simplicity/merkle/

tmr.rs

// SPDX-License-Identifier: CC0-1.0

use crate::merkle::midstate::MidstateExt;
use hashes::sha256::Midstate;

super::impl_mr_type! {
    /// Type Merkle root
    ///
    /// A Merkle root that commits to a type's primitive (unit, sum, product)
    /// and recursively its sub-types.
    ///
    /// Uniquely identifies a type.
    #[derive(Copy, Clone, PartialEq, Eq, Hash, PartialOrd, Ord)]
    pub struct Tmr([u8; 32]);
}

impl Tmr {
    #[rustfmt::skip]
    const UNIT_IV: Midstate = Midstate::new([
        0x50, 0xb3, 0x8c, 0xd7, 0x64, 0x75, 0xff, 0x89,
        0x29, 0x28, 0x8b, 0xfc, 0xd0, 0xd9, 0xdf, 0x0e,
        0x4a, 0x24, 0x1c, 0x0a, 0x57, 0x08, 0x57, 0x2a,
        0xd2, 0x64, 0x19, 0x2a, 0x4f, 0xe6, 0x7b, 0xee,
    ], 64);

    #[rustfmt::skip]
    const SUM_IV: Midstate = Midstate::new([
        0x92, 0x0c, 0xfd, 0x83, 0xcf, 0x96, 0xbb, 0x32,
        0x73, 0x17, 0x36, 0x0f, 0x6d, 0x3a, 0xd7, 0x60,
        0x1e, 0xef, 0x0a, 0x16, 0xdd, 0x53, 0x14, 0x6c,
        0x2e, 0x5d, 0xe3, 0x5f, 0x51, 0xef, 0x8d, 0xa4,
    ], 64);

    #[rustfmt::skip]
    const PROD_IV: Midstate = Midstate::new([
        0xae, 0x99, 0x2a, 0x3e, 0xe0, 0x71, 0x3b, 0xf6,
        0x19, 0x5d, 0x3b, 0xac, 0x1a, 0xf5, 0x05, 0xa7,
        0x29, 0xc1, 0x4d, 0x47, 0x95, 0x58, 0xf0, 0xd6,
        0x29, 0x96, 0x30, 0xf7, 0xfa, 0x97, 0x2e, 0xf8,
    ], 64);

