/rust/registry/src/index.crates.io-1949cf8c6b5b557f/pxfm-0.1.25/src/sincos_dyadic.rs

Source
/*
 * // Copyright (c) Radzivon Bartoshyk 6/2025. 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
 * // 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.
 */
use crate::dyadic_float::{DyadicFloat128, DyadicSign};
use crate::rounding::CpuRound;
use crate::sincos_reduce_tables::ONE_TWENTY_EIGHT_OVER_PI;

pub(crate) fn range_reduction_small_f128(x: f64) -> DyadicFloat128 {
    const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -133,
        mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
    };
    const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
    let prod_hi = x * ONE_TWENTY_EIGHT_OVER_PI_D;
    let kd = prod_hi.cpu_round();

    let mk_f128 = DyadicFloat128::new_from_f64(-kd);
    let x_f128 = DyadicFloat128::new_from_f64(x);
    let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
    let p_hi = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
    let p_mid = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
    let p_lo = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
    let s_hi = p_hi.quick_add(&mk_f128);
    let s_lo = p_mid.quick_add(&p_lo);
    let y = s_hi.quick_add(&s_lo);
    y.quick_mul(&PI_OVER_128_F128)
}

pub(crate) fn range_reduction_small_f128_f128(x: DyadicFloat128) -> (DyadicFloat128, i64) {
    const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -133,
        mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
    };
    const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
    let prod_hi = x.fast_as_f64() * ONE_TWENTY_EIGHT_OVER_PI_D;
    let kd = prod_hi.cpu_round();

    let mk_f128 = DyadicFloat128::new_from_f64(-kd);
    let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
    let p_hi = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
    let p_mid = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
    let p_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
    let p_lo_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.3)));
    let s_hi = p_hi.quick_add(&mk_f128);
    let s_lo = p_mid.quick_add(&p_lo);
    let y = (s_hi + s_lo) + p_lo_lo;
    (y.quick_mul(&PI_OVER_128_F128), kd as i64)
}

// pub(crate) fn range_reduction_small_f128_f128(x: DyadicFloat128) -> (DyadicFloat128, u64) {
//     const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
//         sign: DyadicSign::Pos,
//         exponent: -133,
//         mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
//     };
//     const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
//     let prod_hi = x.fast_as_f64() * ONE_TWENTY_EIGHT_OVER_PI_D;
//     let kd = prod_hi.round();
//
//     let mk_f128 = DyadicFloat128::new_from_f64(-kd);
//     let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
//     let p_hi = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
//     let p_mid = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
//     let p_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
//     let p_lo_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.3)));
//     let s_hi = p_hi.quick_add(&mk_f128);
//     let s_lo = p_mid.quick_add(&p_lo);
//     let s_lo_lo = p_lo_lo.quick_add(&p_lo_lo);
//     let y = s_hi.quick_add(&s_lo).quick_add(&s_lo_lo);
//     (y.quick_mul(&PI_OVER_128_F128), (kd as i64) as u64)
// }

pub(crate) struct SinCosDyadic {
    pub(crate) v_sin: DyadicFloat128,
    pub(crate) v_cos: DyadicFloat128,
}

#[cold]
pub(crate) fn sincos_eval_dyadic(u: &DyadicFloat128) -> SinCosDyadic {
    let u_sq = u.quick_mul(u);

    // sin(u) ~ x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13!
    static SIN_COEFFS: [DyadicFloat128; 7] = [
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -127,
            mantissa: 0x80000000_00000000_00000000_00000000_u128,
        }, // 1
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -130,
            mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
        }, // -1/3!
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x88888888_88888888_88888888_88888889_u128,
        }, // 1/5!
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -140,
            mantissa: 0xd00d00d0_0d00d00d_00d00d00_d00d00d0_u128,
        }, // -1/7!
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -146,
            mantissa: 0xb8ef1d2a_b6399c7d_560e4472_800b8ef2_u128,
        }, // 1/9!
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -153,
            mantissa: 0xd7322b3f_aa271c7f_3a3f25c1_bee38f10_u128,
        }, // -1/11!
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -160,
            mantissa: 0xb092309d_43684be5_1c198e91_d7b4269e_u128,
        }, // 1/13!
    ];

