# Piecewise linear approximation
# Oscar Gustafsson, address@hidden

param inputbits, integer, > 0;
param partitionbits, integer, > 0;
param part1bits, integer;

param integerbitsoffset := 16;
param integerbitsslope := 16;

set Y := {0..(2^partitionbits-1)};
set Z := {0..(2^(inputbits-partitionbits)-1)};
param X{y in Y, z in Z} := 2^(inputbits-partitionbits)*y + z;

param fracweight := 2^(inputbits-partitionbits);

param pi := 3.14159265;

param f{y in Y, z in Z} := sin(X[y,z]/2^inputbits*pi/2);

var p{y in Y}, integer;
var q{y in Y}, integer;

var error>=0;

minimize e: error;

s.t. postive{y in Y, z in Z}: p[y]/(2^integerbitsoffset) + z/fracweight*q[y]/(2^integerbitsslope) - f[y,z] <= error;

s.t. negative{y in Y, z in Z}: -(p[y]/(2^integerbitsoffset) + z/fracweight*q[y]/(2^integerbitsslope) - f[y,z]) <= error;

solve;
display p;
display q;

end;