    /// The TMRs of the types TWO^(2^n) for small values of n
    #[rustfmt::skip]
    pub const TWO_TWO_N: [Tmr; 32] = [
        Tmr([
            0x88, 0x5a, 0x22, 0xde, 0x3e, 0xdb, 0x3f, 0x40,
            0xdb, 0x06, 0x09, 0xc2, 0x40, 0x23, 0x30, 0x3f,
            0xec, 0x67, 0x87, 0xbe, 0x4d, 0x49, 0x21, 0xe4,
            0x5e, 0xe9, 0xd9, 0x83, 0xac, 0xb5, 0xd8, 0x9d,
        ]),
        Tmr([
            0x55, 0x22, 0xba, 0x1c, 0x92, 0x89, 0x4d, 0xf2,
            0x57, 0x23, 0xcf, 0xeb, 0x5a, 0xf2, 0x59, 0xf4,
            0xc5, 0x5a, 0x5c, 0xfc, 0x82, 0x00, 0xd5, 0x9b,
            0xad, 0x09, 0x64, 0x99, 0x7f, 0x9b, 0x2b, 0x04,
        ]),
        Tmr([
            0xfa, 0x28, 0xba, 0x9f, 0x0f, 0x07, 0xb4, 0xfa,
            0xe4, 0xdd, 0x86, 0x23, 0x61, 0x41, 0x12, 0xff,
            0x3b, 0xaf, 0xab, 0xe2, 0x9c, 0x41, 0x5d, 0x2e,
            0x0c, 0x1e, 0xd3, 0xc4, 0x13, 0x51, 0x28, 0xe0,
        ]),
        Tmr([
            0xd3, 0x43, 0xe4, 0xd5, 0xfa, 0xa4, 0xce, 0xa4,
            0x4b, 0xb7, 0x11, 0xef, 0x4b, 0x1b, 0x96, 0xb7,
            0xe0, 0xfb, 0x26, 0xcf, 0xa8, 0x5a, 0x96, 0x04,
            0x39, 0xba, 0x84, 0x58, 0xc0, 0xb6, 0xc5, 0xc3,
        ]),
        Tmr([
            0x62, 0x8c, 0x36, 0x1f, 0x09, 0xcb, 0x2e, 0x5b,
            0xaa, 0xd9, 0xc6, 0xb7, 0x26, 0xa9, 0xfa, 0x95,
            0xd1, 0xda, 0x67, 0x79, 0x7e, 0xe2, 0x4c, 0xcf,
            0x01, 0x41, 0x0c, 0x97, 0x93, 0x39, 0x95, 0x00,
        ]),
        Tmr([
            0xb1, 0xa9, 0xf9, 0x68, 0x78, 0x33, 0xdc, 0x44,
            0xbc, 0x8f, 0x17, 0xd3, 0xcb, 0xc2, 0x55, 0xb7,
            0xaa, 0x49, 0x9a, 0x78, 0xfe, 0xc8, 0x5c, 0xc9,
            0x8a, 0x0c, 0x33, 0x5c, 0x86, 0xed, 0x26, 0xe9,
        ]),
        Tmr([
            0xfd, 0x75, 0xbc, 0xd8, 0xcb, 0x55, 0xa5, 0xe4,
            0x24, 0xe0, 0x92, 0x88, 0xac, 0x8e, 0xb4, 0x29,
            0x42, 0x53, 0x4e, 0xc1, 0x09, 0x9b, 0x72, 0xbe,
            0xce, 0x0e, 0xa2, 0xc5, 0x47, 0x9b, 0xf3, 0xe7,
        ]),
        Tmr([
            0xe3, 0x94, 0xd2, 0xa0, 0x51, 0x6d, 0x73, 0x8d,
            0x6e, 0x04, 0x59, 0xb9, 0x1b, 0xb0, 0xdd, 0x47,
            0x1d, 0x0d, 0xaa, 0x77, 0x96, 0x71, 0xa5, 0x31,
            0x3b, 0x62, 0x14, 0x0e, 0xc7, 0x0a, 0x22, 0x6e,
        ]),
        Tmr([
            0xe4, 0xc4, 0x72, 0x8d, 0x87, 0x67, 0x49, 0xbe,
            0xbe, 0x4d, 0x62, 0x97, 0xdf, 0xad, 0xd4, 0x2c,
            0xe2, 0x68, 0x44, 0x50, 0x0d, 0x96, 0xc5, 0xe9,
            0x14, 0x61, 0x57, 0x50, 0x8e, 0xb9, 0x09, 0x8f,
        ]),
        Tmr([
            0x1a, 0xe5, 0x45, 0xb7, 0xc3, 0xfd, 0x85, 0xfe,
            0x81, 0x6c, 0x70, 0xea, 0x4c, 0x78, 0xb7, 0x41,
            0x9d, 0x8b, 0xe3, 0xc1, 0xfb, 0x3f, 0x72, 0x23,
            0xfa, 0x7d, 0x8d, 0x50, 0x36, 0x75, 0x51, 0x8f,
        ]),
        Tmr([
            0x6a, 0x9c, 0x72, 0x40, 0xe5, 0xd7, 0x1d, 0x5a,
