decmathlib-rs 0.4.0

/* -------------------------------------------------------------------------------------------------- */
/* Port of the Intel Decimal Floating-Point Math Library decimal128 type to Rust.                     */
/* decmathlib-rs - Copyright (C) 2023-2024 Carlos Guzmán Álvarez                                      */
/* -------------------------------------------------------------------------------------------------- */
/* Licensed under the MIT license. See LICENSE file in the project root for full license information. */
/* -------------------------------------------------------------------------------------------------- */
/* Intel® Decimal Floating-Point Math Library - Copyright (c) 2018, Intel Corp.                       */
/* -------------------------------------------------------------------------------------------------- */

use crate::bid_internal::{BID_UINT64, BID_UINT128};

/*
pub (crate) const BID_ROUND_CONST_TABLE: [[u64; 19]; 5] = [
    [	// RN
        0u64,	// 0 extra digits
        5u64,	// 1 extra digits
        50u64,	// 2 extra digits
        500u64,	// 3 extra digits
        5000u64,	// 4 extra digits
        50000u64,	// 5 extra digits
        500000u64,	// 6 extra digits
        5000000u64,	// 7 extra digits
        50000000u64,	// 8 extra digits
        500000000u64,	// 9 extra digits
        5000000000u64,	// 10 extra digits
        50000000000u64,	// 11 extra digits
        500000000000u64,	// 12 extra digits
        5000000000000u64,	// 13 extra digits
        50000000000000u64,	// 14 extra digits
        500000000000000u64,	// 15 extra digits
        5000000000000000u64,	// 16 extra digits
        50000000000000000u64,	// 17 extra digits
        500000000000000000u64	// 18 extra digits
    ],
    [	// RD
        0u64,	// 0 extra digits
        0u64,	// 1 extra digits
        0u64,	// 2 extra digits
        00u64,	// 3 extra digits
        000u64,	// 4 extra digits
        0000u64,	// 5 extra digits
        00000u64,	// 6 extra digits
        000000u64,	// 7 extra digits
        0000000u64,	// 8 extra digits
        00000000u64,	// 9 extra digits
        000000000u64,	// 10 extra digits
        0000000000u64,	// 11 extra digits
        00000000000u64,	// 12 extra digits
        000000000000u64,	// 13 extra digits
        0000000000000u64,	// 14 extra digits
        00000000000000u64,	// 15 extra digits
        000000000000000u64,	// 16 extra digits
        0000000000000000u64,	// 17 extra digits
        00000000000000000u64	// 18 extra digits
    ],
    [	// round to Inf
        0u64,	// 0 extra digits
        9u64,	// 1 extra digits
        99u64,	// 2 extra digits
        999u64,	// 3 extra digits
        9999u64,	// 4 extra digits
        99999u64,	// 5 extra digits
        999999u64,	// 6 extra digits
        9999999u64,	// 7 extra digits
        99999999u64,	// 8 extra digits
        999999999u64,	// 9 extra digits
        9999999999u64,	// 10 extra digits
        99999999999u64,	// 11 extra digits
        999999999999u64,	// 12 extra digits
        9999999999999u64,	// 13 extra digits
        99999999999999u64,	// 14 extra digits
        999999999999999u64,	// 15 extra digits
        9999999999999999u64,	// 16 extra digits
        99999999999999999u64,	// 17 extra digits
        999999999999999999u64	// 18 extra digits
    ],
    [	// RZ
        0u64,	// 0 extra digits
        0u64,	// 1 extra digits
        0u64,	// 2 extra digits
        00u64,	// 3 extra digits
        000u64,	// 4 extra digits
        0000u64,	// 5 extra digits
        00000u64,	// 6 extra digits
        000000u64,	// 7 extra digits
        0000000u64,	// 8 extra digits
        00000000u64,	// 9 extra digits
        000000000u64,	// 10 extra digits
        0000000000u64,	// 11 extra digits
        00000000000u64,	// 12 extra digits
        000000000000u64,	// 13 extra digits
        0000000000000u64,	// 14 extra digits
        00000000000000u64,	// 15 extra digits
        000000000000000u64,	// 16 extra digits
        0000000000000000u64,	// 17 extra digits
        00000000000000000u64	// 18 extra digits
    ],
    [	// round ties away from 0
        0u64,	// 0 extra digits
        5u64,	// 1 extra digits
        50u64,	// 2 extra digits
        500u64,	// 3 extra digits
        5000u64,	// 4 extra digits
        50000u64,	// 5 extra digits
        500000u64,	// 6 extra digits
        5000000u64,	// 7 extra digits
        50000000u64,	// 8 extra digits
        500000000u64,	// 9 extra digits
        5000000000u64,	// 10 extra digits
        50000000000u64,	// 11 extra digits
        500000000000u64,	// 12 extra digits
        5000000000000u64,	// 13 extra digits
        50000000000000u64,	// 14 extra digits
        500000000000000u64,	// 15 extra digits
        5000000000000000u64,	// 16 extra digits
        50000000000000000u64,	// 17 extra digits
        500000000000000000u64	// 18 extra digits
    ]
];
*/