    // cos(u) ~ 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12!
    static COS_COEFFS: [DyadicFloat128; 7] = [
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -127,
            mantissa: 0x80000000_00000000_00000000_00000000_u128,
        }, // 1.0
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -128,
            mantissa: 0x80000000_00000000_00000000_00000000_u128,
        }, // 1/2
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -132,
            mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
        }, // 1/4!
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xb60b60b6_0b60b60b_60b60b60_b60b60b6_u128,
        }, // 1/6!
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -143,
            mantissa: 0xd00d00d0_0d00d00d_00d00d00_d00d00d0_u128,
        }, // 1/8!
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x93f27dbb_c4fae397_780b69f5_333c725b_u128,
        }, // 1/10!
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -156,
            mantissa: 0x8f76c77f_c6c4bdaa_26d4c3d6_7f425f60_u128,
        }, // 1/12!
    ];

    let mut sin_u = SIN_COEFFS[6];
    for i in (0..7).rev() {
        sin_u = sin_u * u_sq + SIN_COEFFS[i];
    }
    sin_u = sin_u * *u;

    let mut cos_u = COS_COEFFS[6];
    for i in (0..7).rev() {
        cos_u = cos_u * u_sq + COS_COEFFS[i];
    }

    SinCosDyadic {
        v_sin: sin_u,
        v_cos: cos_u,
    }
}

/*
   Sage math:
   # Sin K PI over 128
   R = RealField(128)
   π = R.pi()

   def format_hex(value):
       l = hex(value)[2:]
       n = 4
       x = [l[i:i + n] for i in range(0, len(l), n)]
       return "0x" + "_".join(x) + "_u128"

   def print_dyadic(value):
       (s, m, e) = RealField(128)(value).sign_mantissa_exponent();
       print("DyadicFloat128 {")
       print(f"    sign: DyadicSign::{'Pos' if s >= 0 else 'Neg'},")
       print(f"    exponent: {e},")
       print(f"    mantissa: {format_hex(m)},")
       print("},")

   # Generate array entries
   print("pub(crate) static SIN_K_PI_OVER_128_F128: [DyadicFloat128; 65] = [")
   for k in range(65):
       value = R(k) * π / 128
       print_dyadic(value.sin())