            0x83, 0x30, 0xb3, 0xb3, 0xb6, 0x65, 0x0b, 0xc3,
            0x66, 0x6c, 0x3f, 0xef, 0x2e, 0x80, 0x3e, 0xd8,
            0x64, 0xf1, 0x2f, 0xcd, 0x8f, 0xea, 0xc1, 0xca,
        ]),
        Tmr([
            0x0a, 0x2a, 0x58, 0x7a, 0xeb, 0xc9, 0x6b, 0x0e,
            0x3e, 0x26, 0x01, 0x38, 0x2e, 0xb3, 0x2a, 0x9f,
            0x1e, 0x29, 0xc8, 0x50, 0x1c, 0xbd, 0xd8, 0x0e,
            0x87, 0x05, 0xc0, 0xe7, 0xd3, 0xf5, 0xb3, 0x4f,
        ]),
        Tmr([
            0xb3, 0xed, 0xb6, 0xfd, 0x83, 0x8e, 0xc4, 0x05,
            0x7b, 0x76, 0x8c, 0x86, 0xb0, 0xe8, 0xa9, 0x6d,
            0x1c, 0xe3, 0xf1, 0x69, 0x54, 0x31, 0x4d, 0xcd,
            0x3d, 0xbf, 0x72, 0x85, 0xeb, 0xa5, 0x63, 0xa9,
        ]),
        Tmr([
            0xd0, 0x47, 0x4c, 0x0c, 0x1e, 0x2c, 0x09, 0xd9,
            0xc5, 0xf0, 0x50, 0x98, 0x93, 0x57, 0xce, 0x71,
            0xab, 0x5d, 0x90, 0x4e, 0x8e, 0x2e, 0x82, 0x87,
            0x42, 0x86, 0xc0, 0xc2, 0x12, 0xde, 0x3e, 0x71,
        ]),
        Tmr([
            0x37, 0x92, 0x46, 0xdc, 0x86, 0x6d, 0x37, 0x0d,
            0xbf, 0xc9, 0x70, 0x4f, 0xbc, 0x57, 0xcd, 0x7a,
            0x6e, 0xb5, 0xed, 0xe7, 0x97, 0xa0, 0x0c, 0x4a,
            0x72, 0xb3, 0xb4, 0xa5, 0xd9, 0xf0, 0x9f, 0xe1,
        ]),
        Tmr([
            0x8a, 0x59, 0xe8, 0x3f, 0x43, 0xe2, 0xa1, 0xf9,
            0x07, 0xd3, 0xa2, 0x96, 0x67, 0x53, 0x33, 0x6a,
            0x1d, 0xa2, 0x0d, 0x23, 0xfe, 0x63, 0x63, 0x28,
            0x58, 0xf9, 0x4e, 0xc0, 0x7d, 0x19, 0x13, 0xd2,
        ]),
        Tmr([
            0x0f, 0x51, 0x95, 0x68, 0x9f, 0x55, 0x6d, 0x00,
            0xbe, 0x92, 0xfc, 0x2d, 0xc5, 0x7b, 0xcb, 0xb1,
            0x25, 0x62, 0x0f, 0xfc, 0x00, 0x96, 0x3c, 0x09,
            0x14, 0xb1, 0x96, 0x15, 0x1a, 0x77, 0x84, 0x1c,
        ]),
        Tmr([
            0x6d, 0x2a, 0x47, 0x99, 0xa1, 0x6e, 0xb6, 0x78,
            0x4e, 0x49, 0x66, 0xb8, 0x1d, 0xa6, 0x27, 0xd3,
            0x5a, 0xa7, 0x08, 0xfd, 0x97, 0x25, 0xd6, 0x04,
            0x77, 0x7b, 0x14, 0x3e, 0x28, 0xd4, 0xac, 0xf0,
        ]),
        Tmr([
            0x2a, 0x07, 0x5c, 0x50, 0xca, 0x10, 0xe5, 0x00,
            0x92, 0x77, 0x86, 0xca, 0x86, 0xa5, 0x2b, 0xb7,
            0xe5, 0x2d, 0xdb, 0x16, 0x42, 0xe3, 0x77, 0x45,
            0xfb, 0x44, 0x14, 0x91, 0x39, 0xb3, 0x2d, 0x67,
        ]),
        Tmr([
            0xf5, 0x67, 0xc8, 0x1b, 0x82, 0x5d, 0xc9, 0x00,
            0xe0, 0xbc, 0x0c, 0x59, 0xce, 0xa6, 0xaa, 0x1f,
            0x1f, 0x34, 0x28, 0x3f, 0xcb, 0xee, 0xff, 0x73,
            0x2d, 0xb8, 0xe2, 0x17, 0x57, 0x6c, 0x22, 0x55,
        ]),
        Tmr([
            0x0a, 0xee, 0x10, 0x39, 0xd3, 0xc8, 0xaf, 0x91,
            0x41, 0xbc, 0xb9, 0xfd, 0xf3, 0xf8, 0x24, 0x1e,
            0xf9, 0xfd, 0x4b, 0x85, 0x85, 0x3a, 0x79, 0xba,
            0xbc, 0xfb, 0x2a, 0xb4, 0xdb, 0x8e, 0xf3, 0x8c,
        ]),
        Tmr([
            0x30, 0xaa, 0xe9, 0xb8, 0xf2, 0xc6, 0xfa, 0xf0,