pub (crate) const BID_ROUND_CONST_TABLE_128: [[BID_UINT128; 36]; 5] = [
    [	//RN
        BID_UINT128 { w: [0u64, 0u64] },// 0 extra digits
        BID_UINT128 { w: [5u64, 0u64] }, // 1 extra digits
        BID_UINT128 { w: [50u64, 0u64] }, // 2 extra digits
        BID_UINT128 { w: [500u64, 0u64] }, // 3 extra digits
        BID_UINT128 { w: [5000u64, 0u64] },	// 4 extra digits
        BID_UINT128 { w: [50000u64, 0u64] }, // 5 extra digits
        BID_UINT128 { w: [500000u64, 0u64] }, // 6 extra digits
        BID_UINT128 { w: [5000000u64, 0u64] }, // 7 extra digits
        BID_UINT128 { w: [50000000u64, 0u64] },	// 8 extra digits
        BID_UINT128 { w: [500000000u64, 0u64] }, // 9 extra digits
        BID_UINT128 { w: [5000000000u64, 0u64] }, // 10 extra digits
        BID_UINT128 { w: [50000000000u64, 0u64] }, // 11 extra digits
        BID_UINT128 { w: [500000000000u64, 0u64] },	// 12 extra digits
        BID_UINT128 { w: [5000000000000u64, 0u64] }, // 13 extra digits
        BID_UINT128 { w: [50000000000000u64, 0u64] }, // 14 extra digits
        BID_UINT128 { w: [500000000000000u64, 0u64] }, // 15 extra digits
        BID_UINT128 { w: [5000000000000000u64, 0u64] }, // 16 extra digits
        BID_UINT128 { w: [50000000000000000u64, 0u64] }, // 17 extra digits
        BID_UINT128 { w: [500000000000000000u64, 0u64] }, // 18 extra digits
        BID_UINT128 { w: [5000000000000000000u64, 0u64] }, // 19 extra digits
        BID_UINT128 { w: [0xb5e3af16b1880000u64, 2u64] }, //20
        BID_UINT128 { w: [0x1ae4d6e2ef500000u64, 27u64] }, //21
        BID_UINT128 { w: [0xcf064dd59200000u64, 271u64] }, //22
        BID_UINT128 { w: [0x8163f0a57b400000u64, 2710u64] }, //23
        BID_UINT128 { w: [0xde76676d0800000u64, 27105u64] }, //24
        BID_UINT128 { w: [0x8b0a00a425000000u64, 0x422cau64] }, //25
        BID_UINT128 { w: [0x6e64066972000000u64, 0x295be9u64] }, //26
        BID_UINT128 { w: [0x4fe8401e74000000u64, 0x19d971eu64] }, //27
        BID_UINT128 { w: [0x1f12813088000000u64, 0x1027e72fu64] }, //28
        BID_UINT128 { w: [0x36b90be550000000u64, 0xa18f07d7u64] }, //29
        BID_UINT128 { w: [0x233a76f520000000u64, 0x64f964e68u64] }, //30
        BID_UINT128 { w: [0x6048a59340000000u64, 0x3f1bdf1011u64] }, //31
        BID_UINT128 { w: [0xc2d677c080000000u64, 0x27716b6a0adu64] }, //32
        BID_UINT128 { w: [0x9c60ad8500000000u64, 0x18a6e32246c9u64] }, //33
        BID_UINT128 { w: [0x1bc6c73200000000u64, 0xf684df56c3e0u64] }, //34
        BID_UINT128 { w: [0x15c3c7f400000000u64, 0x9a130b963a6c1u64] } //35
    ],
    [	//RD
        BID_UINT128 { w: [0u64, 0u64] }, // 0 extra digits
        BID_UINT128 { w: [0u64, 0u64] }, // 1 extra digits
        BID_UINT128 { w: [0u64, 0u64] }, // 2 extra digits
        BID_UINT128 { w: [00u64, 0u64] }, // 3 extra digits
        BID_UINT128 { w: [000u64, 0u64] }, // 4 extra digits
        BID_UINT128 { w: [0000u64, 0u64] }, // 5 extra digits
        BID_UINT128 { w: [00000u64, 0u64] }, // 6 extra digits
        BID_UINT128 { w: [000000u64, 0u64] }, // 7 extra digits
        BID_UINT128 { w: [0000000u64, 0u64] }, // 8 extra digits
        BID_UINT128 { w: [00000000u64, 0u64] }, // 9 extra digits
        BID_UINT128 { w: [000000000u64, 0u64] }, // 10 extra digits
        BID_UINT128 { w: [0000000000u64, 0u64] }, // 11 extra digits
        BID_UINT128 { w: [00000000000u64, 0u64] }, // 12 extra digits
        BID_UINT128 { w: [000000000000u64, 0u64] }, // 13 extra digits
        BID_UINT128 { w: [0000000000000u64, 0u64] }, // 14 extra digits
        BID_UINT128 { w: [00000000000000u64, 0u64] }, // 15 extra digits
        BID_UINT128 { w: [000000000000000u64, 0u64] }, // 16 extra digits
        BID_UINT128 { w: [0000000000000000u64, 0u64] }, // 17 extra digits
        BID_UINT128 { w: [00000000000000000u64, 0u64] }, // 18 extra digits
        BID_UINT128 { w: [000000000000000000u64, 0u64] }, // 19 extra digits
        BID_UINT128 { w: [0u64, 0u64] }, //20
        BID_UINT128 { w: [0u64, 0u64] }, //21
        BID_UINT128 { w: [0u64, 0u64] }, //22
        BID_UINT128 { w: [0u64, 0u64] }, //23
        BID_UINT128 { w: [0u64, 0u64] }, //24
        BID_UINT128 { w: [0u64, 0u64] }, //25
        BID_UINT128 { w: [0u64, 0u64] }, //26
        BID_UINT128 { w: [0u64, 0u64] }, //27
        BID_UINT128 { w: [0u64, 0u64] }, //28
        BID_UINT128 { w: [0u64, 0u64] }, //29
        BID_UINT128 { w: [0u64, 0u64] }, //30
        BID_UINT128 { w: [0u64, 0u64] }, //31
        BID_UINT128 { w: [0u64, 0u64] }, //32
        BID_UINT128 { w: [0u64, 0u64] }, //33
        BID_UINT128 { w: [0u64, 0u64] }, //34
        BID_UINT128 { w: [0u64, 0u64] }, //35
    ],
    [	//RU
        BID_UINT128{ w: [0u64, 0u64] }, // 0 extra digits
        BID_UINT128{ w: [9u64, 0u64] }, // 1 extra digits
        BID_UINT128{ w: [99u64, 0u64] }, // 2 extra digits
        BID_UINT128{ w: [999u64, 0u64] }, // 3 extra digits
        BID_UINT128{ w: [9999u64, 0u64] }, // 4 extra digits
        BID_UINT128{ w: [99999u64, 0u64] }, // 5 extra digits
        BID_UINT128{ w: [999999u64, 0u64] }, // 6 extra digits
        BID_UINT128{ w: [9999999u64, 0u64] }, // 7 extra digits
        BID_UINT128{ w: [99999999u64, 0u64] }, // 8 extra digits
        BID_UINT128{ w: [999999999u64, 0u64] }, // 9 extra digits
        BID_UINT128{ w: [9999999999u64, 0u64] }, // 10 extra digits
        BID_UINT128{ w: [99999999999u64, 0u64] }, // 11 extra digits
        BID_UINT128{ w: [999999999999u64, 0u64] }, // 12 extra digits
        BID_UINT128{ w: [9999999999999u64, 0u64] }, // 13 extra digits
        BID_UINT128{ w: [99999999999999u64, 0u64] }, // 14 extra digits
        BID_UINT128{ w: [999999999999999u64, 0u64] }, // 15 extra digits
        BID_UINT128{ w: [9999999999999999u64, 0u64] }, // 16 extra digits
        BID_UINT128{ w: [99999999999999999u64, 0u64] }, // 17 extra digits
