/* 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.

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

 */

use super::{cosf, fabsf, logf, sinf, sqrtf};

const INVSQRTPI: f32 = 5.6418961287e-01; /* 0x3f106ebb */

const TPI: f32 = 6.3661974669e-01; /* 0x3f22f983 */

fn common(ix: u32, x: f32, y0: bool) -> f32 {

    let z: f32;

    let s: f32;

    let mut c: f32;

    let mut ss: f32;

    let mut cc: f32;

    /*

     * 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(2.0 * x);

        if s * c < 0.0 {

            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] */

const R02: f32 = 1.5625000000e-02; /* 0x3c800000 */

const R03: f32 = -1.8997929874e-04; /* 0xb947352e */

const R04: f32 = 1.8295404516e-06; /* 0x35f58e88 */

const R05: f32 = -4.6183270541e-09; /* 0xb19eaf3c */

const S01: f32 = 1.5619102865e-02; /* 0x3c7fe744 */

const S02: f32 = 1.1692678527e-04; /* 0x38f53697 */

const S03: f32 = 5.1354652442e-07; /* 0x3509daa6 */

const S04: f32 = 1.1661400734e-09; /* 0x30a045e8 */

/// Zeroth 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 j0f(mut x: f32) -> f32 {

    let z: f32;

    let r: f32;

    let s: f32;

    let mut ix: u32;

    ix = x.to_bits();

    ix &= 0x7fffffff;

    if ix >= 0x7f800000 {

        return 1.0 / (x * x);

    }

    x = fabsf(x);

    if ix >= 0x40000000 {

        /* |x| >= 2 */

        /* large ulp error near zeros */

        return common(ix, x, false);

    }

    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 = 1.0 + z * (S01 + z * (S02 + z * (S03 + z * S04)));

        return (1.0 + x / 2.0) * (1.0 - x / 2.0) + z * (r / s);

    }

    if ix >= 0x21800000 {

        /* |x| >= 2**-60 */

        x = 0.25 * x * x;

    }

    return 1.0 - x;

}

const U00: f32 = -7.3804296553e-02; /* 0xbd9726b5 */

const U01: f32 = 1.7666645348e-01; /* 0x3e34e80d */

const U02: f32 = -1.3818567619e-02; /* 0xbc626746 */

const U03: f32 = 3.4745343146e-04; /* 0x39b62a69 */

const U04: f32 = -3.8140706238e-06; /* 0xb67ff53c */

const U05: f32 = 1.9559013964e-08; /* 0x32a802ba */

const U06: f32 = -3.9820518410e-11; /* 0xae2f21eb */

const V01: f32 = 1.2730483897e-02; /* 0x3c509385 */

const V02: f32 = 7.6006865129e-05; /* 0x389f65e0 */

const V03: f32 = 2.5915085189e-07; /* 0x348b216c */

const V04: f32 = 4.4111031494e-10; /* 0x2ff280c2 */

/// Zeroth 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 y0f(x: f32) -> f32 {

    let z: f32;

    let u: f32;

    let v: f32;

    let ix: u32;

    ix = x.to_bits();

    if (ix & 0x7fffffff) == 0 {

        return -1.0 / 0.0;

    }

    if (ix >> 31) != 0 {

        return 0.0 / 0.0;

    }

    if ix >= 0x7f800000 {

        return 1.0 / x;

    }

    if ix >= 0x40000000 {

        /* |x| >= 2.0 */

        /* large ulp error near zeros */

        return common(ix, x, true);

    }

    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 = 1.0 + 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)

 */

const PR8: [f32; 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 */

];

const PS8: [f32; 5] = [

    1.1653436279e+02, /* 0x42e91198 */

    3.8337448730e+03, /* 0x456f9beb */

    4.0597855469e+04, /* 0x471e95db */

    1.1675296875e+05, /* 0x47e4087c */

    4.7627726562e+04, /* 0x473a0bba */

];

const PR5: [f32; 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 */

];

const PS5: [f32; 5] = [

    6.0753936768e+01, /* 0x42730408 */

    1.0512523193e+03, /* 0x44836813 */

    5.9789707031e+03, /* 0x45bad7c4 */

    9.6254453125e+03, /* 0x461665c8 */

    2.4060581055e+03, /* 0x451660ee */

];

const PR3: [f32; 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 */

];

const PS3: [f32; 5] = [

    3.5856033325e+01, /* 0x420f6c94 */

    3.6151397705e+02, /* 0x43b4c1ca */

    1.1936077881e+03, /* 0x44953373 */

    1.1279968262e+03, /* 0x448cffe6 */

    1.7358093262e+02, /* 0x432d94b8 */

];

const PR2: [f32; 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 */

];

const PS2: [f32; 5] = [

    2.2220300674e+01, /* 0x41b1c32d */

    1.3620678711e+02, /* 0x430834f0 */

    2.7047027588e+02, /* 0x43873c32 */

    1.5387539673e+02, /* 0x4319e01a */

    1.4657617569e+01, /* 0x416a859a */

];

fn pzerof(x: f32) -> f32 {

    let p: &[f32; 6];

    let q: &[f32; 5];

    let z: f32;

    let r: f32;

    let s: f32;

    let mut ix: u32;

    ix = x.to_bits();

    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*/

    {

        p = &PR2;

        q = &PS2;

    }

    z = 1.0 / (x * x);

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

    s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * q[4]))));

    return 1.0 + 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)

 */

const QR8: [f32; 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 */

];

const QS8: [f32; 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 */

];

const QR5: [f32; 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 */

];

const QS5: [f32; 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 */

];

const QR3: [f32; 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 */

];

const QS3: [f32; 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 */

];

const QR2: [f32; 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 */

];

const QS2: [f32; 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 */

];

fn qzerof(x: f32) -> f32 {

    let p: &[f32; 6];

    let q: &[f32; 6];

    let s: f32;

    let r: f32;

    let z: f32;

    let mut ix: u32;

    ix = x.to_bits();

    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*/

    {

        p = &QR2;

        q = &QS2;

    }

    z = 1.0 / (x * x);

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

    s = 1.0 + z * (q[0] + z * (q[1] + z * (q[2] + z * (q[3] + z * (q[4] + z * q[5])))));

    return (-0.125 + r / s) / x;

}