%M = (
      A, sub { return                   $_[0] ** 2 -  22 * $_[0] +   8
+5 },
      B, sub { return                   $_[0] ** 2 +   9 * $_[0] +   2
+0 },
      C, sub { return                   $_[0] ** 2 -  16 * $_[0] -   3
+6 },
      D, sub { return $_[0] ** 3 - 15 * $_[0] ** 2 - 400 * $_[0] - 150
+0 },
      E, sub { return $_[0] ** 3 - 43 * $_[0] ** 2 + 590 * $_[0] - 260
+0 },
      F, sub { return                   $_[0] ** 2 -  19 * $_[0] -  15
+0 },
      G, sub { return $_[0] ** 3 - 98 * $_[0] ** 2 - 199 * $_[0] -  10
+0 },
      H, sub { return                   $_[0] ** 2 -  25 * $_[0] +  14
+4 },
      I, sub { return                   $_[0] ** 2 +  47 * $_[0] -  19
+0 },
      J, sub { return                   $_[0] ** 2 +  22 * $_[0] -   2
+3 },
      K, sub { return                   $_[0] ** 2 +  23 * $_[0] -  79
+8 },
      L, sub { return                   $_[0] ** 2 -  13 * $_[0] -   3
+0 },
      M, sub { return                   $_[0] ** 2 +  37 * $_[0] -  19
+0 },
      N, sub { return                   $_[0] ** 2 -   1 * $_[0] -   3
+0 },
      O, sub { return                   $_[0] ** 2 -   4 * $_[0] -   2
+1 },
      P, sub { return                   $_[0] ** 2 -  11 * $_[0] -   1
+2 },
      Q, sub { return $_[0] ** 3 - 12 * $_[0] ** 2 + 379 * $_[0] - 515
+6 },
      R, sub { return $_[0] ** 3 - 46 * $_[0] ** 2 + 679 * $_[0] - 323
+4 },
      S, sub { return                   $_[0] ** 2 +  44 * $_[0] -  14
+1 },
      T, sub { return                   $_[0] ** 2 -  12 * $_[0] +   3
+2 },
      U, sub { return                   $_[0] ** 2 +   9 * $_[0] -   2
+2 },
      V, sub { return                   $_[0] ** 2 +  14 * $_[0] +   3
+3 },
      W, sub { return                   $_[0] ** 2 +  37 * $_[0] -   1
+2 },
      X, sub { return $_[0] ** 3 + 11 * $_[0] ** 2 + 135 * $_[0] -  14
+2 },
      Y, sub { return                   $_[0] ** 2 -  59 * $_[0] -   1
+4 },
      Z, sub { return                   $_[0] ** 2 +  20 * $_[0] +   6
+4 }
);


$DELTA = 0.045;
$RANGE_LO = 0;
$RANGE_HI = 100;

sub binsearch {
    my($key, $lo, $hi) = @_;
    my($mid) = $lo + ($RANGE_HI - $hi) / $RANGE_HI;

    ++$mid;
    if ($lo/$mid + $DELTA <= 1.0) {
        if (&{$M{$key}}($mid) > 0) {
            return binsearch($key, $mid, $hi);
        } elsif (&{$M{$key}}($mid) < 0) {
            return binsearch($key, $lo + 1, $hi);
        } else {
            $RESULT[$mid]  = ($mid**2 - 13*$mid + 12 ? lc $key : $key)
+;
            $RESULT[$mid] .= ' ' if !($mid**3 - 30*$mid**2 + 269*$mid 
+- 660);

            return binsearch($key, $mid, $hi);
        }
    } else {
        return 0;
    }
}

foreach (keys %M) { # find roots of each equation in range
    binsearch($_, $RANGE_LO, $RANGE_HI);
}

print @RESULT;
print ",\n"; # for canonical JAPH form

[download]

In reply to ObJAPH by jima

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