        BID_UINT128{ w: [999999999999999999u64, 0u64] }, // 18 extra digits
        BID_UINT128{ w: [9999999999999999999u64, 0u64] }, // 19 extra digits
        BID_UINT128{ w: [0x6BC75E2D630FFFFFu64, 0x5u64] }, //20
        BID_UINT128{ w: [0x35C9ADC5DE9FFFFFu64, 0x36u64] }, //21
        BID_UINT128{ w: [0x19E0C9BAB23FFFFFu64, 0x21eu64] }, //22
        BID_UINT128{ w: [0x2C7E14AF67FFFFFu64, 0x152du64] }, //23
        BID_UINT128{ w: [0x1BCECCEDA0FFFFFFu64, 0xd3c2u64] }, //24
        BID_UINT128{ w: [0x1614014849FFFFFFu64, 0x84595u64] }, //25
        BID_UINT128{ w: [0xDCC80CD2E3FFFFFFu64, 0x52b7d2u64] }, //26
        BID_UINT128{ w: [0x9FD0803CE7FFFFFFu64, 0x33B2E3Cu64] }, //27
        BID_UINT128{ w: [0x3E2502610FFFFFFFu64, 0x204FCE5Eu64] }, //28
        BID_UINT128{ w: [0x6D7217CA9FFFFFFFu64, 0x1431E0FAEu64] }, //29
        BID_UINT128{ w: [0x4674EDEA3FFFFFFFu64, 0xC9F2C9CD0u64] }, //30
        BID_UINT128{ w: [0xC0914B267FFFFFFFu64, 0x7E37BE2022u64] }, //31
        BID_UINT128{ w: [0x85ACEF80FFFFFFFFu64, 0x4EE2D6D415Bu64] }, //32
        BID_UINT128{ w: [0x38c15b09ffffffffu64, 0x314dc6448d93u64] }, //33
        BID_UINT128{ w: [0x378d8e63ffffffffu64, 0x1ed09bead87c0u64] }, //34
        BID_UINT128{ w: [0x2b878fe7ffffffffu64, 0x13426172c74d82u64] } //35
    ],
    [	//RZ
        BID_UINT128 { w: [0u64, 0u64] }, // 0 extra digits
        BID_UINT128 { w: [0u64, 0u64] }, // 1 extra digits
        BID_UINT128 { w: [0u64, 0u64] }, // 2 extra digits
        BID_UINT128 { w: [00u64, 0u64] }, // 3 extra digits
        BID_UINT128 { w: [000u64, 0u64] }, // 4 extra digits
        BID_UINT128 { w: [0000u64, 0u64] }, // 5 extra digits
        BID_UINT128 { w: [00000u64, 0u64] }, // 6 extra digits
        BID_UINT128 { w: [000000u64, 0u64] }, // 7 extra digits
        BID_UINT128 { w: [0000000u64, 0u64] }, // 8 extra digits
        BID_UINT128 { w: [00000000u64, 0u64] }, // 9 extra digits
        BID_UINT128 { w: [000000000u64, 0u64] }, // 10 extra digits
        BID_UINT128 { w: [0000000000u64, 0u64] }, // 11 extra digits
        BID_UINT128 { w: [00000000000u64, 0u64] }, // 12 extra digits
        BID_UINT128 { w: [000000000000u64, 0u64] }, // 13 extra digits
        BID_UINT128 { w: [0000000000000u64, 0u64] }, // 14 extra digits
        BID_UINT128 { w: [00000000000000u64, 0u64] }, // 15 extra digits
        BID_UINT128 { w: [000000000000000u64, 0u64] }, // 16 extra digits
        BID_UINT128 { w: [0000000000000000u64, 0u64] }, // 17 extra digits
        BID_UINT128 { w: [00000000000000000u64, 0u64] }, // 18 extra digits
        BID_UINT128 { w: [000000000000000000u64, 0u64] }, // 19 extra digits
        BID_UINT128 { w: [0u64, 0u64] }, //20
        BID_UINT128 { w: [0u64, 0u64] }, //21
        BID_UINT128 { w: [0u64, 0u64] }, //22
        BID_UINT128 { w: [0u64, 0u64] }, //23
        BID_UINT128 { w: [0u64, 0u64] }, //24
        BID_UINT128 { w: [0u64, 0u64] }, //25
        BID_UINT128 { w: [0u64, 0u64] }, //26
        BID_UINT128 { w: [0u64, 0u64] }, //27
        BID_UINT128 { w: [0u64, 0u64] }, //28
        BID_UINT128 { w: [0u64, 0u64] }, //29
        BID_UINT128 { w: [0u64, 0u64] }, //30
        BID_UINT128 { w: [0u64, 0u64] }, //31
        BID_UINT128 { w: [0u64, 0u64] }, //32
        BID_UINT128 { w: [0u64, 0u64] }, //33
        BID_UINT128 { w: [0u64, 0u64] }, //34
        BID_UINT128 { w: [0u64, 0u64] }, //35
    ],
    [	//RN, ties away
        BID_UINT128 { w: [0u64, 0u64] }, // 0 extra digits
        BID_UINT128 { w: [5u64, 0u64] }, // 1 extra digits
        BID_UINT128 { w: [50u64, 0u64] }, // 2 extra digits
        BID_UINT128 { w: [500u64, 0u64] }, // 3 extra digits
        BID_UINT128 { w: [5000u64, 0u64] }, // 4 extra digits
        BID_UINT128 { w: [50000u64, 0u64] }, // 5 extra digits
        BID_UINT128 { w: [500000u64, 0u64] }, // 6 extra digits
        BID_UINT128 { w: [5000000u64, 0u64] }, // 7 extra digits
        BID_UINT128 { w: [50000000u64, 0u64] }, // 8 extra digits
        BID_UINT128 { w: [500000000u64, 0u64] }, // 9 extra digits
        BID_UINT128 { w: [5000000000u64, 0u64] }, // 10 extra digits
        BID_UINT128 { w: [50000000000u64, 0u64] }, // 11 extra digits
        BID_UINT128 { w: [500000000000u64, 0u64] }, // 12 extra digits
        BID_UINT128 { w: [5000000000000u64, 0u64] }, // 13 extra digits
        BID_UINT128 { w: [50000000000000u64, 0u64] }, // 14 extra digits
        BID_UINT128 { w: [500000000000000u64, 0u64] }, // 15 extra digits
        BID_UINT128 { w: [5000000000000000u64, 0u64] }, // 16 extra digits
        BID_UINT128 { w: [50000000000000000u64, 0u64] }, // 17 extra digits
        BID_UINT128 { w: [500000000000000000u64, 0u64] }, // 18 extra digits
        BID_UINT128 { w: [5000000000000000000u64, 0u64] }, // 19 extra digits
        BID_UINT128 { w: [0xb5e3af16b1880000u64, 2u64] }, //20
        BID_UINT128 { w: [0x1ae4d6e2ef500000u64, 27u64] }, //21
        BID_UINT128 { w: [0xcf064dd59200000u64, 271u64] }, //22
        BID_UINT128 { w: [0x8163f0a57b400000u64, 2710u64] }, //23
        BID_UINT128 { w: [0xde76676d0800000u64, 27105u64] }, //24
        BID_UINT128 { w: [0x8b0a00a425000000u64, 0x422cau64] }, //25
        BID_UINT128 { w: [0x6e64066972000000u64, 0x295be9u64] }, //26
        BID_UINT128 { w: [0x4fe8401e74000000u64, 0x19d971eu64] }, //27
        BID_UINT128 { w: [0x1f12813088000000u64, 0x1027e72fu64] }, //28
        BID_UINT128 { w: [0x36b90be550000000u64, 0xa18f07d7u64] }, //29
        BID_UINT128 { w: [0x233a76f520000000u64, 0x64f964e68u64] }, //30
        BID_UINT128 { w: [0x6048a59340000000u64, 0x3f1bdf1011u64] }, //31
        BID_UINT128 { w: [0xc2d677c080000000u64, 0x27716b6a0adu64] }, //32
        BID_UINT128 { w: [0x9c60ad8500000000u64, 0x18a6e32246c9u64] }, //33
        BID_UINT128 { w: [0x1bc6c73200000000u64, 0xf684df56c3e0u64] }, //34
        BID_UINT128 { w: [0x15c3c7f400000000u64, 0x9a130b963a6c1u64] }, //35
    ]
];