            0x7a, 0x62, 0x07, 0x2f, 0x55, 0xb2, 0x96, 0x98,
            0x5d, 0xd7, 0x3b, 0xc1, 0x04, 0x42, 0xc8, 0x02,
            0x79, 0x32, 0xff, 0xf4, 0x1f, 0x2a, 0x2d, 0x72,
        ]),
        Tmr([
            0xbc, 0x14, 0x6c, 0xb5, 0xae, 0x67, 0xe0, 0x0a,
            0x6d, 0x8e, 0x3f, 0xd0, 0x56, 0xfb, 0x7a, 0x72,
            0x82, 0x04, 0x84, 0xc6, 0x1a, 0xcf, 0x17, 0xfe,
            0xcc, 0xf1, 0x30, 0xcb, 0xa6, 0x22, 0xd2, 0x7f,
        ]),
        Tmr([
            0xa8, 0x67, 0xba, 0xcf, 0xf8, 0xd1, 0xc2, 0x5c,
            0x9e, 0x82, 0x4f, 0x1b, 0x63, 0xa4, 0x9c, 0x17,
            0x67, 0x9b, 0xba, 0x8a, 0xd8, 0x76, 0x99, 0xa0,
            0xcd, 0xf7, 0x7d, 0xef, 0x0a, 0x1b, 0x75, 0x11,
        ]),
        Tmr([
            0xc1, 0x28, 0xdc, 0x7e, 0x8d, 0x79, 0x4a, 0x7a,
            0x48, 0x08, 0x14, 0x95, 0xa6, 0xeb, 0x2b, 0x2d,
            0x3c, 0xb6, 0x6b, 0xc0, 0xe0, 0x33, 0x27, 0x3b,
            0xf9, 0xdd, 0xbc, 0x98, 0x6c, 0x22, 0x68, 0x92,
        ]),
        Tmr([
            0x19, 0x9f, 0xfd, 0xe4, 0x7d, 0x27, 0x91, 0xa3,
            0x58, 0xf2, 0x3a, 0xe5, 0x08, 0x25, 0x16, 0xc6,
            0x5e, 0x57, 0xf5, 0x5a, 0xe6, 0x6d, 0xdf, 0x44,
            0x65, 0xba, 0xab, 0x4b, 0xfa, 0x3c, 0x3a, 0x5f,
        ]),
        Tmr([
            0x40, 0x38, 0x09, 0x5d, 0xbb, 0x32, 0xe2, 0x7e,
            0x6e, 0x31, 0x66, 0x52, 0x7b, 0xce, 0xdd, 0xa8,
            0x4e, 0x8b, 0x21, 0xf6, 0xd4, 0x2f, 0x7e, 0x56,
            0xea, 0xff, 0x21, 0x85, 0x6a, 0xd2, 0x04, 0xa2,
        ]),
        Tmr([
            0xc3, 0xa0, 0xa6, 0xf8, 0x7e, 0x6c, 0x3f, 0x02,
            0xbf, 0x98, 0x05, 0x1c, 0xe4, 0x5d, 0x6d, 0x69,
            0x55, 0x38, 0x24, 0x78, 0xf1, 0x0f, 0xa0, 0x6a,
            0xdd, 0x51, 0x30, 0xe5, 0x99, 0x17, 0xf8, 0xc7,
        ]),
        Tmr([
            0x7c, 0x25, 0xbf, 0x44, 0x7a, 0x45, 0xba, 0x13,
            0x23, 0xe8, 0xdb, 0x8b, 0x81, 0x78, 0x87, 0xa8,
            0x85, 0x8b, 0xee, 0x25, 0x6e, 0x5c, 0xa3, 0x52,
            0x8e, 0x79, 0xcf, 0xbc, 0x2d, 0x41, 0x9c, 0xe3,
        ]),
        Tmr([
            0x75, 0xa7, 0x7a, 0x6c, 0x7b, 0x6d, 0xe9, 0x1d,
            0x23, 0xc1, 0x00, 0x4d, 0x8e, 0xb0, 0xb3, 0x5d,
            0x9c, 0xdf, 0x6f, 0xa1, 0xdf, 0xc7, 0xca, 0xbd,
            0x04, 0x66, 0x92, 0xf1, 0xa2, 0x43, 0x14, 0x17,
        ]),
        Tmr([
            0x9f, 0xc2, 0x4a, 0xb6, 0x99, 0x70, 0xf8, 0x66,
            0x6d, 0x7b, 0x1e, 0x52, 0x5a, 0x3a, 0x8e, 0x79,
            0x43, 0x99, 0x76, 0xe7, 0x79, 0x2b, 0xfe, 0x1a,
            0x1b, 0x0d, 0x0d, 0x84, 0xff, 0x03, 0x84, 0x34,
        ]),
        Tmr([
            0x64, 0x25, 0x1a, 0xb9, 0x70, 0x77, 0x17, 0x0e,
            0x19, 0x91, 0x15, 0x76, 0x5e, 0x93, 0x43, 0xe7,
            0x1b, 0x59, 0x0e, 0x41, 0x78, 0x88, 0xf2, 0xa8,
            0x36, 0x43, 0x11, 0xd8, 0x65, 0x40, 0xed, 0xfa,
        ]),
    ];

