pxfm 0.1.4

/*
 * // 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};

pub(crate) static LOG2_STEP_1: [DyadicFloat128; 128] =
    // -log2(r) with 128-bit precision generated by SageMath with:
    // def format_hex(value):
    //     l = hex(value)[2:]
    //     n = 8
    //     x = [l[i:i + n] for i in range(0, len(l), n)]
    //     return "0x" + "_".join(x) + "_u128"
    // for i in range(1, 127):
    //   r = 2^-8 * ceil( 2^8 * (1 - 2^(-8)) / (1 + i*2^(-7)) );
    //   s, m, e = RealField(128)(r).log2().sign_mantissa_exponent();
    //   print("{DyadicSign::Pos,", e, ", format_hex(m), "},");
    /* .step_1 = */
    [
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: 0,
            mantissa: 0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb963dd10_7b993ada_e8c25163_0adb856a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -133,
            mantissa: 0xba1f7430_f9aab1b2_a41b08fb_e05f82d0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -132,
            mantissa: 0x8c25c726_2b57c149_1f06c085_bc1b865d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -132,
            mantissa: 0xbb9ca64e_cac6aaef_2e1c07f0_438ebac0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -132,
            mantissa: 0xeb75e8f8_ff5ff022_aacc0e21_d6541224_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -131,
            mantissa: 0x8dd99530_02a4e866_31514aef_39ce6303_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -131,
            mantissa: 0xa62b07f3_457c4070_50799bea_aab2940c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -131,
            mantissa: 0xbeb024b6_7dda6339_da288fc6_15a727dc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -131,
            mantissa: 0xcb0657cd_5dbe4f6f_22dbbace_d44516ce_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -131,
            mantissa: 0xe3da945b_878e27d0_d939dcee_cdd9ce05_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -131,
            mantissa: 0xfce4aee0_e88b2749_9596a8e2_e84c8f45_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0x84bf1c67_3032495d_243efd93_25954cfe_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0x916d6e15_59a4b696_91d79938_e7226384_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0x9e37db28_66f2850b_22563c9e_d9462091_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xa4a7c31d_c6f9a5d5_3a53ca11_81015ada_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xb19d45fa_1be70855_3eb8023e_ed65d601_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xb823018e_3cfc25f0_ce5cabbd_2d753d9b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xc544c055_fde99333_54dbf16f_b0695ee3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xcbe0e589_e3f6042d_5196a85a_067c6739_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xd930124b_ea9a2c66_f349845e_48955078_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xdfe33d3f_ffa66037_815ef705_cfaef035_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xed61169f_220e97f2_2ba704dc_aa76f41d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -130,
            mantissa: 0xf42be9e9_b09b3def_2062f36b_c14d0d93_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x80ecdde7_d30ea2ed_13288019_4144b02b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x845e706c_afd1bf61_54880de6_3812fd49_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x8b4e029b_1f8ac391_a87c02ea_f36e2c29_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x8ecc164e_a93841ae_9804237e_c8d9431d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x924e6958_9e6b6268_20f81ca9_5d9e7968_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x995ff71b_8773432d_124bc6f1_acf95dc4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0x9cef470a_acfb7bf9_5a5e8e21_bff3336b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xa08300be_1f651473_4e53fa33_29f65894_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xa7b7dd96_762cc3c7_2742d729_6a39eed6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xab591735_abc724e4_f359c554_4bc5e134_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xaefee78f_75707221_6b6c874d_d96e1d75_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xb2a95a4c_c313bb59_21006678_c0a5c390_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xb6587b43_2e47501b_6d40900b_25024b32_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xbdc4f816_7955698f_89e2eb55_3b279b3d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xc1826c86_08fe9951_d58525aa_d392ca50_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xc544c055_fde99333_54dbf16f_b0695ee3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xc90c0049_26e9dbfb_88d5eae3_326327bb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xccd83954_b6359379_46dfa05b_ddfded8c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xd47fcb8c_0852f0c0_bfe9dbeb_f2e8a45e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xd85b3fa7_a3407fa8_7b11f1c5_160c515c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xdc3be2bd_8d837f7f_1339e567_7ec44dd0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xe021c2cf_17ed9bdb_ea2b8c7b_b0ee9c8b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xe40cee16_a2ff21c4_aec56233_2791fe38_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xe7fd7308_d6895b14_71682eba_cca79cfa_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xebf36055_e1abc61e_a5ad5ce9_fb5a7bb6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xefeec4ea_c371584e_32251905_31a852c5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xf3efaff2_9c559a77_da8ad649_da21eab0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xf7f630d8_08fc2ada_4c3e2ea7_c15c3d1e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -129,
