</short>
<descr>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="arccos"/></td><td>calculate reverse cosine</td></tr>
<tr><td><link id="arcsin"/></td><td>calculate reverse sine</td></tr>
<tr><td><link id="arctan2"/></td><td>calculate reverse tangent</td></tr>
<tr><td><link id="cotan"/></td><td>calculate cotangent</td></tr>
<tr><td><link id="sincos"/></td><td>calculate sine and cosine</td></tr>
<tr><td><link id="tan"/></td><td>calculate tangent</td></tr>
</table>
</descr>
</topic>

<topic name="HyperbolicRoutines">
<short>Hyperbolic functions</short>
<descr>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="arcosh"/></td><td>caculate reverse hyperbolic cosine</td></tr>
<tr><td><link id="arsinh"/></td><td>caculate reverse hyperbolic sine</td></tr>
<tr><td><link id="artanh"/></td><td>caculate reverse hyperbolic tangent</td></tr>
<tr><td><link id="cosh"/></td><td>calculate hyperbolic cosine</td></tr>
<tr><td><link id="sinh"/></td><td>calculate hyperbolic sine</td></tr>
<tr><td><link id="tanh"/></td><td>calculate hyperbolic tangent</td></tr>
</table>
</descr>
</topic>

<topic name="ExpLogRoutines">
<short>Exponential and logarithmic functions</short>
<descr>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="intpower"/></td><td>Raise float to integer power</td></tr>
<tr><td><link id="ldexp"/></td><td>Calculate $2^p x$</td></tr>
<tr><td><link id="lnxp1"/></td><td>calculate <var>log(x+1)</var></td></tr>
<tr><td><link id="log10"/></td><td>calculate 10-base log</td></tr>
<tr><td><link id="log2"/></td><td>calculate 2-base log</td></tr>
<tr><td><link id="logn"/></td><td>calculate N-base log</td></tr>
<tr><td><link id="power"/></td><td>raise float to arbitrary power</td></tr>
</table>
</descr>
</topic>

<topic name="NumberConversionRoutines">
<short>Number converting</short>
<descr>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="ceil"/></td><td>Round to infinity</td></tr>
<tr><td><link id="floor"/></td><td>Round to minus infinity</td></tr>
<tr><td><link id="frexp"/></td><td>Return mantissa and exponent</td></tr>
</table>
</descr>
</topic>

<topic name="StatisticalRoutines">
<short>Statistical functions</short>
<descr>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="mean"/></td><td>Mean of values</td></tr>
<tr><td><link id="meanandstddev"/></td><td>Mean and standard deviation of values</td></tr>
<tr><td><link id="momentskewkurtosis"/></td><td>Moments, skew and kurtosis</td></tr>
<tr><td><link id="popnstddev"/></td><td>Population standarddeviation </td></tr>
<tr><td><link id="popnvariance"/></td><td>Population variance</td></tr>
<tr><td><link id="randg"/></td><td>Gaussian distributed randum value</td></tr>
<tr><td><link id="stddev"/></td><td>Standard deviation</td></tr>
<tr><td><link id="sum"/></td><td>Sum of values</td></tr>
<tr><td><link id="sumofsquares"/></td><td>Sum of squared values</td></tr>
<tr><td><link id="sumsandsquares"/></td><td>Sum of values and squared values</td></tr>
<tr><td><link id="totalvariance"/></td><td>Total variance of values</td></tr>
<tr><td><link id="variance"/></td><td>variance of values</td></tr>
</table>
</descr>
</topic>

<topic name="GeometricalRoutines">
<short>Geometrical functions</short>
<descr>
<table>
<th><td>Name</td><td>Description</td></th>
<tr><td><link id="hypot"/></td><td>Hypotenuse of triangle</td></tr>
<tr><td><link id="norm"/></td><td>Euclidian norm</td></tr>
</table>
</descr>
</topic>

<element name="Float">
<short>Float type used in all calls</short>
<descr>
All calculations are done with the Float type. This allows to
recompile the unit with a different float type to obtain a
desired precision. The pointer type <link id="PFloat"/>
is used in functions that accept an array of values of arbitrary length.
</descr>
</element>

<element name="PFloat">
<short>Pointer to <link id="Float"/> type.</short>
</element>

