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@verb #7214:"eqnsolve" this none this rxd #7214
@program #7214:"eqnsolve" this none this
"FLOAT zero = :eqnsolve(STR expr, FLOAT x0, FLOAT x1, FLOAT eps)"
""
"Returns a zero of the expression <expr> in the range [<x0>, <x1>], to an error <epsilon>.  The expression should be in a form \"return 2.0 - log(x);\" -- it must return a floating point number, and use x as its only argument."
"Note that results are not guaranteed (a) if there is no zero in the range, (b) if eps is too big [it should be generally a small number like 1e-6], (c) you commit some evil mathematical mistake like dividing by zero or taking the square root of a negative number, or (d) your equation expression isn't in the correct form."
{expr, x0, x1, eps} = args
"Do argument checking."
typeof(expr) != STR ? raise(E_ARGS, "expr is not a string.") | 0
typeof(x0) != FLOAT ? raise(E_ARGS, "x0 is not a float.") | 0
typeof(x1) != FLOAT ? raise(E_ARGS, "x1 is not a float.") | 0
typeof(eps) != FLOAT ? raise(E_ARGS, "eps is not a float.") | 0
x0 >= x1 ? raise(E_RANGE, "x0 must be less than x1.") | 0
"We're guaranteed termination as the search space halves with each execution."
while (1)
  {compiled, f0} = $no_one:eval(tostr("x = ", x0, "; ", expr))
  compiled ? 0 | raise(E_INVIND, "expr did not compile properly.")
  {compiled, f1} = $no_one:eval(tostr("x = ", x1, "; ", expr))
  compiled ? 0 | raise(E_INVIND, "expr did not compile properly.")
  x = (x0 + x1) / 2.0
  {compiled, f} = $no_one:eval(tostr("x = ", x, "; ", expr))
  compiled ? 0 | raise(E_INVIND, "expr did not compile properly.")
  if (f == 0.0 || abs(x0 - x1) < eps)
    return x
  elseif (f * f0 < 0.0)
    x1 = x
  else
    x0 = x
  endif
endwhile
"Last modified by JS (#7214) on Fri Nov  2 23:03:30 2001 MST."
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