/*

 * // Copyright (c) Radzivon Bartoshyk 8/2025. 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.

 * //

 * // 3.  Neither the name of the copyright holder nor the names of its

 * // contributors may be used to endorse or promote products derived from

 * // this software without specific prior written permission.

 * //

 * // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE

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

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 */

use crate::common::f_fmla;

use crate::double_double::DoubleDouble;

use crate::polyeval::f_estrin_polyeval5;

use crate::sin::{range_reduction_small, sincos_eval};

use crate::sin_helper::sincos_eval_dd;

use crate::sin_table::SIN_K_PI_OVER_128;

use crate::sincos_reduce::LargeArgumentReduction;

#[cold]

#[inline(never)]

fn sinmx_accurate(y: DoubleDouble, sin_k: DoubleDouble, cos_k: DoubleDouble, x: f64) -> f64 {

    let r_sincos = sincos_eval_dd(y);

    // k is an integer and -pi / 256 <= y <= pi / 256.

    // Then sin(x) = sin((k * pi/128 + y)

    //             = sin(y) * cos(k*pi/128) + cos(y) * sin(k*pi/128)

    let sin_k_cos_y = DoubleDouble::quick_mult(r_sincos.v_cos, sin_k);

    let cos_k_sin_y = DoubleDouble::quick_mult(r_sincos.v_sin, cos_k);

    let mut rr = DoubleDouble::full_dd_add(sin_k_cos_y, cos_k_sin_y);

    rr = DoubleDouble::full_add_f64(rr, -x);

    rr.to_f64()

}

#[cold]

fn sinmx_near_zero_hard(x: f64) -> f64 {

    const C: [(u64, u64); 8] = [

        (0xb37137ef120d4bbd, 0xb6db8d4e2aa9f813),

        (0xbc6555555554e720, 0xbfc5555555555555),

        (0x3c01110fff8e3ea0, 0x3f81111111111111),

        (0xbb6314569388b856, 0xbf2a01a01a01a01a),

        (0xbb61f946e615f3cd, 0x3ec71de3a556c723),

        (0x3a8998bc94bd3bf0, 0xbe5ae64567f2d4df),

        (0xba702e73490290eb, 0x3de61245e54b6747),

        (0xba0182df5b1ffd4c, 0xbd6ae4894bb27213),

    ];

    let x2 = DoubleDouble::from_exact_mult(x, x);

    let mut p = DoubleDouble::mul_add(

        x2,

        DoubleDouble::from_bit_pair(C[7]),

        DoubleDouble::from_bit_pair(C[6]),

    );

    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[5]));

    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[4]));

    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[3]));

    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[2]));

    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[1]));

    p = DoubleDouble::mul_add(x2, p, DoubleDouble::from_bit_pair(C[0]));

    p = DoubleDouble::quick_mult_f64(p, x);

    p.to_f64()

}

/// Computes sin(x) - x

///

/// ULP 0.5

pub fn f_sinmx(x: f64) -> f64 {

    let x_e = (x.to_bits() >> 52) & 0x7ff;

    const E_BIAS: u64 = (1u64 << (11 - 1u64)) - 1u64;

    let y: DoubleDouble;

    let k;

    let mut argument_reduction = LargeArgumentReduction::default();

    // |x| < 2^32 (with FMA) or |x| < 2^23 (w/o FMA)

    if x_e < E_BIAS + 16 {

        if x_e < E_BIAS - 6 {

            // |x| < 2^-6

            if x_e < E_BIAS - 32 {

                // |x| < 2^-32

                // Signed zeros.

                if x == 0.0 {

                    return x;

                }

                // For |x| < 2^-32, taylor series sin(x) - x ~ -x^3/6

                let x2 = x * x;

                let c = f_fmla(

                    x2,

                    f64::from_bits(0x3f81111111111111),

                    f64::from_bits(0xbfc5555555555555),

                ) * x2;

                return c * x;

            }

            // Generated by Sollya:

            // d = [2^-26, pi/16];

            // f_sinmx = (sin(x) - x)/x;

