Pastebin: halfpiarea.c

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2016-09-24 21:31

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 /* Computing the value of pi by integrating the area of a (half of a) circle.
 // by Joel Matthew Rees, 1 August 2013
 // Copyright Joel Matthew Rees
 //
 // Fair use acknowledged.
 //
 // All rights to this expression of the method reserved.
 //
 // (Starting from scratch isn't that hard,
 // and you'll like the results better.)
 //
 // Compile with the right libraries:
 // cc -Wall -lm -o halfpiArea halfpiArea.c
 */
 
 
 
 #include <stdio.h>
 #include <stdlib.h>
 #include <math.h>
 
 
 int main( int argc, char * argv[] )
 {
    double area = 0.0;
    double deltaX = 0.025;
    double lastX = -1.0;
    double x;
    double almostPi;
 
    if ( argc > 1 )
    {  deltaX = strtod( argv[ 1 ], NULL );
    }
 
    /* Note that starting from the half delta converges at least one decimal digit faster.
    // (That's because the height of the rectangle crosses the circle at midpoint, 
    // rather than left edge or right. Draw the pictures to see why.
    // This is right edge, but changing to midpoint or left edge is trivial.) 
    */
    for ( x = -1.0 + deltaX; x <= 1.0; x += deltaX )
    {
       double ysquared = 1.0 - ( x * x );
       double y = sqrt( ysquared );
       /* deltaX = x - lastX; */
       lastX = x;
       area += deltaX * y;
       if ( deltaX > 0.00005 )
       {  printf( "(%17.15g,%17.15g): %17.15g\n", x, y, area );
       }
    }
 
    almostPi = area * 2;
    printf( "Almost Pi: %17.15g\n", almostPi );
    return EXIT_SUCCESS;
 }