plonky2/evm/src/cpu/kernel/asm/fields/fp6_mul.asm

// cost: 156
global mul_fp6:
    /// initial stack: c0, c0_, c1, c1_, c2, c2_, d0, d0_, d1, d1_, d2, d2_, retdest
    /// final   stack: e0, e0_, e1, e1_, e2, e2_

    /// C = C0 + C1t + C2t^2 
    ///   = (c0 + c0_i) + (c1 + c1_i)t + (c2 + c2_i)t^2
    ///
    /// D = D0 + D1t + D2t^2
    ///   = (d0 + d0_i) + (d1 + d1_i)t + (d2 + d2_i)t^2
    ///
    /// E = E0 + E1t + E2t^2 = CD
    
    /// E0 = C0D0 + i9(C1D2 + C2D1)
    ///
    /// C0D0 = (c0d0 - c0_d0_) + (c0d0_ + c0_d0)i
    ///
    /// C1D2 = (c1d2 - c1_d2_) + (c1d2_ + c1_d2)i
    /// C2D1 = (c2d1 - c2_d1_) + (c2d1_ + c2_d1)i
    ///
    /// CDX  = C1D2 + C2D1
    ///      = (c1d2 + c2d1 - c1_d2_ - c2_d1_) + (c1d2_ + c1_d2 + c2d1_ + c2_d1)i
    ///
    /// i9(CDX) = (9CDX - CDX_) + (CDX + 9CDX_)i
    ///
    /// E0  = 9CDX  - CDX_ + C0D0
    /// E0_ = 9CDX_ + CDX  + C0D0_
    ///
    /// E1 = C0D1 + C1D0 + i9(C2D2)
    ///
    /// C0D1 = (c0d1 - c0_d1_) + (c0d1_ + c0_d1)i
    /// C1D0 = (c1d0 - c1_d0_) + (c1d0_ + c1_d0)i
    ///
    /// CD01  = c0d1  + c1d0  - (c0_d1_ + c1_d0_)
    /// CD01_ = c0d1_ + c0_d1 +  c1d0_  + c1_d0
    ///
    ///    C2D2  = (c2d2 - c2_d2_) + (c2d2_ + c2_d2)i
    /// i9(C2D2) = (9C2D2 - C2D2_) + (C2D2 + 9C2D2_)i
    ///
    /// E1  = 9C2D2 -  C2D2_ + CD01
    /// E1_ =  C2D2 + 9C2D2_ + CD01_
    ///
    /// E2 = C0D2 + C1D1 + C2D0
    ///
    /// C0D2 = (c0d2 - c0_d2_) + (c0d2_ + c0_d2)i
    /// C1D1 = (c1d1 - c1_d1_) + (c1d1_ + c1_d1)i
    /// C2D0 = (c2d0 - c2_d0_) + (c2d0_ + c2_d0)i
    ///
    /// E2  = c0d2  + c1d1  + c2d0  - (c0_d2_ + c1_d1_ + c2_d0_)
    /// E2_ = c0d2_ + c0_d2 + c1d1_ +  c1_d1  + c2d0_  + c2_d0

    // E2
    // make c0_d2_ + c1_d1_ + c2_d0_
    DUP8
    DUP7
    MULFP254
    DUP11
    DUP6
    MULFP254
    ADDFP254
    DUP13
    DUP4
    MULFP254
    ADDFP254
    // make c0d2 + c1d1 + c2d0
    DUP12
    DUP3
    MULFP254
    DUP11
    DUP6
    MULFP254
    ADDFP254
    DUP9
    DUP8
    MULFP254
    ADDFP254
    // stack: c0d2  + c1d1  + c2d0, c0_d2_ + c1_d1_ + c2_d0_
    SUBFP254
    SWAP12

