OpenCores
URL https://opencores.org/ocsvn/openrisc_me/openrisc_me/trunk

Subversion Repositories openrisc_me

[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.18.0/] [newlib/] [libm/] [math/] [ef_jn.c] - Blame information for rev 207

Details | Compare with Previous | View Log

Line No. Rev Author Line
1 207 jeremybenn
/* ef_jn.c -- float version of e_jn.c.
2
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3
 */
4
 
5
/*
6
 * ====================================================
7
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8
 *
9
 * Developed at SunPro, a Sun Microsystems, Inc. business.
10
 * Permission to use, copy, modify, and distribute this
11
 * software is freely granted, provided that this notice
12
 * is preserved.
13
 * ====================================================
14
 */
15
 
16
#include "fdlibm.h"
17
 
18
#ifdef __STDC__
19
static const float
20
#else
21
static float
22
#endif
23
invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
24
two   =  2.0000000000e+00, /* 0x40000000 */
25
one   =  1.0000000000e+00; /* 0x3F800000 */
26
 
27
#ifdef __STDC__
28
static const float zero  =  0.0000000000e+00;
29
#else
30
static float zero  =  0.0000000000e+00;
31
#endif
32
 
33
#ifdef __STDC__
34
        float __ieee754_jnf(int n, float x)
35
#else
36
        float __ieee754_jnf(n,x)
37
        int n; float x;
38
#endif
39
{
40
        __int32_t i,hx,ix, sgn;
41
        float a, b, temp, di;
42
        float z, w;
43
 
44
    /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
45
     * Thus, J(-n,x) = J(n,-x)
46
     */
47
        GET_FLOAT_WORD(hx,x);
48
        ix = 0x7fffffff&hx;
49
    /* if J(n,NaN) is NaN */
50
        if(FLT_UWORD_IS_NAN(ix)) return x+x;
51
        if(n<0){
52
                n = -n;
53
                x = -x;
54
                hx ^= 0x80000000;
55
        }
56
        if(n==0) return(__ieee754_j0f(x));
57
        if(n==1) return(__ieee754_j1f(x));
58
        sgn = (n&1)&(hx>>31);   /* even n -- 0, odd n -- sign(x) */
59
        x = fabsf(x);
60
        if(FLT_UWORD_IS_ZERO(ix)||FLT_UWORD_IS_INFINITE(ix))
61
            b = zero;
62
        else if((float)n<=x) {
63
                /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
64
            a = __ieee754_j0f(x);
65
            b = __ieee754_j1f(x);
66
            for(i=1;i<n;i++){
67
                temp = b;
68
                b = b*((float)(i+i)/x) - a; /* avoid underflow */
69
                a = temp;
70
            }
71
        } else {
72
            if(ix<0x30800000) { /* x < 2**-29 */
73
    /* x is tiny, return the first Taylor expansion of J(n,x)
74
     * J(n,x) = 1/n!*(x/2)^n  - ...
75
     */
76
                if(n>33)        /* underflow */
77
                    b = zero;
78
                else {
79
                    temp = x*(float)0.5; b = temp;
80
                    for (a=one,i=2;i<=n;i++) {
81
                        a *= (float)i;          /* a = n! */
82
                        b *= temp;              /* b = (x/2)^n */
83
                    }
84
                    b = b/a;
85
                }
86
            } else {
87
                /* use backward recurrence */
88
                /*                      x      x^2      x^2
89
                 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
90
                 *                      2n  - 2(n+1) - 2(n+2)
91
                 *
92
                 *                      1      1        1
93
                 *  (for large x)   =  ----  ------   ------   .....
94
                 *                      2n   2(n+1)   2(n+2)
95
                 *                      -- - ------ - ------ -
96
                 *                       x     x         x
97
                 *
98
                 * Let w = 2n/x and h=2/x, then the above quotient
99
                 * is equal to the continued fraction:
100
                 *                  1
101
                 *      = -----------------------
102
                 *                     1
103
                 *         w - -----------------
104
                 *                        1
105
                 *              w+h - ---------
106
                 *                     w+2h - ...
107
                 *
108
                 * To determine how many terms needed, let
109
                 * Q(0) = w, Q(1) = w(w+h) - 1,
110
                 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
111
                 * When Q(k) > 1e4      good for single
112
                 * When Q(k) > 1e9      good for double
113
                 * When Q(k) > 1e17     good for quadruple
114
                 */
115
            /* determine k */
116
                float t,v;
117
                float q0,q1,h,tmp; __int32_t k,m;
118
                w  = (n+n)/(float)x; h = (float)2.0/(float)x;
119
                q0 = w;  z = w+h; q1 = w*z - (float)1.0; k=1;
120
                while(q1<(float)1.0e9) {
121
                        k += 1; z += h;
122
                        tmp = z*q1 - q0;
123
                        q0 = q1;
124
                        q1 = tmp;
125
                }
126
                m = n+n;
127
                for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
128
                a = t;
129
                b = one;
130
                /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
131
                 *  Hence, if n*(log(2n/x)) > ...
132
                 *  single 8.8722839355e+01
133
                 *  double 7.09782712893383973096e+02
134
                 *  long double 1.1356523406294143949491931077970765006170e+04
135
                 *  then recurrent value may overflow and the result is
136
                 *  likely underflow to zero
137
                 */
138
                tmp = n;
139
                v = two/x;
140
                tmp = tmp*__ieee754_logf(fabsf(v*tmp));
141
                if(tmp<(float)8.8721679688e+01) {
142
                    for(i=n-1,di=(float)(i+i);i>0;i--){
143
                        temp = b;
144
                        b *= di;
145
                        b  = b/x - a;
146
                        a = temp;
147
                        di -= two;
148
                    }
149
                } else {
150
                    for(i=n-1,di=(float)(i+i);i>0;i--){
151
                        temp = b;
152
                        b *= di;
153
                        b  = b/x - a;
154
                        a = temp;
155
                        di -= two;
156
                    /* scale b to avoid spurious overflow */
157
                        if(b>(float)1e10) {
158
                            a /= b;
159
                            t /= b;
160
                            b  = one;
161
                        }
162
                    }
163
                }
164
                b = (t*__ieee754_j0f(x)/b);
165
            }
166
        }
167
        if(sgn==1) return -b; else return b;
168
}
169
 