<element name="TPaymentTime">
<short>Type used in financial (interest) calculations.</short>
</element>
<element name="TPaymentTime.PTEndOfPeriod">
<short>End of period.</short>
</element>
<element name="TPaymentTime.PTStartOfPeriod">
<short>Start of period.</short>
</element>

<element name="EInvalidArgument">
<short>Exception raised when invalid arguments are passed to a function.</short>
</element>

<element name="arccos">
<short></short>
<descr>
<var>Arccos</var> returns the inverse cosine of its argument <var>x</var>. The
argument <var>x</var> should lie between -1 and 1 (borders included). 
</descr>
<errors>
If the argument <var>x</var> is not in the allowed range, an
<var>EInvalidArgument</var> exception is raised.
</errors>
<seealso>
<link id="arcsin"/>
<link id="arcosh"/>
<link id="arsinh"/>
<link id="artanh"/>
</seealso>
<example file="mathex/ex1"/>
</element>

<element name="arcosh">
<short></short>
<descr>
<var>Arcosh</var> returns the inverse hyperbolic cosine of its argument <var>x</var>. 
The argument <var>x</var> should be larger than 1. 

The <var>arccosh</var> variant of this function is supplied for Delphi 
compatibility.
</descr>
<errors>
If the argument <var>x</var> is not in the allowed range, an <var>EInvalidArgument</var>
exception is raised.
</errors>
<seealso>
<link id="cosh"/>
<link id="sinh"/>
<link id="arcsin"/>
<link id="arsinh"/>
<link id="artanh"/>,
<link id="tanh"/>
</seealso>
<example file="mathex/ex3"/>
</element>

<element name="arcsin">
<short></short>
<descr>
<var>Arcsin</var> returns the inverse sine of its argument <var>x</var>. The
argument <var>x</var> should lie between -1 and 1. 
</descr>
<errors>
If the argument <var>x</var> is not in the allowed range, an <var>EInvalidArgument</var>
exception is raised.
</errors>
<seealso>
<link id="arccos"/>
<link id="arcosh"/>
<link id="arsinh"/>
<link id="artanh"/>
</seealso>
<example file="mathex/ex2"/>
</element>


<element name="arctan2">
<short></short>
<descr>
<var>arctan2</var> calculates <var>arctan(y/x)</var>, and returns an angle in the
correct quadrant. The returned angle will be in the range $-\pi$ to
$\pi$ radians.
The values of <var>x</var> and <var>y</var> must be between -2\^{}64 and 2\^{}64,
moreover <var>x</var> should be different from zero.

On Intel systems this function is implemented with the native intel
<var>fpatan</var> instruction.
</descr>
<errors>
If <var>x</var> is zero, an overflow error will occur.
</errors>
<seealso>
<link id="arccos"/>
<link id="arcosh"/>
<link id="arsinh"/>
<link id="artanh"/>
</seealso>
<example file="mathex/ex6"/>
</element>

<element name="arsinh">
<short></short>
<descr>
<var>arsinh</var> returns the inverse hyperbolic sine of its argument <var>x</var>. 

The <var>arscsinh</var> variant of this function is supplied for Delphi 
compatibility.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="arcosh"/>
<link id="arccos"/>
<link id="arcsin"/>
<link id="artanh"/>
</seealso>
<example file="mathex/ex4"/>
</element>


<element name="artanh">
<short></short>
<descr>
<var>artanh</var> returns the inverse hyperbolic tangent of its argument <var>x</var>,
where <var>x</var> should lie in the interval [-1,1], borders included.

The <var>arctanh</var> variant of this function is supplied for Delphi compatibility.
</descr>
<errors>
In case <var>x</var> is not in the interval [-1,1], an <var>EInvalidArgument</var>
exception is raised.
</errors>
<seealso>
<link id="arcosh"/>
<link id="arccos"/>
<link id="arcsin"/>
<link id="artanh"/>
</seealso>
<example file="mathex/ex5"/>
</element>


<element name="ceil">
<short></short>
<descr>
<var>Ceil</var> returns the lowest integer number greater than or equal to <var>x</var>.
The absolute value of <var>x</var> should be less than <var>maxint</var>.
</descr>
<errors>
If the asolute value of <var>x</var> is larger than maxint, an overflow error will
occur.
</errors>
<seealso>
<link id="floor"/>
</seealso>
<example file="mathex/ex7"/>
</element>

