use.std::math::ecgfp5::base_field

#! Given an encoded elliptic curve point `w` s.t. it's expressed using
#! an element ∈ GF(p^5) | p = 2^64 - 2^32 + 1, this routine verifies whether
#! given point can be successfully decoded or not
#!
#! Expected stack state
#!
#! [w0, w1, w2, w3, w4, ...]
#!
#! Final stack state
#!
#! [flg, ...]
#!
#! If w can be decoded, flg = 1
#! Else flg = 0
#!
#! Note, if w = (0, 0, 0, 0, 0), it can be successfully decoded to point
#! at infinity i.e. flg = 1, in that case.
#!
#! See https://github.com/pornin/ecgfp5/blob/ce059c6/python/ecGFp5.py#L1043-L1052
#! for reference implementation
export.validate
    repeat.5
        dup.4
    end

    exec.base_field::square
    sub.2 # = e

    exec.base_field::square
    swap
    sub.1052
    swap # = delta

    exec.base_field::legendre
    eq.1
    movdn.5

    push.1
    repeat.5
        swap
        eq.0
        and
    end

    or
end

#! Given an encoded elliptic curve point `w` s.t. it's expressed using
#! an element ∈ GF(p^5) | p = 2^64 - 2^32 + 1, this routine attempts to decode
#! it into x, y coordinates, along with boolean field element denoting whether it's
#! point-at-infinity or not.
#!
#! Expected stack state
#!
#! [w0, w1, w2, w3, w4, ...]
#!
#! Final state state
#!
#! [x0, x1, x2, x3, x4, y0, y1, y2, y3, y4, inf, flg, ...]
#!
#! If `w` has be decoded, flg = 1
#! Else flg = 0 and x, y = (0, 0)
#!
#! Note, when w = (0, 0, 0, 0, 0), it will be successfully decoded to
#! point-at-infinity i.e. x, y = (0, 0) and flg = 1
#!
#! See https://github.com/pornin/ecgfp5/blob/ce059c6/python/ecGFp5.py#L1022-L1041
#! for reference implementation
export.decode
    repeat.5
        dup.4
    end

    exec.base_field::square
    sub.2 # = e

    repeat.5
        dup.4
    end

    exec.base_field::square
    swap
    sub.1052
    swap # = delta

    exec.base_field::sqrt # = (r, c)

    repeat.5
        dup.10
    end

    repeat.5
        dup.9
    end

    exec.base_field::add
    push.0.0.0.0.9223372034707292161
    exec.base_field::mul # = x1

    repeat.5
        movup.9
    end

    repeat.5
        movup.15
    end

    exec.base_field::sub
    push.0.0.0.0.9223372034707292161
    exec.base_field::mul # = x2

    repeat.5
        movup.9
    end

    repeat.5
        dup.4
    end

    exec.base_field::legendre
    eq.1

    if.true
        repeat.5
            movup.5
            drop
        end
    else
        repeat.5
            drop
        end
    end # = x

    repeat.5
        dup.10
    end

    repeat.5
        dup.9
    end

    exec.base_field::mul
    repeat.5
        movup.4
        neg
    end # = y

    dup.10
    not # = inf

    push.1
    repeat.5
        movup.13
        eq.0
        and
    end

    movup.12
    or # = c

    swap

    repeat.5
        movup.6
    end

    repeat.5
        movup.11
    end

    add.6148914689804861441 # = x
end

#! Given an elliptic curve point as Weierstraß coordinates (X, Y) along with
#! boolean field element `inf`, denoting whether this is point-at-infinity or not,
#! this routine encodes it to a single element ∈ GF(p^5) | p = 2^64 - 2^32 + 1
#!
#! Expected stack state
#!
#! [x0, x1, x2, x3, x4, y0, y1, y2, y3, y4, inf, ...]
#!
#! Final stack state
#!
#! [w0, w1, w2, w3, w4, ...]
#!
#! Note, when inf = 1, encoded point w = (0, 0, 0, 0, 0)
#!
#! See https://github.com/pornin/ecgfp5/blob/ce059c6/python/ecGFp5.py#L1214-L1216
#! for reference implementation.
export.encode
    push.0.0.0.0.6148914689804861441 # = a/ 3

    exec.base_field::sub # = (a/ 3) - x

    repeat.5
        movup.9
    end

    exec.base_field::div # = w = y/ ((a/ 3) - x)

