/* 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 <errno.h>

#include <float.h>

#include <math.h>

#include <math-narrow-eval.h>

#include <math_private.h>

#include <math-underflow.h>

static const float

two   =  2.0000000000e+00, /* 0x40000000 */

one   =  1.0000000000e+00; /* 0x3F800000 */

static const float zero  =  0.0000000000e+00;

float

__ieee754_jnf(int n, float x)

{

    float ret;

    {

	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(__builtin_expect(ix>0x7f800000, 0)) return x+x;

	if(n<0){

		n = -n;

		x = -x;

		hx ^= 0x80000000;

	}

	if(n==0) return(__ieee754_j0f(x));

	if(n==1) return(__ieee754_j1f(x));

	sgn = (n&1)&(hx>>31);	/* even n -- 0, odd n -- sign(x) */

	x = fabsf(x);

	SET_RESTORE_ROUNDF (FE_TONEAREST);

	if(__builtin_expect(ix==0||ix>=0x7f800000, 0))	/* if x is 0 or inf */

	    return sgn == 1 ? -zero : zero;

	else if((float)n<=x) {

		/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */

	    a = __ieee754_j0f(x);

	    b = __ieee754_j1f(x);

	    for(i=1;i

		temp = b;

		b = b*((double)(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*__ieee754_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;

			}

		    }

		}

		/* j0() and j1() suffer enormous loss of precision at and

		 * near zero; however, we know that their zero points never

		 * coincide, so just choose the one further away from zero.

		 */

		z = __ieee754_j0f (x);

		w = __ieee754_j1f (x);

		if (fabsf (z) >= fabsf (w))

		  b = (t * z / b);

		else

		  b = (t * w / a);

	    }

	}

	if(sgn==1) ret = -b; else ret = b;

	ret = math_narrow_eval (ret);

    }

    if (ret == 0)

      {

	ret = math_narrow_eval (__copysignf (FLT_MIN, ret) * FLT_MIN);

	__set_errno (ERANGE);

      }

    else

	math_check_force_underflow (ret);

    return ret;

}

strong_alias (__ieee754_jnf, __jnf_finite)

float

__ieee754_ynf(int n, float x)

{

    float ret;

    {

	int32_t i,hx,ix;

	uint32_t ib;

	int32_t sign;

	float a, b, temp;

	GET_FLOAT_WORD(hx,x);

	ix = 0x7fffffff&hx;

    /* if Y(n,NaN) is NaN */

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

	sign = 1;

	if(n<0){

		n = -n;

		sign = 1 - ((n&1)<<1);

	}

	if(n==0) return(__ieee754_y0f(x));

	if(__builtin_expect(ix==0, 0))

		return -sign/zero;

	if(__builtin_expect(hx<0, 0)) return zero/(zero*x);

	SET_RESTORE_ROUNDF (FE_TONEAREST);

	if(n==1) {

	    ret = sign*__ieee754_y1f(x);

	    goto out;

	}

	if(__builtin_expect(ix==0x7f800000, 0)) return zero;

	a = __ieee754_y0f(x);

	b = __ieee754_y1f(x);

	/* quit if b is -inf */

	GET_FLOAT_WORD(ib,b);

	for(i=1;i

	    temp = b;

	    b = ((double)(i+i)/x)*b - a;

	    GET_FLOAT_WORD(ib,b);

	    a = temp;

	}

	/* If B is +-Inf, set up errno accordingly.  */

	if (! isfinite (b))

	  __set_errno (ERANGE);

	if(sign>0) ret = b; else ret = -b;

    }

 out:

    if (isinf (ret))

	ret = __copysignf (FLT_MAX, ret) * FLT_MAX;

    return ret;

}

strong_alias (__ieee754_ynf, __ynf_finite)