   print("];")
*/
pub(crate) static SIN_K_PI_OVER_128_F128: [DyadicFloat128; 65] = [
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: 0,
        mantissa: 0x0_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -133,
        mantissa: 0xc90a_afbd_1b33_efc9_c539_edcb_fda0_cf2c_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -132,
        mantissa: 0xc8fb_2f88_6ec0_9f37_6a17_954b_2b7c_5171_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -131,
        mantissa: 0x96a9_0496_70cf_ae65_f775_7409_4d3c_35c4_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -131,
        mantissa: 0xc8bd_35e1_4da1_5f0e_c739_6c89_4bbf_7389_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -131,
        mantissa: 0xfab2_72b5_4b98_71a2_7047_29ae_56d7_8a37_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -130,
        mantissa: 0x9640_8374_7309_d113_000a_89a1_1e07_c1ff_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -130,
        mantissa: 0xaf10_a224_59fe_32a6_3fee_f3bb_58b1_f10d_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -130,
        mantissa: 0xc7c5_c1e3_4d30_55b2_5cc8_c00e_4fcc_d850_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -130,
        mantissa: 0xe05c_1353_f27b_17e5_0ebc_61ad_e6ca_83cc_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -130,
        mantissa: 0xf8cf_cbd9_0af8_d57a_4221_dc4b_a772_598d_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0x888e_9315_8fb3_bb04_9841_56f5_5334_4306_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0x94a0_3176_acf8_2d45_ae4b_a773_da6b_f754_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xa09a_e4a0_bb30_0a19_2f89_5f44_a303_cc0b_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xac7c_d3ad_58fe_e7f0_811f_9539_84ef_f83e_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xb844_2987_d22c_f576_9cc3_ef36_746d_e3b8_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xc3ef_1535_754b_168d_3122_c2a5_9efd_dc37_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xcf7b_ca1d_476c_516d_a812_90bd_baad_62e4_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xdae8_804f_0ae6_015b_362c_b974_182e_3030_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xe633_74c9_8e22_f0b4_2872_ce1b_fc7a_d1cc_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xf15a_e9c0_37b1_d8f0_6c48_e9e3_420b_0f1d_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -129,
        mantissa: 0xfc5d_26df_c4d5_cfda_27c0_7c91_1290_b8d1_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0x839c_3cc9_17ff_6cb4_bfd7_9717_f288_0abf_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0x88f5_9aa0_da59_1421_b892_ca83_61d8_c84c_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0x8e39_d9cd_7346_4364_bba4_cfec_bff5_4868_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0x9368_2a66_e896_f544_b178_2191_1e71_c16e_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0x987f_bfe7_0b81_a708_19ce_c845_ac87_a5c6_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0x9d7f_d149_0285_c9e3_e25e_3954_9638_ae67_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xa267_9928_48ee_b0c0_3b51_67ee_359a_234e_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xa736_55df_1f2f_489e_149f_6e75_9934_68a2_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xabeb_49a4_6764_fd15_1bec_da80_89c1_a94c_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xb085_baa8_e966_f6da_e4ca_d00d_5c94_bcd1_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xb504_f333_f9de_6484_597d_89b3_754a_be9f_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xb968_41bf_7ffc_b21a_9de1_e3b2_2b8b_f4db_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xbdae_f913_557d_76f0_ac85_320f_528d_6d5c_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xc1d8_705f_fcbb_6e90_bdf0_715c_b8b2_0bd7_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xc5e4_0358_a8ba_05a7_43da_25d9_9267_326b_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xc9d1_124c_931f_da7a_8335_241b_e169_3225_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xcd9f_023f_9c3a_059e_23af_31db_7179_a4a9_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xd14d_3d02_313c_0eed_744f_ea20_e8ab_ef92_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xd4db_3148_750d_1819_f630_e8b6_dac8_3e68_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xd848_52c0_a80f_fcdb_24b9_fe00_6635_74a4_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xdb94_1a28_cb71_ec87_2c19_b632_53da_43fb_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xdebe_0563_7ca9_4cfb_4b19_aa71_fec3_ae6c_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xe1c5_978c_05ed_8691_f4e8_a837_2f8c_5810_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xe4aa_5909_a08f_a7b4_1227_85ae_67f5_515c_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xe76b_d7a1_e63b_9786_1251_2952_9d48_a92f_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xea09_a68a_6e49_cd62_15ad_45b4_a1b5_e823_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xec83_5e79_946a_3145_7e61_0231_ac1d_6181_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xeed8_9db6_6611_e307_86f8_c20f_b664_b01b_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xf109_0827_b437_25fd_6712_7db3_5b28_7315_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xf314_4762_4708_8f74_a548_6bdc_455d_56a3_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xf4fa_0ab6_316e_d2ec_163c_5c7f_03b7_18c5_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xf6ba_073b_424b_19e8_2c79_1f59_cc1f_fc23_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xf853_f7dc_9186_b952_c7ad_c6b4_9888_91ba_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xf9c7_9d63_272c_4628_4504_ae08_d19b_2981_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xfb14_be7f_bae5_8156_2172_a361_fd2a_722f_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xfc3b_27d3_8a5d_49ab_2567_78ff_cb5c_1769_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xfd3a_abf8_4528_b50b_eae6_bd95_1c1d_abbd_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xfe13_2387_0cfe_9a3d_90cd_1d95_9db6_74ef_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xfec4_6d1e_8929_2cf0_4139_0efd_c726_e9ef_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xff4e_6d68_0c41_d0a9_0f66_8633_f1ab_858a_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xffb1_0f1b_cb6b_ef1d_421e_8eda_af59_453e_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -128,
        mantissa: 0xffec_4304_2668_65d9_5657_5523_6696_1732_u128,
    },
    DyadicFloat128 {
        sign: DyadicSign::Pos,
        exponent: -127,
        mantissa: 0x8000_0000_0000_0000_0000_0000_0000_0000_u128,
    },
];