    /// The TMRs of the types (TWO^8)^<(2^(N + 1)) for small values of n
    #[rustfmt::skip]
    pub const BUFFER8_TWO_N_PLUS_ONE: [Tmr; 16] = [
        Tmr([
            0x66, 0x8c, 0x79, 0xa6, 0xf0, 0xe0, 0x86, 0xa6,
            0x2d, 0x73, 0xf0, 0xc6, 0x52, 0xb1, 0x5c, 0x56,
            0xb1, 0xd3, 0x53, 0x68, 0xe1, 0xff, 0xad, 0x76,
            0xc9, 0xd4, 0xdb, 0xae, 0xb5, 0x2d, 0xe6, 0x2f,
        ]),
        Tmr([
            0x9f, 0x91, 0xf5, 0x19, 0x9b, 0xb8, 0x16, 0x7a,
            0x3b, 0x6c, 0xf8, 0xd0, 0x39, 0x75, 0x6e, 0x1b,
            0x33, 0x18, 0x42, 0x6e, 0xef, 0x3a, 0x9b, 0xa0,
            0x90, 0x2c, 0x91, 0xdc, 0x5f, 0x7e, 0x63, 0x39,
        ]),
        Tmr([
            0x16, 0x98, 0x45, 0xb0, 0xe2, 0xf0, 0x4a, 0x83,
            0x76, 0xfe, 0x91, 0x14, 0xbd, 0x35, 0x3a, 0x29,
            0xe9, 0xb7, 0x80, 0x42, 0xb7, 0x70, 0x1b, 0xa1,
            0x6d, 0x02, 0xc4, 0x62, 0x18, 0xef, 0x8b, 0xdf,
        ]),
        Tmr([
            0xbd, 0x59, 0x57, 0x8c, 0x45, 0x78, 0xfe, 0xc4,
            0xef, 0x2a, 0x29, 0xc1, 0xad, 0xea, 0x4c, 0xe1,
            0x30, 0x6c, 0x1a, 0x2b, 0x10, 0xd6, 0x18, 0xbc,
            0x58, 0x44, 0x67, 0x84, 0x17, 0x97, 0x3b, 0x8e,
        ]),
        Tmr([
            0x88, 0xd1, 0x8c, 0x11, 0x5f, 0x86, 0x54, 0x40,
            0x5f, 0xd7, 0x1d, 0xe8, 0x7e, 0x6f, 0xf0, 0x80,
            0x6c, 0x5d, 0xa7, 0x97, 0xca, 0xaf, 0x48, 0xe2,
            0x47, 0xea, 0xcc, 0x43, 0x99, 0x96, 0x89, 0x1a,
        ]),
        Tmr([
            0x90, 0x65, 0x22, 0xe1, 0x6d, 0xf3, 0x6f, 0x83,
            0xa4, 0x50, 0x32, 0x8a, 0xf8, 0x4e, 0x2f, 0x3e,
            0x52, 0xf6, 0xd6, 0x49, 0xa7, 0x88, 0xe3, 0xb2,
            0x1c, 0xca, 0xe3, 0xcd, 0x9a, 0x24, 0x66, 0x77,
        ]),
        Tmr([
            0x3a, 0xba, 0x4c, 0xce, 0x0e, 0x46, 0xc5, 0x54,
            0xb4, 0x4f, 0x70, 0x21, 0x3d, 0x4d, 0x8b, 0xd8,
            0xe8, 0xf1, 0x7e, 0x2b, 0xd1, 0x7b, 0xdf, 0xb7,
            0x15, 0x0a, 0xdf, 0xfd, 0x9a, 0xdf, 0x80, 0x9d,
        ]),
        Tmr([
            0x7d, 0x81, 0x2a, 0xf0, 0x44, 0xcb, 0x04, 0xd2,
            0xaf, 0x4f, 0xc8, 0xe9, 0xb5, 0x30, 0x66, 0x03,
            0x9b, 0xd5, 0x89, 0x2a, 0x56, 0xa5, 0xd5, 0x64,
