Floor | <. 0 0 0 | Lesser Of (Min) |
<.y gives the floor of y , that is,
the largest integer less than or equal to y . Thus:<. 4.6 4 _4 _4.6 4 4 _4 _5The implied comparison with integers is tolerant, as discussed under Equal (=), and is controlled by <.!.t . See below for complex arguments. |
x<.y is the lesser of x and y .
For example:3 <. 4 _4 3 _4 <./7 8 5 9 2 2 <./\7 8 5 9 2 7 7 5 5 2 |
floor=: j./@(ip+(c2>c1),c1+:c2) '`c1 c2 fp ip'=:(1:>+/@fp)`(>:/@fp)`(+.-ip)`(<.@+.)As developed by McDonnell [10], this function has the following properties:
Convexity: | If (<.z1)=(<.z2) and z3 lies on the line between z1 to z2, then (<.z3)=(<.z1) . |
Translatability: | If z4 is a Gaussian integer, then (z4+<.z5)=(<.z4+z5) . |
Compatibility: | (<.x j.0)=((<.x)j.0) and (<.0 j.x)=(0 j.(<.x)) |
(>.&.- ; <.) 4.6 4 _4 _4.6 +---------+---------+ |4 4 _4 _5|4 4 _4 _5| +---------+---------+The expression <.x+0.5 gives the integer nearest to the real argument x . The number of digits needed to represent a positive integer is given by one plus the floor of its base ten logarithm:
a ,. (,. 1:+<.) 10^. a=: 9 10 11 99 100 101 9 0.954243 1 10 1 2 11 1.04139 2 99 1.99564 2 100 2 3 101 2.00432 3