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

Subversion Repositories openrisc_me

[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.17.0/] [newlib/] [libm/] [math/] [ef_jn.c] - Blame information for rev 455

Go to most recent revision | Details | Compare with Previous | View Log

Line No. Rev Author Line
1 148 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.