use strict;

sub reference_mapping {  # look-up table for verification purpose
    return substr("111222223333444444",$_[0]-1,1);
}

sub sentence2chapter_fa { # Fourier approximation 
    my $t = shift;
    die "$t not in range [1..18]" if ($t<1 || $t>18);
    return int ( 3.3 + 
		 -0.210463 * cos(0.31 * $t)  -1.319957 * sin(0.31 * $t) + 
		 -0.165006 * cos(0.63 * $t)  -0.475488 * sin(0.63 * $t) + 
		 -0.018111 * cos(0.94 * $t)  -0.365714 * sin(0.94 * $t) +
		  0.143325 * cos(1.26 * $t)  -0.368175 * sin(1.26 * $t)
		 );
}


sub heavyside {
    return $_[0] <= 0 ? 0 : 1; 
}

sub sentence2chapter_hs { # Heavyside approach
    my $t = shift;
    die "$t not in range [1..18]" if ($t<1 || $t>18);
    return heavyside($t       ) +
	   heavyside($t -  3.5) +
	   heavyside($t -  8.5) +
	   heavyside($t - 12.5);
}


print "Sentence Interpolation (delta)  Comment\n";
print "---------FA-(d)---HS-(d)---------------\n";

for my $sentence ( 1..18 ) {              # verification loop
    my $ref_chapter  = reference_mapping($sentence);
    my $fa           = sentence2chapter_fa($sentence);
    my $hs           = sentence2chapter_hs($sentence);
    my $comment      = $ref_chapter == $fa && $ref_chapter == $hs ? "ok" : "err";

    printf("%4d ->  %2d (%d)   %2d (%d)        %s\n", 
	   $sentence, 
	   $fa, 
	   $fa - $ref_chapter,
	   $hs,
	   $hs - $ref_chapter,
	   $comment);
}

__END__
Sentence Interpolation (delta)  Comment
---------FA-(d)---HS-(d)---------------
   1 ->   1 (0)    1 (0)        ok
   2 ->   1 (0)    1 (0)        ok
   3 ->   1 (0)    1 (0)        ok
   4 ->   2 (0)    2 (0)        ok
   5 ->   2 (0)    2 (0)        ok
   6 ->   2 (0)    2 (0)        ok
   7 ->   2 (0)    2 (0)        ok
   8 ->   2 (0)    2 (0)        ok
   9 ->   3 (0)    3 (0)        ok
  10 ->   3 (0)    3 (0)        ok
  11 ->   3 (0)    3 (0)        ok
  12 ->   3 (0)    3 (0)        ok
  13 ->   4 (0)    4 (0)        ok
  14 ->   4 (0)    4 (0)        ok
  15 ->   4 (0)    4 (0)        ok
  16 ->   4 (0)    4 (0)        ok
  17 ->   4 (0)    4 (0)        ok
  18 ->   4 (0)    4 (0)        ok