    movup.5
    if.true
        repeat.5
            drop
        end

        push.0.0.0.0.0
    end
end

#! Given two elliptic curve points ( say a, b ) as Weierstraß coordinates (X, Y) on stack,
#! this routine computes elliptic curve point c, resulting from a + b.
#!
#! Following point addition formula is complete and it works when two points are
#! same/ different or input operands are point-at-infinity.
#!
#! Expected stack state
#!
#! [x1_0, x1_1, x1_2, x1_3, x1_4, y1_0, y1_1, y1_2, y1_3, y1_4, inf1, x2_0, x2_1, x2_2, x2_3, x2_4, y2_0, y2_1, y2_2, y2_3, y2_4, inf2, ...]
#!
#! s.t. x1_{0..5} -> x1, y1_{0..5} -> y1 |> a = (x1, y1, inf1)
#!      x2_{0..5} -> x2, y2_{0..5} -> y2 |> b = (x2, y2, inf2)
#!
#! Final stack state
#!
#! [x3_0, x3_1, x3_2, x3_3, x3_4, y3_0, y3_1, y3_2, y3_3, y3_4, inf3, ...]
#!
#! Read point addition section ( on page 8 ) of https://ia.cr/2022/274
#! For reference implementation see https://github.com/pornin/ecgfp5/blob/ce059c6/python/ecGFp5.py#L1228-L1255
export.add.10
    loc_storew.0
    dropw
    loc_store.1 # cached x1

    loc_storew.2
    dropw
    loc_store.3 # cached y1

    loc_store.4 # cached inf1

    loc_storew.5
    dropw
    loc_store.6 # cached x2

    loc_storew.7
    dropw
    loc_store.8 # cached y2

    loc_store.9 # cached inf2

    loc_load.6
    push.0.0.0.0
    loc_loadw.5 # bring x2

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x1

    exec.base_field::eq
    dup

    if.true
        loc_load.1
        push.0.0.0.0
        loc_loadw.0 # bring x1

        exec.base_field::square

        repeat.5
            movup.4
            mul.3
        end

        add.6148914689804861439
        swap
        add.263
        swap
    else
        loc_load.3
        push.0.0.0.0
        loc_loadw.2 # bring y1

        loc_load.8
        push.0.0.0.0
        loc_loadw.7 # bring y2

        exec.base_field::sub
    end # = λ0

    dup.5

    if.true
        loc_load.3
        push.0.0.0.0
        loc_loadw.2 # bring y1

        repeat.5
            movup.4
            mul.2
        end
    else
        loc_load.1
        push.0.0.0.0
        loc_loadw.0 # bring x1

        loc_load.6
        push.0.0.0.0
        loc_loadw.5 # bring x2

        exec.base_field::sub
    end # = λ1

    repeat.5
        movup.9
    end

    exec.base_field::div # = λ

    repeat.5
        dup.4
    end

    exec.base_field::square # = λ^2

    loc_load.6
    push.0.0.0.0
    loc_loadw.5 # bring x2

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x1

    exec.base_field::add

    repeat.5
        movup.9
    end

    exec.base_field::sub # compute x3

    repeat.5
        dup.4
    end

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x1

    exec.base_field::sub

    repeat.5
        movup.14
    end

    exec.base_field::mul

    loc_load.3
    push.0.0.0.0
    loc_loadw.2 # bring y1

    repeat.5
        movup.9
    end

    exec.base_field::sub # compute y3

    movup.10

    loc_load.3
    push.0.0.0.0
    loc_loadw.2 # bring y1

    loc_load.8
    push.0.0.0.0
    loc_loadw.7 # bring y2

    exec.base_field::neq

    and # compute inf3

    movdn.5

    # finalize selection of y3

    loc_load.8
    push.0.0.0.0
    loc_loadw.7 # bring y2

    loc_load.4 # bring inf1

    if.true
        repeat.5
            movup.5
            drop
        end
    else
        repeat.5
            drop
        end
    end

    loc_load.3
    push.0.0.0.0
    loc_loadw.2 # bring y1

    loc_load.9 # bring inf2

    if.true
        repeat.5
            movup.5
            drop
        end
    else
        repeat.5
            drop
        end
    end

    # finalize selection of x3

    repeat.5
        movup.10
    end

    loc_load.6
    push.0.0.0.0
    loc_loadw.5 # bring x2

    loc_load.4 # bring inf1

    if.true
        repeat.5
            movup.5
            drop
        end
    else
        repeat.5
            drop
        end
    end