Coverage Report

Created: 2025-11-05 08:08

Line	Count	Source
1		/*
2		* // Copyright (c) Radzivon Bartoshyk 6/2025. All rights reserved.
3		* //
4		* // Redistribution and use in source and binary forms, with or without modification,
5		* // are permitted provided that the following conditions are met:
6		* //
7		* // 1. Redistributions of source code must retain the above copyright notice, this
8		* // list of conditions and the following disclaimer.
9		* //
10		* // 2. Redistributions in binary form must reproduce the above copyright notice,
11		* // this list of conditions and the following disclaimer in the documentation
12		* // and/or other materials provided with the distribution.
13		* //
14		* // 3. Neither the name of the copyright holder nor the names of its
15		* // contributors may be used to endorse or promote products derived from
16		* // this software without specific prior written permission.
17		* //
18		* // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
19		* // AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
20		* // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
21		* // DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
22		* // FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
23		* // DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
24		* // SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
25		* // CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
26		* // OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
27		* // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28		*/
29		use crate::dyadic_float::{DyadicFloat128, DyadicSign};
30		use crate::rounding::CpuRound;
31		use crate::sincos_reduce_tables::ONE_TWENTY_EIGHT_OVER_PI;
32
33	0	pub(crate) fn range_reduction_small_f128(x: f64) -> DyadicFloat128 {
34		const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
35		sign: DyadicSign::Pos,
36		exponent: -133,
37		mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
38		};
39		const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
40	0	let prod_hi = x * ONE_TWENTY_EIGHT_OVER_PI_D;
41	0	let kd = prod_hi.cpu_round();
42
43	0	let mk_f128 = DyadicFloat128::new_from_f64(-kd);
44	0	let x_f128 = DyadicFloat128::new_from_f64(x);
45	0	let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
46	0	let p_hi = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
47	0	let p_mid = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
48	0	let p_lo = x_f128.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
49	0	let s_hi = p_hi.quick_add(&mk_f128);
50	0	let s_lo = p_mid.quick_add(&p_lo);
51	0	let y = s_hi.quick_add(&s_lo);
52	0	y.quick_mul(&PI_OVER_128_F128)
53	0	}
54
55	0	pub(crate) fn range_reduction_small_f128_f128(x: DyadicFloat128) -> (DyadicFloat128, i64) {
56		const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
57		sign: DyadicSign::Pos,
58		exponent: -133,
59		mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
60		};
61		const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
62	0	let prod_hi = x.fast_as_f64() * ONE_TWENTY_EIGHT_OVER_PI_D;
63	0	let kd = prod_hi.cpu_round();
64
65	0	let mk_f128 = DyadicFloat128::new_from_f64(-kd);
66	0	let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
67	0	let p_hi = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
68	0	let p_mid = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
69	0	let p_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
70	0	let p_lo_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.3)));
71	0	let s_hi = p_hi.quick_add(&mk_f128);