    // E0, E0_
    // make CDX_ = c1d2_ + c1_d2 + c2d1_ + c2_d1
    DUP1
    DUP5
    MULFP254
    DUP13
    DUP7
    MULFP254
    ADDFP254
    DUP12
    DUP8
    MULFP254
    ADDFP254
    DUP11
    DUP9
    MULFP254
    ADDFP254
    // make C0D0_ = c0d0_ + c0_d0
    DUP10
    DUP4
    MULFP254
    DUP10
    DUP6
    MULFP254
    ADDFP254
    // make CDX = c1d2 + c2d1 - c1_d2_ - c2_d1_
    DUP13
    DUP10
    MULFP254
    DUP4
    DUP9
    MULFP254
    ADDFP254
    DUP15
    DUP8
    MULFP254
    DUP14
    DUP11
    MULFP254
    ADDFP254
    SUBFP254
    // make C0D0 = c0d0 - c0_d0_
    DUP12
    DUP7
    MULFP254
    DUP12
    DUP7
    MULFP254
    SUBFP254
    // stack:               C0D0 , CDX , C0D0_, CDX_
    DUP4
    DUP3
    // stack:  CDX , CDX_ , C0D0 , CDX , C0D0_, CDX_
    PUSH 9
    MULFP254
    SUBFP254
    ADDFP254
    // stack: 9CDX - CDX_ + C0D0 , CDX , C0D0_, CDX_
    SWAP12
    SWAP3
    // stack:               CDX_ , CDX , C0D0_
    PUSH 9
    MULFP254
    ADDFP254
    ADDFP254
    // stack:              9CDX_ + CDX + C0D0_
    SWAP11

    // E1, E1_
    // make C2D2_ = c2d2_ + c2_d2
    DUP14
    DUP10
    MULFP254
    DUP4
    DUP10
    MULFP254
    ADDFP254
    // make C2D2  = c2d2  - c2_d2_
    DUP4
    DUP11
    MULFP254
    DUP16
    DUP11
    MULFP254
    SUBFP254
    // make CD01 = c0d1 + c1d0 - (c0_d1_ + c1_d0_)
    DUP4
    DUP10
    MULFP254
    DUP16
    DUP9
    MULFP254
    ADDFP254
    DUP13
    DUP10
    MULFP254
    DUP5
    DUP9
    MULFP254
    ADDFP254
    SUBFP254
    // stack:                      CD01, C2D2, C2D2_
    DUP3
    DUP3
    // stack:       C2D2 , C2D2_ , CD01, C2D2, C2D2_
    PUSH 9
    MULFP254
    SUBFP254
    ADDFP254
    // stack: E1 = 9C2D2 - C2D2_ + CD01, C2D2, C2D2_
    SWAP15
    SWAP2
    // stack:                    C2D2_ , C2D2
    PUSH 9
    MULFP254
    ADDFP254
    // stack:               9C2D2_ + C2D2
    // make CD01_ = c0d1_ + c0_d1 +  c1d0_  + c1_d0
    DUP12
    DUP10
    MULFP254
    DUP5
    DUP10
    MULFP254
    ADDFP254
    DUP4
    DUP9
    MULFP254
    ADDFP254
    DUP3
    DUP8
    MULFP254
    ADDFP254
    // stack:       CD01_ , 9C2D2_ + C2D2
    ADDFP254
    // stack: E1_ = CD01_ + 9C2D2_ + C2D2
    SWAP15
    // E2_
    // stack: d2, d1_, d1, d0_, d2_, c0, c0_, c1, c1_, c2, c2_, d0
    SWAP7
    MULFP254
    // stack: c1d1_, d1, d0_, d2_, c0, c0_, d2, c1_, c2, c2_, d0
    SWAP7
    MULFP254
    // stack: c1_d1, d0_, d2_, c0, c0_, d2, c1d1_, c2, c2_, d0
    SWAP7
    MULFP254
    // stack: c2d0_, d2_, c0, c0_, d2, c1d1_, c1_d1, c2_, d0
    SWAP2
    MULFP254
    // stack: c0d2_, c2d0_, c0_, d2, c1d1_, c1_d1, c2_, d0
    ADDFP254
    // stack: c0d2_ + c2d0_, c0_, d2, c1d1_, c1_d1, c2_, d0
    SWAP2
    MULFP254
    // stack: c0_d2, c0d2_ + c2d0_, c1d1_, c1_d1, c2_, d0
    ADDFP254
    ADDFP254
    ADDFP254
    // stack: c0_d2 + c0d2_ + c2d0_ + c1d1_ + c1_d1, c2_, d0
    SWAP2
    MULFP254
    ADDFP254
    SWAP6
    JUMP