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go / go / 352996a381701cfa0c16e8de29cbde8f3922182f / . / src / crypto / elliptic / p256_asm_s390x.s
blob: 96b59be23fb778c2a7e71da2f6c7495983033a37 [file] [log] [blame]
// Copyright 2016 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
#include "textflag.h"
DATA p256ordK0<>+0x00(SB)/4, $0xee00bc4f
DATA p256ord<>+0x00(SB)/8, $0xffffffff00000000
DATA p256ord<>+0x08(SB)/8, $0xffffffffffffffff
DATA p256ord<>+0x10(SB)/8, $0xbce6faada7179e84
DATA p256ord<>+0x18(SB)/8, $0xf3b9cac2fc632551
DATA p256<>+0x00(SB)/8, $0xffffffff00000001 // P256
DATA p256<>+0x08(SB)/8, $0x0000000000000000 // P256
DATA p256<>+0x10(SB)/8, $0x00000000ffffffff // P256
DATA p256<>+0x18(SB)/8, $0xffffffffffffffff // P256
DATA p256<>+0x20(SB)/8, $0x0c0d0e0f1c1d1e1f // SEL d1 d0 d1 d0
DATA p256<>+0x28(SB)/8, $0x0c0d0e0f1c1d1e1f // SEL d1 d0 d1 d0
DATA p256<>+0x30(SB)/8, $0x0000000010111213 // SEL 0 d1 d0 0
DATA p256<>+0x38(SB)/8, $0x1415161700000000 // SEL 0 d1 d0 0
DATA p256<>+0x40(SB)/8, $0x18191a1b1c1d1e1f // SEL d1 d0 d1 d0
DATA p256<>+0x48(SB)/8, $0x18191a1b1c1d1e1f // SEL d1 d0 d1 d0
DATA p256mul<>+0x00(SB)/8, $0xffffffff00000001 // P256
DATA p256mul<>+0x08(SB)/8, $0x0000000000000000 // P256
DATA p256mul<>+0x10(SB)/8, $0x00000000ffffffff // P256
DATA p256mul<>+0x18(SB)/8, $0xffffffffffffffff // P256
DATA p256mul<>+0x20(SB)/8, $0x1c1d1e1f00000000 // SEL d0 0 0 d0
DATA p256mul<>+0x28(SB)/8, $0x000000001c1d1e1f // SEL d0 0 0 d0
DATA p256mul<>+0x30(SB)/8, $0x0001020304050607 // SEL d0 0 d1 d0
DATA p256mul<>+0x38(SB)/8, $0x1c1d1e1f0c0d0e0f // SEL d0 0 d1 d0
DATA p256mul<>+0x40(SB)/8, $0x040506071c1d1e1f // SEL 0 d1 d0 d1
DATA p256mul<>+0x48(SB)/8, $0x0c0d0e0f1c1d1e1f // SEL 0 d1 d0 d1
DATA p256mul<>+0x50(SB)/8, $0x0405060704050607 // SEL 0 0 d1 d0
DATA p256mul<>+0x58(SB)/8, $0x1c1d1e1f0c0d0e0f // SEL 0 0 d1 d0
DATA p256mul<>+0x60(SB)/8, $0x0c0d0e0f1c1d1e1f // SEL d1 d0 d1 d0
DATA p256mul<>+0x68(SB)/8, $0x0c0d0e0f1c1d1e1f // SEL d1 d0 d1 d0
DATA p256mul<>+0x70(SB)/8, $0x141516170c0d0e0f // SEL 0 d1 d0 0
DATA p256mul<>+0x78(SB)/8, $0x1c1d1e1f14151617 // SEL 0 d1 d0 0
DATA p256mul<>+0x80(SB)/8, $0x00000000fffffffe // (1*2^256)%P256
DATA p256mul<>+0x88(SB)/8, $0xffffffffffffffff // (1*2^256)%P256
DATA p256mul<>+0x90(SB)/8, $0xffffffff00000000 // (1*2^256)%P256
DATA p256mul<>+0x98(SB)/8, $0x0000000000000001 // (1*2^256)%P256
GLOBL p256ordK0<>(SB), 8, $4
GLOBL p256ord<>(SB), 8, $32
GLOBL p256<>(SB), 8, $80
GLOBL p256mul<>(SB), 8, $160
// func hasVectorFacility() bool
TEXT ·hasVectorFacility(SB), NOSPLIT, $24-1
MOVD $x-24(SP), R1
XC $24, 0(R1), 0(R1) // clear the storage
MOVD $2, R0 // R0 is the number of double words stored -1
WORD $0xB2B01000 // STFLE 0(R1)
XOR R0, R0 // reset the value of R0
MOVBZ z-8(SP), R1
AND $0x40, R1
BEQ novector
vectorinstalled:
// check if the vector instruction has been enabled
VLEIB $0, $0xF, V16
VLGVB $0, V16, R1
CMPBNE R1, $0xF, novector
MOVB $1, ret+0(FP) // have vx
RET
novector:
MOVB $0, ret+0(FP) // no vx
RET
// ---------------------------------------
// iff cond == 1 val <- -val
// func p256NegCond(val *p256Point, cond int)
#define P1ptr R1
#define CPOOL R4
#define Y1L V0
#define Y1H V1
#define T1L V2
#define T1H V3
#define PL V30
#define PH V31
#define ZER V4
#define SEL1 V5
#define CAR1 V6
TEXT ·p256NegCond(SB), NOSPLIT, $0
MOVD val+0(FP), P1ptr
MOVD $p256mul<>+0x00(SB), CPOOL
VL 16(CPOOL), PL
VL 0(CPOOL), PH
VL 32(P1ptr), Y1H
VL 48(P1ptr), Y1L
VLREPG cond+8(FP), SEL1
VZERO ZER
VCEQG SEL1, ZER, SEL1
VSCBIQ Y1L, PL, CAR1
VSQ Y1L, PL, T1L
VSBIQ PH, Y1H, CAR1, T1H
VSEL Y1L, T1L, SEL1, Y1L
VSEL Y1H, T1H, SEL1, Y1H
VST Y1H, 32(P1ptr)
VST Y1L, 48(P1ptr)
RET
#undef P1ptr
#undef CPOOL
#undef Y1L
#undef Y1H
#undef T1L
#undef T1H
#undef PL
#undef PH
#undef ZER
#undef SEL1
#undef CAR1
// ---------------------------------------
// if cond == 0 res <- b; else res <- a
// func p256MovCond(res, a, b *p256Point, cond int)
#define P3ptr R1
#define P1ptr R2
#define P2ptr R3
#define X1L V0
#define X1H V1
#define Y1L V2
#define Y1H V3
#define Z1L V4
#define Z1H V5
#define X2L V6
#define X2H V7
#define Y2L V8
#define Y2H V9
#define Z2L V10
#define Z2H V11
#define ZER V18
#define SEL1 V19
TEXT ·p256MovCond(SB), NOSPLIT, $0
MOVD res+0(FP), P3ptr
MOVD a+8(FP), P1ptr
MOVD b+16(FP), P2ptr
VLREPG cond+24(FP), SEL1
VZERO ZER
VCEQG SEL1, ZER, SEL1
VL 0(P1ptr), X1H
VL 16(P1ptr), X1L
VL 32(P1ptr), Y1H
VL 48(P1ptr), Y1L
VL 64(P1ptr), Z1H
VL 80(P1ptr), Z1L
VL 0(P2ptr), X2H
VL 16(P2ptr), X2L
VL 32(P2ptr), Y2H
VL 48(P2ptr), Y2L
VL 64(P2ptr), Z2H
VL 80(P2ptr), Z2L
VSEL X2L, X1L, SEL1, X1L
VSEL X2H, X1H, SEL1, X1H
VSEL Y2L, Y1L, SEL1, Y1L
VSEL Y2H, Y1H, SEL1, Y1H
VSEL Z2L, Z1L, SEL1, Z1L
VSEL Z2H, Z1H, SEL1, Z1H
VST X1H, 0(P3ptr)
VST X1L, 16(P3ptr)
VST Y1H, 32(P3ptr)
VST Y1L, 48(P3ptr)
VST Z1H, 64(P3ptr)
VST Z1L, 80(P3ptr)
RET
#undef P3ptr
#undef P1ptr
#undef P2ptr
#undef X1L
#undef X1H
#undef Y1L
#undef Y1H
#undef Z1L
#undef Z1H
#undef X2L
#undef X2H
#undef Y2L
#undef Y2H
#undef Z2L
#undef Z2H
#undef ZER
#undef SEL1
// ---------------------------------------
// Constant time table access
// Indexed from 1 to 15, with -1 offset
// (index 0 is implicitly point at infinity)
// func p256Select(point *p256Point, table []p256Point, idx int)
#define P3ptr R1
#define P1ptr R2
#define COUNT R4
#define X1L V0
#define X1H V1
#define Y1L V2
#define Y1H V3
#define Z1L V4
#define Z1H V5
#define X2L V6
#define X2H V7
#define Y2L V8
#define Y2H V9
#define Z2L V10
#define Z2H V11
#define ONE V18
#define IDX V19
#define SEL1 V20
#define SEL2 V21
TEXT ·p256Select(SB), NOSPLIT, $0
MOVD point+0(FP), P3ptr
MOVD table+8(FP), P1ptr
VLREPB idx+(32+7)(FP), IDX
