/* e_jnf.c -- float version of e_jn.c.
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */

/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice 
 * is preserved.
 * ====================================================
 */

#include "math.h"
#include "math_private.h"

static const float
two   =  2.0000000000e+00, /* 0x40000000 */
one   =  1.0000000000e+00; /* 0x3F800000 */

static const float zero  =  0.0000000000e+00;

float
jnf(int n, float x)
{
        int32_t i,hx,ix, sgn;
        float a, b, temp, di;
        float z, w;

    /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
     * Thus, J(-n,x) = J(n,-x)
     */
        GET_FLOAT_WORD(hx,x);
        ix = 0x7fffffff&hx;
    /* if J(n,NaN) is NaN */
        if(ix>0x7f800000) return x+x;
        if(n<0){                
                n = -n;
                x = -x;
                hx ^= 0x80000000;
        }
        if(n==0) return(j0f(x));
        if(n==1) return(j1f(x));
        sgn = (n&1)&(hx>>31);   /* even n -- 0, odd n -- sign(x) */
        x = fabsf(x);
        if(ix==0||ix>=0x7f800000)       /* if x is 0 or inf */
            b = zero;
        else if((float)n<=x) {   
                /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
            a = j0f(x);
            b = j1f(x);
            for(i=1;i<n;i++){
                temp = b;
                b = b*((float)(i+i)/x) - a; /* avoid underflow */
                a = temp;
            }
        } else {
            if(ix<0x30800000) { /* x < 2**-29 */
    /* x is tiny, return the first Taylor expansion of J(n,x) 
     * J(n,x) = 1/n!*(x/2)^n  - ...
     */
                if(n>33)        /* underflow */
                    b = zero;
                else {
                    temp = x*(float)0.5; b = temp;
                    for (a=one,i=2;i<=n;i++) {
                        a *= (float)i;          /* a = n! */
                        b *= temp;              /* b = (x/2)^n */
                    }
                    b = b/a;
                }
            } else {
                /* use backward recurrence */
                /*                      x      x^2      x^2       
                 *  J(n,x)/J(n-1,x) =  ----   ------   ------   .....
                 *                      2n  - 2(n+1) - 2(n+2)
                 *
                 *                      1      1        1       
                 *  (for large x)   =  ----  ------   ------   .....
                 *                      2n   2(n+1)   2(n+2)
                 *                      -- - ------ - ------ - 
                 *                       x     x         x
                 *
                 * Let w = 2n/x and h=2/x, then the above quotient
                 * is equal to the continued fraction:
                 *                  1
                 *      = -----------------------
                 *                     1
                 *         w - -----------------
                 *                        1
                 *              w+h - ---------
                 *                     w+2h - ...
                 *
                 * To determine how many terms needed, let
                 * Q(0) = w, Q(1) = w(w+h) - 1,
                 * Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
                 * When Q(k) > 1e4      good for single 
                 * When Q(k) > 1e9      good for double 
                 * When Q(k) > 1e17     good for quadruple 
                 */
            /* determine k */
                float t,v;
                float q0,q1,h,tmp; int32_t k,m;
                w  = (n+n)/(float)x; h = (float)2.0/(float)x;
                q0 = w;  z = w+h; q1 = w*z - (float)1.0; k=1;
                while(q1<(float)1.0e9) {
                        k += 1; z += h;
                        tmp = z*q1 - q0;
                        q0 = q1;
                        q1 = tmp;
                }
                m = n+n;
                for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
                a = t;
                b = one;
                /*  estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
                 *  Hence, if n*(log(2n/x)) > ...
                 *  single 8.8722839355e+01
                 *  double 7.09782712893383973096e+02
                 *  long double 1.1356523406294143949491931077970765006170e+04
                 *  then recurrent value may overflow and the result is 
                 *  likely underflow to zero
                 */
                tmp = n;
                v = two/x;
                tmp = tmp*logf(fabsf(v*tmp));
                if(tmp<(float)8.8721679688e+01) {
                    for(i=n-1,di=(float)(i+i);i>0;i--){
                        temp = b;
                        b *= di;
                        b  = b/x - a;
                        a = temp;
                        di -= two;
                    }
                } else {
                    for(i=n-1,di=(float)(i+i);i>0;i--){
                        temp = b;
                        b *= di;
                        b  = b/x - a;
                        a = temp;
                        di -= two;
                    /* scale b to avoid spurious overflow */
                        if(b>(float)1e10) {
                            a /= b;
                            t /= b;
                            b  = one;
                        }
                    }
                }
                b = (t*j0f(x)/b);
            }
        }
        if(sgn==1) return -b; else return b;
}

float
ynf(int n, float x) 
{
        int32_t i,hx,ix,ib;
        int32_t sign;
        float a, b, temp;

        GET_FLOAT_WORD(hx,x);
        ix = 0x7fffffff&hx;
    /* if Y(n,NaN) is NaN */
        if(ix>0x7f800000) return x+x;
        if(ix==0) return -one/zero;
        if(hx<0) return zero/zero;
        sign = 1;
        if(n<0){
                n = -n;
                sign = 1 - ((n&1)<<1);
        }
        if(n==0) return(y0f(x));
        if(n==1) return(sign*y1f(x));
        if(ix==0x7f800000) return zero;

        a = y0f(x);
        b = y1f(x);
        /* quit if b is -inf */
        GET_FLOAT_WORD(ib,b);
        for(i=1;i<n&&ib!=0xff800000;i++){ 
            temp = b;
            b = ((float)(i+i)/x)*b - a;
            GET_FLOAT_WORD(ib,b);
            a = temp;
        }
        if(sign>0) return b; else return -b;
}