# Category : C Source Code

Archive : CEPHES22.ZIP

Filename : MOD2PI.C

*

* -- Steve Moshier

*/

#define TPI 6.283185307179586476925

main()

{

char s[40];

double a, n, t, x, y, z;

int lflg;

double floor(), ldexp(), sin();

x = TPI/4.0;

t = 1.0;

loop:

t = 2.0 * t;

/* Stop testing at a point beyond which the integer part of

* x/2pi cannot be represented exactly by a double precision number.

* The library trigonometry functions will probably give up long before

* this point is reached.

*/

if( t > 1.0e16 )

exit(0);

/* Adjust the following to choose a nontrivial x

* where test function(x) has a slope of about 1 or more.

*/

x = TPI * t + 0.5;

z = x;

lflg = 0;

inlup:

/* floor() returns the largest integer less than its argument.

* If you do not have this, or AINT(), then you may convert x/TPI

* to a long integer and then back to double; but in that case

* x will be limited to the largest value that will fit into a

* long integer.

*/

n = floor( z/TPI );

/* Carefully subtract 2 pi n from x.

* This is done by subtracting n * 2**k in such a way that there

* is no arithmetic cancellation error at any step. The k are the

* bits in the number 2 pi.

*

* If you do not have ldexp(), then you may multiply or

* divide n by an appropriate power of 2 after each step.

* For example:

* a = z - 4*n;

* a -= 2*n;

* n /= 4;

* a -= n; n/4

* n /= 8;

* a -= n; n/32

* etc.

* This will only work if division by a power of 2 is exact.

*/

a = z - ldexp(n, 2); /* 4n */

a -= ldexp( n, 1); /* 2n */

a -= ldexp( n, -2 ); /* n/4 */

a -= ldexp( n, -5 ); /* n/32 */

a -= ldexp( n, -9 ); /* n/512 */

a += ldexp( n, -15 ); /* add n/32768 */

a -= ldexp( n, -17 ); /* n/131072 */

a -= ldexp( n, -18 );

a -= ldexp( n, -20 );

a -= ldexp( n, -22 );

a -= ldexp( n, -24 );

a -= ldexp( n, -28 );

a -= ldexp( n, -32 );

a -= ldexp( n, -37 );

a -= ldexp( n, -39 );

a -= ldexp( n, -40 );

a -= ldexp( n, -42 );

a -= ldexp( n, -46 );

a -= ldexp( n, -47 );

/* Subtract what is left of 2 pi n after all the above reductions.

*/

a -= 2.44929359829470635445e-16 * n;

/* If the test is extended too far, it is possible

* to have chosen the wrong value of n. The following

* will fix that, but at some reduction in accuracy.

*/

if( (a > TPI) || (a < -1e-11) )

{

z = a;

lflg += 1;

printf( "Warning! Reduction failed on first try.\n" );

goto inlup;

}

if( a < 0.0 )

{

printf( "Warning! Reduced value < 0\n" );

a += TPI;

}

/* Compute the test function at x and at a = x mod 2 pi.

*/

y = sin(x);

z = sin(a);

printf( "sin(%.15e) error = %.3e\n", x, y-z );

goto loop;

}

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