            0x1c, 0x5c, 0x58, 0xc8, 0x6e, 0xed, 0x8a, 0x35,
        ]),
        Tmr([
            0x23, 0x0e, 0xa9, 0x70, 0x03, 0x3e, 0x47, 0xc5,
            0x61, 0x68, 0x1e, 0xe7, 0x20, 0x58, 0xb9, 0xc0,
            0x75, 0x5b, 0x8d, 0x87, 0x22, 0x80, 0x18, 0x4f,
            0x2e, 0x3f, 0xe3, 0x93, 0xc0, 0x47, 0x8f, 0x1a,
        ]),
        Tmr([
            0x6e, 0x90, 0x88, 0x04, 0x20, 0x46, 0x2b, 0x84,
            0xf2, 0x16, 0x30, 0x2a, 0x09, 0x56, 0x9c, 0xc8,
            0xd4, 0x47, 0x54, 0x4a, 0xcd, 0x8a, 0xbc, 0x53,
            0xd8, 0xa7, 0xcf, 0x21, 0x9b, 0x44, 0x9c, 0x95,
        ]),
        Tmr([
            0x7a, 0xd1, 0x5d, 0xed, 0x85, 0x02, 0xa6, 0xf1,
            0x1e, 0xb8, 0xa4, 0x9b, 0x25, 0xc8, 0xd7, 0x62,
            0xa0, 0xfe, 0x00, 0x4f, 0xb5, 0x7d, 0x73, 0x43,
            0xbd, 0xf4, 0x90, 0xed, 0x7e, 0xd2, 0xf4, 0x07,
        ]),
        Tmr([
            0xaa, 0x30, 0x30, 0x15, 0x71, 0xcf, 0x8d, 0x2d,
            0x64, 0xe9, 0x65, 0x4b, 0x0c, 0xbd, 0xe0, 0x54,
            0x01, 0x77, 0xab, 0xc2, 0xf2, 0xef, 0xfb, 0x7f,
            0x05, 0x2e, 0x27, 0xa8, 0xcc, 0xcc, 0xee, 0x62,
        ]),
        Tmr([
            0x28, 0x6d, 0x4d, 0x57, 0x6d, 0xb8, 0xe8, 0x45,
            0x00, 0x9c, 0x74, 0x84, 0xe0, 0x0a, 0x9f, 0xa3,
            0xf3, 0x18, 0xa8, 0x21, 0x9e, 0x38, 0x66, 0x2c,
            0xda, 0x11, 0x75, 0x78, 0x22, 0xe4, 0x53, 0xbb,
        ]),
        Tmr([
            0x10, 0x56, 0xa7, 0x17, 0xdc, 0x0c, 0x86, 0xb7,
            0x49, 0x97, 0x5e, 0x9c, 0x36, 0x4a, 0xb5, 0xa6,
            0x64, 0x77, 0xc4, 0x2d, 0xe1, 0x6e, 0x5b, 0x05,
            0x29, 0x81, 0x4f, 0x4c, 0xba, 0x95, 0x7c, 0xb3,
        ]),
        Tmr([
            0x94, 0x59, 0x0e, 0xf5, 0x66, 0x10, 0xaa, 0x7f,
            0xec, 0x46, 0x5b, 0x72, 0x32, 0xab, 0xa3, 0xf4,
            0x7c, 0x94, 0x2b, 0x8e, 0x8d, 0xc8, 0x76, 0x82,
            0x51, 0xd3, 0x70, 0x2c, 0x99, 0xb9, 0xef, 0xef,
        ]),
        Tmr([
            0xd0, 0x7f, 0x71, 0xb7, 0xcd, 0x48, 0xb8, 0x50,
            0xad, 0x09, 0x06, 0x8b, 0x9b, 0x48, 0xe0, 0xf8,
            0x5f, 0x84, 0xc0, 0x1b, 0x34, 0x58, 0x6a, 0x51,
            0x34, 0x61, 0xfa, 0xf7, 0x6d, 0x54, 0x34, 0x64,
        ]),
    ];

