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[/] [or1k/] [trunk/] [newlib/] [newlib/] [libm/] [math/] [ef_jn.c] - Blame information for rev 1775

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1 39 lampret 
/* ef_jn.c -- float version of e_jn.c.
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 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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 */
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/*
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 * ====================================================
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 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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 *
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 * Developed at SunPro, a Sun Microsystems, Inc. business.
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 * Permission to use, copy, modify, and distribute this
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 * software is freely granted, provided that this notice
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 * is preserved.
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 * ====================================================
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 */
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#include "fdlibm.h"
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#ifdef __STDC__
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static const float
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#else
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static float
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#endif
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invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */
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two   =  2.0000000000e+00, /* 0x40000000 */
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one   =  1.0000000000e+00; /* 0x3F800000 */
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#ifdef __STDC__
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static const float zero  =  0.0000000000e+00;
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#else
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static float zero  =  0.0000000000e+00;
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#endif
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#ifdef __STDC__
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        float __ieee754_jnf(int n, float x)
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#else
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        float __ieee754_jnf(n,x)
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        int n; float x;
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#endif
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{
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        __int32_t i,hx,ix, sgn;
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        float a, b, temp, di;
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        float z, w;
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    /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
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     * Thus, J(-n,x) = J(n,-x)
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     */
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        GET_FLOAT_WORD(hx,x);
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        ix = 0x7fffffff&hx;
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    /* if J(n,NaN) is NaN */
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        if(ix>0x7f800000) return x+x;
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        if(n<0){
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                n = -n;
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                x = -x;
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                hx ^= 0x80000000;
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        }
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        if(n==0) return(__ieee754_j0f(x));
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        if(n==1) return(__ieee754_j1f(x));
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        sgn = (n&1)&(hx>>31);   /* even n -- 0, odd n -- sign(x) */
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        x = fabsf(x);
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        if(ix==0||ix>=0x7f800000)        /* if x is 0 or inf */
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            b = zero;
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        else if((float)n<=x) {
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                /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
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            a = __ieee754_j0f(x);
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            b = __ieee754_j1f(x);
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            for(i=1;i<n;i++){
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                temp = b;
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                b = b*((float)(i+i)/x) - a; /* avoid underflow */
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                a = temp;
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            }
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        } else {
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            if(ix<0x30800000) { /* x < 2**-29 */
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    /* x is tiny, return the first Taylor expansion of J(n,x)
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     * J(n,x) = 1/n!*(x/2)^n  - ...
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     */
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                if(n>33)        /* underflow */
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                    b = zero;
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                else {
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                    temp = x*(float)0.5; b = temp;
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                    for (a=one,i=2;i<=n;i++) {
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                        a *= (float)i;          /* a = n! */
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                        b *= temp;              /* b = (x/2)^n */
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                    }
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                    b = b/a;
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                }
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            } else {
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                /* use backward recurrence */
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                /*                      x      x^2      x^2
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                 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
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                 *                      2n  - 2(n+1) - 2(n+2)
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                 *
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                 *                      1      1        1
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                 *  (for large x)   =  ----  ------   ------   .....
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                 *                      2n   2(n+1)   2(n+2)
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                 *                      -- - ------ - ------ -
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                 *                       x     x         x
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                 *
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                 * Let w = 2n/x and h=2/x, then the above quotient
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                 * is equal to the continued fraction:
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                 *                  1
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                 *      = -----------------------
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                 *                     1
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                 *         w - -----------------
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                 *                        1
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                 *              w+h - ---------
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                 *                     w+2h - ...
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                 *
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                 * To determine how many terms needed, let
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                 * Q(0) = w, Q(1) = w(w+h) - 1,
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                 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
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                 * When Q(k) > 1e4      good for single
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                 * When Q(k) > 1e9      good for double
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                 * When Q(k) > 1e17     good for quadruple
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                 */
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            /* determine k */
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                float t,v;
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                float q0,q1,h,tmp; __int32_t k,m;
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                w  = (n+n)/(float)x; h = (float)2.0/(float)x;
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                q0 = w;  z = w+h; q1 = w*z - (float)1.0; k=1;
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                while(q1<(float)1.0e9) {
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                        k += 1; z += h;
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                        tmp = z*q1 - q0;
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                        q0 = q1;
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                        q1 = tmp;
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                }
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                m = n+n;
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                for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
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                a = t;
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                b = one;
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                /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
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                 *  Hence, if n*(log(2n/x)) > ...
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                 *  single 8.8722839355e+01
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                 *  double 7.09782712893383973096e+02
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                 *  long double 1.1356523406294143949491931077970765006170e+04
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                 *  then recurrent value may overflow and the result is
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                 *  likely underflow to zero
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                 */
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                tmp = n;
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                v = two/x;
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                tmp = tmp*__ieee754_logf(fabsf(v*tmp));
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                if(tmp<(float)8.8721679688e+01) {
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                    for(i=n-1,di=(float)(i+i);i>0;i--){
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                        temp = b;
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                        b *= di;
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                        b  = b/x - a;
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                        a = temp;
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                        di -= two;
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                    }
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                } else {
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                    for(i=n-1,di=(float)(i+i);i>0;i--){
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                        temp = b;
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                        b *= di;
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                        b  = b/x - a;
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                        a = temp;
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                        di -= two;
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                    /* scale b to avoid spurious overflow */
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                        if(b>(float)1e10) {
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                            a /= b;
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                            t /= b;
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                            b  = one;
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                        }
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                    }
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                }
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                b = (t*__ieee754_j0f(x)/b);
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            }
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        }
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        if(sgn==1) return -b; else return b;
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}
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#ifdef __STDC__
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        float __ieee754_ynf(int n, float x)
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#else
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        float __ieee754_ynf(n,x)
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        int n; float x;
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#endif
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{
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        __int32_t i,hx,ix,ib;
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        __int32_t sign;
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        float a, b, temp;
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        GET_FLOAT_WORD(hx,x);
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        ix = 0x7fffffff&hx;
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    /* if Y(n,NaN) is NaN */
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        if(ix>0x7f800000) return x+x;
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        if(ix==0) return -one/zero;
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        if(hx<0) return zero/zero;
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        sign = 1;
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        if(n<0){
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                n = -n;
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                sign = 1 - ((n&1)<<1);
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        }
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        if(n==0) return(__ieee754_y0f(x));
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        if(n==1) return(sign*__ieee754_y1f(x));
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        if(ix==0x7f800000) return zero;
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        a = __ieee754_y0f(x);
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        b = __ieee754_y1f(x);
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        /* quit if b is -inf */
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        GET_FLOAT_WORD(ib,b);
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        for(i=1;i<n&&ib!=0xff800000;i++){
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            temp = b;
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            b = ((float)(i+i)/x)*b - a;
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            GET_FLOAT_WORD(ib,b);
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            a = temp;
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        }
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        if(sign>0) return b; else return -b;
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}

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