/* rpn udf:  min
/* purpose:  find minimum of a function
/* user's function is "fn"
/* lower limit stored in "a"
/* upper limit stored in "b"
/* step size stored in "dx"
/* desired accuracy is in "dxlim"
/* call to find minimum is "min"
/* upon exit, stack contains value of x at which minimum occurs
/*
/* Michael Borland, 1988
0 sto dx sto dxlim sto a sto b sto dx sto f0 sto f1 
  sto x0 sto x1
cle

udf
min
a sto x0 fn sto f0 pop  a dx + sto x1 fn sto f1 pop  loop1

udf
viewState
dx "dx = %e " 1 fprf pop
x0 "x0 = %e " 1 fprf pop
f0 "f0 = %e " 1 fprf pop
x1 "x1 = %e " 1 fprf pop
f1 "f1 = %e\n" 1 fprf pop

udf
loop1
viewState
stopNow 1 == pop pop ? :
f0 f1 < pop pop ? reset_steps : test_end advance loop1 $ $

udf
test_end
0 sto stopNow pop 
x1 b > pop pop ? 1 sto stopNow pop : test_end1 $

udf
test_end1
dx dxlim < pop pop ? x0 1 sto stopNow pop :  $

udf
advance
x1 sto x0 dx + sto x1 pop   f1 sto f0 pop   x1 fn sto f1 pop

udf
reset_steps
x0 dx - sto x0 fn sto f0 pop dx 2 / sto dx  x0 + sto x1 fn sto f1 pop
"subdivided\n" 1 puts
viewState
loop1

udf
fn
1.5 - sqr 2 -

-10 sto a 10 sto b 1 sto dx 1e-8 sto dxlim cle