            mantissa: 0xfc025746_86680cc6_bcb9bfa9_852e0d35_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x800a1995_f0019518_ce032f41_d1e774e8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x8215ea5c_d3e4c4c7_9b39ffee_bc29372a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x8424a633_5c777e0b_87f95f1b_efb6f806_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x86365578_62acb7ce_b987b42e_3bb332a1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x884b00ae_f726cec5_139a7ba8_3bf2d136_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x8a62b07f_3457c407_050799be_aaab2941_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x8c7d6db7_169e0cda_8bd74461_7e9b7d52_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x8e9b414b_5a92a606_046ad444_333ceb10_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x90bc3458_61bf3d52_ef4c737f_ba4f5d66_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x92e05023_1df57d6f_ae441c09_d761c549_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x95079e1a_0382dc79_6e36aa9c_e90a3879_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x973227d6_027ebd8a_0efca1a1_84e93809_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x973227d6_027ebd8a_0efca1a1_84e93809_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x995ff71b_8773432d_124bc6f1_acf95dc4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x9b9115db_83a3dd2d_352bea51_e58ea9e8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x9dc58e34_7d37696d_266d6cdc_959153bc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0x9ffd6a73_a78eaf35_4527d82c_8214ddca_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xa238b516_0413106e_404cabb7_6d600e3c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xa238b516_0413106e_404cabb7_6d600e3c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xa47778c9_8bcc86a1_cab7d2ec_23f0eef3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xa6b9c06e_6211646b_761c48dd_859de2d3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xa8ff9718_10a5e181_7fd3b7d7_e5d148bb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xab49080e_cda53208_c27c6780_d92b4d11_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xad961ed0_cb91d406_db502402_c94092cd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xad961ed0_cb91d406_db502402_c94092cd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xafe6e713_93eeda29_3432ef6b_732b6843_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xb23b6cc5_6cc84c99_bb324da7_e046e792_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xb493bc0e_c9954243_b21709ce_430c8e24_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xb493bc0e_c9954243_b21709ce_430c8e24_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xb6efe153_c7e319f6_e91ad16e_cff10111_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xb94fe935_b83e3eb5_ce31e481_cd797e79_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xbbb3e094_b3d228d3_da3e961a_96c580fa_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xbbb3e094_b3d228d3_da3e961a_96c580fa_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xbe1bd491_3f3fda43_f396598a_ae91499a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xc087d28d_fb2febb8_ae4cceb0_f621941b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xc087d28d_fb2febb8_ae4cceb0_f621941b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xc2f7e831_632b6670_6c1855c4_2078f81b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xc56c2367_9b4d206e_169535fb_8bf577c8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xc56c2367_9b4d206e_169535fb_8bf577c8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xc7e49264_4d64237e_3b24cecc_60217942_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xca6143a4_9626d820_3dc2687f_cf939696_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xca6143a4_9626d820_3dc2687f_cf939696_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xcce245f1_031e41fa_0a62e6ad_d1a901a0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xcf67a85f_a1f89a04_5bb6e231_38ad51e1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xcf67a85f_a1f89a04_5bb6e231_38ad51e1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xd1f17a56_21fb01ac_7fc60a51_03092bae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xd47fcb8c_0852f0c0_bfe9dbeb_f2e8a45e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xd47fcb8c_0852f0c0_bfe9dbeb_f2e8a45e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xd712ac0c_f811659d_8e2d7d37_8127d823_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xd9aa2c3b_0ea3cbc1_5c1a7f14_b168b365_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xd9aa2c3b_0ea3cbc1_5c1a7f14_b168b365_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xdc465cd1_55a90942_b7579f0f_8d3d514b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xdc465cd1_55a90942_b7579f0f_8d3d514b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xdee74ee6_4b0c38d3_b087205e_b55aea85_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe18d13ee_805a4de3_424a2623_d60dfb16_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe18d13ee_805a4de3_424a2623_d60dfb16_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe437bdbf_5254459c_4d3a591a_e6854787_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe437bdbf_5254459c_4d3a591a_e6854787_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe6e75e91_b9cca551_8dcdb6b2_4c5c5cdf_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe99c0905_36ece983_33ac7d9e_bba8a53c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xe99c0905_36ece983_33ac7d9e_bba8a53c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xec55d022_d80e3d27_fb2eede4_b59d8959_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xec55d022_d80e3d27_fb2eede4_b59d8959_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xef14c760_5d60654c_308b4546_66de8f99_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xef14c760_5d60654c_308b4546_66de8f99_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xf1d902a3_7aaa5085_8383cb0c_e23bebd4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xf1d902a3_7aaa5085_8383cb0c_e23bebd4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xf4a29645_38813c67_64fc87b4_a41f7b70_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xf4a29645_38813c67_64fc87b4_a41f7b70_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xf7719715_7665f689_3f5d7d82_b65c5686_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xf7719715_7665f689_3f5d7d82_b65c5686_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xfa461a5e_8f4b759d_6476077b_9fbd41ae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xfa461a5e_8f4b759d_6476077b_9fbd41ae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -128,
            mantissa: 0xfd2035e9_221ef5d0_0e3909ff_d0d61778_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: 0,
            mantissa: 0_u128,
        },
    ];

pub(crate) static LOG2_STEP_2: [DyadicFloat128; 193] =
    // -log2(r) for the second step, generated by SageMath with:
    //
    // for i in range(-2^6, 2^7 + 1):
    //   r = 2^-16 * round( 2^16 / (1 + i*2^(-14)) );
    //   s, m, e = RealField(128)(r).log2().sign_mantissa_exponent();
    //   print("{DyadicSign::Neg," if s == 1 else "{DyadicSign::Pos,", e, ",
    //         format_hex(m), "},");
    /* .step_2 = */
    [