<element name="cosh">
<short></short>
<descr>
<var>Cosh</var> returns the hyperbolic cosine of it's argument {x}.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="arcosh"/>
<link id="sinh"/>
<link id="arsinh"/>
</seealso>
<example file="mathex/ex8"/>
</element>


<element name="cotan">
<short></short>
<descr>
<var>Cotan</var> returns the cotangent of it's argument <var>x</var>. <var>x</var> should
be different from zero.
</descr>
<errors>
If <var>x</var> is zero then a overflow error will occur.
</errors>
<seealso>
<link id="tanh"/>
</seealso>
<example file="mathex/ex9"/>
</element>


<element name="cycletorad">
<short></short>
<descr>
<var>Cycletorad</var> transforms it's argument <var>cycle</var>
(an angle expressed in cycles) to radians.
(1 cycle is $2 \pi$ radians).
</descr>
<errors>
None.
</errors>
<seealso>
<link id="degtograd"/>
<link id="degtorad"/>
<link id="radtodeg"/>,
<link id="radtograd"/>
<link id="radtocycle"/>
</seealso>
<example file="mathex/ex10"/>
</element>


<element name="degtograd">
<short></short>
<descr>
<var>Degtograd</var> transforms it's argument <var>deg</var> (an angle in degrees)
to grads.

(90 degrees is 100 grad.)
</descr>
<errors>
None.
</errors>
<seealso>
<link id="cycletorad"/>
<link id="degtorad"/>
<link id="radtodeg"/>,
<link id="radtograd"/>
<link id="radtocycle"/>
</seealso>
<example file="mathex/ex11"/>
</element>


<element name="degtorad">
<short></short>
<descr>
<var>Degtorad</var> converts it's argument <var>deg</var> (an angle in degrees) to
radians.

(pi radians is 180 degrees)
</descr>
<errors>
None.
</errors>
<seealso>
<link id="cycletorad"/>
<link id="degtograd"/>
<link id="radtodeg"/>,
<link id="radtograd"/>
<link id="radtocycle"/>
</seealso>
<example file="mathex/ex12"/>
</element>


<element name="floor">
<short></short>
<descr>
<var>Floor</var> returns the largest integer smaller than or equal to <var>x</var>.
The absolute value of <var>x</var> should be less than <var>maxint</var>.
</descr>
<errors>
If <var>x</var> is larger than <var>maxint</var>, an overflow will occur.
</errors>
<seealso>
<link id="ceil"/>
</seealso>
<example file="mathex/ex13"/>
</element>


<element name="frexp">
<short></short>
<descr>
<var>Frexp</var> returns the mantissa and exponent of it's argument
<var>x</var> in <var>mantissa</var> and <var>exponent</var>.
</descr>
<errors>
None
</errors>
<seealso>
</seealso>
<example file="mathex/ex14"/>
</element>


<element name="gradtodeg">
<short></short>
<descr>
<var>Gradtodeg</var> converts its argument <var>grad</var> (an angle in grads)
to degrees.

(100 grad is 90 degrees)
</descr>
<errors>
None.
</errors>
<seealso>
<link id="cycletorad"/>
<link id="degtograd"/>
<link id="radtodeg"/>,
<link id="radtograd"/>
<link id="radtocycle"/>
<link id="gradtorad"/>
</seealso>
<example file="mathex/ex15"/>
</element>


<element name="gradtorad">
<short></short>
<descr>
<var>Gradtorad</var> converts its argument <var>grad</var> (an angle in grads)
to radians.

(200 grad is pi degrees).
</descr>
<errors>
None.
</errors>
<seealso>
<link id="cycletorad"/>
<link id="degtograd"/>
<link id="radtodeg"/>,
<link id="radtograd"/>
<link id="radtocycle"/>
<link id="gradtodeg"/>
</seealso>
<example file="mathex/ex16"/>
</element>


<element name="hypot">
<short></short>
<descr>
<var>Hypot</var> returns the hypotenuse of the triangle where the sides
adjacent to the square angle have lengths <var>x</var> and <var>y</var>.