72	0	let s_lo = p_mid.quick_add(&p_lo);
73	0	let y = (s_hi + s_lo) + p_lo_lo;
74	0	(y.quick_mul(&PI_OVER_128_F128), kd as i64)
75	0	}
76
77		// pub(crate) fn range_reduction_small_f128_f128(x: DyadicFloat128) -> (DyadicFloat128, u64) {
78		// const PI_OVER_128_F128: DyadicFloat128 = DyadicFloat128 {
79		// sign: DyadicSign::Pos,
80		// exponent: -133,
81		// mantissa: 0xc90f_daa2_2168_c234_c4c6_628b_80dc_1cd1_u128,
82		// };
83		// const ONE_TWENTY_EIGHT_OVER_PI_D: f64 = f64::from_bits(0x40445f306dc9c883);
84		// let prod_hi = x.fast_as_f64() * ONE_TWENTY_EIGHT_OVER_PI_D;
85		// let kd = prod_hi.round();
86		//
87		// let mk_f128 = DyadicFloat128::new_from_f64(-kd);
88		// let over_pi3 = ONE_TWENTY_EIGHT_OVER_PI[3];
89		// let p_hi = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.0)));
90		// let p_mid = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.1)));
91		// let p_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.2)));
92		// let p_lo_lo = x.quick_mul(&DyadicFloat128::new_from_f64(f64::from_bits(over_pi3.3)));
93		// let s_hi = p_hi.quick_add(&mk_f128);
94		// let s_lo = p_mid.quick_add(&p_lo);
95		// let s_lo_lo = p_lo_lo.quick_add(&p_lo_lo);
96		// let y = s_hi.quick_add(&s_lo).quick_add(&s_lo_lo);
97		// (y.quick_mul(&PI_OVER_128_F128), (kd as i64) as u64)
98		// }
99
100		pub(crate) struct SinCosDyadic {
101		pub(crate) v_sin: DyadicFloat128,
102		pub(crate) v_cos: DyadicFloat128,
103		}
104
105		#[cold]
106	0	pub(crate) fn sincos_eval_dyadic(u: &DyadicFloat128) -> SinCosDyadic {
107	0	let u_sq = u.quick_mul(u);
108
109		// sin(u) ~ x - x^3/3! + x^5/5! - x^7/7! + x^9/9! - x^11/11! + x^13/13!
110		static SIN_COEFFS: [DyadicFloat128; 7] = [
111		DyadicFloat128 {
112		sign: DyadicSign::Pos,
113		exponent: -127,
114		mantissa: 0x80000000_00000000_00000000_00000000_u128,
115		}, // 1
116		DyadicFloat128 {
117		sign: DyadicSign::Neg,
118		exponent: -130,
119		mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
120		}, // -1/3!
121		DyadicFloat128 {
122		sign: DyadicSign::Pos,
123		exponent: -134,
124		mantissa: 0x88888888_88888888_88888888_88888889_u128,
125		}, // 1/5!
126		DyadicFloat128 {
127		sign: DyadicSign::Neg,
128		exponent: -140,
129		mantissa: 0xd00d00d0_0d00d00d_00d00d00_d00d00d0_u128,
130		}, // -1/7!
131		DyadicFloat128 {
132		sign: DyadicSign::Pos,
133		exponent: -146,
134		mantissa: 0xb8ef1d2a_b6399c7d_560e4472_800b8ef2_u128,
135		}, // 1/9!
136		DyadicFloat128 {
137		sign: DyadicSign::Neg,
138		exponent: -153,
139		mantissa: 0xd7322b3f_aa271c7f_3a3f25c1_bee38f10_u128,
140		}, // -1/11!
141		DyadicFloat128 {
142		sign: DyadicSign::Pos,
143		exponent: -160,
144		mantissa: 0xb092309d_43684be5_1c198e91_d7b4269e_u128,
145		}, // 1/13!
146		];
147
148		// cos(u) ~ 1 - x^2/2 + x^4/4! - x^6/6! + x^8/8! - x^10/10! + x^12/12!
149		static COS_COEFFS: [DyadicFloat128; 7] = [
150		DyadicFloat128 {
151		sign: DyadicSign::Pos,
152		exponent: -127,
153		mantissa: 0x80000000_00000000_00000000_00000000_u128,
154		}, // 1.0
155		DyadicFloat128 {
156		sign: DyadicSign::Neg,
157		exponent: -128,
158		mantissa: 0x80000000_00000000_00000000_00000000_u128,
159		}, // 1/2
160		DyadicFloat128 {
161		sign: DyadicSign::Pos,
162		exponent: -132,
163		mantissa: 0xaaaaaaaa_aaaaaaaa_aaaaaaaa_aaaaaaab_u128,
164		}, // 1/4!
165		DyadicFloat128 {
166		sign: DyadicSign::Neg,
167		exponent: -137,
168		mantissa: 0xb60b60b6_0b60b60b_60b60b60_b60b60b6_u128,
169		}, // 1/6!
170		DyadicFloat128 {
171		sign: DyadicSign::Pos,
172		exponent: -143,
173		mantissa: 0xd00d00d0_0d00d00d_00d00d00_d00d00d0_u128,
