/* e_j0f.c -- float version of e_j0.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-barriers.h>

#include <math_private.h>

static float pzerof(float), qzerof(float);

static const float

huge	= 1e30,

one	= 1.0,

invsqrtpi=  5.6418961287e-01, /* 0x3f106ebb */

tpi      =  6.3661974669e-01, /* 0x3f22f983 */

		/* R0/S0 on [0, 2.00] */

R02  =  1.5625000000e-02, /* 0x3c800000 */

R03  = -1.8997929874e-04, /* 0xb947352e */

R04  =  1.8295404516e-06, /* 0x35f58e88 */

R05  = -4.6183270541e-09, /* 0xb19eaf3c */

S01  =  1.5619102865e-02, /* 0x3c7fe744 */

S02  =  1.1692678527e-04, /* 0x38f53697 */

S03  =  5.1354652442e-07, /* 0x3509daa6 */

S04  =  1.1661400734e-09; /* 0x30a045e8 */

static const float zero = 0.0;

float

__ieee754_j0f(float x)

{

	float z, s,c,ss,cc,r,u,v;

	int32_t hx,ix;

	GET_FLOAT_WORD(hx,x);

	ix = hx&0x7fffffff;

	if(ix>=0x7f800000) return one/(x*x);

	x = fabsf(x);

	if(ix >= 0x40000000) {	/* |x| >= 2.0 */

		__sincosf (x, &s, &c);

		ss = s-c;

		cc = s+c;

		if(ix<0x7f000000) {  /* make sure x+x not overflow */

		    z = -__cosf(x+x);

		    if ((s*c)

		    else	    ss = z/cc;

		}

	/*

	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)

	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)

	 */

		if(ix>0x48000000) z = (invsqrtpi*cc)/sqrtf(x);

		else {

		    u = pzerof(x); v = qzerof(x);

		    z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);

		}

		return z;

	}

	if(ix<0x39000000) {	/* |x| < 2**-13 */

	    math_force_eval(huge+x);		/* raise inexact if x != 0 */

	    if(ix<0x32000000) return one;	/* |x|<2**-27 */

	    else	      return one - (float)0.25*x*x;

	}

	z = x*x;

	r =  z*(R02+z*(R03+z*(R04+z*R05)));

	s =  one+z*(S01+z*(S02+z*(S03+z*S04)));

	if(ix < 0x3F800000) {	/* |x| < 1.00 */

	    return one + z*((float)-0.25+(r/s));

	} else {

	    u = (float)0.5*x;

	    return((one+u)*(one-u)+z*(r/s));

	}

}

strong_alias (__ieee754_j0f, __j0f_finite)

static const float

u00  = -7.3804296553e-02, /* 0xbd9726b5 */

u01  =  1.7666645348e-01, /* 0x3e34e80d */

u02  = -1.3818567619e-02, /* 0xbc626746 */

u03  =  3.4745343146e-04, /* 0x39b62a69 */

u04  = -3.8140706238e-06, /* 0xb67ff53c */

u05  =  1.9559013964e-08, /* 0x32a802ba */

u06  = -3.9820518410e-11, /* 0xae2f21eb */

v01  =  1.2730483897e-02, /* 0x3c509385 */

v02  =  7.6006865129e-05, /* 0x389f65e0 */

v03  =  2.5915085189e-07, /* 0x348b216c */

v04  =  4.4111031494e-10; /* 0x2ff280c2 */

float

__ieee754_y0f(float x)

{

	float z, s,c,ss,cc,u,v;

	int32_t hx,ix;

	GET_FLOAT_WORD(hx,x);

	ix = 0x7fffffff&hx;

    /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0, y0(0) is -inf.  */

	if(ix>=0x7f800000) return  one/(x+x*x);

	if(ix==0) return -1/zero; /* -inf and divide by zero exception.  */

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

	if(ix >= 0x40000000) {  /* |x| >= 2.0 */

	/* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0))

	 * where x0 = x-pi/4

	 *      Better formula:

	 *              cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4)

	 *                      =  1/sqrt(2) * (sin(x) + cos(x))

	 *              sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4)

	 *                      =  1/sqrt(2) * (sin(x) - cos(x))

	 * To avoid cancellation, use

	 *              sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x))

	 * to compute the worse one.

