text: /* 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.
   * ====================================================
   */
  
  /*
   * See e_j0.c for complete comments.
   */
  
  #include "math.h"
  #include "math_private.h"
  
  static inline float pzerof(float), qzerof(float);
  
  static const volatile float vone = 1,  vzero = 0;
  
  static const float
  huge 	= 1e30,
  zero	= 0.0,
  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 */
  
  float
  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 */
  		s = sinf(x);
  		c = cosf(x);
  		ss = s-c;
  		cc = s+c;
  		if(ix<0x7f000000) {  /* make sure x+x not overflow */
  		    z = -cosf(x+x);
  		    if ((s*c)<zero) cc = z/ss;
  		    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>0x58000000) z = (invsqrtpi*cc)/sqrtf(x); /* |x|>2**49 */
  		else {
  		    u = pzerof(x); v = qzerof(x);
  		    z = invsqrtpi*(u*cc-v*ss)/sqrtf(x);
  		}
  		return z;
  	}
  	if(ix<0x3b000000) {	/* |x| < 2**-9 */
  	    if(huge+x>one) {	/* raise inexact if x != 0 */
  	        if(ix<0x39800000) return one;	/* |x|<2**-12 */
  	        else 	      return one - x*x/4;
  	    }
  	}
  	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));
  	}
  }
  
  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
  y0f(float x) 
  {
  	float z, s,c,ss,cc,u,v;
  	int32_t hx,ix;
  
  	GET_FLOAT_WORD(hx,x);
          ix = 0x7fffffff&hx;
  	if(ix>=0x7f800000) return  vone/(x+x*x);
  	if(ix==0) return -one/vzero;
  	if(hx<0) return vzero/vzero;
          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.
           */
                  s = sinf(x);
                  c = cosf(x);
                  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)<zero) cc = z/ss;
                      else            ss = z/cc;
                  }
                  if(ix>0x58000000) z = (invsqrtpi*ss)/sqrtf(x); /* |x|>2**49 */
                  else {
                      u = pzerof(x); v = qzerof(x);
                      z = invsqrtpi*(u*ss+v*cc)/sqrtf(x);
                  }
                  return z;
  	}
  	if(ix<=0x39000000) {	/* x < 2**-13 */
  	    return(u00 + tpi*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*(j0f(x)*logf(x)));
  }
  
  /* 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 inline float
  pzerof(float x)
  {
  	const float *p,*q;
  	float z,r,s;
  	int32_t ix;
  	GET_FLOAT_WORD(ix,x);
  	ix &= 0x7fffffff;
  	if(ix>=0x41000000)     {p = pR8; q= pS8;}
  	else if(ix>=0x409173eb){p = pR5; q= pS5;}
  	else if(ix>=0x4036d917){p = pR3; q= pS3;}
  	/* else ix >= 0x40000000 */
  	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 inline float
  qzerof(float x)
  {
  	const float *p,*q;
  	float s,r,z;
  	int32_t ix;
  	GET_FLOAT_WORD(ix,x);
  	ix &= 0x7fffffff;
  	if(ix>=0x41000000)     {p = qR8; q= qS8;}
  	else if(ix>=0x409173eb){p = qR5; q= qS5;}
  	else if(ix>=0x4036d917){p = qR3; q= qS3;}
  	/* else ix >= 0x40000000 */
  	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;
  }
  