pub (crate) const BID_RECIPROCALS10_128: [BID_UINT128; 36] = [
    BID_UINT128{ w: [0u64, 0u64] },	                                    // 0 extra digits
    BID_UINT128{ w: [0x3333333333333334u64, 0x3333333333333333u64] },	// 1 extra digit
    BID_UINT128{ w: [0x51eb851eb851eb86u64, 0x051eb851eb851eb8u64] },	// 2 extra digits
    BID_UINT128{ w: [0x3b645a1cac083127u64, 0x0083126e978d4fdfu64] },	// 3 extra digits
    BID_UINT128{ w: [0x4af4f0d844d013aau64, 0x00346dc5d6388659u64] },	//  10^(-4) * 2^131
    BID_UINT128{ w: [0x08c3f3e0370cdc88u64, 0x0029f16b11c6d1e1u64] },	//  10^(-5) * 2^134
    BID_UINT128{ w: [0x6d698fe69270b06du64, 0x00218def416bdb1au64] },	//  10^(-6) * 2^137
    BID_UINT128{ w: [0xaf0f4ca41d811a47u64, 0x0035afe535795e90u64] },	//  10^(-7) * 2^141
    BID_UINT128{ w: [0xbf3f70834acdaea0u64, 0x002af31dc4611873u64] },	//  10^(-8) * 2^144
    BID_UINT128{ w: [0x65cc5a02a23e254du64, 0x00225c17d04dad29u64] },	//  10^(-9) * 2^147
    BID_UINT128{ w: [0x6fad5cd10396a214u64, 0x0036f9bfb3af7b75u64] },	// 10^(-10) * 2^151
    BID_UINT128{ w: [0xbfbde3da69454e76u64, 0x002bfaffc2f2c92au64] },	// 10^(-11) * 2^154
    BID_UINT128{ w: [0x32fe4fe1edd10b92u64, 0x00232f33025bd422u64] },	// 10^(-12) * 2^157
    BID_UINT128{ w: [0x84ca19697c81ac1cu64, 0x00384b84d092ed03u64] },	// 10^(-13) * 2^161
    BID_UINT128{ w: [0x03d4e1213067bce4u64, 0x002d09370d425736u64] },	// 10^(-14) * 2^164
    BID_UINT128{ w: [0x3643e74dc052fd83u64, 0x0024075f3dceac2bu64] },	// 10^(-15) * 2^167
    BID_UINT128{ w: [0x56d30baf9a1e626bu64, 0x0039a5652fb11378u64] },	// 10^(-16) * 2^171
    BID_UINT128{ w: [0x12426fbfae7eb522u64, 0x002e1dea8c8da92du64] },	// 10^(-17) * 2^174
    BID_UINT128{ w: [0x41cebfcc8b9890e8u64, 0x0024e4bba3a48757u64] },	// 10^(-18) * 2^177
    BID_UINT128{ w: [0x694acc7a78f41b0du64, 0x003b07929f6da558u64] },	// 10^(-19) * 2^181
    BID_UINT128{ w: [0xbaa23d2ec729af3eu64, 0x002f394219248446u64] },	// 10^(-20) * 2^184
    BID_UINT128{ w: [0xfbb4fdbf05baf298u64, 0x0025c768141d369eu64] },	// 10^(-21) * 2^187
    BID_UINT128{ w: [0x2c54c931a2c4b759u64, 0x003c7240202ebdcbu64] },	// 10^(-22) * 2^191
    BID_UINT128{ w: [0x89dd6dc14f03c5e1u64, 0x00305b66802564a2u64] },	// 10^(-23) * 2^194
    BID_UINT128{ w: [0xd4b1249aa59c9e4eu64, 0x0026af8533511d4eu64] },	// 10^(-24) * 2^197
    BID_UINT128{ w: [0x544ea0f76f60fd49u64, 0x003de5a1ebb4fbb1u64] },	// 10^(-25) * 2^201
    BID_UINT128{ w: [0x76a54d92bf80caa1u64, 0x00318481895d9627u64] },	// 10^(-26) * 2^204
    BID_UINT128{ w: [0x921dd7a89933d54eu64, 0x00279d346de4781fu64] },	// 10^(-27) * 2^207
    BID_UINT128{ w: [0x8362f2a75b862215u64, 0x003f61ed7ca0c032u64] },	// 10^(-28) * 2^211
    BID_UINT128{ w: [0xcf825bb91604e811u64, 0x0032b4bdfd4d668eu64] },	// 10^(-29) * 2^214
    BID_UINT128{ w: [0x0c684960de6a5341u64, 0x00289097fdd7853fu64] },	// 10^(-30) * 2^217
    BID_UINT128{ w: [0x3d203ab3e521dc34u64, 0x002073accb12d0ffu64] },	// 10^(-31) * 2^220
    BID_UINT128{ w: [0x2e99f7863b696053u64, 0x0033ec47ab514e65u64] },	// 10^(-32) * 2^224
    BID_UINT128{ w: [0x587b2c6b62bab376u64, 0x002989d2ef743eb7u64] },	// 10^(-33) * 2^227
    BID_UINT128{ w: [0xad2f56bc4efbc2c5u64, 0x00213b0f25f69892u64] },	// 10^(-34) * 2^230
    BID_UINT128{ w: [0x0f2abc9d8c9689d1u64, 0x01a95a5b7f87a0efu64] },	// 35 extra digits
];

