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

/// inputs:
///     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
///
/// output:
///     E = E0 + E1t + E2t^2 = CD
///       = (e0 + e0_i) + (e1 + e1_i)t + (e2 + e2_i)t^2
///
/// initial stack: c0, c0_, c1, c1_, c2, c2_, d0, d0_, d1, d1_, d2, d2_, retdest
/// final   stack: e0, e0_, e1, e1_, e2, e2_

/// computations:
///
/// 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
///
/// CD12 = C1D2 + C2D1
///      = (c1d2 + c2d1 - c1_d2_ - c2_d1_) + (c1d2_ + c1_d2 + c2d1_ + c2_d1)i
///
/// i9(CD12) = (9CD12 - CD12_) + (CD12 + 9CD12_)i
///
/// e0  = 9CD12  - CD12_ + C0D0
/// e0_ = 9CD12_ + CD12  + 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


// cost: 157
global mul_fp6:
    // 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
    // stack: e2 = c0d2  + c1d1  + c2d0 - (c0_d2_ + c1_d1_ + c2_d0_)
    SWAP12

    // e0, e0_
    // make CD12_ = 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 CD12 = 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 , CD12 , C0D0_, CD12_
    DUP4
    DUP3
    // stack:       CD12 , CD12_ , C0D0 , CD12 , C0D0_, CD12_
    PUSH 9
    MULFP254
    SUBFP254
    ADDFP254
    // stack: e0 = 9CD12 - CD12_ + C0D0 , CD12 , C0D0_, CD12_
    SWAP12
    SWAP3
    // stack:                     CD12_ , CD12 , C0D0_
    PUSH 9
    MULFP254
    ADDFP254
    ADDFP254
    // stack:              e0_ = 9CD12_ + CD12 + 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
    // stack:  e2_ = c2_d0 + c0_d2 + c0d2_ + c2d0_ + c1d1_ + c1_d1
    SWAP6

    // stack: retdest, e0, e0_, e1, e1_, e2, e2_
    JUMP
comments 2022-10-25 17:14:15 -04:00			`/// inputs:`
			`/// C = C0 + C1t + C2t^2`
			`/// = (c0 + c0_i) + (c1 + c1_i)t + (c2 + c2_i)t^2`
better comments 2022-10-22 16:17:51 -04:00			`///`
comments 2022-10-25 17:14:15 -04:00			`/// D = D0 + D1t + D2t^2`
			`/// = (d0 + d0_i) + (d1 + d1_i)t + (d2 + d2_i)t^2`
better comments 2022-10-22 16:17:51 -04:00			`///`
comments 2022-10-25 17:14:15 -04:00			`/// output:`
			`/// E = E0 + E1t + E2t^2 = CD`
			`/// = (e0 + e0_i) + (e1 + e1_i)t + (e2 + e2_i)t^2`
better comments 2022-10-22 16:17:51 -04:00			`///`
comments 2022-10-25 17:14:15 -04:00			`/// initial stack: c0, c0_, c1, c1_, c2, c2_, d0, d0_, d1, d1_, d2, d2_, retdest`
			`/// final stack: e0, e0_, e1, e1_, e2, e2_`

