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Improved documentation, moved to float.gd, added IsRealFloat filter, … #2016

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Dec 18, 2017
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Improved documentation, moved to float.gd, added IsRealFloat filter, … #2016

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3f489dc
Improved documentation, moved to float.gd, added IsRealFloat filter, …
laurentbartholdi Dec 11, 2017
99b5e22
Added SignBit and SignFloat, documented RootsFloat
laurentbartholdi Dec 14, 2017
70eae78
Removed misleading reference to standard library in documentation of …
laurentbartholdi Dec 14, 2017
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182 changes: 12 additions & 170 deletions doc/ref/floats.xml
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Original file line number Diff line number Diff line change
Expand Up @@ -162,85 +162,7 @@ false
]]></Example>
<P/>

<ManSection>
<Heading>Mathematical operations</Heading>
<Attr Name="Cos" Arg="x"/>
<Attr Name="Sin" Arg="x"/>
<Attr Name="SinCos" Arg="x"/>
<Attr Name="Tan" Arg="x"/>
<Attr Name="Sec" Arg="x"/>
<Attr Name="Csc" Arg="x"/>
<Attr Name="Cot" Arg="x"/>
<Attr Name="Asin" Arg="x"/>
<Attr Name="Acos" Arg="x"/>
<Attr Name="Atan" Arg="x"/>
<Oper Name="Atan2" Arg="y x"/>
<Attr Name="Cosh" Arg="x"/>
<Attr Name="Sinh" Arg="x"/>
<Attr Name="Tanh" Arg="x"/>
<Attr Name="Sech" Arg="x"/>
<Attr Name="Csch" Arg="x"/>
<Attr Name="Coth" Arg="x"/>
<Attr Name="Asinh" Arg="x"/>
<Attr Name="Acosh" Arg="x"/>
<Attr Name="Atanh" Arg="x"/>
<Oper Name="Log" Arg="x"/>
<Attr Name="Log2" Arg="x"/>
<Attr Name="Log10" Arg="x"/>
<Attr Name="Log1p" Arg="x"/>
<Attr Name="Exp" Arg="x"/>
<Attr Name="Exp2" Arg="x"/>
<Attr Name="Exp10" Arg="x"/>
<Attr Name="Expm1" Arg="x"/>
<Attr Name="CubeRoot" Arg="x"/>
<Attr Name="Square" Arg="x"/>
<Oper Name="Hypothenuse" Arg="x y"/>
<Attr Name="Ceil" Arg="x"/>
<Attr Name="Floor" Arg="x"/>
<Attr Name="Round" Arg="x"/>
<Attr Name="Trunc" Arg="x"/>
<Attr Name="Frac" Arg="x"/>
<Attr Name="SignFloat" Arg="x"/>
<Attr Name="Erf" Arg="x"/>
<Attr Name="Zeta" Arg="x"/>
<Attr Name="Gamma" Arg="x"/>
<Description>
Usual mathematical functions.
</Description>
</ManSection>

<ManSection>
<Oper Name="EqFloat" Arg="x y"/>
<Returns>Whether the floateans <A>x</A> and <A>y</A> are equal</Returns>
<Description>
This function compares two floating-point numbers, and returns
<K>true</K> if they are equal, and <K>false</K> otherwise; with the
exception that <K>NaN</K> is always considered to be different from
itself.
</Description>
</ManSection>

<ManSection>
<Attr Name="PrecisionFloat" Arg="x"/>
<Returns>The precision of <A>x</A></Returns>
<Description>
This function returns the precision, counted in number of binary digits,
of the floating-point number <A>x</A>.
</Description>
</ManSection>

<ManSection>
<Prop Name="IsPInfinity" Arg="x"/>
<Prop Name="IsNInfinity" Arg="x"/>
<Prop Name="IsXInfinity" Arg="x"/>
<Prop Name="IsFinite" Arg="x" Label="float"/>
<Prop Name="IsNaN" Arg="x"/>
<Description>
Returns <K>true</K> if the floating-point number <A>x</A> is
respectively <M>+\infty</M>, <M>-\infty</M>, <M>\pm\infty</M>,
finite, or `not a number', such as the result of <C>0.0/0.0</C>.
</Description>
</ManSection>
<#Include Label="Float">

<ManSection>
<Var Name="FLOAT" Label="constants"/>
Expand All @@ -267,7 +189,9 @@ false
</Description>
</ManSection>

<#Include Label="Float">
<#Include Label="Float-Extra">
<#Include Label="Float-Infinities">
<#Include Label="Float-Math-Commands">

</Section>

Expand Down Expand Up @@ -307,30 +231,18 @@ optional second argument requesting a precision in binary digits.