	 */

		__sincosf (x, &s, &c);

		ss = s-c;

		cc = s+c;

	/*

	 * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x)

	 * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x)

	 */

		if(ix<0x7f000000) {  /* make sure x+x not overflow */

		    z = -__cosf(x+x);

		    if ((s*c)

		    else            ss = z/cc;

		}

		if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x);

		else {

		    u = pzerof(x); v = qzerof(x);

		    z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);

		}

		return z;

	}

	if(ix<=0x39800000) {	/* x < 2**-13 */

	    return(u00 + tpi*__ieee754_logf(x));

	}

	z = x*x;

	u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06)))));

	v = one+z*(v01+z*(v02+z*(v03+z*v04)));

	return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x)));

}

strong_alias (__ieee754_y0f, __y0f_finite)

/* The asymptotic expansions of pzero is

 *	1 - 9/128 s^2 + 11025/98304 s^4 - ...,	where s = 1/x.

 * For x >= 2, We approximate pzero by

 *	pzero(x) = 1 + (R/S)

 * where  R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10

 *	  S = 1 + pS0*s^2 + ... + pS4*s^10

 * and

 *	| pzero(x)-1-R/S | <= 2  ** ( -60.26)

 */

static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */

  0.0000000000e+00, /* 0x00000000 */

 -7.0312500000e-02, /* 0xbd900000 */

 -8.0816707611e+00, /* 0xc1014e86 */

 -2.5706311035e+02, /* 0xc3808814 */

 -2.4852163086e+03, /* 0xc51b5376 */

 -5.2530439453e+03, /* 0xc5a4285a */

};

static const float pS8[5] = {

  1.1653436279e+02, /* 0x42e91198 */

  3.8337448730e+03, /* 0x456f9beb */

  4.0597855469e+04, /* 0x471e95db */

  1.1675296875e+05, /* 0x47e4087c */

  4.7627726562e+04, /* 0x473a0bba */

};

static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */

 -1.1412546255e-11, /* 0xad48c58a */

 -7.0312492549e-02, /* 0xbd8fffff */

 -4.1596107483e+00, /* 0xc0851b88 */

 -6.7674766541e+01, /* 0xc287597b */

 -3.3123129272e+02, /* 0xc3a59d9b */

 -3.4643338013e+02, /* 0xc3ad3779 */

};

static const float pS5[5] = {

  6.0753936768e+01, /* 0x42730408 */

  1.0512523193e+03, /* 0x44836813 */

  5.9789707031e+03, /* 0x45bad7c4 */

  9.6254453125e+03, /* 0x461665c8 */

  2.4060581055e+03, /* 0x451660ee */

};

static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */

 -2.5470459075e-09, /* 0xb12f081b */

 -7.0311963558e-02, /* 0xbd8fffb8 */

 -2.4090321064e+00, /* 0xc01a2d95 */

 -2.1965976715e+01, /* 0xc1afba52 */

 -5.8079170227e+01, /* 0xc2685112 */

 -3.1447946548e+01, /* 0xc1fb9565 */

};

static const float pS3[5] = {

  3.5856033325e+01, /* 0x420f6c94 */

  3.6151397705e+02, /* 0x43b4c1ca */

  1.1936077881e+03, /* 0x44953373 */

  1.1279968262e+03, /* 0x448cffe6 */

  1.7358093262e+02, /* 0x432d94b8 */

};

static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */

 -8.8753431271e-08, /* 0xb3be98b7 */

 -7.0303097367e-02, /* 0xbd8ffb12 */

 -1.4507384300e+00, /* 0xbfb9b1cc */

 -7.6356959343e+00, /* 0xc0f4579f */

 -1.1193166733e+01, /* 0xc1331736 */

 -3.2336456776e+00, /* 0xc04ef40d */

};

static const float pS2[5] = {

  2.2220300674e+01, /* 0x41b1c32d */

  1.3620678711e+02, /* 0x430834f0 */

  2.7047027588e+02, /* 0x43873c32 */

  1.5387539673e+02, /* 0x4319e01a */

  1.4657617569e+01, /* 0x416a859a */

};

static float

pzerof(float x)

{

	const float *p,*q;

	float z,r,s;

	int32_t ix;

	GET_FLOAT_WORD(ix,x);

	ix &= 0x7fffffff;

	/* ix >= 0x40000000 for all calls to this function.  */

	if(ix>=0x41000000)     {p = pR8; q= pS8;}

	else if(ix>=0x40f71c58){p = pR5; q= pS5;}

	else if(ix>=0x4036db68){p = pR3; q= pS3;}

	else {p = pR2; q= pS2;}

	z = one/(x*x);

	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));

	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4]))));

	return one+ r/s;

}

/* For x >= 8, the asymptotic expansions of qzero is

 *	-1/8 s + 75/1024 s^3 - ..., where s = 1/x.