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xb9061559_18954401_b5cfed58_337e848a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xb6264958_a3c7fa2b_ffaf2ac1_b1d20910_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xb34671e4_39aa448e_52521a39_50ea2ed8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xb0668efb_7ef48ab7_f87e1abd_ee10fd95_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xad86a09e_185af0e8_fbd43bbc_c24c5e43_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xaaa6a6cb_aa8d57ce_2f4f5d48_f9796742_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xa7c6a183_da375c3d_3477fd67_c1cab6b3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xa4e690c6_4c0056f0_7b4d33eb_381fe558_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0xa2067492_a48b5c43_3ce25e48_cb498dea_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x9f264ce8_88773bed_70b0fcc9_e4330983_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x9c4619c7_9c5e80bf_bc9e4267_d3189b22_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x9965db2f_84d7705f_5fb3d896_326615c4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x9685911f_e6740b02_178b5831_1e96d323_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x93a53b98_65c20b2a_006bf8b6_cf73d847_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x90c4da98_a74ae561_7019f6e6_4a580a02_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x8de46e20_4f93c7f6_cb5733cf_0eb4191d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x8b03f62f_031d9ab8_56148d4f_c5e415b6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x882372c4_6664feaf_fe5370f4_25872623_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x8542e3e0_1de24ddf_21b72a14_57ee70d6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -135,
            mantissa: 0x81aa211f_1e332fcf_abff4f89_968bed0b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xfd92f0cf_88d75f24_86410a67_6480a5a7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xf7d1886b_2a876289_44280889_021970e4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xf2100910_6a42bc14_32eb139d_9812090d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xec4e72be_90cd2d2d_bef9dd41_e8e42810_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xe68cc574_e6e1e5d7_689d08ca_6c7c3eb1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xe0cb0132_b5338423_01ef259a_7f69821d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xdb0925f7_446c13a9_e22cea71_b7bb8467_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xd54733c1_dd2d0d04_0e5bb273_03f542fe_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xcf852a91_c80f553f_57453c8d_5dc64ce1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xc9c30a66_4da33d56_6cc7add1_fc09ef92_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xc400d33e_b67081a7_e678d728_0de1c07f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xbe3e851a_4af6496d_419bbeb2_239bdc39_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xb87c1ff8_53ab2631_d4676d1d_81755809_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xb2b9a3d8_18fd1349_b69dfef7_ac2e2890_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xacf710b8_e3517548_9f72fa0a_8fccabc0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xa7346699_fb051978_b8bfe6a3_addb988e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0xa171a57a_a86c3551_67862c8e_c9dcd60d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0x9baecd5a_33d265ee_09bd3370_909e28a6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0x95ebde37_e57aaf84_a96bc611_b991419b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0x9028d813_059f7cdc_a50bb80f_203f0d62_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0x8a65baea_dc729ec5_4d36cd47_4f65a317_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -136,
            mantissa: 0x84a286be_b21d4b8c_779be241_ef4874a3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xfdbe771b_9d803cea_0e76a962_fa65ace3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xf237b2ae_f4e62e5a_d3d35627_464a5267_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xe6b0c035_fa8b328c_162ef4b0_e838c363_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xdb299faf_3e7cd74f_77bb10b9_76b3b9ca_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xcfa25119_50b77014_209853ce_e70bc58b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xc41ad472_c12614d3_63f9b57c_baf2e58d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xb89329ba_1fa2a0fd_4fca1c93_1bd6e6d6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xad0b50ed_fbf5b265_26d26e43_4a53490a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0xa1834a0c_e5d6a82d_c55e0790_78dc86a0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0x95fb1515_6ceba1b5_f05b9d5b_d28f540b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -137,
            mantissa: 0x8a72b206_20c97d84_8ef87f1a_11cdb727_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -138,
            mantissa: 0xfdd441bb_21e7b069_9d687011_4c1183cf_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -138,
            mantissa: 0xe6c2c334_99ba16c4_63d514ff_f97e86f3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -138,
            mantissa: 0xcfb0e875_c7cc5929_11a38190_1eadd883_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -138,
            mantissa: 0xb89eb17b_cabe1857_a9d69d37_bc0a5bac_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -138,
            mantissa: 0xa18c1e43_c10c6898_2dc97c9f_fefd2497_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -138,
            mantissa: 0x8a792eca_c911cf92_0dcdc8af_cb2ac09a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -139,
            mantissa: 0xe6cbc61c_020c8446_dd454eb3_a1489470_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -139,
            mantissa: 0xb8a47615_0dfe4470_87803586_4d84b319_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -139,
            mantissa: 0x8a7c6d7a_f1de7942_7ce595cc_53b8342c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -140,
            mantissa: 0xb8a7588f_d29b1baa_4710b590_49899141_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -141,
            mantissa: 0xb8a8c9d8_be9ae994_5957f633_309d74e3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: 0,
            mantissa: 0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -141,
            mantissa: 0xb8abac81_ab576f3b_8268aba0_30b1adf6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -140,
            mantissa: 0xb8ad1de1_ac9ea6a5_1511cba2_fb213a10_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -139,
            mantissa: 0x8a82eb77_08262500_6379fb9f_d9bc6235_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -139,
            mantissa: 0xb8b000b8_c65957cc_b6fe1bf6_01ee27d5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -139,
            mantissa: 0xe6ddcebb_d72d3f7f_8c6e6069_3a14e6d0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -138,
            mantissa: 0x8a862ac3_0095c084_e9bcfd0c_62eaa2ca_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -138,