<Section><Heading>Complex arithmetic</Heading>

Complex arithmetic may be implemented in packages, and is present
in <Package>float</Package>. Complex numbers are treated as usual
numbers; they may be input with an extra "i" as in <C>-0.5+0.866i</C>.
Complex arithmetic may be implemented in packages, and is present in
<Package>float</Package>. Complex numbers are treated as usual
numbers; they may be input with an extra "i" as in
<C>-0.5+0.866i</C>. They may also be created using <Ref
Oper="NewFloat"/> with three arguments: the float filter, the real
part, and the imaginary part.
<P/>

Methods should then be implemented for <C>Norm</C>, <C>RealPart</C>,
<C>ImaginaryPart</C>, <C>ComplexConjugate</C>, ...

<ManSection>
<Attr Name="ComplexI" Arg="x"/>
<Description>
Returns a floatean with the same precision and representation,
whose value equals the imaginary unit <C>i</C>.
</Description>
</ManSection>

<ManSection>
<Attr Name="Argument" Arg="z" Label="for complex numbers" />
<Description>
Returns the argument of the complex number <A>z</A>.
<!-- Define what the argument is? -->
</Description>
</ManSection>

<#Include Label="Float-Complex">

</Section>

Expand All @@ -348,77 +260,7 @@ Note the usual convention that intervals are compared as
in <M>[a,b]\le[c,d]</M> if and only if <M>a\le c</M> and <M>b\le
d</M>.

<ManSection>
<Attr Name="Sup" Arg="interval"/>
<Description>
Returns the supremum of the interval.
</Description>
</ManSection>
<ManSection>
<Attr Name="Inf" Arg="interval"/>
<Description>
Returns the infimum of the interval.
</Description>
</ManSection>
<ManSection>
<Attr Name="Mid" Arg="interval"/>
<Description>
Returns the midpoint of the interval.
</Description>
</ManSection>
<ManSection>
<Attr Name="AbsoluteDiameter" Arg="interval"/>
<Description>
Returns the absolute diameter of the interval.
<!-- FIXME: what does that mean? -->
</Description>
</ManSection>
<ManSection>
<Attr Name="RelativeDiameter" Arg="interval"/>
<Description>
Returns the relative diameter of the interval.
<!-- FIXME: what does that mean? -->
</Description>
</ManSection>
<ManSection>
<Oper Name="Overlaps" Arg="interval1 interval2"/>
<Description>
Returns <K>true</K> if the two intervals overlap.
<!-- FIXME: is that correct? -->
</Description>
</ManSection>
<ManSection>
<Oper Name="IsDisjoint" Arg="interval1 interval2"/>
<Description>
Returns <K>true</K> if the two intervals are disjoint.
</Description>
</ManSection>
<ManSection>
<Oper Name="IsSubset" Arg="interval1 interval2" Label="for floatean intervals"/>
<Description>
Returns <K>true</K> if the first interval contains the second.
</Description>
</ManSection>
<ManSection>
<Oper Name="IncreaseInterval" Arg="interval delta"/>
<Description>
Returns an interval with same midpoint but absolute diameter increased by
<A>delta</A>.
</Description>
</ManSection>
<ManSection>
<Oper Name="BlowupInterval" Arg="interval ratio"/>
<Description>
Returns an interval with same midpoint but relative diameter increased by
<A>ratio</A>.
</Description>
</ManSection>
<ManSection>
<Oper Name="BisectInterval" Arg="interval"/>
<Description>
Returns a list of two intervals whose union equals <A>interval</A>.
</Description>
</ManSection>
<#Include Label="Float-Intervals">

</Section>

Expand Down
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