/* ef_jn.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 "fdlibm.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 (FLT_UWORD_IS_NAN(ix))
        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 (FLT_UWORD_IS_ZERO(ix) || FLT_UWORD_IS_INFINITE(ix))
        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 (ix == 0)
        return __math_divzerof(1);

    if (ix > 0x7f800000)
        return x+x;

    if (hx < 0)
        return __math_invalidf(x);

    if (ix == 0x7f800000)
        return 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));

    a = y0f(x);
    b = y1f(x);
    /* quit if b is -inf */
    GET_FLOAT_WORD(ib, b);
    for (i = 1; i < n && ib != (__int32_t)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;
}

_MATH_ALIAS_f_if(jn)

_MATH_ALIAS_f_if(yn)