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x1

    loc_load.9 # bring inf2

    if.true
        repeat.5
            movup.5
            drop
        end
    else
        repeat.5
            drop
        end
    end

    # finalize selection of inf3

    movup.10
    loc_load.9 # bring inf2
    loc_load.4 # bring inf1
    cdrop

    loc_load.4 # bring inf1
    loc_load.9 # bring inf2
    cdrop

    movdn.10
end

#! Given one elliptic curve point ( say a ) as Weierstraß coordinates (X, Y) on stack,
#! this routine computes elliptic curve point b s.t. b = 2 * a.
#!
#! Following point doubling formula is complete and it works only when input operand is
#! a non-infinity point, then resulting point b should also be non-infinity.
#!
#! Note, result of add(a, b) = double(a) | a = b
#!
#! Expected stack state
#!
#! [x0, x1, x2, x3, x4, y0, y1, y2, y3, y4, inf, ...]
#!
#! s.t. x{0..5} -> x, y{0..5} -> y |> a = (x, y, inf)
#!
#! Final stack state
#!
#! [x'0, x'1, x'2, x'3, x'4, y'0, y'1, y'2, y'3, y'4, inf, ...]
#!
#! Read point addition section ( on page 8 ) of https://ia.cr/2022/274
#! For reference implementation see https://github.com/pornin/ecgfp5/blob/ce059c6/python/ecGFp5.py#L1270-L1280
export.double.5
    loc_storew.0
    dropw
    loc_store.1 # cached x

    loc_storew.2
    dropw
    loc_store.3 # cached y

    loc_store.4 # cached inf

    loc_load.3
    push.0.0.0.0
    loc_loadw.2 # bring y

    repeat.5
        movup.4
        mul.2
    end # compute λ1

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x

    exec.base_field::square

    repeat.5
        movup.4
        mul.3
    end

    add.6148914689804861439
    swap
    add.263
    swap # compute λ0

    exec.base_field::div # compute λ

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x

    repeat.5
        movup.4
        mul.2
    end

    repeat.5
        dup.9
    end

    exec.base_field::square
    exec.base_field::sub # compute x'

    repeat.5
        dup.4
    end

    loc_load.1
    push.0.0.0.0
    loc_loadw.0 # bring x

    exec.base_field::sub

    repeat.5
        movup.14
    end

    exec.base_field::mul

    loc_load.3
    push.0.0.0.0
    loc_loadw.2 # bring y

    repeat.5
        movup.9
    end

    exec.base_field::sub # compute y'

    repeat.5
        movup.9
    end

    loc_load.4
    movdn.10
end

#! Given an elliptic curve point ( say a ) as Weierstraß coordinates (X, Y) and a 319 -bit scalar ( say e )
#! on stack, this routine computes elliptic curve point b s.t. b =  e * a, using double-and-add technique.
#!
#! Scalar e should be lesser than 1067993516717146951041484916571792702745057740581727230159139685185762082554198619328292418486241 ( prime number ).
#! Note, scalar e should be provided as 10 limbs on stack, each of 32 -bit, representing it in radix-2^32 form.
#!
#! Given a scalar e ( as arbitrary width big integer ), following python code snippet should convert it to desired input form
#!
#! [(a >> (32*i)) & 0xffff_ffff for i in range(10)]
#!
#! Expected stack state
#!
#! [x0, x1, x2, x3, x4, y0, y1, y2, y3, y4, inf, e0, e1, e2, e3, e4, e5, e6, e7, e8, e9, ...]
#!
#! Point a = (x, y, inf)
#! Scalar e = (e0, e1, e2, e3, e4, e5, e6, e7, e8, e9)
#!
#! Final stack state
#!
#! [x'0, x'1, x'2, x'3, x'4, y'0, y'1, y'2, y'3, y'4, inf, ...]
#!
#! Point b = (x', y' inf') | b = e * a
#!
#! See https://github.com/itzmeanjan/secp256k1/blob/cbbe199/point.py#L174-L186 for source of inpiration.
export.mul.10
    loc_storew.0
    dropw
    loc_store.1 # cached base_x

    loc_storew.2
    dropw
    loc_store.3 # cached base_y

    loc_store.4 # cached base_inf

    push.0.0.0.0
    loc_storew.5
    dropw
    push.0
    loc_store.6 # initialize and cache res_x