174		}, // 1/8!
175		DyadicFloat128 {
176		sign: DyadicSign::Neg,
177		exponent: -149,
178		mantissa: 0x93f27dbb_c4fae397_780b69f5_333c725b_u128,
179		}, // 1/10!
180		DyadicFloat128 {
181		sign: DyadicSign::Pos,
182		exponent: -156,
183		mantissa: 0x8f76c77f_c6c4bdaa_26d4c3d6_7f425f60_u128,
184		}, // 1/12!
185		];
186
187	0	let mut sin_u = SIN_COEFFS[6];
188	0	for i in (0..7).rev() {
189	0	sin_u = sin_u * u_sq + SIN_COEFFS[i];
190	0	}
191	0	sin_u = sin_u * *u;
192
193	0	let mut cos_u = COS_COEFFS[6];
194	0	for i in (0..7).rev() {
195	0	cos_u = cos_u * u_sq + COS_COEFFS[i];
196	0	}
197
198	0	SinCosDyadic {
199	0	v_sin: sin_u,
200	0	v_cos: cos_u,
201	0	}
202	0	}
203
204		/*
205		Sage math:
206		# Sin K PI over 128
207		R = RealField(128)
208		π = R.pi()
209
210		def format_hex(value):
211		l = hex(value)[2:]
212		n = 4
213		x = [l[i:i + n] for i in range(0, len(l), n)]
214		return "0x" + "_".join(x) + "_u128"
215
216		def print_dyadic(value):
217		(s, m, e) = RealField(128)(value).sign_mantissa_exponent();
218		print("DyadicFloat128 {")
219		print(f" sign: DyadicSign::{'Pos' if s >= 0 else 'Neg'},")
220		print(f" exponent: {e},")
221		print(f" mantissa: {format_hex(m)},")
222		print("},")
223
224		# Generate array entries
225		print("pub(crate) static SIN_K_PI_OVER_128_F128: [DyadicFloat128; 65] = [")
226		for k in range(65):
227		value = R(k) * π / 128
228		print_dyadic(value.sin())
229
230		print("];")
231		*/
232		pub(crate) static SIN_K_PI_OVER_128_F128: [DyadicFloat128; 65] = [
233		DyadicFloat128 {
234		sign: DyadicSign::Pos,
235		exponent: 0,
236		mantissa: 0x0_u128,
237		},
238		DyadicFloat128 {
239		sign: DyadicSign::Pos,
240		exponent: -133,
241		mantissa: 0xc90a_afbd_1b33_efc9_c539_edcb_fda0_cf2c_u128,
242		},
243		DyadicFloat128 {
244		sign: DyadicSign::Pos,
245		exponent: -132,
246		mantissa: 0xc8fb_2f88_6ec0_9f37_6a17_954b_2b7c_5171_u128,
247		},
248		DyadicFloat128 {
249		sign: DyadicSign::Pos,
250		exponent: -131,
251		mantissa: 0x96a9_0496_70cf_ae65_f775_7409_4d3c_35c4_u128,
252		},
253		DyadicFloat128 {
254		sign: DyadicSign::Pos,
255		exponent: -131,
256		mantissa: 0xc8bd_35e1_4da1_5f0e_c739_6c89_4bbf_7389_u128,
257		},
258		DyadicFloat128 {
259		sign: DyadicSign::Pos,
260		exponent: -131,
261		mantissa: 0xfab2_72b5_4b98_71a2_7047_29ae_56d7_8a37_u128,
262		},
263		DyadicFloat128 {
264		sign: DyadicSign::Pos,
265		exponent: -130,
266		mantissa: 0x9640_8374_7309_d113_000a_89a1_1e07_c1ff_u128,
267		},
268		DyadicFloat128 {
269		sign: DyadicSign::Pos,
270		exponent: -130,
271		mantissa: 0xaf10_a224_59fe_32a6_3fee_f3bb_58b1_f10d_u128,
272		},
273		DyadicFloat128 {
274		sign: DyadicSign::Pos,
275		exponent: -130,
276		mantissa: 0xc7c5_c1e3_4d30_55b2_5cc8_c00e_4fcc_d850_u128,
277		},
278		DyadicFloat128 {
279		sign: DyadicSign::Pos,
280		exponent: -130,
281		mantissa: 0xe05c_1353_f27b_17e5_0ebc_61ad_e6ca_83cc_u128,
282		},
283		DyadicFloat128 {
284		sign: DyadicSign::Pos,
285		exponent: -130,
286		mantissa: 0xf8cf_cbd9_0af8_d57a_4221_dc4b_a772_598d_u128,
287		},
288		DyadicFloat128 {
289		sign: DyadicSign::Pos,
290		exponent: -129,
291		mantissa: 0x888e_9315_8fb3_bb04_9841_56f5_5334_4306_u128,
292		},
293		DyadicFloat128 {
294		sign: DyadicSign::Pos,
295		exponent: -129,
296		mantissa: 0x94a0_3176_acf8_2d45_ae4b_a773_da6b_f754_u128,
297		},
298		DyadicFloat128 {
299		sign: DyadicSign::Pos,
300		exponent: -129,
301		mantissa: 0xa09a_e4a0_bb30_0a19_2f89_5f44_a303_cc0b_u128,
302		},
303		DyadicFloat128 {
304		sign: DyadicSign::Pos,
305		exponent: -129,
306		mantissa: 0xac7c_d3ad_58fe_e7f0_811f_9539_84ef_f83e_u128,
