/*
 *  ======================================================================
 *  math.c -- demonstrate simple math library functions and application of
 *            errno.h for checking range and domain errors.
 *
 *  Math Functions used here : fabs(x), sin(x), tan(x), atan2(y,x),
 *                             floor(x), and log(x).
 *  User defined functions   : trunc(x) -- truncate small values of x.
 *  ======================================================================
 *
 *  Copyright (C) 1994-96 by Mark Austin and David Mazzoni.
 *                                                                     
 *  This software is provided "as is" without express or implied warranty.
 *  Permission is granted to use this software on any computer system,
 *  and to redistribute it freely, subject to the following restrictions:
 * 
 *  1. The authors are not responsible for the consequences of use of
 *     this software, even if they arise from defects in the software.
 *  2. The origin of this software must not be misrepresented, either
 *     by explicit claim or by omission.
 *  3. Altered versions must be plainly marked as such, and must not
 *     be misrepresented as being the original software.
 *  4. This notice is to remain intact.
 *  ======================================================================
 */

#include <stdio.h>
#include <math.h>
#include <errno.h>  /* to allow checking of int errno */

static const float kfEpsilon = 1E-5; /* precision for loops & truncation */

/* Define a function to truncate small values to 0 */

double trunc( double dValToTruncate ) {
   if( fabs( dValToTruncate ) < kfEpsilon )
      return 0.0;
   else
      return dValToTruncate;
}

int main( void ) {
double dAngle;  /* for angles in this example      */
double dTang;   /* for the tangent of a test angle */
double dLimit;  /* limit for angles                */
double dNum;    /* for PI fraction calculation     */
double dY1, dY2, dY3;      

 /* [a] : Find and print the sin of angles from 0 to PI in PI/6 increments */

    dLimit = M_PI + kfEpsilon;                                         

    for( dAngle = 0.0; dAngle < dLimit; dAngle += M_PI/6 )
       printf( "sin(%4.2g) = %-4.2g\n", dAngle, trunc( sin( dAngle ) ) );

 /* [b] : Find the tangent of -3 PI / 4 */

    dTang = tan( -3*M_PI_4 );
    printf( "The tangent of %g (-3PI/4) radians is %g\n", -3*M_PI_4, dTang);

 /* [c] : Find the angle with tangent -root2 / -root2 in the third quadrant */

    dAngle = atan2( -M_SQRT2, -M_SQRT2 );
    printf( "The angle with tangent %g/%g is %g\n",
            -M_SQRT2, -M_SQRT2, dAngle );
    printf( "Checking, this value should be %g\n", -3*M_PI_4 );

 /* [d] : Find a rational expression in terms of PI (we know its a fraction of 4). */

    dNum = floor( dAngle*4/M_PI );
    printf( "Expressed as a PI fraction this is %g PI / %g\n", dNum, 4.0 );

 /* [e] : test for domain and range errors in math functions */

    /* [e.1] : domain error: for negative argument to log(x) */

    printf( "\nCurrent value of errno: %i", errno );
    dY1 = log( -1 );
    printf( "\nValue of dY1 after log(-1) is %f : errno = %i", dY1, errno );
    if( EDOM == errno ) { /* EDOM #defined in errno.h above */
        printf( "\nDomain error occured in log function." );
        errno = 0;        /* reset error status */
    }

    /* [e.2] : range error: for log( 0 ) */

    dY2 = log( 0 );
    printf( "\nValue of dY2 after log(0) is %f : errno = %i", dY2, errno );
    if( ERANGE == errno || EDOM == errno ) {
        printf( "\nRange or domain error occured in log function." );
        errno = 0;        /* reset error status */
    }
    printf( "\n" );

    /* [e.3] : range/overflow error: for 10^1000 */

    dY3 = pow( 10.0, 1000.0 );
    printf( "\nValue of dY3 after pow(10, 1000) is %f : errno = %i", dY3, errno );
    if( ERANGE == errno ) {
        printf( "\nRange error occured in pow() function." );
        errno = 0;       /* reset error status */
    }
    printf( "\n" );

 /* [f] : Simulate sequence of calculations containing error conditions */

    dY1 = 1.0/0.0;
    dY2 = 2.0*dY1;
    dY3 = dY2/dY1;
    printf( "Value of dY1 = 1.0/0.0 = %f\n", dY1 );
    printf( "         dY2 = 2.0*dY1 = %f\n", dY2 );
    printf( "         dY3 = dY2/dY1 = %f\n", dY3 );
}