/* origin: FreeBSD /usr/src/lib/msun/src/e_j0f.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.
 * ====================================================
 */

#define _GNU_SOURCE
#include "libm.h"

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

static const float invsqrtpi = 5.6418961287e-01, /* 0x3f106ebb */
    tpi = 6.3661974669e-01;                      /* 0x3f22f983 */

static float common(uint32_t ix, float x, int y0) {
  float z, s, c, ss, 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)
   */
  s = sinf(x);
  c = cosf(x);
  if (y0)
    c = -c;
  cc = s + c;
  if (ix < 0x7f000000) {
    ss = s - c;
    z = -cosf(2 * x);
    if (s * c < 0)
      cc = z / ss;
    else
      ss = z / cc;
    if (ix < 0x58800000) {
      if (y0)
        ss = -ss;
      cc = pzerof(x) * cc - qzerof(x) * ss;
    }
  }
  return invsqrtpi * cc / sqrtf(x);
}

/* R0/S0 on [0, 2.00] */
static const float 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, r, s;
  uint32_t ix;

  GET_FLOAT_WORD(ix, x);
  ix &= 0x7fffffff;
  if (ix >= 0x7f800000)
    return 1 / (x * x);
  x = fabsf(x);

  if (ix >= 0x40000000) { /* |x| >= 2 */
    /* large ulp error near zeros */
    return common(ix, x, 0);
  }
  if (ix >= 0x3a000000) { /* |x| >= 2**-11 */
    /* up to 4ulp error near 2 */
    z = x * x;
    r = z * (R02 + z * (R03 + z * (R04 + z * R05)));
    s = 1 + z * (S01 + z * (S02 + z * (S03 + z * S04)));
    return (1 + x / 2) * (1 - x / 2) + z * (r / s);
  }
  if (ix >= 0x21800000) /* |x| >= 2**-60 */
    x = 0.25f * x * x;
  return 1 - x;
}

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, u, v;
  uint32_t ix;

  GET_FLOAT_WORD(ix, x);
  if ((ix & 0x7fffffff) == 0)
    return -1 / 0.0f;
  if (ix >> 31)
    return 0 / 0.0f;
  if (ix >= 0x7f800000)
    return 1 / x;
  if (ix >= 0x40000000) { /* |x| >= 2.0 */
    /* large ulp error near zeros */
    return common(ix, x, 1);
  }
  if (ix >= 0x39000000) { /* x >= 2**-13 */
    /* large ulp error at x ~= 0.89 */
    z = x * x;
    u = u00 +
        z * (u01 + z * (u02 + z * (u03 + z * (u04 + z * (u05 + z * u06)))));
    v = 1 + z * (v01 + z * (v02 + z * (v03 + z * v04)));
    return u / v + tpi * (j0f(x) * logf(x));
  }
  return u00 + tpi * 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 float pzerof(float x) {
  const float *p, *q;
  float_t z, r, s;
  uint32_t ix;

  GET_FLOAT_WORD(ix, x);
  ix &= 0x7fffffff;
  if (ix >= 0x41000000) {
    p = pR8;
    q = pS8;
  } else if (ix >= 0x40f71c58) {
    p = pR5;
    q = pS5;
  } else if (ix >= 0x4036db68) {
    p = pR3;
    q = pS3;
  } else /*ix >= 0x40000000*/ {
    p = pR2;
    q = pS2;
  }
  z = 1.0f / (x * x);
  r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
  s = 1.0f + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));
  return 1.0f + 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_t s, r, z;
  uint32_t ix;

  GET_FLOAT_WORD(ix, x);
  ix &= 0x7fffffff;
  if (ix >= 0x41000000) {
    p = qR8;
    q = qS8;
  } else if (ix >= 0x40f71c58) {
    p = qR5;
    q = qS5;
  } else if (ix >= 0x4036db68) {
    p = qR3;
    q = qS3;
  } else /*ix >= 0x40000000*/ {
    p = qR2;
    q = qS2;
  }
  z = 1.0f / (x * x);
  r = p[0] + z * (p[1] + z * (p[2] + z * (p[3] + z * (p[4] + z * p[5]))));
  s = 1.0f +
      z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));
  return (-.125f + r / s) / x;
}