pub(crate) const BID_POWER10_TABLE_128: [BID_UINT128; 39] = [
    BID_UINT128 { w: [0x0000000000000001u64, 0x0000000000000000u64] },	// 10^0
    BID_UINT128 { w: [0x000000000000000au64, 0x0000000000000000u64] },	// 10^1
    BID_UINT128 { w: [0x0000000000000064u64, 0x0000000000000000u64] },	// 10^2
    BID_UINT128 { w: [0x00000000000003e8u64, 0x0000000000000000u64] },	// 10^3
    BID_UINT128 { w: [0x0000000000002710u64, 0x0000000000000000u64] },	// 10^4
    BID_UINT128 { w: [0x00000000000186a0u64, 0x0000000000000000u64] },	// 10^5
    BID_UINT128 { w: [0x00000000000f4240u64, 0x0000000000000000u64] },	// 10^6
    BID_UINT128 { w: [0x0000000000989680u64, 0x0000000000000000u64] },	// 10^7
    BID_UINT128 { w: [0x0000000005f5e100u64, 0x0000000000000000u64] },	// 10^8
    BID_UINT128 { w: [0x000000003b9aca00u64, 0x0000000000000000u64] },	// 10^9
    BID_UINT128 { w: [0x00000002540be400u64, 0x0000000000000000u64] },	// 10^10
    BID_UINT128 { w: [0x000000174876e800u64, 0x0000000000000000u64] },	// 10^11
    BID_UINT128 { w: [0x000000e8d4a51000u64, 0x0000000000000000u64] },	// 10^12
    BID_UINT128 { w: [0x000009184e72a000u64, 0x0000000000000000u64] },	// 10^13
    BID_UINT128 { w: [0x00005af3107a4000u64, 0x0000000000000000u64] },	// 10^14
    BID_UINT128 { w: [0x00038d7ea4c68000u64, 0x0000000000000000u64] },	// 10^15
    BID_UINT128 { w: [0x002386f26fc10000u64, 0x0000000000000000u64] },	// 10^16
    BID_UINT128 { w: [0x016345785d8a0000u64, 0x0000000000000000u64] },	// 10^17
    BID_UINT128 { w: [0x0de0b6b3a7640000u64, 0x0000000000000000u64] },	// 10^18
    BID_UINT128 { w: [0x8ac7230489e80000u64, 0x0000000000000000u64] },	// 10^19
    BID_UINT128 { w: [0x6bc75e2d63100000u64, 0x0000000000000005u64] },	// 10^20
    BID_UINT128 { w: [0x35c9adc5dea00000u64, 0x0000000000000036u64] },	// 10^21
    BID_UINT128 { w: [0x19e0c9bab2400000u64, 0x000000000000021eu64] },	// 10^22
    BID_UINT128 { w: [0x02c7e14af6800000u64, 0x000000000000152du64] },	// 10^23
    BID_UINT128 { w: [0x1bcecceda1000000u64, 0x000000000000d3c2u64] },	// 10^24
    BID_UINT128 { w: [0x161401484a000000u64, 0x0000000000084595u64] },	// 10^25
    BID_UINT128 { w: [0xdcc80cd2e4000000u64, 0x000000000052b7d2u64] },	// 10^26
    BID_UINT128 { w: [0x9fd0803ce8000000u64, 0x00000000033b2e3cu64] },	// 10^27
    BID_UINT128 { w: [0x3e25026110000000u64, 0x00000000204fce5eu64] },	// 10^28
    BID_UINT128 { w: [0x6d7217caa0000000u64, 0x00000001431e0faeu64] },	// 10^29
    BID_UINT128 { w: [0x4674edea40000000u64, 0x0000000c9f2c9cd0u64] },	// 10^30
    BID_UINT128 { w: [0xc0914b2680000000u64, 0x0000007e37be2022u64] },	// 10^31
    BID_UINT128 { w: [0x85acef8100000000u64, 0x000004ee2d6d415bu64] },	// 10^32
    BID_UINT128 { w: [0x38c15b0a00000000u64, 0x0000314dc6448d93u64] },	// 10^33
    BID_UINT128 { w: [0x378d8e6400000000u64, 0x0001ed09bead87c0u64] },	// 10^34
    BID_UINT128 { w: [0x2b878fe800000000u64, 0x0013426172c74d82u64] },	// 10^35
    BID_UINT128 { w: [0xb34b9f1000000000u64, 0x00c097ce7bc90715u64] },	// 10^36
    BID_UINT128 { w: [0x00f436a000000000u64, 0x0785ee10d5da46d9u64] },	// 10^37
    BID_UINT128 { w: [0x098a224000000000u64, 0x4b3b4ca85a86c47au64] },	// 10^38
];