            mantissa: 0xa19dca8e_85918b6d_73b21420_9a5234a7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -138,
            mantissa: 0xb8b5c6c3_5e142a9b_347d4ca3_109fe4db_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -138,
            mantissa: 0xcfce1f64_6dca7745_37a62c48_783bb066_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -138,
            mantissa: 0xe6e6d474_9883fbe3_0794b643_7fb56344_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -138,
            mantissa: 0xfdffe5f6_c232f658_1cb9a45e_d90318e6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0x8a8ca9f6_e7762d0f_bc118e5d_bbef7dbc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0x96198f2e_5173e93b_b4c0fb95_35907cf8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xa1a6a2a3_113fe246_c051d2c5_f00a9bb9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xad33e456_9918a8d5_55326987_8c1e5110_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xb8c1544a_5b4e2caf_bc906750_b0ce372c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xc44ef27f_ca41bdd8_4c50eaa6_3be294b6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xcfdcbef8_58660da1_b6cb28db_8c065b44_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xdb6ab9b5_783f2fc5_70479336_830ceb05_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xe6f8e2b8_9c629b7a_2a458c83_1f6aeb49_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xf2873a03_37772c8a_6489ba5b_d391e206_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -137,
            mantissa: 0xfe15bf96_bc35246b_13f6fda5_10aeec3b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0x84d239ba_4eb315a9_2f9a0ef9_e8250836_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0x8a99aacf_26f2a8a7_389019e8_22b70f1e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0x9061330a_a04f87ae_308beeff_a12cf669_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0x9628d26d_7448a43f_9886a71b_25a2085d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0x9bf088f8_5c65a56b_70ba9ceb_e0b969c3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xa1b856ac_1236e85b_cd855dc7_05ea2bea_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xa7803b89_4f5580e0_7736196b_11afb331_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xad483790_cd6339fa_94c99761_b8eab3d8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xb3104ac3_460a9668_6194b8c0_40814736_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xb8d87521_72fed130_edde8d24_c7a999cc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xbea0b6ac_0dfbde2f_ea6b01eb_de42f1d0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xc4690f63_d0c66aa1_7ef732b6_9334cf50_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xca317f49_752bddae_2ba86275_fcfc2d72_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xcffa065d_b50258f6_b56ea44e_185bf99f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xd5c2a4a1_4a28b920_1d5c3bbe_b6902bfe_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xdb8b5a14_ee86965f_a2f2bb9e_156b0f37_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xe15426b9_5c0c4506_d166eb8d_a06ab5ef_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xe71d0a8f_4cb2d60f_97dc7bae_4219de0f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xece60597_7a7c17a8_6c9a8e76_98f416c4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xf2af17d2_9f7295c0_7b3a20aa_5289695e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xf8784141_75a99a93_ddcf578e_e2c2897b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -136,
            mantissa: 0xfe4181e4_b73d2f37_e10ebd96_c3ec30ec_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x82056cde_8f290e13_a9b7baec_b34ba577_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x8430f56d_5e1edfd1_2da910dc_61c182da_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x8715b5a8_f27bed90_faca09dc_7e0ba8b5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x89fa8180_19a2cace_0d723876_173c0947_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x8cdf58f3_30b64515_4e6651df_154e8f8c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x8fc43c02_94dd8af3_ee54b77d_3bc34b6d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x92a92aae_a3442c3d_ad07dde9_b5f92cce_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x958e24f7_b91a1a53_261aacf9_44b638f0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x98732ade_3393a868_232f5d64_a85b219d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x9b583c62_6fe98bc9_f3a958bb_706093fc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0x9e3d5984_cb58dc25_c9eaa059_e7b0333a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xa1228245_a32313cf_1e154029_663243c0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xa407b6a5_548e1006_16515200_e283d006_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xa6ecf6a4_3ce4113d_f498168a_3337ca4f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xa9d24242_b973bb63_8a04a89f_0548a10f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xacb79981_27901623_afaad01f_25772805_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xaf9cfc5f_e4908d31_c4f47950_543fe0b8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xb2826adf_4dd0f08e_338655e6_77d0d3ec_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xb567e4ff_c0b174cc_f8ac2ce1_9d009541_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xb84d6ac1_9a96b35c_344d5e7d_d7b2f465_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xbb32fc25_38e9aaca_bd6a217f_b4598ec7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xbe18992a_f917bf0e_bc21ff36_8f562b75_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xc0fe41d3_3892b9cc_4944139c_cbf2cb9a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xc3e3f61e_54d0ca9c_1369970c_8b67e6b5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xc6c9b60c_ab4c8752_099b370e_2d04a530_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xc9af819e_9984ec44_0b81c3d4_8aff589f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xcc9558d4_7cfd5c90_9f22b809_93be311b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xcf7b3bae_b33da265_ac29209c_8d8985ae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xd2612a2d_99d1ef47_3cbb6a52_0292351d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xd5472451_8e4adc56_43de9ae4_0507ef24_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xd82d2a1a_ee3d6a97_69677b90_2ea4df3a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xdb133b8a_17430339_db7a3aff_74967bd5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xddf9589f_66f977de_25990c82_a0066ac6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xe0df815b_3b0302dd_0d424aac_f4babf55_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xe30c278d_9936c595_f8e3e7eb_5a7bdebb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xe5f264ad_b62d5810_5ef8bf5a_df5deebe_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xe8d8ad75_590bdf92_331d1996_5368fc82_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xebbf01e4_df85219e_901c30c4_27e358b8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xeea561fc_a7504dc1_aeac7e98_57253b06_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xf18bcdbd_0e28fdd7_e2113e58_93ab5b40_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xf4724526_71cf3654_9a4efc80_ae977826_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xf758c839_30076689_6bf3ba83_19332c9f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xfa3f56f5_a69a68ed_1d732d30_2e75018b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -135,