			`/// computations:`
better comments 2022-10-22 16:17:51 -04:00			`///`
comments 2022-10-25 17:14:15 -04:00			`/// E0 = C0D0 + i9(C1D2 + C2D1)`
better comments 2022-10-22 16:17:51 -04:00			`///`
			`/// C0D0 = (c0d0 - c0_d0_) + (c0d0_ + c0_d0)i`
			`///`
			`/// C1D2 = (c1d2 - c1_d2_) + (c1d2_ + c1_d2)i`
			`/// C2D1 = (c2d1 - c2_d1_) + (c2d1_ + c2_d1)i`
			`///`
			`/// CD12 = C1D2 + C2D1`
			`/// = (c1d2 + c2d1 - c1_d2_ - c2_d1_) + (c1d2_ + c1_d2 + c2d1_ + c2_d1)i`
			`///`
			`/// i9(CD12) = (9CD12 - CD12_) + (CD12 + 9CD12_)i`
			`///`
			`/// e0 = 9CD12 - CD12_ + C0D0`
			`/// e0_ = 9CD12_ + CD12 + C0D0_`
			`///`
			`///`
comments 2022-10-25 17:14:15 -04:00			`/// E1 = C0D1 + C1D0 + i9(C2D2)`
better comments 2022-10-22 16:17:51 -04:00			`///`
			`/// 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_`
			`///`
			`///`
comments 2022-10-25 17:14:15 -04:00			`/// E2 = C0D2 + C1D1 + C2D0`
better comments 2022-10-22 16:17:51 -04:00			`///`
			`/// 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`
fp6 test passes 2022-10-22 13:16:07 -04:00
fp6 mul 2022-10-20 16:18:41 -04:00
better comments 2022-10-22 16:17:51 -04:00			`// cost: 157`
			`global mul_fp6:`
			`// e2`
new fp6 2022-10-22 09:53:16 -04:00			`// make c0_d2_ + c1_d1_ + c2_d0_`
			`DUP8`
			`DUP7`
			`MULFP254`
			`DUP11`
			`DUP6`
			`MULFP254`
			`ADDFP254`
			`DUP13`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP4`
			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`ADDFP254`
			`// make c0d2 + c1d1 + c2d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP12`
new fp6 2022-10-22 09:53:16 -04:00			`DUP3`
			`MULFP254`
			`DUP11`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP6`
			`MULFP254`
			`ADDFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP9`
			`DUP8`
			`MULFP254`
			`ADDFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: c0d2 + c1d1 + c2d0 , c0_d2_ + c1_d1_ + c2_d0_`
new fp6 2022-10-22 09:53:16 -04:00			`SUBFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: e2 = c0d2 + c1d1 + c2d0 - (c0_d2_ + c1_d1_ + c2_d0_)`
new fp6 2022-10-22 09:53:16 -04:00			`SWAP12`
fp6 test passes 2022-10-22 13:16:07 -04:00
better comments 2022-10-22 16:17:51 -04:00			`// e0, e0_`
better comments 2022-10-22 13:28:12 -04:00			`// make CD12_ = c1d2_ + c1_d2 + c2d1_ + c2_d1`
new fp6 2022-10-22 09:53:16 -04:00			`DUP1`
			`DUP5`
			`MULFP254`
			`DUP13`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP7`
			`MULFP254`
			`ADDFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP12`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP8`
			`MULFP254`
			`ADDFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP11`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP9`
			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`ADDFP254`
			`// make C0D0_ = c0d0_ + c0_d0`
			`DUP10`
			`DUP4`
			`MULFP254`
			`DUP10`
			`DUP6`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`ADDFP254`
better comments 2022-10-22 13:28:12 -04:00			`// make CD12 = c1d2 + c2d1 - c1_d2_ - c2_d1_`
new fp6 2022-10-22 09:53:16 -04:00			`DUP13`
			`DUP10`
			`MULFP254`
			`DUP4`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP9`
			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`ADDFP254`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP15`
			`DUP8`
			`MULFP254`
			`DUP14`
new fp6 2022-10-22 09:53:16 -04:00			`DUP11`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`ADDFP254`
			`SUBFP254`
			`// make C0D0 = c0d0 - c0_d0_`
new fp6 2022-10-22 09:53:16 -04:00			`DUP12`
			`DUP7`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP12`
			`DUP7`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`SUBFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: C0D0 , CD12 , C0D0_, CD12_`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP4`
			`DUP3`
better comments 2022-10-22 16:17:51 -04:00			`// stack: CD12 , CD12_ , C0D0 , CD12 , C0D0_, CD12_`
fp6 mul 2022-10-20 16:18:41 -04:00			`PUSH 9`
			`MULFP254`
			`SUBFP254`
			`ADDFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: e0 = 9CD12 - CD12_ + C0D0 , CD12 , C0D0_, CD12_`
new fp6 2022-10-22 09:53:16 -04:00			`SWAP12`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP3`
better comments 2022-10-22 16:17:51 -04:00			`// stack: CD12_ , CD12 , C0D0_`