pub (crate) const BID_RECIP_SCALE: [i32; 36] = [
    129 - 128,	// 1
    129 - 128,	// 1/10
    129 - 128,	// 1/10^2
    129 - 128,	// 1/10^3
    3,	        // 131 - 128
    6,	        // 134 - 128
    9,	        // 137 - 128
    13,	        // 141 - 128
    16,	        // 144 - 128
    19,	        // 147 - 128
    23,	        // 151 - 128
    26,	        // 154 - 128
    29,	        // 157 - 128
    33,	        // 161 - 128
    36,	        // 164 - 128
    39,	        // 167 - 128
    43,	        // 171 - 128
    46,	        // 174 - 128
    49,	        // 177 - 128
    53,	        // 181 - 128
    56,	        // 184 - 128
    59,	        // 187 - 128
    63,	        // 191 - 128

    66,	        // 194 - 128
    69,	        // 197 - 128
    73,	        // 201 - 128
    76,	        // 204 - 128
    79,	        // 207 - 128
    83,	        // 211 - 128
    86,	        // 214 - 128
    89,	        // 217 - 128
    92,	        // 220 - 128
    96,	        // 224 - 128
    99,	        // 227 - 128
    102,        // 230 - 128
    109,        // 237 - 128, 1/10^35
];

/// tables used in computation
pub (crate) const BID_ESTIMATE_DECIMAL_DIGITS: [i32; 129] = [
    1,	//2^0 =1     < 10^0
    1,	//2^1 =2     < 10^1
    1,	//2^2 =4     < 10^1
    1,	//2^3 =8     < 10^1
    2,	//2^4 =16    < 10^2
    2,	//2^5 =32    < 10^2
    2,	//2^6 =64    < 10^2
    3,	//2^7 =128   < 10^3
    3,	//2^8 =256   < 10^3
    3,	//2^9 =512   < 10^3
    4,	//2^10=1024  < 10^4
    4,	//2^11=2048  < 10^4
    4,	//2^12=4096  < 10^4
    4,	//2^13=8192  < 10^4
    5,	//2^14=16384 < 10^5
    5,	//2^15=32768 < 10^5

    5,	//2^16=65536     < 10^5
    6,	//2^17=131072    < 10^6
    6,	//2^18=262144    < 10^6
    6,	//2^19=524288    < 10^6
    7,	//2^20=1048576   < 10^7
    7,	//2^21=2097152   < 10^7
    7,	//2^22=4194304   < 10^7
    7,	//2^23=8388608   < 10^7
    8,	//2^24=16777216  < 10^8
    8,	//2^25=33554432  < 10^8
    8,	//2^26=67108864  < 10^8
    9,	//2^27=134217728 < 10^9
    9,	//2^28=268435456 < 10^9
    9,	//2^29=536870912 < 10^9
    10,	//2^30=1073741824< 10^10
    10,	//2^31=2147483648< 10^10

    10,	//2^32=4294967296     < 10^10
    10,	//2^33=8589934592     < 10^10
    11,	//2^34=17179869184    < 10^11
    11,	//2^35=34359738368    < 10^11
    11,	//2^36=68719476736    < 10^11
    12,	//2^37=137438953472   < 10^12
    12,	//2^38=274877906944   < 10^12
    12,	//2^39=549755813888   < 10^12
    13,	//2^40=1099511627776  < 10^13
    13,	//2^41=2199023255552  < 10^13
    13,	//2^42=4398046511104  < 10^13
    13,	//2^43=8796093022208  < 10^13
    14,	//2^44=17592186044416 < 10^14
    14,	//2^45=35184372088832 < 10^14
    14,	//2^46=70368744177664 < 10^14
    15,	//2^47=140737488355328< 10^15

    15,	//2^48=281474976710656    < 10^15
    15,	//2^49=562949953421312    < 10^15
    16,	//2^50=1125899906842624   < 10^16
    16,	//2^51=2251799813685248   < 10^16
    16,	//2^52=4503599627370496   < 10^16
    16,	//2^53=9007199254740992   < 10^16
    17,	//2^54=18014398509481984  < 10^17
    17,	//2^55=36028797018963968  < 10^17
    17,	//2^56=72057594037927936  < 10^17
    18,	//2^57=144115188075855872 < 10^18
    18,	//2^58=288230376151711744 < 10^18
    18,	//2^59=576460752303423488 < 10^18
    19,	//2^60=1152921504606846976< 10^19
    19,	//2^61=2305843009213693952< 10^19
    19,	//2^62=4611686018427387904< 10^19
    19,	//2^63=9223372036854775808< 10^19

    20,	//2^64=18446744073709551616
    20,	//2^65=36893488147419103232
    20,	//2^66=73786976294838206464
    21,	//2^67=147573952589676412928
    21,	//2^68=295147905179352825856
    21,	//2^69=590295810358705651712
    22,	//2^70=1180591620717411303424
    22,	//2^71=2361183241434822606848
    22,	//2^72=4722366482869645213696
    22,	//2^73=9444732965739290427392
    23,	//2^74=18889465931478580854784
    23,	//2^75=37778931862957161709568
    23,	//2^76=75557863725914323419136
    24,	//2^77=151115727451828646838272
    24,	//2^78=302231454903657293676544
    24,	//2^79=604462909807314587353088