            mantissa: 0xfd25f15c_33558362_ba179c5d_bcceec01_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x80064bb6_9a0533c0_5543f53b_8ad85039_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x8179a494_8347996b_e971a556_5b93cb67_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x82ed0348_045f379d_5b399644_ba714691_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x846067d1_4c3b8982_5079f1e0_ec4b8496_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x85d3d230_89ce40b0_6aba4990_a32e8873_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x87474265_ec0b4548_e16770c3_a404291c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x88bab871_a1e8b61c_1edb7ffb_1d6b3eab_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x8a2e3453_da5ee8cd_603243e1_ba7c7865_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x8ba1b60c_c46869f6_57ea5c03_ea4621dd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x8d153d9c_8f01fd4a_d3534cbf_43bd7fd8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x8e88cb03_692a9dbc_62c8c807_5dc91cd5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x8ffc5e41_81e37d9e_04bb70a5_e3db7b85_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x916ff757_083006c7_d3875ba3_2159547a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x9286adfc_a91ba28d_5c94c80e_7a8f66b1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x93fa514b_a0517623_52d313c4_7b4f91db_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x956dfa72_866fc57d_80829e9f_3957a4c3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x96e1a971_8a824be5_1cd49179_72015ae7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x98555e48_db96fcd2_1af23c29_ef3032da_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x99c918f8_a8be040e_e7f7bf24_0be67b80_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x9b3cd981_2109c5dc_2bbe3cd4_f7d868fa_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x9cb09fe2_738edf14_8c75d6a4_c5ae460d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x9e246c1c_cf642550_750fb989_c9a06186_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0x9f983e30_63a2a709_de787e24_4901bdf9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa10c161d_5f65abc0_1ba3205f_f729efa4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa27ff3e3_f1cab41b_a864d2a0_38fb19cd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa3f3d784_49f17a11_fb21f083_a5fec56d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa567c0fe_96fbf109_594c5552_bcc377f5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa6dbb053_080e45fc_aeb35a35_3fc5a503_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa84fa581_cc4edf9f_67a5c051_30c0f330_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xa9c3a08b_12e65e81_4de5cafd_e1caf46f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xab37a16f_0aff9d32_686fce3d_160e88fd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xacaba82d_e3c7b066_de1375b3_af6749a6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xadc2b114_c632da56_24356904_8ac4affe_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xaf36c213_19b80ea2_d6796227_dcd39551_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb0aad8ec_cfb38d51_abc92653_86172074_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb21ef5a2_175ac65e_0caac9f1_7896f2ce_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb3931833_1fe56492_1c65a3c7_f828972b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb50740a0_188d4daa_abdc6644_6a4286d9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb67b6ee9_308ea27b_2f3bbe8e_8d72abec_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -134,
            mantissa: 0xb7efa30e_9727bf11_b67dbdd7_f03d168c_u128,
        },
    ];

pub(crate) static LOG2_STEP_3: [DyadicFloat128; 161] =
    // -log2(r) for the third step, generated by SageMath with:
    //
    // for i in range(-80, 81):
    //   r = 2^-21 * round( 2^21 / (1 + i*2^(-21)) );
    //   s, m, e = RealField(128)(r).log2().sign_mantissa_exponent();
    //   print("{DyadicSign::Neg," if (s == 1) else "{DyadicSign::Pos,", e, ",
    //         format_hex(m), "},");
    /* .step_3 = */
    [
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xe6d3a96b_978fc16e_26f2c63c_0827ccbb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xe3f107a9_fbfc50ca_4b56fe66_7c8ec091_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xe10e65d1_4b937265_647d7618_1aec10fc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xde2bc3e1_8653b4f5_99e8f4d5_379eca79_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xdb4921da_ac3ba730_f07da899_90c20623_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xd8667fbc_bd49d7cd_4a812184_8531851a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xd583dd87_b97cd580_679a4d85_4ae13619_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xd2a13b3b_a0d32eff_e4d17407_2487a514_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xcfbe98d8_734b7301_3c90319d_969b54be_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xccdbf65e_30e43039_c6a173b0_9ba301e6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xc9f953cc_d99bf55e_b8317428_d7d8d06b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xc716b124_6d715125_23cdb51b_cc2061cd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xc4340e64_ec62d241_f964fc78_084fd515_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xc1516b8e_566f076a_06474fb1_5ccbb015_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xbe6ec8a0_ab947f51_f525ef6d_0b75b1c3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xbb8c259b_ebd1c8ae_4e13532d_f7ee8da7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xb8a98280_17257233_76832500_d72a9027_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xb5c6df4d_2d8e0a95_b14a3d28_5e592ba0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xb2e43c03_2f0a2089_1e9e9dc9_711f6e20_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xb00198a2_1b9842c1_bc176e97_4f255fac_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xad1ef529_f336fff3_64acf87f_c0f648e6_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xaa3c519a_b5e4e6d1_d0b8a157_4433e1f8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xa759adf4_63a08610_95f4e785_371c69a9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xa4770a36_fc686c63_277d5db0_0363a46f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0xa1946662_803b287c_d5cea669_485ec36c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0x9eb1c276_ef174910_cec66fda_04833322_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -142,