    push.0.0.0.0
    loc_storew.7
    dropw
    push.0
    loc_store.8 # initialize and cache res_y

    push.1
    loc_store.9 # initialize and cache res_inf

    repeat.10
        repeat.32
            dup
            push.1
            u32and

            if.true
                # bring base
                loc_load.4

                loc_load.3
                push.0.0.0.0
                loc_loadw.2

                loc_load.1
                push.0.0.0.0
                loc_loadw.0

                # bring res
                loc_load.9

                loc_load.8
                push.0.0.0.0
                loc_loadw.7

                loc_load.6
                push.0.0.0.0
                loc_loadw.5

                exec.add

                # write back res
                loc_storew.5
                dropw
                loc_store.6

                loc_storew.7
                dropw
                loc_store.8

                loc_store.9
            end

            # bring base
            loc_load.4

            loc_load.3
            push.0.0.0.0
            loc_loadw.2

            loc_load.1
            push.0.0.0.0
            loc_loadw.0

            exec.double

            # write back base
            loc_storew.0
            dropw
            loc_store.1

            loc_storew.2
            dropw
            loc_store.3

            loc_store.4

            u32shr.1
        end

        drop
    end

    # bring res
    loc_load.9

    loc_load.8
    push.0.0.0.0
    loc_loadw.7

    loc_load.6
    push.0.0.0.0
    loc_loadw.5
end

#! Given a 319 -bit scalar ( say e ) on stack, this routine computes elliptic curve point
#! b s.t. b =  e * G, using double-and-add technique | G = conventional group generator point.
#!
#! Group generator point https://github.com/pornin/ecgfp5/blob/ce059c6/rust/src/curve.rs#L67-L83
#!
#! Scalar e should be lesser than N ( = 1067993516717146951041484916571792702745057740581727230159139685185762082554198619328292418486241 ).
#! Note, scalar e should be provided as 10 limbs on stack, each of 32 -bit, representing it in radix-2^32 form.
#!
#! Given a 319 -bit scalar e, following python code snippet should convert it to
#! desired input form i.e. radix-2^32 representation, having ten 32 -bit limbs
#!
#! [(e >> (32*i)) & 0xffff_ffff for i in range(10)]
#!
#! Expected stack state
#!
#! [e0, e1, e2, e3, e4, e5, e6, e7, e8, e9, ...]
#!
#! Scalar e = (e0, e1, e2, e3, e4, e5, e6, e7, e8, e9)
#!
#! Final stack state
#!
#! [x0, x1, x2, x3, x4, y0, y1, y2, y3, y4, inf, ...]
#!
#! Point b = (x, y, inf) | b = e * G
#!
#! See https://github.com/itzmeanjan/secp256k1/blob/cbbe199/point.py#L174-L186 for source of inpiration.
export.gen_mul.8
    loc_storew.0
    dropw
    loc_storew.1
    dropw
    push.0.0
    movup.3
    movup.3
    loc_storew.2
    dropw # cache 319 -bit scalar, having 10 limbs, each of 32 -bit width

    push.0.0.0.0.0
    loc_storew.3
    dropw
    loc_store.4 # initialize and cache res_x

    push.0.0.0.0.0
    loc_storew.5
    dropw
    loc_store.6 # initialize and cache res_y