The function uses Pythagoras' rule for this.
</descr>
<errors>
None.
</errors>
<seealso>
</seealso>
<example file="mathex/ex17"/>
</element>


<element name="intpower">
<short></short>
<descr>
<var>Intpower</var> returns <var>base</var> to the power <var>exponent</var>,
where exponent is an integer value.
</descr>
<errors>
If <var>base</var> is zero and the exponent is negative, then an
overflow error will occur.
</errors>
<seealso>
<link id="power"/>
</seealso>
<example file="mathex/ex18"/>
</element>


<element name="ldexp">
<short></short>
<descr>
<var>Ldexp</var> returns $2^p x$.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="lnxp1"/>
<link id="log10"/>
<link id="log2"/>
<link id="logn"/>
</seealso>
<example file="mathex/ex19"/>
</element>


<element name="lnxp1">
<short></short>
<descr>
<var>Lnxp1</var> returns the natural logarithm of <var>1+X</var>. The result
is more precise for small values of <var>x</var>. <var>x</var> should be larger
than -1.
</descr>
<errors>
If $x\leq -1$ then an <var>EInvalidArgument</var> exception will be raised.
</errors>
<seealso>
<link id="ldexp"/>
<link id="log10"/>
<link id="log2"/>
<link id="logn"/>
</seealso>
<example file="mathex/ex20"/>
</element>

<element name="log10">
<short></short>
<descr>
<var>Log10</var> returns the 10-base logarithm of <var>X</var>.
</descr>
<errors>
If <var>x</var> is less than or equal to 0 an 'invalid fpu operation' error
will occur.
</errors>
<seealso>
<link id="ldexp"/>
<link id="lnxp1"/>
<link id="log2"/>
<link id="logn"/>
</seealso>
<example file="mathex/ex21"/>
</element>


<element name="log2">
<short></short>
<descr>
<var>Log2</var> returns the 2-base logarithm of <var>X</var>.
</descr>
<errors>
If <var>x</var> is less than or equal to 0 an 'invalid fpu operation' error
will occur.
</errors>
<seealso>
<link id="ldexp"/>
<link id="lnxp1"/>
<link id="log10"/>
<link id="logn"/>
</seealso>
<example file="mathex/ex22"/>
</element>


<element name="logn">
<short></short>
<descr>
<var>Logn</var> returns the n-base logarithm of <var>X</var>.
</descr>
<errors>
If <var>x</var> is less than or equal to 0 an 'invalid fpu operation' error
will occur.
</errors>
<seealso>
<link id="ldexp"/>
<link id="lnxp1"/>
<link id="log10"/>
<link id="log2"/>
</seealso>
<example file="mathex/ex23"/>
</element>

<element name="max">
<short></short>
<descr>
<var>Max</var> returns the maximum of <var>Int1</var> and <var>Int2</var>.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="min"/>
<link id="maxIntValue"/>
<link id="maxvalue"/>
</seealso>
<example file="mathex/ex24"/>
</element>

<element name="maxIntValue">
<short></short>
<descr>
<var>MaxIntValue</var> returns the largest integer out of the <var>Data</var>
array.

This function is provided for Delphi compatibility, use the <link id="maxvalue"/>
function instead.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="maxvalue"/>
<link id="minvalue"/>
<link id="minIntValue"/>
</seealso>
<example file="mathex/ex25"/>
</element>


<element name="maxvalue">
<short></short>
<descr>
<var>Maxvalue</var> returns the largest value in the <var>data</var> 
array with integer or float values. The return value has 
the same type as the elements of the array.

The third and fourth forms accept a pointer to an array of <var>N</var> 
integer or float values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="maxIntValue"/>
<link id="minvalue"/>
<link id="minIntValue"/>
</seealso>
<example file="mathex/ex26"/>
</element>

<element name="mean">
<short></short>
<descr>
<var>Mean</var> returns the average value of <var>data</var>.

The second form accepts a pointer to an array of <var>N</var> values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="meanandstddev"/>
<link id="momentskewkurtosis"/>
<link id="sum"/>
</seealso>
<example file="mathex/ex27"/>
</element>

<element name="meanandstddev">
<short></short>
<descr>
<var>meanandstddev</var> calculates the mean and standard deviation of <var>data</var>
and returns the result in <var>mean</var> and <var>stddev</var>, respectively.
Stddev is zero if there is only one value.

The second form accepts a pointer to an array of <var>N</var> values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="mean"/>
<link id="sum"/>
<link id="sumofsquares"/>
<link id="momentskewkurtosis"/>
</seealso>
<example file="mathex/ex28"/>
</element>


<element name="min">
<short></short>
<descr>
<var>min</var> returns the smallest value of <var>Int1</var> and <var>Int2</var>;
</descr>
<errors>
None.
</errors>
<seealso>
<link id="max"/>
</seealso>
<example file="mathex/ex29"/>
</element>

<element name="minIntValue">
<short></short>
<descr>
<var>MinIntvalue</var> returns the smallest value in the <var>Data</var> array.