            mantissa: 0x9bcf1e74_48fb5cd2_1da36f6e_be3851db_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
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        DyadicFloat128 {
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            exponent: -142,
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        DyadicFloat128 {
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            exponent: -142,
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        DyadicFloat128 {
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            exponent: -142,
            mantissa: 0x90448d82_debe5194_d934c388_57eee4f3_u128,
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        DyadicFloat128 {
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            exponent: -142,
            mantissa: 0x8d61e90c_cfb481b1_c27b427b_4fbfc7db_u128,
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        DyadicFloat128 {
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            exponent: -142,
            mantissa: 0x8a7f447f_aba9fd2b_6e13de50_2b142b39_u128,
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        DyadicFloat128 {
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            exponent: -142,
            mantissa: 0x879c9fdb_729d52b3_f4e40620_6614e2ba_u128,
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        DyadicFloat128 {
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            exponent: -142,
            mantissa: 0x84b9fb20_248d10fd_4d320daa_3312ea6c_u128,
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        DyadicFloat128 {
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            exponent: -142,
            mantissa: 0x81d7564d_c177c6b9_4aa528fc_9d433c1a_u128,
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        DyadicFloat128 {
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            exponent: -143,
            mantissa: 0xfde962c8_92b80533_3c8ad047_559b1622_u128,
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        DyadicFloat128 {
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            exponent: -143,
            mantissa: 0xf82418c7_7870a69f_acf765a8_fc5bcc31_u128,
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        DyadicFloat128 {
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            mantissa: 0xf25ece98_34168f1a_be238832_edd27f20_u128,
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        DyadicFloat128 {
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            mantissa: 0xec99843a_c5a6dc07_02644bfc_a329b708_u128,
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            mantissa: 0xd58458f7_66d647ce_0951ef23_9abbb959_u128,
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        DyadicFloat128 {
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            mantissa: 0xcfbf0db3_25cf43ad_686c430c_89143d35_u128,
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            exponent: -143,
            mantissa: 0xc9f9c240_baa15447_ba79c248_afd42c12_u128,
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            exponent: -143,
            mantissa: 0xc43476a0_254996fd_ad19e0a9_2f115327_u128,
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        DyadicFloat128 {
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            exponent: -143,
            mantissa: 0xbe6f2ad1_65c5292f_a8ad6ac3_b0c99520_u128,
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        DyadicFloat128 {
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            exponent: -143,
            mantissa: 0xb8a9ded4_7c11283d_d0567d4a_9cc5e6a1_u128,
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        DyadicFloat128 {
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            exponent: -143,
            mantissa: 0xb2e492a9_682ab188_01f87c65_4b231443_u128,
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        DyadicFloat128 {
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        DyadicFloat128 {
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            exponent: -144,
            mantissa: 0xfde9ba10_90ab7feb_41127e3a_88eb6741_u128,
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            exponent: -144,
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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            exponent: -148,
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        DyadicFloat128 {
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            exponent: -148,
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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            mantissa: 0xb8aa523e_a755fe32_ee400e8c_68838733_u128,
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
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        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xc435af55_45f9e18e_b136b5ac_e0d6f74d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xc7185e6f_2a3dbd56_a979e6c4_34fad480_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xc9fb0da0_242c8b50_0794df56_00c90a5a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xccddbce8_33c7bcd8_a86d8081_4ac18cf1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xcfc06c47_5910c34e_8b8ac57a_9cca2d56_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xd2a31bbd_9409100f_d314c7e0_3140001f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xd585cb4a_e4b2147a_c3d4c40e_20b5ec89_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xd8687aef_4b0d41ed_c5351d72_9060644e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xdb4b2aaa_c71c09c7_614162e1_e12e445d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xde2dda7d_58dfdd66_44a652ea_df8ede85_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xe1108a67_005a2e29_3eb1e02a_f3e52c3c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xe3f33a67_bd8c6d6f_415335a2_53a82aa2_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -142,
