projects / uclibc-ng.git / blame
| Commit | Line | Data |
|---|---|---|
| 1077fa4d EA |
1 | /* ynf.c |
| 2 | * | |
| 3 | * Bessel function of second kind of integer order | |
| 4 | * | |
| 5 | * | |
| 6 | * | |
| 7 | * SYNOPSIS: | |
| 8 | * | |
| 9 | * float x, y, ynf(); | |
| 10 | * int n; | |
| 11 | * | |
| 12 | * y = ynf( n, x ); | |
| 13 | * | |
| 14 | * | |
| 15 | * | |
| 16 | * DESCRIPTION: | |
| 17 | * | |
| 18 | * Returns Bessel function of order n, where n is a | |
| 19 | * (possibly negative) integer. | |
| 20 | * | |
| 21 | * The function is evaluated by forward recurrence on | |
| 22 | * n, starting with values computed by the routines | |
| 23 | * y0() and y1(). | |
| 24 | * | |
| 25 | * If n = 0 or 1 the routine for y0 or y1 is called | |
| 26 | * directly. | |
| 27 | * | |
| 28 | * | |
| 29 | * | |
| 30 | * ACCURACY: | |
| 31 | * | |
| 32 | * | |
| 33 | * Absolute error, except relative when y > 1: | |
| 34 | * | |
| 35 | * arithmetic domain # trials peak rms | |
| 36 | * IEEE 0, 30 10000 2.3e-6 3.4e-7 | |
| 37 | * | |
| 38 | * | |
| 39 | * ERROR MESSAGES: | |
| 40 | * | |
| 41 | * message condition value returned | |
| 42 | * yn singularity x = 0 MAXNUMF | |
| 43 | * yn overflow MAXNUMF | |
| 44 | * | |
| 45 | * Spot checked against tables for x, n between 0 and 100. | |
| 46 | * | |
| 47 | */ | |
| 48 | \f | |
| 49 | /* | |
| 50 | Cephes Math Library Release 2.2: June, 1992 | |
| 51 | Copyright 1984, 1987, 1992 by Stephen L. Moshier | |
| 52 | Direct inquiries to 30 Frost Street, Cambridge, MA 02140 | |
| 53 | */ | |
| 54 | ||
| 55 | #include <math.h> | |
| 56 | extern float MAXNUMF, MAXLOGF; | |
| 57 | ||
| 58 | float y0f(float), y1f(float), logf(float); | |
| 59 | ||
| 60 | float ynf( int nn, float xx ) | |
| 61 | { | |
| 62 | float x, an, anm1, anm2, r, xinv; | |
| 63 | int k, n, sign; | |
| 64 | ||
| 65 | x = xx; | |
| 66 | n = nn; | |
| 67 | if( n < 0 ) | |
| 68 | { | |
| 69 | n = -n; | |
| 70 | if( (n & 1) == 0 ) /* -1**n */ | |
| 71 | sign = 1; | |
| 72 | else | |
| 73 | sign = -1; | |
| 74 | } | |
| 75 | else | |
| 76 | sign = 1; | |
| 77 | ||
| 78 | ||
| 79 | if( n == 0 ) | |
| 80 | return( sign * y0f(x) ); | |
| 81 | if( n == 1 ) | |
| 82 | return( sign * y1f(x) ); | |
| 83 | ||
| 84 | /* test for overflow */ | |
| 85 | if( x <= 0.0 ) | |
| 86 | { | |
| 87 | mtherr( "ynf", SING ); | |
| 88 | return( -MAXNUMF ); | |
| 89 | } | |
| 90 | if( (x < 1.0) || (n > 29) ) | |
| 91 | { | |
| 92 | an = (float )n; | |
| 93 | r = an * logf( an/x ); | |
| 94 | if( r > MAXLOGF ) | |
| 95 | { | |
| 96 | mtherr( "ynf", OVERFLOW ); | |
| 97 | return( -MAXNUMF ); | |
| 98 | } | |
| 99 | } | |
| 100 | ||
| 101 | /* forward recurrence on n */ | |
| 102 | ||
| 103 | anm2 = y0f(x); | |
| 104 | anm1 = y1f(x); | |
| 105 | k = 1; | |
| 106 | r = 2 * k; | |
| 107 | xinv = 1.0/x; | |
| 108 | do | |
| 109 | { | |
| 110 | an = r * anm1 * xinv - anm2; | |
| 111 | anm2 = anm1; | |
| 112 | anm1 = an; | |
| 113 | r += 2.0; | |
| 114 | ++k; | |
| 115 | } | |
| 116 | while( k < n ); | |
| 117 | ||
| 118 | ||
| 119 | return( sign * an ); | |
| 120 | } |