/* 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.

 * ====================================================

 */

use super::{fabsf, j0f, j1f, logf, y0f, y1f};

/// Integer order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the first kind (f32).

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]

pub fn jnf(n: i32, mut x: f32) -> f32 {

    let mut ix: u32;

    let mut nm1: i32;

    let mut sign: bool;

    let mut i: i32;

    let mut a: f32;

    let mut b: f32;

    let mut temp: f32;

    ix = x.to_bits();

    sign = (ix >> 31) != 0;

    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 = !sign;

    } else {

        nm1 = n - 1;

    }

    if nm1 == 0 {

        return j1f(x);

    }

    sign &= (n & 1) != 0; /* even n: 0, odd n: signbit(x) */

    x = fabsf(x);

    if ix == 0 || ix == 0x7f800000 {

        /* if x is 0 or inf */

        b = 0.0;

    } else if (nm1 as f32) < x {

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

        a = j0f(x);

        b = j1f(x);

        i = 0;

        while i < nm1 {

            i += 1;

            temp = b;

            b = b * (2.0 * (i as f32) / 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 = 0.5 * x;

        b = temp;

        a = 1.0;

        i = 2;

        while i <= nm1 + 1 {

            a *= i as f32; /* a = n! */

            b *= temp; /* b = (x/2)^n */

            i += 1;

        }

        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 */

        let mut t: f32;

        let mut q0: f32;

        let mut q1: f32;

        let mut w: f32;

        let h: f32;

        let mut z: f32;

        let mut tmp: f32;

        let nf: f32;

        let mut k: i32;

        nf = (nm1 as f32) + 1.0;

        w = 2.0 * nf / x;

        h = 2.0 / x;

        z = w + h;

        q0 = w;

        q1 = w * z - 1.0;

        k = 1;

        while q1 < 1.0e4 {

            k += 1;

            z += h;

            tmp = z * q1 - q0;

            q0 = q1;

            q1 = tmp;

        }

        t = 0.0;

        i = k;

        while i >= 0 {

            t = 1.0 / (2.0 * ((i as f32) + nf) / x - t);

            i -= 1;

        }

        a = t;

        b = 1.0;

        /*  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 < 88.721679688 {

            i = nm1;

            while i > 0 {

                temp = b;

                b = 2.0 * (i as f32) * b / x - a;

                a = temp;

                i -= 1;

            }

        } else {

            i = nm1;

            while i > 0 {

                temp = b;

                b = 2.0 * (i as f32) * b / x - a;

                a = temp;

                /* scale b to avoid spurious overflow */

                let x1p60 = f32::from_bits(0x5d800000); // 0x1p60 == 2^60

                if b > x1p60 {

                    a /= b;

                    t /= b;

                    b = 1.0;

                }

                i -= 1;

            }

        }

        z = j0f(x);

        w = j1f(x);

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

            b = t * z / b;

        } else {

            b = t * w / a;

        }

    }

    if sign { -b } else { b }

}

/// Integer order of the [Bessel function](https://en.wikipedia.org/wiki/Bessel_function) of the second kind (f32).

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]

pub fn ynf(n: i32, x: f32) -> f32 {

    let mut ix: u32;

    let mut ib: u32;

    let nm1: i32;

    let mut sign: bool;

    let mut i: i32;

    let mut a: f32;

    let mut b: f32;

    let mut temp: f32;

    ix = x.to_bits();

    sign = (ix >> 31) != 0;

    ix &= 0x7fffffff;

    if ix > 0x7f800000 {

        /* nan */

        return x;

    }

    if sign && ix != 0 {

        /* x < 0 */

        return 0.0 / 0.0;

    }

    if ix == 0x7f800000 {

        return 0.0;

    }

    if n == 0 {

        return y0f(x);

    }

    if n < 0 {

        nm1 = -(n + 1);

        sign = (n & 1) != 0;

    } else {

        nm1 = n - 1;

        sign = false;

    }

    if nm1 == 0 {

        if sign {

            return -y1f(x);

        } else {

            return y1f(x);

        }

    }

    a = y0f(x);

    b = y1f(x);

    /* quit if b is -inf */

    ib = b.to_bits();

    i = 0;

    while i < nm1 && ib != 0xff800000 {

        i += 1;

        temp = b;

        b = (2.0 * (i as f32) / x) * b - a;

        ib = b.to_bits();

        a = temp;

    }

    if sign { -b } else { b }

}