    25,	//2^80=1208925819614629174706176
    25,	//2^81=2417851639229258349412352
    25,	//2^82=4835703278458516698824704
    25,	//2^83=9671406556917033397649408
    26,	//2^84=19342813113834066795298816
    26,	//2^85=38685626227668133590597632
    26,	//2^86=77371252455336267181195264
    27,	//2^87=154742504910672534362390528
    27,	//2^88=309485009821345068724781056
    27,	//2^89=618970019642690137449562112
    28,	//2^90=1237940039285380274899124224
    28,	//2^91=2475880078570760549798248448
    28,	//2^92=4951760157141521099596496896
    28,	//2^93=9903520314283042199192993792
    29,	//2^94=19807040628566084398385987584
    29,	//2^95=39614081257132168796771975168
    29,	//2^96=79228162514264337593543950336

    30,	//2^97=158456325028528675187087900672
    30,	//2^98=316912650057057350374175801344
    30,	//2^99=633825300114114700748351602688
    31,	//2^100=1267650600228229401496703205376
    31,	//2^101=2535301200456458802993406410752
    31,	//2^102=5070602400912917605986812821504
    32,	//2^103=10141204801825835211973625643008
    32,	//2^104=20282409603651670423947251286016
    32,	//2^105=40564819207303340847894502572032
    32,	//2^106=81129638414606681695789005144064
    33,	//2^107=162259276829213363391578010288128
    33,	// 2^108
    33,	// 2^109
    34,	// 2^110
    34,	// 2^111
    34,	// 2^112
    35,	// 2^113
    35,	// 2^114
    35,	// 2^115
    35,	// 2^116
    36,	// 2^117
    36,	// 2^118
    36,	// 2^119
    37,	// 2^120
    37,	// 2^121
    37,	// 2^122
    38,	// 2^123
    38,	// 2^124
    38,	// 2^125
    38,	// 2^126
    39,	// 2^127
    39	// 2^128
];