 * We approximate pzero by

 *	qzero(x) = s*(-1.25 + (R/S))

 * where  R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10

 *	  S = 1 + qS0*s^2 + ... + qS5*s^12

 * and

 *	| qzero(x)/s +1.25-R/S | <= 2  ** ( -61.22)

 */

static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */

  0.0000000000e+00, /* 0x00000000 */

  7.3242187500e-02, /* 0x3d960000 */

  1.1768206596e+01, /* 0x413c4a93 */

  5.5767340088e+02, /* 0x440b6b19 */

  8.8591972656e+03, /* 0x460a6cca */

  3.7014625000e+04, /* 0x471096a0 */

};

static const float qS8[6] = {

  1.6377603149e+02, /* 0x4323c6aa */

  8.0983447266e+03, /* 0x45fd12c2 */

  1.4253829688e+05, /* 0x480b3293 */

  8.0330925000e+05, /* 0x49441ed4 */

  8.4050156250e+05, /* 0x494d3359 */

 -3.4389928125e+05, /* 0xc8a7eb69 */

};

static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */

  1.8408595828e-11, /* 0x2da1ec79 */

  7.3242180049e-02, /* 0x3d95ffff */

  5.8356351852e+00, /* 0x40babd86 */

  1.3511157227e+02, /* 0x43071c90 */

  1.0272437744e+03, /* 0x448067cd */

  1.9899779053e+03, /* 0x44f8bf4b */

};

static const float qS5[6] = {

  8.2776611328e+01, /* 0x42a58da0 */

  2.0778142090e+03, /* 0x4501dd07 */

  1.8847289062e+04, /* 0x46933e94 */

  5.6751113281e+04, /* 0x475daf1d */

  3.5976753906e+04, /* 0x470c88c1 */

 -5.3543427734e+03, /* 0xc5a752be */

};

static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */

  4.3774099900e-09, /* 0x3196681b */

  7.3241114616e-02, /* 0x3d95ff70 */

  3.3442313671e+00, /* 0x405607e3 */

  4.2621845245e+01, /* 0x422a7cc5 */

  1.7080809021e+02, /* 0x432acedf */

  1.6673394775e+02, /* 0x4326bbe4 */

};

static const float qS3[6] = {

  4.8758872986e+01, /* 0x42430916 */

  7.0968920898e+02, /* 0x44316c1c */

  3.7041481934e+03, /* 0x4567825f */

  6.4604252930e+03, /* 0x45c9e367 */

  2.5163337402e+03, /* 0x451d4557 */

 -1.4924745178e+02, /* 0xc3153f59 */

};

static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */

  1.5044444979e-07, /* 0x342189db */

  7.3223426938e-02, /* 0x3d95f62a */

  1.9981917143e+00, /* 0x3fffc4bf */

  1.4495602608e+01, /* 0x4167edfd */

  3.1666231155e+01, /* 0x41fd5471 */

  1.6252708435e+01, /* 0x4182058c */

};

static const float qS2[6] = {

  3.0365585327e+01, /* 0x41f2ecb8 */

  2.6934811401e+02, /* 0x4386ac8f */

  8.4478375244e+02, /* 0x44533229 */

  8.8293585205e+02, /* 0x445cbbe5 */

  2.1266638184e+02, /* 0x4354aa98 */

 -5.3109550476e+00, /* 0xc0a9f358 */

};

static float

qzerof(float x)

{

	const float *p,*q;

	float s,r,z;

	int32_t ix;

	GET_FLOAT_WORD(ix,x);

	ix &= 0x7fffffff;

	/* ix >= 0x40000000 for all calls to this function.  */

	if(ix>=0x41000000)     {p = qR8; q= qS8;}

	else if(ix>=0x40f71c58){p = qR5; q= qS5;}

	else if(ix>=0x4036db68){p = qR3; q= qS3;}

	else {p = qR2; q= qS2;}

	z = one/(x*x);

	r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5]))));

	s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5])))));

	return (-(float).125 + r/s)/x;

}