170
#ifdef __STDC__
171
        float __ieee754_ynf(int n, float x)
172
#else
173
        float __ieee754_ynf(n,x)
174
        int n; float x;
175
#endif
176
{
177
        __int32_t i,hx,ix,ib;
178
        __int32_t sign;
179
        float a, b, temp;
180
 
181
        GET_FLOAT_WORD(hx,x);
182
        ix = 0x7fffffff&hx;
183
    /* if Y(n,NaN) is NaN */
184
        if(FLT_UWORD_IS_NAN(ix)) return x+x;
185
        if(FLT_UWORD_IS_ZERO(ix)) return -one/zero;
186
        if(hx<0) return zero/zero;
187
        sign = 1;
188
        if(n<0){
189
                n = -n;
190
                sign = 1 - ((n&1)<<1);
191
        }
192
        if(n==0) return(__ieee754_y0f(x));
193
        if(n==1) return(sign*__ieee754_y1f(x));
194
        if(FLT_UWORD_IS_INFINITE(ix)) return zero;
195
 
196
        a = __ieee754_y0f(x);
197
        b = __ieee754_y1f(x);
198
        /* quit if b is -inf */
199
        GET_FLOAT_WORD(ib,b);
200
        for(i=1;i<n&&ib!=0xff800000;i++){
201
            temp = b;
202
            b = ((float)(i+i)/x)*b - a;
203
            GET_FLOAT_WORD(ib,b);
204
            a = temp;
205
        }
206
        if(sign>0) return b; else return -b;
207
}

powered by: WebSVN 2.1.0

© copyright 1999-2024 OpenCores.org, equivalent to Oliscience, all rights reserved. OpenCores®, registered trademark.