/* origin: FreeBSD /usr/src/lib/msun/src/e_jnf.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"

float jnf(int n, float x) {
  uint32_t ix;
  int nm1, sign, i;
  float a, b, temp;

  GET_FLOAT_WORD(ix, x);
  sign = ix >> 31;
  ix &= 0x7fffffff;
  if (ix > 0x7f800000) /* nan */
    return x;

  /* J(-n,x) = J(n,-x), use |n|-1 to avoid overflow in -n */
  if (n == 0)
    return j0f(x);
  if (n < 0) {
    nm1 = -(n + 1);
    x = -x;
    sign ^= 1;
  } else
    nm1 = n - 1;
  if (nm1 == 0)
    return j1f(x);

  sign &= n; /* even n: 0, odd n: signbit(x) */
  x = fabsf(x);
  if (ix == 0 || ix == 0x7f800000) /* if x is 0 or inf */
    b = 0.0f;
  else if (nm1 < 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 = 0; i < nm1;) {
      i++;
      temp = b;
      b = b * (2.0f * i / x) - a;
      a = temp;
    }
  } else {
    if (ix < 0x35800000) { /* x < 2**-20 */
      /* x is tiny, return the first Taylor expansion of J(n,x)
       * J(n,x) = 1/n!*(x/2)^n  - ...
       */
      if (nm1 > 8) /* underflow */
        nm1 = 8;
      temp = 0.5f * x;
      b = temp;
      a = 1.0f;
      for (i = 2; i <= nm1 + 1; 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, q0, q1, w, h, z, tmp, nf;
      int k;

      nf = nm1 + 1.0f;
      w = 2 * nf / x;
      h = 2 / x;
      z = w + h;
      q0 = w;
      q1 = w * z - 1.0f;
      k = 1;
      while (q1 < 1.0e4f) {
        k += 1;
        z += h;
        tmp = z * q1 - q0;
        q0 = q1;
        q1 = tmp;
      }
      for (t = 0.0f, i = k; i >= 0; i--)
        t = 1.0f / (2 * (i + nf) / x - t);
      a = t;
      b = 1.0f;
      /*  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 = nf * logf(fabsf(w));
      if (tmp < 88.721679688f) {
        for (i = nm1; i > 0; i--) {
          temp = b;
          b = 2.0f * i * b / x - a;
          a = temp;
        }
      } else {
        for (i = nm1; i > 0; i--) {
          temp = b;
          b = 2.0f * i * b / x - a;
          a = temp;
          /* scale b to avoid spurious overflow */
          if (b > 0x1p60f) {
            a /= b;
            t /= b;
            b = 1.0f;
          }
        }
      }
      z = j0f(x);
      w = j1f(x);
      if (fabsf(z) >= fabsf(w))
        b = t * z / b;
      else
        b = t * w / a;
    }
  }
  return sign ? -b : b;
}

float ynf(int n, float x) {
  uint32_t ix, ib;
  int nm1, sign, i;
  float a, b, temp;

  GET_FLOAT_WORD(ix, x);
  sign = ix >> 31;
  ix &= 0x7fffffff;
  if (ix > 0x7f800000) /* nan */
    return x;
  if (sign && ix != 0) /* x < 0 */
    return 0 / 0.0f;
  if (ix == 0x7f800000)
    return 0.0f;

  if (n == 0)
    return y0f(x);
  if (n < 0) {
    nm1 = -(n + 1);
    sign = n & 1;
  } else {
    nm1 = n - 1;
    sign = 0;
  }
  if (nm1 == 0)
    return sign ? -y1f(x) : y1f(x);

  a = y0f(x);
  b = y1f(x);
  /* quit if b is -inf */
  GET_FLOAT_WORD(ib, b);
  for (i = 0; i < nm1 && ib != 0xff800000;) {
    i++;
    temp = b;
    b = (2.0f * i / x) * b - a;
    GET_FLOAT_WORD(ib, b);
    a = temp;
  }
  return sign ? -b : b;
}