307		},
308		DyadicFloat128 {
309		sign: DyadicSign::Pos,
310		exponent: -129,
311		mantissa: 0xb844_2987_d22c_f576_9cc3_ef36_746d_e3b8_u128,
312		},
313		DyadicFloat128 {
314		sign: DyadicSign::Pos,
315		exponent: -129,
316		mantissa: 0xc3ef_1535_754b_168d_3122_c2a5_9efd_dc37_u128,
317		},
318		DyadicFloat128 {
319		sign: DyadicSign::Pos,
320		exponent: -129,
321		mantissa: 0xcf7b_ca1d_476c_516d_a812_90bd_baad_62e4_u128,
322		},
323		DyadicFloat128 {
324		sign: DyadicSign::Pos,
325		exponent: -129,
326		mantissa: 0xdae8_804f_0ae6_015b_362c_b974_182e_3030_u128,
327		},
328		DyadicFloat128 {
329		sign: DyadicSign::Pos,
330		exponent: -129,
331		mantissa: 0xe633_74c9_8e22_f0b4_2872_ce1b_fc7a_d1cc_u128,
332		},
333		DyadicFloat128 {
334		sign: DyadicSign::Pos,
335		exponent: -129,
336		mantissa: 0xf15a_e9c0_37b1_d8f0_6c48_e9e3_420b_0f1d_u128,
337		},
338		DyadicFloat128 {
339		sign: DyadicSign::Pos,
340		exponent: -129,
341		mantissa: 0xfc5d_26df_c4d5_cfda_27c0_7c91_1290_b8d1_u128,
342		},
343		DyadicFloat128 {
344		sign: DyadicSign::Pos,
345		exponent: -128,
346		mantissa: 0x839c_3cc9_17ff_6cb4_bfd7_9717_f288_0abf_u128,
347		},
348		DyadicFloat128 {
349		sign: DyadicSign::Pos,
350		exponent: -128,
351		mantissa: 0x88f5_9aa0_da59_1421_b892_ca83_61d8_c84c_u128,
352		},
353		DyadicFloat128 {
354		sign: DyadicSign::Pos,
355		exponent: -128,
356		mantissa: 0x8e39_d9cd_7346_4364_bba4_cfec_bff5_4868_u128,
357		},
358		DyadicFloat128 {
359		sign: DyadicSign::Pos,
360		exponent: -128,
361		mantissa: 0x9368_2a66_e896_f544_b178_2191_1e71_c16e_u128,
362		},
363		DyadicFloat128 {
364		sign: DyadicSign::Pos,
365		exponent: -128,
366		mantissa: 0x987f_bfe7_0b81_a708_19ce_c845_ac87_a5c6_u128,
367		},
368		DyadicFloat128 {
369		sign: DyadicSign::Pos,
370		exponent: -128,
371		mantissa: 0x9d7f_d149_0285_c9e3_e25e_3954_9638_ae67_u128,
372		},
373		DyadicFloat128 {
374		sign: DyadicSign::Pos,
375		exponent: -128,
376		mantissa: 0xa267_9928_48ee_b0c0_3b51_67ee_359a_234e_u128,
377		},
378		DyadicFloat128 {
379		sign: DyadicSign::Pos,
380		exponent: -128,
381		mantissa: 0xa736_55df_1f2f_489e_149f_6e75_9934_68a2_u128,
382		},
383		DyadicFloat128 {
384		sign: DyadicSign::Pos,
385		exponent: -128,
386		mantissa: 0xabeb_49a4_6764_fd15_1bec_da80_89c1_a94c_u128,
387		},
388		DyadicFloat128 {
389		sign: DyadicSign::Pos,
390		exponent: -128,
391		mantissa: 0xb085_baa8_e966_f6da_e4ca_d00d_5c94_bcd1_u128,
392		},
393		DyadicFloat128 {
394		sign: DyadicSign::Pos,
395		exponent: -128,
396		mantissa: 0xb504_f333_f9de_6484_597d_89b3_754a_be9f_u128,
397		},
398		DyadicFloat128 {
399		sign: DyadicSign::Pos,
400		exponent: -128,
401		mantissa: 0xb968_41bf_7ffc_b21a_9de1_e3b2_2b8b_f4db_u128,
402		},
403		DyadicFloat128 {
404		sign: DyadicSign::Pos,
405		exponent: -128,
406		mantissa: 0xbdae_f913_557d_76f0_ac85_320f_528d_6d5c_u128,
407		},
408		DyadicFloat128 {
409		sign: DyadicSign::Pos,
410		exponent: -128,
411		mantissa: 0xc1d8_705f_fcbb_6e90_bdf0_715c_b8b2_0bd7_u128,
412		},
413		DyadicFloat128 {
414		sign: DyadicSign::Pos,
415		exponent: -128,
416		mantissa: 0xc5e4_0358_a8ba_05a7_43da_25d9_9267_326b_u128,
417		},
418		DyadicFloat128 {
419		sign: DyadicSign::Pos,
420		exponent: -128,
421		mantissa: 0xc9d1_124c_931f_da7a_8335_241b_e169_3225_u128,
422		},
423		DyadicFloat128 {
424		sign: DyadicSign::Pos,
425		exponent: -128,
426		mantissa: 0xcd9f_023f_9c3a_059e_23af_31db_7179_a4a9_u128,
427		},
428		DyadicFloat128 {
429		sign: DyadicSign::Pos,
430		exponent: -128,
431		mantissa: 0xd14d_3d02_313c_0eed_744f_ea20_e8ab_ef92_u128,