    /// The TMR of the `Ctx8` type used by the SHA256 jets.
    #[rustfmt::skip]
    pub const CTX8: Tmr = Tmr([
        0x8d, 0x5c, 0xe5, 0xf6, 0xeb, 0xfc, 0x70, 0x61,
        0xe7, 0x91, 0x16, 0xbd, 0xf6, 0x6f, 0xb4, 0xe4,
        0xc6, 0xca, 0x32, 0xa0, 0x1c, 0xda, 0x48, 0xf6,
        0xed, 0xc1, 0x0a, 0xee, 0xfd, 0x31, 0x0e, 0x8c,
    ]);

    /// The TMR for the unit type
    pub const fn unit() -> Tmr {
        Self::from_byte_array(Self::UNIT_IV.to_parts().0)
    }

    /// The TMR for the successor of a type.
    ///
    /// Given a type `X`, we define its successor `S X` as `1 + X`.
    /// In Rust notation this would be `Option<X>`.
    pub fn successor(self) -> Tmr {
        Self::SUM_IV
            .zz_update_2x32(Tmr::unit(), self)
            .into_merkle_root()
    }

    /// The TMR for the sum of two types, whose TMRs are given
    pub fn sum(tmr1: Tmr, tmr2: Tmr) -> Tmr {
        Self::SUM_IV
            .update_64(&super::concat(tmr1, tmr2))
            .into_merkle_root()
    }

    /// The TMR for the sum of two types, whose TMRs are given
    ///
    /// This function is slow but can be used in a const context. If you do not
    /// need to run in a const context, use [`Self::sum`] instead.
    pub const fn sum_unoptimized(tmr1: Tmr, tmr2: Tmr) -> Tmr {
        Self::from_byte_array(
            Self::SUM_IV
                .update_2x32_unoptimized(tmr1.as_byte_array(), tmr2.as_byte_array())
                .to_parts()
                .0,
        )
    }

    /// The TMR for the product of two types, whose TMRs are given
    pub fn product(tmr1: Tmr, tmr2: Tmr) -> Tmr {
        Self::PROD_IV.zz_update_2x32(tmr1, tmr2).into_merkle_root()
    }

    /// The TMR for the product of two types, whose TMRs are given
    ///
    /// This function is slow but can be used in a const context. If you do not
    /// need to run in a const context, use [`Self::product`] instead.
    pub const fn product_unoptimized(tmr1: Tmr, tmr2: Tmr) -> Tmr {
        Self::from_byte_array(
            Self::PROD_IV
                .update_2x32_unoptimized(tmr1.as_byte_array(), tmr2.as_byte_array())
                .to_parts()
                .0,
        )
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    use crate::jet::Jet;
    use crate::merkle::bip340_iv;
    use crate::types::{self, Final};

    #[test]
    fn ivs() {
        fn check_iv(target: Midstate, s: &'static str) {
            let name = s.trim_start_matches("Simplicity\x1fType\x1f");
            // Uncomment this if the IVs ever change
            /*
            let target = Tmr(bip340_iv(s.as_bytes()));
            println!("    #[rustfmt::skip]");
            println!("    const {}_IV: Midstate = Midstate::new([", name.to_ascii_uppercase());
            print!("       "); for ch in &target.0[0..8] { print!(" 0x{:02x},", ch); }; println!();
            print!("       "); for ch in &target.0[8..16] { print!(" 0x{:02x},", ch); }; println!();
            print!("       "); for ch in &target.0[16..24] { print!(" 0x{:02x},", ch); }; println!();
            print!("       "); for ch in &target.0[24..32] { print!(" 0x{:02x},", ch); }; println!();
            println!("    ], 64);");
            println!();
            */
            assert_eq!(
                target,
                bip340_iv(s.as_bytes()),
                "mismatch on IV for {}",
                name
            );
        }

        check_iv(Tmr::UNIT_IV, "Simplicity\x1fType\x1funit");
        check_iv(Tmr::SUM_IV, "Simplicity\x1fType\x1fsum");
        check_iv(Tmr::PROD_IV, "Simplicity\x1fType\x1fprod");
    }

