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diff --git a/libm/float/k0f.c b/libm/float/k0f.c
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-/* k0f.c
- *
- * Modified Bessel function, third kind, order zero
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0f();
- *
- * y = k0f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns modified Bessel function of the third kind
- * of order zero of the argument.
- *
- * The range is partitioned into the two intervals [0,8] and
- * (8, infinity). Chebyshev polynomial expansions are employed
- * in each interval.
- *
- *
- *
- * ACCURACY:
- *
- * Tested at 2000 random points between 0 and 8. Peak absolute
- * error (relative when K0 > 1) was 1.46e-14; rms, 4.26e-15.
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 7.8e-7 8.5e-8
- *
- * ERROR MESSAGES:
- *
- * message condition value returned
- * K0 domain x <= 0 MAXNUM
- *
- */
- /* k0ef()
- *
- * Modified Bessel function, third kind, order zero,
- * exponentially scaled
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, k0ef();
- *
- * y = k0ef( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns exponentially scaled modified Bessel function
- * of the third kind of order zero of the argument.
- *
- *
- *
- * ACCURACY:
- *
- * Relative error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 30 30000 8.1e-7 7.8e-8
- * See k0().
- *
- */
-
-/*
-Cephes Math Library Release 2.0: April, 1987
-Copyright 1984, 1987 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-#include <math.h>
-
-/* Chebyshev coefficients for K0(x) + log(x/2) I0(x)
- * in the interval [0,2]. The odd order coefficients are all
- * zero; only the even order coefficients are listed.
- *
- * lim(x->0){ K0(x) + log(x/2) I0(x) } = -EUL.
- */
-
-static float A[] =
-{
- 1.90451637722020886025E-9f,
- 2.53479107902614945675E-7f,
- 2.28621210311945178607E-5f,
- 1.26461541144692592338E-3f,
- 3.59799365153615016266E-2f,
- 3.44289899924628486886E-1f,
--5.35327393233902768720E-1f
-};
-
-
-
-/* Chebyshev coefficients for exp(x) sqrt(x) K0(x)
- * in the inverted interval [2,infinity].
- *
- * lim(x->inf){ exp(x) sqrt(x) K0(x) } = sqrt(pi/2).
- */
-
-static float B[] = {
--1.69753450938905987466E-9f,
- 8.57403401741422608519E-9f,
--4.66048989768794782956E-8f,
- 2.76681363944501510342E-7f,
--1.83175552271911948767E-6f,
- 1.39498137188764993662E-5f,
--1.28495495816278026384E-4f,
- 1.56988388573005337491E-3f,
--3.14481013119645005427E-2f,
- 2.44030308206595545468E0f
-};
-
-/* k0.c */
-
-extern float MAXNUMF;
-
-#ifdef ANSIC
-float chbevlf(float, float *, int);
-float expf(float), i0f(float), logf(float), sqrtf(float);
-#else
-float chbevlf(), expf(), i0f(), logf(), sqrtf();
-#endif
-
-
-float k0f( float xx )
-{
-float x, y, z;
-
-x = xx;
-if( x <= 0.0f )
- {
- mtherr( "k0f", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x <= 2.0f )
- {
- y = x * x - 2.0f;
- y = chbevlf( y, A, 7 ) - logf( 0.5f * x ) * i0f(x);
- return( y );
- }
-z = 8.0f/x - 2.0f;
-y = expf(-x) * chbevlf( z, B, 10 ) / sqrtf(x);
-return(y);
-}
-
-
-
-float k0ef( float xx )
-{
-float x, y;
-
-
-x = xx;
-if( x <= 0.0f )
- {
- mtherr( "k0ef", DOMAIN );
- return( MAXNUMF );
- }
-
-if( x <= 2.0f )
- {
- y = x * x - 2.0f;
- y = chbevlf( y, A, 7 ) - logf( 0.5f * x ) * i0f(x);
- return( y * expf(x) );
- }
-
-y = chbevlf( 8.0f/x - 2.0f, B, 10 ) / sqrtf(x);
-return(y);
-}