            mantissa: 0xe6d5ea7f_90780c97_611abb08_33305fe1_u128,
        },
    ];

pub(crate) static LOG2_STEP_4: [DyadicFloat128; 130] =
    // -log2(r) for the fourth step, generated by SageMath with:
    //
    // for i in range(-65, 65):
    //   r = 2^-28 * round( 2^28 / (1 + i*2^(-28)) );
    //   s, m, e = RealField(128)(r).log2().sign_mantissa_exponent();
    //   print("{DyadicSign::Neg," if (s == 1) else "{DyadicSign::Pos,", e, ",
    //         format_hex(m), "},");
    /* .step_4 = */
    [
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xbb8ce299_0b5d0b90_ef1bffe5_65ce0a46_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xb8aa39b8_07a576e4_bea32445_60ca3d99_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xb5c790d6_d5c354df_8b91f71c_eefa31a2_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xb2e4e7f5_75b6a57b_9096e3d6_84001c0e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xb0023f13_e77f68b3_086054c7_94367f36_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xad1f9632_2b1d9e80_2d9cb330_94afe4de_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xaa3ced50_409146dd_3afa673c_fb3698f3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xa75a446e_27da61c4_6b27d803_3e4c6450_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xa4779b8b_e0f8ef2f_f8d36b84_d52a477b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0xa194f2a9_6becef1a_1eab86ae_37c03565_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x9eb249c6_c8b6617d_175e8d56_deb4ce2c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x9bcfa0e3_f7554653_1d9ae241_436519da_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x98ecf800_f7c99d96_6c0ee71a_dfe44325_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x960a4f1d_ca136741_3d68fc7c_2efb522f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x9327a63a_6e32a34d_cc5781e8_ac28e749_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x9044fd56_e42751b6_5388d5ce_d3a0f5af_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x8d625473_2bf17275_0dab5588_224c7e4a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x8a7fab8f_45910584_356d5d59_15c94a70_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x879d02ab_31060ade_057d4871_2c69a6a7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x84ba59c6_ee50827c_b88970ea_e5341d60_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -149,
            mantissa: 0x81d7b0e2_7d706c5a_89402fcb_bfe331bb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xfdea0ffb_bccb90e3_649fba08_79ca348b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xf824be32_22612d78_dccd9edf_bab6f777_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xf25f6c68_2ba1ae69_f066b9aa_4636478e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xec9a1a9d_d88d13ab_14c7b3cb_21578781_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xe6d4c8d3_29235d30_bf4d347b_528f56e1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xe10f7708_1d648aef_6553e0c9_e1b70799_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xdb4a253c_b5509cdb_7c385b9b_d80c1375_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xd584d370_f0e792e9_795745ac_402f919d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xcfbf81a4_d0296d0d_d20d3d8c_2625ac1b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xc9fa2fd8_53162b3c_fbb6dfa2_97551554_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xc434de0b_79adcd6b_6bb0c62c_a2867d91_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xbe6f8c3e_43f0538d_9757893d_57e40877_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xb8aa3a70_b1ddbd97_f407bebd_c8f8c28e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xb2e4e8a2_c3760b7e_f71dfa6d_08b016be_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xad1f96d4_78b93d37_15f6cde0_2b5543ce_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xa75a4505_d1a752b4_c5eec882_4692d1e9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0xa194f336_ce404bec_7c627794_7172081a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0x9bcfa167_6e8428d2_aeae662d_c45a61ce_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0x960a4f97_b272e95b_d22f1d3b_59110455_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0x9044fdc7_9a0c8d7c_5c412380_4ab83462_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0x8a7fabf7_25511528_c240fd95_b5cecb89_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -150,
            mantissa: 0x84ba5a26_54408055_798b2dea_b82fadc4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xfdea10aa_4db59ded_eef86988_e2227ddb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xf25f6d07_3a400203_62e1207c_0209b090_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xe6d4c963_6e202cd4_39897891_13ec7bee_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xdb4a25be_e9561e49_5daa6556_5e562909_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xcfbf8219_abe1d64b_b9fcd606_2a84acbd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xc434de73_b5c354c4_3939b586_c46792b3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xb8aa3acd_06fa999b_c619ea6a_7a9ee85e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xad1f9725_9f87a4bb_4b5656ef_9e7a27fd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0xa194f37d_7f6a760b_b3a7d900_83f7239c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0x960a4fd4_a6a30d75_e9c74a33_81c0f016_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -151,
            mantissa: 0x8a7fac2b_15316ae2_d86d7fca_f12ed012_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -152,
            mantissa: 0xfdea1101_962b1c76_d4a6956a_5c863e0f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -152,
            mantissa: 0xe6d4c9ab_909eeed1_1462ef19_2f547877_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -152,
            mantissa: 0xcfbf8254_19be4ca6_45819d2f_1d72eb8b_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -152,
            mantissa: 0xb8aa3afb_318935c8_3d742790_eedbe719_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -152,
            mantissa: 0xa194f3a0_d7ffaa08_d1ac0d7b_70d74492_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -152,
            mantissa: 0x8a7fac45_0d21a939_d79ac583_75f83d0c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -153,
            mantissa: 0xe6d4c9cf_a1de665a_49637b2b_ac367e87_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -153,
            mantissa: 0xb8aa3b12_46d08f69_1cc4b5ee_dcc78b35_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -153,