pub (crate) const BID_POWER10_INDEX_BINEXP_128: [BID_UINT128; 125] = [
    BID_UINT128 { w: [0x000000000000000au64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000000000000au64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000000000000au64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000000000000au64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000000064u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000000064u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000000064u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000003e8u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000003e8u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000003e8u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000002710u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000002710u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000002710u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000002710u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000186a0u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000186a0u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000186a0u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000f4240u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000f4240u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000000000f4240u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000989680u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000989680u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000989680u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000000989680u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000005f5e100u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000005f5e100u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0000000005f5e100u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000003b9aca00u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000003b9aca00u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000003b9aca00u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000002540be400u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000002540be400u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000002540be400u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00000002540be400u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000174876e800u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000174876e800u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000174876e800u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000e8d4a51000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000e8d4a51000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000000e8d4a51000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000009184e72a000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000009184e72a000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000009184e72a000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x000009184e72a000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00005af3107a4000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00005af3107a4000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00005af3107a4000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00038d7ea4c68000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00038d7ea4c68000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x00038d7ea4c68000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x002386f26fc10000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x002386f26fc10000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x002386f26fc10000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x002386f26fc10000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x016345785d8a0000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x016345785d8a0000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x016345785d8a0000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0de0b6b3a7640000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0de0b6b3a7640000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x0de0b6b3a7640000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x8ac7230489e80000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x8ac7230489e80000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x8ac7230489e80000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x8ac7230489e80000u64, 0x0000000000000000u64] },
    BID_UINT128 { w: [0x6bc75e2d63100000u64, 0x0000000000000005u64] },	// 10^20
    BID_UINT128 { w: [0x6bc75e2d63100000u64, 0x0000000000000005u64] },	// 10^20
    BID_UINT128 { w: [0x6bc75e2d63100000u64, 0x0000000000000005u64] },	// 10^20
    BID_UINT128 { w: [0x35c9adc5dea00000u64, 0x0000000000000036u64] },	// 10^21
    BID_UINT128 { w: [0x35c9adc5dea00000u64, 0x0000000000000036u64] },	// 10^21
    BID_UINT128 { w: [0x35c9adc5dea00000u64, 0x0000000000000036u64] },	// 10^21
    BID_UINT128 { w: [0x19e0c9bab2400000u64, 0x000000000000021eu64] },	// 10^22
    BID_UINT128 { w: [0x19e0c9bab2400000u64, 0x000000000000021eu64] },	// 10^22
    BID_UINT128 { w: [0x19e0c9bab2400000u64, 0x000000000000021eu64] },	// 10^22
    BID_UINT128 { w: [0x19e0c9bab2400000u64, 0x000000000000021eu64] },	// 10^22
    BID_UINT128 { w: [0x02c7e14af6800000u64, 0x000000000000152du64] },	// 10^23
    BID_UINT128 { w: [0x02c7e14af6800000u64, 0x000000000000152du64] },	// 10^23
    BID_UINT128 { w: [0x02c7e14af6800000u64, 0x000000000000152du64] },	// 10^23
    BID_UINT128 { w: [0x1bcecceda1000000u64, 0x000000000000d3c2u64] },	// 10^24
    BID_UINT128 { w: [0x1bcecceda1000000u64, 0x000000000000d3c2u64] },	// 10^24
    BID_UINT128 { w: [0x1bcecceda1000000u64, 0x000000000000d3c2u64] },	// 10^24
    BID_UINT128 { w: [0x161401484a000000u64, 0x0000000000084595u64] },	// 10^25
    BID_UINT128 { w: [0x161401484a000000u64, 0x0000000000084595u64] },	// 10^25
    BID_UINT128 { w: [0x161401484a000000u64, 0x0000000000084595u64] },	// 10^25
    BID_UINT128 { w: [0x161401484a000000u64, 0x0000000000084595u64] },	// 10^25
    BID_UINT128 { w: [0xdcc80cd2e4000000u64, 0x000000000052b7d2u64] },	// 10^26
    BID_UINT128 { w: [0xdcc80cd2e4000000u64, 0x000000000052b7d2u64] },	// 10^26
    BID_UINT128 { w: [0xdcc80cd2e4000000u64, 0x000000000052b7d2u64] },	// 10^26
    BID_UINT128 { w: [0x9fd0803ce8000000u64, 0x00000000033b2e3cu64] },	// 10^27
    BID_UINT128 { w: [0x9fd0803ce8000000u64, 0x00000000033b2e3cu64] },	// 10^27
    BID_UINT128 { w: [0x9fd0803ce8000000u64, 0x00000000033b2e3cu64] },	// 10^27
    BID_UINT128 { w: [0x3e25026110000000u64, 0x00000000204fce5eu64] },	// 10^28
    BID_UINT128 { w: [0x3e25026110000000u64, 0x00000000204fce5eu64] },	// 10^28
    BID_UINT128 { w: [0x3e25026110000000u64, 0x00000000204fce5eu64] },	// 10^28
    BID_UINT128 { w: [0x3e25026110000000u64, 0x00000000204fce5eu64] },	// 10^28
    BID_UINT128 { w: [0x6d7217caa0000000u64, 0x00000001431e0faeu64] },	// 10^29
    BID_UINT128 { w: [0x6d7217caa0000000u64, 0x00000001431e0faeu64] },	// 10^29
    BID_UINT128 { w: [0x6d7217caa0000000u64, 0x00000001431e0faeu64] },	// 10^29
    BID_UINT128 { w: [0x4674edea40000000u64, 0x0000000c9f2c9cd0u64] },	// 10^30
    BID_UINT128 { w: [0x4674edea40000000u64, 0x0000000c9f2c9cd0u64] },	// 10^30
    BID_UINT128 { w: [0x4674edea40000000u64, 0x0000000c9f2c9cd0u64] },	// 10^30
    BID_UINT128 { w: [0xc0914b2680000000u64, 0x0000007e37be2022u64] },	// 10^31
    BID_UINT128 { w: [0xc0914b2680000000u64, 0x0000007e37be2022u64] },	// 10^31
    BID_UINT128 { w: [0xc0914b2680000000u64, 0x0000007e37be2022u64] },	// 10^31
    BID_UINT128 { w: [0x85acef8100000000u64, 0x000004ee2d6d415bu64] },	// 10^32
    BID_UINT128 { w: [0x85acef8100000000u64, 0x000004ee2d6d415bu64] },	// 10^32
    BID_UINT128 { w: [0x85acef8100000000u64, 0x000004ee2d6d415bu64] },	// 10^32
    BID_UINT128 { w: [0x85acef8100000000u64, 0x000004ee2d6d415bu64] },	// 10^32
    BID_UINT128 { w: [0x38c15b0a00000000u64, 0x0000314dc6448d93u64] },	// 10^33
    BID_UINT128 { w: [0x38c15b0a00000000u64, 0x0000314dc6448d93u64] },	// 10^33
    BID_UINT128 { w: [0x38c15b0a00000000u64, 0x0000314dc6448d93u64] },	// 10^33, entry 112
    BID_UINT128 { w: [0x378d8e6400000000u64, 0x0001ed09bead87c0u64] },	// 10^34
    BID_UINT128 { w: [0x378d8e6400000000u64, 0x0001ed09bead87c0u64] },	// 10^34
    BID_UINT128 { w: [0x378d8e6400000000u64, 0x0001ed09bead87c0u64] },	// 10^34
    BID_UINT128 { w: [0x2b878fe800000000u64, 0x0013426172c74d82u64] },	// 10^35
    BID_UINT128 { w: [0x2b878fe800000000u64, 0x0013426172c74d82u64] },	// 10^35
    BID_UINT128 { w: [0x2b878fe800000000u64, 0x0013426172c74d82u64] },	// 10^35
    BID_UINT128 { w: [0x2b878fe800000000u64, 0x0013426172c74d82u64] },	// 10^35
    BID_UINT128 { w: [0xb34b9f1000000000u64, 0x00c097ce7bc90715u64] },	// 10^36
    BID_UINT128 { w: [0x00f436a000000000u64, 0x0785ee10d5da46d9u64] },	// 10^37
    BID_UINT128 { w: [0x00f436a000000000u64, 0x0785ee10d5da46d9u64] },	// 10^37
    BID_UINT128 { w: [0x00f436a000000000u64, 0x0785ee10d5da46d9u64] },	// 10^37
    BID_UINT128 { w: [0x098a224000000000u64, 0x4b3b4ca85a86c47au64] },	// 10^38
    BID_UINT128 { w: [0x098a224000000000u64, 0x4b3b4ca85a86c47au64] },	// 10^38
    BID_UINT128 { w: [0x098a224000000000u64, 0x4b3b4ca85a86c47au64] },	// 10^38
    BID_UINT128 { w: [0x098a224000000000u64, 0x4b3b4ca85a86c47au64] },	// 10^38
];

pub (crate) const BID_SHORT_RECIP_SCALE: [i32; 18] = [
    1,
    65 - 64,
    69 - 64,
    71 - 64,
    75 - 64,
    78 - 64,
    81 - 64,
    85 - 64,
    88 - 64,
    91 - 64,
    95 - 64,
    98 - 64,
    101 - 64,
    105 - 64,
    108 - 64,
    111 - 64,
    115 - 64,	//114 - 64
    118 - 64
];


pub (crate) const BID_RECIPROCALS10_64: [BID_UINT64; 18] = [
    1u64,	                // dummy value for 0 extra digits
    0x3333333333333334u64,	// 1 extra digit
    0x51eb851eb851eb86u64,
    0x20c49ba5e353f7cfu64,
    0x346dc5d63886594bu64,
    0x29f16b11c6d1e109u64,
    0x218def416bdb1a6eu64,
    0x35afe535795e90b0u64,
    0x2af31dc4611873c0u64,
    0x225c17d04dad2966u64,
    0x36f9bfb3af7b7570u64,
    0x2bfaffc2f2c92ac0u64,
    0x232f33025bd42233u64,
    0x384b84d092ed0385u64,
    0x2d09370d42573604u64,
    0x24075f3dceac2b37u64,
    0x39a5652fb1137857u64,
    0x2e1dea8c8da92d13u64
];