    #[test]
    #[allow(clippy::needless_range_loop)]
    fn const_powers_of_2() {
        fn check_pow(target: Tmr, i: usize, expected_tmrs: &[Tmr]) {
            // Uncomment this if the IVs ever change
            /*
            let target = tmrs[i];
            println!("    Tmr([");
            print!("       "); for ch in &target.0[0..8] { print!(" 0x{:02x},", ch); }; println!();
            print!("       "); for ch in &target.0[8..16] { print!(" 0x{:02x},", ch); }; println!();
            print!("       "); for ch in &target.0[16..24] { print!(" 0x{:02x},", ch); }; println!();
            print!("       "); for ch in &target.0[24..32] { print!(" 0x{:02x},", ch); }; println!();
            println!("    ]),");
            */
            assert_eq!(target, expected_tmrs[i], "mismatch on TMR for TWO^(2^{i})");
        }

        let n = Tmr::TWO_TWO_N.len();
        types::Context::with_context(|ctx| {
            let tmrs = types::Type::powers_of_two(&ctx, n)
                .iter()
                .filter_map(types::Type::tmr)
                .collect::<Vec<Tmr>>();
            debug_assert_eq!(tmrs.len(), n);
            for i in 0..n {
                check_pow(Tmr::TWO_TWO_N[i], i, &tmrs);
            }
        });
    }

    #[test]
    fn direct_constructors() {
        let unit = Tmr::unit();
        let bit1 = Tmr::sum(unit, unit);
        let bit2 = Tmr::sum_unoptimized(unit, unit);
        assert_eq!(bit1, bit2);
        assert_eq!(bit1, Tmr::TWO_TWO_N[0]);

        let dbit1 = Tmr::product(bit1, bit1);
        let dbit2 = Tmr::product_unoptimized(bit1, bit1);
        assert_eq!(dbit1, dbit2);
        assert_eq!(dbit1, Tmr::TWO_TWO_N[1]);
    }

    #[test]
    fn const_buffer8() {
        use std::sync::Arc;

        let two_8_tmr = Tmr::TWO_TWO_N[3];
        let buf_0_tmr = two_8_tmr.successor();

        let two_8 = Final::two_two_n_fixed::<3>();
        let buf_0 = Arc::clone(&two_8).successor();

        assert_eq!(buf_0, Final::buffer8_two_n_plus_one(0).unwrap());
        assert_eq!(two_8.tmr(), two_8_tmr);
        assert_eq!(buf_0.tmr(), buf_0_tmr);
        assert_eq!(buf_0_tmr, Tmr::BUFFER8_TWO_N_PLUS_ONE[0]);

        let mut tmr = buf_0_tmr;
        let mut fin = buf_0;
        assert_eq!(Tmr::BUFFER8_TWO_N_PLUS_ONE.len(), 16);
        for n in 1..Tmr::BUFFER8_TWO_N_PLUS_ONE.len() {
            tmr = Tmr::product(Tmr::TWO_TWO_N[n + 3].successor(), tmr);
            fin = Final::product(Final::two_two_n(n + 3).unwrap().successor(), fin);

            assert_eq!(fin.tmr(), tmr);
            assert_eq!(fin, Final::buffer8_two_n_plus_one(n).unwrap());
            assert_eq!(tmr, Tmr::BUFFER8_TWO_N_PLUS_ONE[n]);

            // For the case of n == 5, i.e. a 63-byte buffer (63 = 2^(n + 1) - 1),
            // we can check against the SHA256 Ctx8 type to make sure that our
            // computations are actually correct.
            if n == 5 {
                let extra_ctx_stuff = Final::product(
                    Final::two_two_n_fixed::<6>(), // 2^64
                    Final::two_two_n_fixed::<8>(), // 2^256
                );
                let synthetic_ctx_ty = Final::product(Arc::clone(&fin), extra_ctx_stuff);
                let actual_ctx_ty = crate::jet::Core::Sha256Ctx8Init.target_ty().to_final();
                assert_eq!(synthetic_ctx_ty, actual_ctx_ty,);
                assert_eq!(synthetic_ctx_ty, Final::ctx8());
                assert_eq!(synthetic_ctx_ty.tmr(), Tmr::CTX8);
            }
        }
    }
}