テンプレート:Numのソースを表示

<includeonly>{{#switch:{{#expr:{{{1}}}}}|INF=INF|-INF=-INF|{{#ifexpr:({{{1}}})=trunc({{{1}}})|{{#expr:trunc({{{1}}})}}|{{#switch:1|{{#expr:({{{1}}})>0}}={{num/1|({{{1}}})}}|{{#expr:({{{1}}})<0}}=-({{num/1|-({{{1}}})}})|0}}}}}}</includeonly><noinclude>
This template has as parameter an expression and produces a decimal number. If the expression produces a number of type integer, the template returns exactly that integer. If the expression produces a float, the template returns the result with a format that is accepted in an expression, and with an accuracy such the system would round it to the same float; thus if applied to a result of the template, the template returns the same.

The format (in the examples shown with [[Template:Numfh]]) is ordinary decimal format, because scientific notation with a fixed normalisation in general does not allow a representation of the exact float, see [[Help:Calculation accuracy#Reconstruction of an internal number]]. 

For any float, 17 significant digits are enough to reconstruct it. Therefore we get for example:

*{{xpsoc|numfh|(2-2^-52)*2^-20}}
*{{xpsoc|numfh|(2-2^-52)*2^10}}
*{{xpsoc|numfh|(2-2^-52)*2^20}}

For numbers with a decimal point, trailing zeros are avoided:
*{{xpsoc|numfh|1e-3/8}}
*{{xpsoc|numfh|1e-10/8}}
*{{xpsoc|numfh|1e-20/8}}
*{{xpsoc|numfh|.00000000000000000000125}}
Large floats:
*{{xpsoc|numfh|3^39}}
Numbers of type integer have up to 19 digits:
*{{xpsoc|numfh|trunc3^trunc39}}