            // Q = fpminimax(f_sinmx, [|0, 2, 4, 6, 8, 10, 12|], [|127, 127, D...|], d);

            let x2 = DoubleDouble::from_exact_mult(x, x);

            let p = f_estrin_polyeval5(

                x2.hi,

                f64::from_bits(0x3f81111111111111),

                f64::from_bits(0xbf2a01a01a019d2f),

                f64::from_bits(0x3ec71de3a5269512),

                f64::from_bits(0xbe5ae642b76ba0f5),

                f64::from_bits(0x3de6035da3c7eaed),

            );

            let mut c = DoubleDouble::mul_f64_add(

                x2,

                p,

                DoubleDouble::from_bit_pair((0xbc655542976eb2af, 0xbfc5555555555555)),

            );

            c = DoubleDouble::mul_add(

                x2,

                c,

                DoubleDouble::from_bit_pair((0x34b215c35dc9e9be, 0xb832bde584573661)),

            );

            c = DoubleDouble::quick_mult_f64(c, x);

            let err = f_fmla(

                x2.hi,

                f64::from_bits(0x3cc0000000000000), // 2^-51

                f64::from_bits(0x3bc0000000000000), // 2^-67

            );

            let ub = c.hi + (c.lo + err);

            let lb = c.hi + (c.lo - err);

            if ub == lb {

                return c.to_f64();

            }

            return sinmx_near_zero_hard(x);

        }

        // // Small range reduction.

        (y, k) = range_reduction_small(x);

    } else {

        // Inf or NaN

        if x_e > 2 * E_BIAS {

            // sin(+-Inf) = NaN

            return x + f64::NAN;

        }

        // Large range reduction.

        (k, y) = argument_reduction.reduce(x);

    }

    let r_sincos = sincos_eval(y);

    // cos(k * pi/128) = sin(k * pi/128 + pi/2) = sin((k + 64) * pi/128).

    let sk = SIN_K_PI_OVER_128[(k & 255) as usize];

    let ck = SIN_K_PI_OVER_128[((k.wrapping_add(64)) & 255) as usize];

    let sin_k = DoubleDouble::from_bit_pair(sk);

    let cos_k = DoubleDouble::from_bit_pair(ck);

    let sin_k_cos_y = DoubleDouble::quick_mult(r_sincos.v_cos, sin_k);

    let cos_k_sin_y = DoubleDouble::quick_mult(r_sincos.v_sin, cos_k);

    // sin_k_cos_y is always >> cos_k_sin_y

    let mut rr = DoubleDouble::from_exact_add(sin_k_cos_y.hi, cos_k_sin_y.hi);

    rr.lo += sin_k_cos_y.lo + cos_k_sin_y.lo;

    rr = DoubleDouble::from_exact_add(rr.hi, rr.lo);

    rr = DoubleDouble::full_add_f64(rr, -x);

    let rlp = rr.lo + r_sincos.err;

    let rlm = rr.lo - r_sincos.err;

    let r_upper = rr.hi + rlp; // (rr.lo + ERR);

    let r_lower = rr.hi + rlm; // (rr.lo - ERR);

    // Ziv's accuracy test

    if r_upper == r_lower {

        return rr.to_f64();

    }

    sinmx_accurate(y, sin_k, cos_k, x)

}

#[cfg(test)]

mod tests {

    use super::*;

    #[test]

    fn f_sinf_test() {

        assert_eq!(f_sinmx(0.0), 0.0);

        assert_eq!(f_sinmx(1.0), -0.1585290151921035);

        assert_eq!(f_sinmx(0.3), -0.0044797933386604245);

        assert_eq!(f_sinmx(-1.0), 0.1585290151921035);

        assert_eq!(f_sinmx(-0.3), 0.0044797933386604245);

        assert_eq!(f_sinmx(std::f64::consts::PI / 2.), -0.5707963267948966);

        assert!(f_sinmx(f64::INFINITY).is_nan());

        assert!(f_sinmx(f64::NEG_INFINITY).is_nan());

    }

}