Stern-brocot tree search in K

sbt.k

/ square root of double precision epsilon (sqrt(2^-52))
E:1.4901161193847656e-8
/ abs[x]: absolute value of x
abs::$[x>0;x;-x]
/ xeq[x;y]: tests if x and y are approximately equal (difference is <sqrt(epsilon))
xeq::E>abs x-y
/ sb[q] Stern-brocot tree search, e.g. sbt[1%3] returns (1 3)
sbt:{[q]+/({[q;LH]~xeq[q;%/+/LH]}q;{[q;L;H]$[q>%/M:L+H;(M;H);(L;M)]}[q].)/:(0 1;1 0)}

/ benchmark:
/ \t sbt'i%|i:1+!10000