432		},
433		DyadicFloat128 {
434		sign: DyadicSign::Pos,
435		exponent: -128,
436		mantissa: 0xd4db_3148_750d_1819_f630_e8b6_dac8_3e68_u128,
437		},
438		DyadicFloat128 {
439		sign: DyadicSign::Pos,
440		exponent: -128,
441		mantissa: 0xd848_52c0_a80f_fcdb_24b9_fe00_6635_74a4_u128,
442		},
443		DyadicFloat128 {
444		sign: DyadicSign::Pos,
445		exponent: -128,
446		mantissa: 0xdb94_1a28_cb71_ec87_2c19_b632_53da_43fb_u128,
447		},
448		DyadicFloat128 {
449		sign: DyadicSign::Pos,
450		exponent: -128,
451		mantissa: 0xdebe_0563_7ca9_4cfb_4b19_aa71_fec3_ae6c_u128,
452		},
453		DyadicFloat128 {
454		sign: DyadicSign::Pos,
455		exponent: -128,
456		mantissa: 0xe1c5_978c_05ed_8691_f4e8_a837_2f8c_5810_u128,
457		},
458		DyadicFloat128 {
459		sign: DyadicSign::Pos,
460		exponent: -128,
461		mantissa: 0xe4aa_5909_a08f_a7b4_1227_85ae_67f5_515c_u128,
462		},
463		DyadicFloat128 {
464		sign: DyadicSign::Pos,
465		exponent: -128,
466		mantissa: 0xe76b_d7a1_e63b_9786_1251_2952_9d48_a92f_u128,
467		},
468		DyadicFloat128 {
469		sign: DyadicSign::Pos,
470		exponent: -128,
471		mantissa: 0xea09_a68a_6e49_cd62_15ad_45b4_a1b5_e823_u128,
472		},
473		DyadicFloat128 {
474		sign: DyadicSign::Pos,
475		exponent: -128,
476		mantissa: 0xec83_5e79_946a_3145_7e61_0231_ac1d_6181_u128,
477		},
478		DyadicFloat128 {
479		sign: DyadicSign::Pos,
480		exponent: -128,
481		mantissa: 0xeed8_9db6_6611_e307_86f8_c20f_b664_b01b_u128,
482		},
483		DyadicFloat128 {
484		sign: DyadicSign::Pos,
485		exponent: -128,
486		mantissa: 0xf109_0827_b437_25fd_6712_7db3_5b28_7315_u128,
487		},
488		DyadicFloat128 {
489		sign: DyadicSign::Pos,
490		exponent: -128,
491		mantissa: 0xf314_4762_4708_8f74_a548_6bdc_455d_56a3_u128,
492		},
493		DyadicFloat128 {
494		sign: DyadicSign::Pos,
495		exponent: -128,
496		mantissa: 0xf4fa_0ab6_316e_d2ec_163c_5c7f_03b7_18c5_u128,
497		},
498		DyadicFloat128 {
499		sign: DyadicSign::Pos,
500		exponent: -128,
501		mantissa: 0xf6ba_073b_424b_19e8_2c79_1f59_cc1f_fc23_u128,
502		},
503		DyadicFloat128 {
504		sign: DyadicSign::Pos,
505		exponent: -128,
506		mantissa: 0xf853_f7dc_9186_b952_c7ad_c6b4_9888_91ba_u128,
507		},
508		DyadicFloat128 {
509		sign: DyadicSign::Pos,
510		exponent: -128,
511		mantissa: 0xf9c7_9d63_272c_4628_4504_ae08_d19b_2981_u128,
512		},
513		DyadicFloat128 {
514		sign: DyadicSign::Pos,
515		exponent: -128,
516		mantissa: 0xfb14_be7f_bae5_8156_2172_a361_fd2a_722f_u128,
517		},
518		DyadicFloat128 {
519		sign: DyadicSign::Pos,
520		exponent: -128,
521		mantissa: 0xfc3b_27d3_8a5d_49ab_2567_78ff_cb5c_1769_u128,
522		},
523		DyadicFloat128 {
524		sign: DyadicSign::Pos,
525		exponent: -128,
526		mantissa: 0xfd3a_abf8_4528_b50b_eae6_bd95_1c1d_abbd_u128,
527		},
528		DyadicFloat128 {
529		sign: DyadicSign::Pos,
530		exponent: -128,
531		mantissa: 0xfe13_2387_0cfe_9a3d_90cd_1d95_9db6_74ef_u128,
532		},
533		DyadicFloat128 {
534		sign: DyadicSign::Pos,
535		exponent: -128,
536		mantissa: 0xfec4_6d1e_8929_2cf0_4139_0efd_c726_e9ef_u128,
537		},
538		DyadicFloat128 {
539		sign: DyadicSign::Pos,
540		exponent: -128,
541		mantissa: 0xff4e_6d68_0c41_d0a9_0f66_8633_f1ab_858a_u128,
542		},
543		DyadicFloat128 {
544		sign: DyadicSign::Pos,
545		exponent: -128,
546		mantissa: 0xffb1_0f1b_cb6b_ef1d_421e_8eda_af59_453e_u128,
547		},
548		DyadicFloat128 {
549		sign: DyadicSign::Pos,
550		exponent: -128,
551		mantissa: 0xffec_4304_2668_65d9_5657_5523_6696_1732_u128,
552		},
553		DyadicFloat128 {
554		sign: DyadicSign::Pos,
555		exponent: -127,
556		mantissa: 0x8000_0000_0000_0000_0000_0000_0000_0000_u128,
557		},
558		];