#include <reg51.h>
/*
 * 1/(1+x) = 1 + sum( (-x)^i, 0<=i<=n )
 * S = 1 - x + x^2 - x^3 + x^4 - x^5
 *   = 1 - x( 1 - x + x^2 - x^3 + x^4 )
 *   = 1 - x( 1 - x( 1 - x + x^2 - x^3 ))
 *   = 1 - x( 1 - x( 1 - x( 1 - x + x^2 )))
 *   = 1 - x( 1 - x( 1 - x( 1 - x( 1 - x ))))
 *  S0 = 1 - x
 *  Si+1 = 1 - x*Si
 *  Considering scale:
 *  S = (m - m * x / m + m * x^2 / m^2 - m * x^3 / m^3 + m * x^4 / m^4 - m * x^5 / m^5)/m =
 *  = ( m - x(m - m*x/m + m*x^2/m^2 + m*x^3/m^3 + ... )/m)/m
 *  = ( m - x(m - x(m - m*x/m + m*x^2/m^2 + m*x^3/m^3)/m)/m)/m
 *  = ( m - x(m - x(m - x( m - x(m-x)/m)/m)/m)/m)/m
 *  S0 = m - x;
 *  Si+1 = m - x*Si/m;
 */

typedef unsigned int uint16_t;
typedef unsigned char uint8_t;

main( ) {

    uint16_t num, x, m = 100;
    uint8_t j;
    // m is a scale.
    for( x = 0; x< 100; x++ ) {
        num = m - x;
        for( j = 0; j < 50; j++ )
            num = m - x*num/m;
        P3 = num; // For analyzer.
    }
    while(1);
}