    push.1
    loc_store.7 # initialize and cache res_inf

    push.0.8623373087021137817.12280941316336150722.16498106075800537106.17561351883262171669.14191612778916076371.18286383079848041790.5863339128417000744.11451759428629996034.14179124258460441178.4768624678334228939
    push.0.16248535820734672314.12843058077554438509.14604603115652880441.1861370543582612103.12413761366396265525.4176022593458990041.3883454194479152564.14208568149880154517.30496475895846659.10372352552633189742
    push.0.2877809984845595236.8124729848406989261.2903444924486455483.6139401771336820486.11258486910517561409.11269995078679563195.4075713964805364983.11272694349658053421.17286345916541825175.5239921069304273244
    push.0.17641185070824107975.14889445785061292430.7405791732550181507.4195033912468829473.5893024420900179836.9198199668142261635.13255077950461830861.3315714462260585145.5358622364758307393.721593612819002908
    push.0.17218153792253988554.398898134320123335.14691321837712781231.14813642725547346961.7022468048599869463.13425501193148363047.8102520424076163562.4818391030611537206.3117791970810252983.3664867151911665097
    push.0.9768740144997694838.18337438909916942052.13287690569608682189.1749912136742008160.16874873892224416289.13753848043314362441.4990704782108972448.15940429530085642075.10014152261700797213.8271724616203496328
    push.0.15137575290038364568.834448034475692680.17725871744982540755.17720761966581073520.15617784849739721933.13143846705867213452.6387719880838102748.15637132133232092065.17395668299430845447.4976508673457147220
    push.0.14448869278120871938.2440192432902894712.9065627619858283302.7476463190805008531.12433592364249876790.7326369368968030334.10492708378186270656.8590652592090351714.11478014260122655233.5102808632757846047
    push.0.9652768576975789451.2169826252445647515.8515692953826676326.12790755226033428483.10499532484372206399.1752808319082265622.1461287152438866664.16156917747677348345.1913114203733512691.4220966228724218121
    push.0.15678769274395291067.3644569546435216629.8279510540289007754.14347910311032351181.11017801090920149683.17092277456226211965.16027019793415245260.6242090196981371796.13195765456550520156.18329307820651300136
    push.0.15660277884414351657.4747038350935563407.16563445468461400225.9202649824211012050.16989226289451019470.16269357368883802812.14601257932273902054.11922650544629087011.3837671014910122842.10542030917794106031
    push.0.16679682878508344885.4260113432582040236.6657572838446037989.17057619578187970416.9557888942099085229.16766876175803959905.8797349954628290450.9735674650584728206.16707168790898826743.2957163603751591175
    push.0.12731950592067067806.15132000389362928180.2301212109204980010.11858193693385253107.2787225233368024015.15608358023222707950.5664305148663915403.14236763768002019539.11718445275434263967.10887359501593613247
    push.0.12906063996958603900.1561861388017124445.9769071188656310541.9108206805299149795.828335823705130147.11630764285144089035.13798633568618668074.10120521355198906717.78547975849802565.9032713792450238388
    push.0.2932017870248423748.12862241115656865401.5691212362156829751.10513473720672864882.5811042078412067511.458337204753456641.13679640590869584883.3442439947769535104.10679288079271307010.16403385062095364376
    push.0.2960040779968781381.13743098123458581162.16796911018466257282.3963340258774352059.9493732769165536890.17565729304514950270.14558776703731825254.16603544858443598146.1290832334148046531.7196562104405968541
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    repeat.2 # process first 8 limbs of scalar
        repeat.4 # process 4 consecutive 32 -bit limbs
            repeat.32 # process each 32 -bit limb
                push.0.0.0.0
                loc_loadw.0

                dup
                push.1
                u32and
                movdn.4

                u32shr.1

                loc_storew.0
                dropw

                if.true
                    # base already on stack top
                    # bring res from memory
                    loc_load.7

                    loc_load.6
                    push.0.0.0.0
                    loc_loadw.5

                    loc_load.4
                    push.0.0.0.0
                    loc_loadw.3

                    exec.add

                    # write back res
                    loc_storew.3
                    dropw
                    loc_store.4

                    loc_storew.5
                    dropw
                    loc_store.6

                    loc_store.7
                else
                    dropw
                    dropw
                    push.0
                    dropw
                end
            end

            push.0.0.0.0
            loc_loadw.0

            drop
            push.0
            movdn.3

            loc_storew.0
            dropw
        end

        push.0.0.0.0
        loc_loadw.1
        loc_storew.0
        dropw
    end

    repeat.2 # process last 2 limbs of scalar
        repeat.32 # process each of last two 32 -bit limbs
            push.0.0.0.0
            loc_loadw.2

            dup
            push.1
            u32and
            movdn.4

            u32shr.1

            loc_storew.2
            dropw

            if.true
                # base already on stack top
                # bring res from memory
                loc_load.7

                loc_load.6
                push.0.0.0.0
                loc_loadw.5

                loc_load.4
                push.0.0.0.0
                loc_loadw.3

                exec.add

                # write back res
                loc_storew.3
                dropw
                loc_store.4

                loc_storew.5
                dropw
                loc_store.6

                loc_store.7
            else
                dropw
                dropw
                push.0
                dropw
            end
        end

        push.0.0.0.0
        loc_loadw.2

        drop
        push.0
        movdn.3

        loc_storew.2
        dropw
    end

    # bring res back to stack
    loc_load.7

    loc_load.6
    push.0.0.0.0
    loc_loadw.5

    loc_load.4
    push.0.0.0.0
    loc_loadw.3
end