This function is provided for Delphi compatibility, use <var>minvalue</var>
instead.
</descr>
<errors>
None
</errors>
<seealso>
<link id="minvalue"/>
<link id="maxIntValue"/>
<link id="maxvalue"/>
</seealso>
<example file="mathex/ex30"/>
</element>


<element name="minvalue">
<short></short>
<descr>
<var>Minvalue</var> returns the smallest value in the <var>data</var> 
array with integer or float values. The return value has 
the same type as the elements of the array.

The third and fourth forms accept a pointer to an array of <var>N</var> 
integer or float values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="maxIntValue"/>
<link id="maxvalue"/>
<link id="minIntValue"/>
</seealso>
<example file="mathex/ex31"/>
</element>


<element name="momentskewkurtosis">
<short></short>
<descr>
<var>momentskewkurtosis</var> calculates the 4 first moments of the distribution
of valuesin <var>data</var> and returns them in <var>m1</var>,<var>m2</var>,<var>m3</var> and
<var>m4</var>, as well as the <var>skew</var> and <var>kurtosis</var>.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="mean"/>
<link id="meanandstddev"/>
</seealso>
<example file="mathex/ex32"/>
</element>

<element name="norm">
<short></short>
<descr>
<var>Norm</var> calculates the Euclidian norm of the array of data.
This equals <var>sqrt(sumofsquares(data))</var>.

The second form accepts a pointer to an array of <var>N</var> values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="sumofsquares"/>
</seealso>
<example file="mathex/ex33"/>
</element>


<element name="popnstddev">
<short></short>
<descr>
<var>Popnstddev</var> returns the square root of the population variance of
the values in the  <var>Data</var> array. It returns zero if there is only one value.

The second form of this function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="popnvariance"/>
<link id="mean"/>
<link id="meanandstddev"/>
<link id="stddev"/>,
<link id="momentskewkurtosis"/>
</seealso>
<example file="mathex/ex35"/>
</element>


<element name="popnvariance">
<short></short>
<descr>
<var>Popnvariance</var> returns the square root of the population variance of
the values in the  <var>Data</var> array. It returns zero if there is only one value.

The second form of this function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="popnstddev"/>
<link id="mean"/>
<link id="meanandstddev"/>
<link id="stddev"/>,
<link id="momentskewkurtosis"/>
</seealso>
<example file="mathex/ex36"/>
</element>


<element name="power">
<short></short>
<descr>
<var>power</var> raises <var>base</var> to the power <var>power</var>. This is equivalent
to <var>exp(power*ln(base))</var>. Therefore <var>base</var> should be non-negative.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="intpower"/>
</seealso>
<example file="mathex/ex34"/>
</element>


<element name="radtocycle">
<short></short>
<descr>
<var>Radtocycle</var> converts its argument <var>rad</var> (an angle expressed in
radians) to an angle in cycles.

(1 cycle equals 2 pi radians)
</descr>
<errors>
None.
</errors>
<seealso>
<link id="degtograd"/>
<link id="degtorad"/>
<link id="radtodeg"/>,
<link id="radtograd"/>
<link id="cycletorad"/>
</seealso>
<example file="mathex/ex37"/>
</element>


<element name="radtodeg">
<short></short>
<descr>
<var>Radtodeg</var> converts its argument <var>rad</var> (an angle expressed in
radians) to an angle in degrees.

(180 degrees equals pi radians)
</descr>
<errors>
None.
</errors>
<seealso>
<link id="degtograd"/>
<link id="degtorad"/>
<link id="radtocycle"/>,
<link id="radtograd"/>
<link id="cycletorad"/>
</seealso>
<example file="mathex/ex38"/>
</element>


<element name="radtograd">
<short></short>
<descr>
<var>Radtodeg</var> converts its argument <var>rad</var> (an angle expressed in
radians) to an angle in grads.

