[Jprogramming] jwiki/Essays/FFT

[Bo Jacoby]

<henryhrich at nc.rr.com> wrote: "My roots-of-unity verb was designed to get higher accuracy than simpler approaches."

The verb
   PoU=:_1^+: NB. Power of Unity

is not contaminated by transcendental numbers such as (2p1) or transcendental functions such as monadic (^). If (y) is rational then (PoU y) is algebraic, so transcendence is not needed. The precision seems OK, even without the use of ((**|)&.+.) 

   n,.PoU(n=.i.8)%8
0                   1
1   0.707107j0.707107
2                 0j1
3  _0.707107j0.707107
4                  _1
5 _0.707107j_0.707107
6                0j_1
7  0.707107j_0.707107