テンプレート:Truncのソースを表示

<includeonly>{{trunc/1|{{formatnum:{{{1}}}|R}}|{{formatnum:{{{2|}}}|R}}}}</includeonly><noinclude>

This template produces an expression for the truncated value of a given expression. If the value is in the range of integer-type numbers (in the range {{numf|trunc-2^63}} through {{numf|trunc(2^63-1024)+trunc1023}}), the resulting expression is of type integer.

The template also serves as a tool to enter an integer larger than {{numf|2^53}}, avoiding rounding to float: split the digits up into two parameters, each forming an integer not larger than that limit, and avoiding leading zeros in the second parameter. If the latter requires a larger first parameter: for every trailing 0 it can be a factor 2 larger then mentioned (see also [[Help:Calculation accuracy#Integers]]). To enter an integer smaller than -{{numf|2^53}} explicitly, do the same with a minus sign before each part.
 
Thus, when applying <code>#expr</code>, if the value is in the range of integer-type numbers the exact result is produced. The reason for not applying <code>#expr</code> in this template is:
*for integer-type numbers: in subsequent use in another expression the value would be rounded to float
*for floats: they would be rounded to 14 digits

==Examples==
Integer-type expressions (unchanged):
*{{xpsopocc|numf|trunc|trunc(2^63-1024)+trunc1023}}

Explicit integer values in the range of type integer:
*{{xpsoc|trunc|123|4567890123456789}}
*{{xpsoc|trunc|1234|567890123456789}}
*{{xpsoc|trunc|123456|7890123456789}}
*{{xpsoc|trunc|1234567|890123456789}}
*{{xpsoc|trunc|12345678|90123456789}}
*{{xpsoc|trunc|1234567890|123456789}}
*{{xpsoc|trunc|12345678901|23456789}}
*{{xpsoc|trunc|123456789012|3456789}}
*{{xpsoc|trunc|1234567890123|456789}}
*{{xpsoc|trunc|12345678901234|56789}}
*{{xpsoc|trunc|123456789012345|6789}}
*{{xpsoc|trunc|1234567890123456|789}}

*{{xpsopocc|numf|trunc|123|4567890123456789}}
*{{xpsopocc|numf|trunc|1234|567890123456789}}
*{{xpsopocc|numf|trunc|123456|7890123456789}}
*{{xpsopocc|numf|trunc|1234567|890123456789}}
*{{xpsopocc|numf|trunc|12345678|90123456789}}
*{{xpsopocc|numf|trunc|1234567890|123456789}}
*{{xpsopocc|numf|trunc|12345678901|23456789}}
*{{xpsopocc|numf|trunc|123456789012|3456789}}
*{{xpsopocc|numf|trunc|1234567890123|456789}}
*{{xpsopocc|numf|trunc|12345678901234|56789}}
*{{xpsopocc|numf|trunc|123456789012345|6789}}
*{{xpsopocc|numf|trunc|1234567890123456|789}}

*{{xpsopocc|numf|trunc|9e17|1}} (to avoid leading zeros in the second parameter, the first parameter is almost 100 times as large as 9,007,199,254,740,992. However, for every trailing 0 it can be a factor 2 larger then this number; in this case there are 17 trailing zeros; since the factor 100 is less than 2^17 the first parameter is exactly representable as float).

*{{xpsopocc|numf|trunc|-123|-4567890123456789}}

Float expressions with integer values in the range of type integer (the template converts them to type integer):
*{{xpsoocc|#expr:|trunc|-2^63}}

Float expressions with a non-integer value  (the template applies the mathematical trunc function and returns a result of type integer)::
*{{xpsopocc|numf|trunc|98.7}}
*{{xpsopocc|numf|trunc|20/3}}
*{{xpsopocc|numf|trunc|1e6/3}}

Floats outside the range of type integer (unchanged):
*{{xpsopocc|numfh|trunc|123.45e20}}
:Compare the operator trunc:
:*{{xpsoc|numf|trunc123.45e20}}

----
A leading zero in the second parameter is ignored:
*{{xpsopocc|numf|trunc|123456789|0123456789}}

If one of the integers is too large, it is rounded in the conversion to float, making the result inaccurate:
*{{xpsopocc|numf|trunc|1|234567890123456789}}
*{{xpsopocc|numf|trunc|12|34567890123456789}}
*{{xpsopocc|numf|trunc|12345678901234567|89}}
*{{xpsopocc|numf|trunc|123456789012345678|9}}

[[Category:Mathematical templates|{{PAGENAME}}]]</noinclude>