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diff --git a/libm/float/j1f.c b/libm/float/j1f.c
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-/* j1f.c
- *
- * Bessel function of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * float x, y, j1f();
- *
- * y = j1f( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of order one of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a polynomial approximation
- * 2
- * (w - r ) x P(w)
- * 1
- * 2
- * is used, where w = x and r is the first zero of the function.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x R(1/x^2) - 3pi/4. The function is
- *
- * j0(x) = Modulus(x) cos( Phase(x) ).
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 1.2e-7 2.5e-8
- * IEEE 2, 32 100000 2.0e-7 5.3e-8
- *
- *
- */
- /* y1.c
- *
- * Bessel function of second kind of order one
- *
- *
- *
- * SYNOPSIS:
- *
- * double x, y, y1();
- *
- * y = y1( x );
- *
- *
- *
- * DESCRIPTION:
- *
- * Returns Bessel function of the second kind of order one
- * of the argument.
- *
- * The domain is divided into the intervals [0, 2] and
- * (2, infinity). In the first interval a rational approximation
- * R(x) is employed to compute
- *
- * 2
- * y0(x) = (w - r ) x R(x^2) + 2/pi (ln(x) j1(x) - 1/x) .
- * 1
- *
- * Thus a call to j1() is required.
- *
- * In the second interval, the modulus and phase are approximated
- * by polynomials of the form Modulus(x) = sqrt(1/x) Q(1/x)
- * and Phase(x) = x + 1/x S(1/x^2) - 3pi/4. Then the function is
- *
- * y0(x) = Modulus(x) sin( Phase(x) ).
- *
- *
- *
- *
- * ACCURACY:
- *
- * Absolute error:
- * arithmetic domain # trials peak rms
- * IEEE 0, 2 100000 2.2e-7 4.6e-8
- * IEEE 2, 32 100000 1.9e-7 5.3e-8
- *
- * (error criterion relative when |y1| > 1).
- *
- */
-
-
-/*
-Cephes Math Library Release 2.2: June, 1992
-Copyright 1984, 1987, 1989, 1992 by Stephen L. Moshier
-Direct inquiries to 30 Frost Street, Cambridge, MA 02140
-*/
-
-
-#include <math.h>
-
-
-static float JP[5] = {
--4.878788132172128E-009f,
- 6.009061827883699E-007f,
--4.541343896997497E-005f,
- 1.937383947804541E-003f,
--3.405537384615824E-002f
-};
-
-static float YP[5] = {
- 8.061978323326852E-009f,
--9.496460629917016E-007f,
- 6.719543806674249E-005f,
--2.641785726447862E-003f,
- 4.202369946500099E-002f
-};
-
-static float MO1[8] = {
- 6.913942741265801E-002f,
--2.284801500053359E-001f,
- 3.138238455499697E-001f,
--2.102302420403875E-001f,
- 5.435364690523026E-003f,
- 1.493389585089498E-001f,
- 4.976029650847191E-006f,
- 7.978845453073848E-001f
-};
-
-static float PH1[8] = {
--4.497014141919556E+001f,
- 5.073465654089319E+001f,
--2.485774108720340E+001f,
- 7.222973196770240E+000f,
--1.544842782180211E+000f,
- 3.503787691653334E-001f,
--1.637986776941202E-001f,
- 3.749989509080821E-001f
-};
-
-static float YO1 = 4.66539330185668857532f;
-static float Z1 = 1.46819706421238932572E1f;
-
-static float THPIO4F = 2.35619449019234492885f; /* 3*pi/4 */
-static float TWOOPI = 0.636619772367581343075535f; /* 2/pi */
-extern float PIO4;
-
-
-float polevlf(float, float *, int);
-float logf(float), sinf(float), cosf(float), sqrtf(float);
-
-float j1f( float xx )
-{
-float x, w, z, p, q, xn;
-
-
-x = xx;
-if( x < 0 )
- x = -xx;
-
-if( x <= 2.0f )
- {
- z = x * x;
- p = (z-Z1) * x * polevlf( z, JP, 4 );
- return( p );
- }
-
-q = 1.0f/x;
-w = sqrtf(q);
-
-p = w * polevlf( q, MO1, 7);
-w = q*q;
-xn = q * polevlf( w, PH1, 7) - THPIO4F;
-p = p * cosf(xn + x);
-return(p);
-}
-
-
-
-
-extern float MAXNUMF;
-
-float y1f( float xx )
-{
-float x, w, z, p, q, xn;
-
-
-x = xx;
-if( x <= 2.0f )
- {
- if( x <= 0.0f )
- {
- mtherr( "y1f", DOMAIN );
- return( -MAXNUMF );
- }
- z = x * x;
- w = (z - YO1) * x * polevlf( z, YP, 4 );
- w += TWOOPI * ( j1f(x) * logf(x) - 1.0f/x );
- return( w );
- }
-
-q = 1.0f/x;
-w = sqrtf(q);
-
-p = w * polevlf( q, MO1, 7);
-w = q*q;
-xn = q * polevlf( w, PH1, 7) - THPIO4F;
-p = p * sinf(xn + x);
-return(p);
-}