// origin: FreeBSD /usr/src/lib/msun/src/s_exp2f.c

//-

// Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>

// All rights reserved.

//

// Redistribution and use in source and binary forms, with or without

// modification, are permitted provided that the following conditions

// are met:

// 1. Redistributions of source code must retain the above copyright

//    notice, this list of conditions and the following disclaimer.

// 2. Redistributions in binary form must reproduce the above copyright

//    notice, this list of conditions and the following disclaimer in the

//    documentation and/or other materials provided with the distribution.

//

// THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND

// ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE

// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE

// ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE

// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL

// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS

// OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)

// HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT

// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY

// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF

// SUCH DAMAGE.

const TBLSIZE: usize = 16;

static EXP2FT: [u64; TBLSIZE] = [

    0x3fe6a09e667f3bcd,

    0x3fe7a11473eb0187,

    0x3fe8ace5422aa0db,

    0x3fe9c49182a3f090,

    0x3feae89f995ad3ad,

    0x3fec199bdd85529c,

    0x3fed5818dcfba487,

    0x3feea4afa2a490da,

    0x3ff0000000000000,

    0x3ff0b5586cf9890f,

    0x3ff172b83c7d517b,

    0x3ff2387a6e756238,

    0x3ff306fe0a31b715,

    0x3ff3dea64c123422,

    0x3ff4bfdad5362a27,

    0x3ff5ab07dd485429,

];

// exp2f(x): compute the base 2 exponential of x

//

// Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927.

//

// Method: (equally-spaced tables)

//

//   Reduce x:

//     x = k + y, for integer k and |y| <= 1/2.

//     Thus we have exp2f(x) = 2**k * exp2(y).

//

//   Reduce y:

//     y = i/TBLSIZE + z for integer i near y * TBLSIZE.

//     Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z),

//     with |z| <= 2**-(TBLSIZE+1).

//

//   We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a

//   degree-4 minimax polynomial with maximum error under 1.4 * 2**-33.

//   Using double precision for everything except the reduction makes

//   roundoff error insignificant and simplifies the scaling step.

//

//   This method is due to Tang, but I do not use his suggested parameters:

//

//      Tang, P.  Table-driven Implementation of the Exponential Function

//      in IEEE Floating-Point Arithmetic.  TOMS 15(2), 144-157 (1989).

/// Exponential, base 2 (f32)

///

/// Calculate `2^x`, that is, 2 raised to the power `x`.

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

pub fn exp2f(mut x: f32) -> f32 {

    let redux = f32::from_bits(0x4b400000) / TBLSIZE as f32;

    let p1 = f32::from_bits(0x3f317218);

    let p2 = f32::from_bits(0x3e75fdf0);

    let p3 = f32::from_bits(0x3d6359a4);

    let p4 = f32::from_bits(0x3c1d964e);

    // double_t t, r, z;

    // uint32_t ix, i0, k;

    let x1p127 = f32::from_bits(0x7f000000);

    /* Filter out exceptional cases. */

    let ui = f32::to_bits(x);

    let ix = ui & 0x7fffffff;

    if ix > 0x42fc0000 {

        /* |x| > 126 */

        if ix > 0x7f800000 {

            /* NaN */

            return x;

        }

        if ui >= 0x43000000 && ui < 0x80000000 {

            /* x >= 128 */

            x *= x1p127;

            return x;

        }

        if ui >= 0x80000000 {

            /* x < -126 */

            if ui >= 0xc3160000 || (ui & 0x0000ffff != 0) {

                force_eval!(f32::from_bits(0x80000001) / x);

            }

            if ui >= 0xc3160000 {

                /* x <= -150 */

                return 0.0;

            }

        }

    } else if ix <= 0x33000000 {

        /* |x| <= 0x1p-25 */

        return 1.0 + x;

    }

    /* Reduce x, computing z, i0, and k. */

    let ui = f32::to_bits(x + redux);

    let mut i0 = ui;

    i0 += TBLSIZE as u32 / 2;

    let k = i0 / TBLSIZE as u32;

    let ukf = f64::from_bits(((0x3ff + k) as u64) << 52);

    i0 &= TBLSIZE as u32 - 1;

    let mut uf = f32::from_bits(ui);

    uf -= redux;

    let z: f64 = (x - uf) as f64;

    /* Compute r = exp2(y) = exp2ft[i0] * p(z). */

    let r: f64 = f64::from_bits(i!(EXP2FT, i0 as usize));

    let t: f64 = r as f64 * z;

    let r: f64 = r + t * (p1 as f64 + z * p2 as f64) + t * (z * z) * (p3 as f64 + z * p4 as f64);

    /* Scale by 2**k */

    (r * ukf) as f32

}