fp6 mul 2022-10-20 16:18:41 -04:00			`PUSH 9`
			`MULFP254`
			`ADDFP254`
			`ADDFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: e0_ = 9CD12_ + CD12 + C0D0_`
new fp6 2022-10-22 09:53:16 -04:00			`SWAP11`
fp6 test passes 2022-10-22 13:16:07 -04:00
better comments 2022-10-22 16:17:51 -04:00			`// e1, e1_`
fp6 mul 2022-10-20 16:18:41 -04:00			`// make C2D2_ = c2d2_ + c2_d2`
new fp6 2022-10-22 09:53:16 -04:00			`DUP14`
			`DUP10`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP4`
			`DUP10`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`ADDFP254`
			`// make C2D2 = c2d2 - c2_d2_`
new fp6 2022-10-22 09:53:16 -04:00			`DUP4`
			`DUP11`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP16`
			`DUP11`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`SUBFP254`
new fp6 2022-10-22 09:53:16 -04:00			`// make CD01 = c0d1 + c1d0 - (c0_d1_ + c1_d0_)`
			`DUP4`
			`DUP10`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP16`
			`DUP9`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`ADDFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP13`
			`DUP10`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`DUP5`
			`DUP9`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
			`ADDFP254`
			`SUBFP254`
new fp6 2022-10-22 09:53:16 -04:00			`// stack: CD01, C2D2, C2D2_`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP3`
			`DUP3`
new fp6 2022-10-22 09:53:16 -04:00			`// stack: C2D2 , C2D2_ , CD01, C2D2, C2D2_`
fp6 mul 2022-10-20 16:18:41 -04:00			`PUSH 9`
			`MULFP254`
			`SUBFP254`
			`ADDFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: e1 = 9C2D2 - C2D2_ + CD01, C2D2, C2D2_`
new fp6 2022-10-22 09:53:16 -04:00			`SWAP15`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP2`
new fp6 2022-10-22 09:53:16 -04:00			`// stack: C2D2_ , C2D2`
fp6 mul 2022-10-20 16:18:41 -04:00			`PUSH 9`
			`MULFP254`
			`ADDFP254`
better comments 2022-10-22 13:28:12 -04:00			`// stack: 9C2D2_ + C2D2`
fp6 mul 2022-10-20 16:18:41 -04:00			`// make CD01_ = c0d1_ + c0_d1 + c1d0_ + c1_d0`
new fp6 2022-10-22 09:53:16 -04:00			`DUP12`
			`DUP10`
			`MULFP254`
			`DUP5`
			`DUP10`
fp6 mul 2022-10-20 16:18:41 -04:00			`MULFP254`
new fp6 2022-10-22 09:53:16 -04:00			`ADDFP254`
fp6 mul 2022-10-20 16:18:41 -04:00			`DUP4`
			`DUP9`
			`MULFP254`
			`ADDFP254`
			`DUP3`
			`DUP8`
			`MULFP254`
			`ADDFP254`
			`// stack: CD01_ , 9C2D2_ + C2D2`
			`ADDFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: e1_ = CD01_ + 9C2D2_ + C2D2`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP15`
cleanup comments 2022-10-22 13:44:01 -04:00
better comments 2022-10-22 16:17:51 -04:00			`// e2_`
new fp6 2022-10-22 09:53:16 -04:00			`// stack: d2, d1_, d1, d0_, d2_, c0, c0_, c1, c1_, c2, c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP7`
			`MULFP254`
cleanup comments 2022-10-22 13:44:01 -04:00			`// stack: c1d1_, d1, d0_, d2_, c0, c0_, d2, c1_, c2, c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP7`
			`MULFP254`
cleanup comments 2022-10-22 13:44:01 -04:00			`// stack: c1_d1, d0_, d2_, c0, c0_, d2, c1d1_, c2, c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP7`
			`MULFP254`
minor 2022-10-25 17:11:33 -04:00			`// stack: c2d0_, d2_, c0, c0_, d2, c1d1_, c1_d1 , c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP2`
			`MULFP254`
minor 2022-10-25 17:11:33 -04:00			`// stack: c0d2_ , c2d0_, c0_, d2, c1d1_, c1_d1 , c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`ADDFP254`
minor 2022-10-25 17:11:33 -04:00			`// stack: c0d2_ + c2d0_, c0_, d2, c1d1_, c1_d1 , c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP2`
			`MULFP254`
clean up test 2022-10-25 16:59:32 -04:00			`// stack: c0_d2 , c0d2_ + c2d0_ , c1d1_ , c1_d1 , c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`ADDFP254`
			`ADDFP254`
			`ADDFP254`
minor 2022-10-25 17:11:33 -04:00			`// stack: c0_d2 + c0d2_ + c2d0_ + c1d1_ + c1_d1 , c2_, d0`
fp6 mul 2022-10-20 16:18:41 -04:00			`SWAP2`
			`MULFP254`
			`ADDFP254`
better comments 2022-10-22 16:17:51 -04:00			`// stack: e2_ = c2_d0 + c0_d2 + c0d2_ + c2d0_ + c1d1_ + c1_d1`
new fp6 2022-10-22 09:53:16 -04:00			`SWAP6`
better comments 2022-10-22 16:17:51 -04:00
			`// stack: retdest, e0, e0_, e1, e1_, e2, e2_`
fp6 test passes 2022-10-22 13:16:07 -04:00			`JUMP`