(200 grads equals pi radians)
</descr>
<errors>
None.
</errors>
<seealso>
<link id="degtograd"/>
<link id="degtorad"/>
<link id="radtocycle"/>,
<link id="radtodeg"/>
<link id="cycletorad"/>
</seealso>
<example file="mathex/ex39"/>
</element>


<element name="randg">
<short></short>
<descr>
<var>randg</var> returns a random number which - when produced in large
quantities - has a Gaussian distribution with mean <var>mean</var> and 
standarddeviation <var>stddev</var>. 
</descr>
<errors>
None.
</errors>
<seealso>
<link id="mean"/>
<link id="stddev"/>
<link id="meanandstddev"/>
</seealso>
<example file="mathex/ex40"/>
</element>


<element name="sincos">
<short></short>
<descr>
<var>Sincos</var> calculates the sine and cosine of the angle <var>theta</var>,
and returns the result in <var>sinus</var> and <var>cosinus</var>.

On Intel hardware, This calculation will be faster than making 2 calls
to clculatet he sine and cosine separately.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="arcsin"/>
<link id="arccos"/>.
</seealso>
<example file="mathex/ex41"/>
</element>


<element name="sinh">
<short></short>
<descr>
<var>Sinh</var> returns the hyperbolic sine of its argument <var>x</var>.
</descr>
<errors>
</errors>
<seealso>
<link id="cosh"/>
<link id="arsinh"/>
<link id="tanh"/>
<link id="artanh"/>
</seealso>
<example file="mathex/ex42"/>
</element>


<element name="stddev">
<short></short>
<descr>
<var>Stddev</var> returns the standard deviation of the values in <var>Data</var>.
It returns zero if there is only one value.

The second form of the function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="mean"/>
<link id="meanandstddev"/>
<link id="variance"/>
<link id="totalvariance"/>
</seealso>
<example file="mathex/ex43"/>
</element>


<element name="sum">
<short></short>
<descr>
<var>Sum</var> returns the sum of the values in the <var>data</var> array.

The second form of the function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="sumofsquares"/>
<link id="sumsandsquares"/>
<link id="totalvariance"/>
, <link id="variance"/>
</seealso>
<example file="mathex/ex44"/>
</element>


<element name="sumofsquares">
<short></short>
<descr>
<var>Sumofsquares</var> returns the sum of the squares of the values in the <var>data</var> 
array.

The second form of the function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="sum"/>
<link id="sumsandsquares"/>
<link id="totalvariance"/>
, <link id="variance"/>
</seealso>
<example file="mathex/ex45"/>
</element>


<element name="sumsandsquares">
<short></short>
<descr>
<var>sumsandsquares</var> calculates the sum of the values and the sum of 
the squares of the values in the <var>data</var> array and returns the
results in <var>sum</var> and <var>sumofsquares</var>.

The second form of the function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="sum"/>
<link id="sumofsquares"/>
<link id="totalvariance"/>
, <link id="variance"/>
</seealso>
<example file="mathex/ex46"/>
</element>


<element name="tan">
<short></short>
<descr>
<var>Tan</var> returns the tangent of <var>x</var>.
</descr>
<errors>
If <var>x</var> (normalized) is pi/2 or 3pi/2 then an overflow will occur.
</errors>
<seealso>
<link id="tanh"/>
<link id="arcsin"/>
<link id="sincos"/>
<link id="arccos"/>
</seealso>
<example file="mathex/ex47"/>
</element>


<element name="tanh">
<short></short>
<descr>
<var>Tanh</var> returns the hyperbolic tangent of <var>x</var>.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="arcsin"/>
<link id="sincos"/>
<link id="arccos"/>
</seealso>
<example file="mathex/ex48"/>
</element>


<element name="totalvariance">
<short></short>
<descr>
<var>TotalVariance</var> returns the total variance of the values in the 
<var>data</var> array. It returns zero if there is only one value.

The second form of the function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="variance"/>
<link id="stddev"/>
<link id="mean"/>
</seealso>
<example file="mathex/ex49"/>
</element>


<element name="variance">
<short></short>
<descr>
<var>Variance</var> returns the variance of the values in the 
<var>data</var> array. It returns zero if there is only one value.

The second form of the function accepts a pointer to an array of <var>N</var>
values.
</descr>
<errors>
None.
</errors>
<seealso>
<link id="totalvariance"/>
<link id="stddev"/>
<link id="mean"/>
</seealso>
<example file="mathex/ex50"/>
</element>

</module>
</package>
</fpdoc-descriptions>