            mantissa: 0x8a7fac52_0919cd43_d43bf48a_42745836_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -154,
            mantissa: 0xb8aa3b1d_d1743f1c_3557bdcf_592619eb_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Neg,
            exponent: -155,
            mantissa: 0xb8aa3b23_96c617ae_6bdc2e83_d3ebb0c4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: 0,
            mantissa: 0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -155,
            mantissa: 0xb8aa3b2f_2169ca44_2d5b4005_0e44e8ab_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -154,
            mantissa: 0xb8aa3b34_e6bba447_b8560371_b8f04afe_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -153,
            mantissa: 0x8a7fac6c_010a1f14_c79a43cc_c70459cc_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -153,
            mantissa: 0xb8aa3b40_715f59c0_22c25632_f519f77f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -153,
            mantissa: 0xe6d4ca17_c45d8282_42c10a31_4e35fb9e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -152,
            mantissa: 0x8a7fac78_fd024cdb_be5a212e_d7b949e4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -152,
            mantissa: 0xa194f3e7_892a4fde_12dcf94e_f5c5b918_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -152,
            mantissa: 0xb8aa3b57_86a6ca76_49781013_e57110ce_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -152,
            mantissa: 0xcfbf82c8_f577bcd2_8cba70c0_85c12cb3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -152,
            mantissa: 0xe6d4ca3b_d59d2721_07332f3f_b09328b8_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -152,
            mantissa: 0xfdea11b0_2717098f_e3716824_3a9d8b14_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0x8a7fac92_f4f2b226_a6022054_79b93722_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0x960a504e_8f041bc3_b5bd7358_52c0d583_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xa194f40a_e1bfc1b6_36324863_0b0d812d_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xad1f97c7_ed25a415_3ca83f0e_02b823c0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xb8aa3b85_b135c2f7_de66fb46_974bc4fd_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xc434df44_2df01e75_30b6254e_23c69fc2_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xcfbf8303_6354b6a4_48dd69ba_009b370c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xdb4a26c3_51638b9c_3c247973_83b16af5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xe6d4ca83_f81c9d74_1fd309b8_00678db7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xf25f6e45_577fec43_0930d418_c79378a3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -151,
            mantissa: 0xfdea1207_6f8d7820_0d85967b_2783a12c_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0x84ba5ae5_2022a091_210c898c_360016ed_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0x8a7facc6_e4d3a3b0_5e19883e_ef2605ab_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0x9044fea9_05d9c579_488dacc6_629300ae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0x960a508b_833505f7_6b0cdebd_3264e3e3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0x9bcfa26e_5ce56536_503b07e7_ff788dc2_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xa194f451_92eae341_82bc1435_696a69d1_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xa75a4635_25458024_8d33f1be_0e96fb1f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xad1f9819_13f53bea_fa4690c4_8c1b66c9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xb2e4e9fd_5efa16a0_5497e3b5_7dd5fe75_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xb8aa3be2_06541050_26cbdf27_7e66cad5_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xbe6f8dc7_0a032905_fb8679db_27301625_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xc434dfac_6a0760cd_5d6bacbb_1056f6aa_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xc9fa3192_2660b7b1_d71f72db_d0c3d936_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xcfbf8378_3f0f2dbe_f345c97b_fe230ba2_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xd584d55e_b412c300_3c82b004_2ce54751_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xdb4a2745_856b7781_3d7a2806_f0403bae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xe10f792c_b3194b4d_80d03540_da2f18ae_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xe6d4cb14_3d1c3e70_9128dd98_7b73194f_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xec9a1cfc_237450f5_f928291e_63940e14_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xf25f6ee4_662182e9_4372220d_20e0e78a_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xf824c0cd_0523d455_faaad4c9_407040c7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -150,
            mantissa: 0xfdea12b6_007b4547_a9764fe1_4e20e9e4_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x81d7b24f_ac13eae4_ed3c5206_ea4d3942_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x84ba5b44_8614c2f4_0c2af218_aea6da27_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x879d0439_8e402ad6_f6d912ac_383aaeba_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x8a7fad2e_c4962293_7298bf5c_ca8b3d95_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x8d625624_2916aa2f_44bc04da_a8808214_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x9044ff19_bbc1c1b0_3294f0eb_14683198_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x9327a80f_7c97691c_01759268_4ff600c3_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x960a5105_6b97a078_76aff941_9c43e8b9_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x98ecf9fb_88c267cb_5796367b_39d26c63_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x9bcfa2f1_d417bf1a_697a5c2e_6888ddaa_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0x9eb24be8_4d97a66b_71ae7d89_67b5a2b7_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xa194f4de_f5421dc4_3584aecf_760e7b39_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xa4779dd5_cb17252a_7a4f0558_d1b0c59e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xa75a46cc_cf16bca4_055f9792_b821c455_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xaa3cefc4_0140e436_9c087cff_664ee311_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xad1f98bb_61959be8_039bce36_188dfc04_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xb00241b2_f014e3be_016ba4e3_0a9d9d21_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xb2e4eaaa_acbebbbe_5aca1bc7_77a54d5e_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xb5c793a2_979323ee_d5094eb9_9a35d1f0_u128,
        },
        DyadicFloat128 {
            sign: DyadicSign::Pos,
            exponent: -149,
            mantissa: 0xb8aa3c9a_b0921c55_357b5aa4_ac49738d_u128,
        },
    ];