123 lines
2.7 KiB
C
123 lines
2.7 KiB
C
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/* Program to test range reduction of trigonometry functions
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*
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* -- Steve Moshier
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*/
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#include "mconf.h"
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#ifdef ANSIPROT
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extern double floor ( double );
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extern double ldexp ( double, int );
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extern double sin ( double );
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#else
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double floor(), ldexp(), sin();
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#endif
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#define TPI 6.283185307179586476925
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main()
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{
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char s[40];
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double a, n, t, x, y, z;
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int lflg;
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x = TPI/4.0;
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t = 1.0;
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loop:
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t = 2.0 * t;
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/* Stop testing at a point beyond which the integer part of
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* x/2pi cannot be represented exactly by a double precision number.
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* The library trigonometry functions will probably give up long before
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* this point is reached.
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*/
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if( t > 1.0e16 )
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exit(0);
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/* Adjust the following to choose a nontrivial x
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* where test function(x) has a slope of about 1 or more.
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*/
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x = TPI * t + 0.5;
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z = x;
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lflg = 0;
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inlup:
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/* floor() returns the largest integer less than its argument.
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* If you do not have this, or AINT(), then you may convert x/TPI
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* to a long integer and then back to double; but in that case
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* x will be limited to the largest value that will fit into a
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* long integer.
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*/
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n = floor( z/TPI );
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/* Carefully subtract 2 pi n from x.
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* This is done by subtracting n * 2**k in such a way that there
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* is no arithmetic cancellation error at any step. The k are the
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* bits in the number 2 pi.
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*
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* If you do not have ldexp(), then you may multiply or
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* divide n by an appropriate power of 2 after each step.
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* For example:
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* a = z - 4*n;
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* a -= 2*n;
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* n /= 4;
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* a -= n; n/4
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* n /= 8;
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* a -= n; n/32
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* etc.
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* This will only work if division by a power of 2 is exact.
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*/
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a = z - ldexp(n, 2); /* 4n */
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a -= ldexp( n, 1); /* 2n */
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a -= ldexp( n, -2 ); /* n/4 */
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a -= ldexp( n, -5 ); /* n/32 */
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a -= ldexp( n, -9 ); /* n/512 */
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a += ldexp( n, -15 ); /* add n/32768 */
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a -= ldexp( n, -17 ); /* n/131072 */
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a -= ldexp( n, -18 );
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a -= ldexp( n, -20 );
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a -= ldexp( n, -22 );
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a -= ldexp( n, -24 );
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a -= ldexp( n, -28 );
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a -= ldexp( n, -32 );
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a -= ldexp( n, -37 );
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a -= ldexp( n, -39 );
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a -= ldexp( n, -40 );
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a -= ldexp( n, -42 );
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a -= ldexp( n, -46 );
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a -= ldexp( n, -47 );
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/* Subtract what is left of 2 pi n after all the above reductions.
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*/
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a -= 2.44929359829470635445e-16 * n;
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/* If the test is extended too far, it is possible
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* to have chosen the wrong value of n. The following
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* will fix that, but at some reduction in accuracy.
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*/
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if( (a > TPI) || (a < -1e-11) )
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{
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z = a;
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lflg += 1;
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printf( "Warning! Reduction failed on first try.\n" );
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goto inlup;
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}
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if( a < 0.0 )
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{
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printf( "Warning! Reduced value < 0\n" );
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a += TPI;
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}
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/* Compute the test function at x and at a = x mod 2 pi.
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*/
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y = sin(x);
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z = sin(a);
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printf( "sin(%.15e) error = %.3e\n", x, y-z );
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goto loop;
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}
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