VREPIB $1, ONE
VREPIB $1, SEL2
MOVD $1, COUNT
VZERO X1H
VZERO X1L
VZERO Y1H
VZERO Y1L
VZERO Z1H
VZERO Z1L
loop_select:
VL 0(P1ptr), X2H
VL 16(P1ptr), X2L
VL 32(P1ptr), Y2H
VL 48(P1ptr), Y2L
VL 64(P1ptr), Z2H
VL 80(P1ptr), Z2L
VCEQG SEL2, IDX, SEL1
VSEL X2L, X1L, SEL1, X1L
VSEL X2H, X1H, SEL1, X1H
VSEL Y2L, Y1L, SEL1, Y1L
VSEL Y2H, Y1H, SEL1, Y1H
VSEL Z2L, Z1L, SEL1, Z1L
VSEL Z2H, Z1H, SEL1, Z1H
VAB SEL2, ONE, SEL2
ADDW $1, COUNT
ADD $96, P1ptr
CMPW COUNT, $17
BLT loop_select
VST X1H, 0(P3ptr)
VST X1L, 16(P3ptr)
VST Y1H, 32(P3ptr)
VST Y1L, 48(P3ptr)
VST Z1H, 64(P3ptr)
VST Z1L, 80(P3ptr)
RET
#undef P3ptr
#undef P1ptr
#undef COUNT
#undef X1L
#undef X1H
#undef Y1L
#undef Y1H
#undef Z1L
#undef Z1H
#undef X2L
#undef X2H
#undef Y2L
#undef Y2H
#undef Z2L
#undef Z2H
#undef ONE
#undef IDX
#undef SEL1
#undef SEL2
// ---------------------------------------
// Constant time table access
// Indexed from 1 to 15, with -1 offset
// (index 0 is implicitly point at infinity)
// func p256SelectBase(point *p256Point, table []p256Point, idx int)
#define P3ptr R1
#define P1ptr R2
#define COUNT R4
#define X1L V0
#define X1H V1
#define Y1L V2
#define Y1H V3
#define Z1L V4
#define Z1H V5
#define X2L V6
#define X2H V7
#define Y2L V8
#define Y2H V9
#define Z2L V10
#define Z2H V11
#define ONE V18
#define IDX V19
#define SEL1 V20
#define SEL2 V21
TEXT ·p256SelectBase(SB), NOSPLIT, $0
MOVD point+0(FP), P3ptr
MOVD table+8(FP), P1ptr
VLREPB idx+(32+7)(FP), IDX
VREPIB $1, ONE
VREPIB $1, SEL2
MOVD $1, COUNT
VZERO X1H
VZERO X1L
VZERO Y1H
VZERO Y1L
VZERO Z1H
VZERO Z1L
loop_select:
VL 0(P1ptr), X2H
VL 16(P1ptr), X2L
VL 32(P1ptr), Y2H
VL 48(P1ptr), Y2L
VL 64(P1ptr), Z2H
VL 80(P1ptr), Z2L
VCEQG SEL2, IDX, SEL1
VSEL X2L, X1L, SEL1, X1L
VSEL X2H, X1H, SEL1, X1H
VSEL Y2L, Y1L, SEL1, Y1L
VSEL Y2H, Y1H, SEL1, Y1H
VSEL Z2L, Z1L, SEL1, Z1L
VSEL Z2H, Z1H, SEL1, Z1H
VAB SEL2, ONE, SEL2
ADDW $1, COUNT
ADD $96, P1ptr
CMPW COUNT, $65
BLT loop_select
VST X1H, 0(P3ptr)
VST X1L, 16(P3ptr)
VST Y1H, 32(P3ptr)
VST Y1L, 48(P3ptr)
VST Z1H, 64(P3ptr)
VST Z1L, 80(P3ptr)
RET
#undef P3ptr
#undef P1ptr
#undef COUNT
#undef X1L
#undef X1H
#undef Y1L
#undef Y1H
#undef Z1L
#undef Z1H
#undef X2L
#undef X2H
#undef Y2L
#undef Y2H
#undef Z2L
#undef Z2H
#undef ONE
#undef IDX
#undef SEL1
#undef SEL2
// ---------------------------------------
// func p256FromMont(res, in []byte)
#define res_ptr R1
#define x_ptr R2
#define CPOOL R4
#define T0 V0
#define T1 V1
#define T2 V2
#define TT0 V3
#define TT1 V4
#define ZER V6
#define SEL1 V7
#define SEL2 V8
#define CAR1 V9
#define CAR2 V10
#define RED1 V11
#define RED2 V12
#define PL V13
#define PH V14
TEXT ·p256FromMont(SB), NOSPLIT, $0
MOVD res+0(FP), res_ptr
MOVD in+24(FP), x_ptr
VZERO T2
VZERO ZER
MOVD $p256<>+0x00(SB), CPOOL
VL 16(CPOOL), PL
VL 0(CPOOL), PH
VL 48(CPOOL), SEL2
VL 64(CPOOL), SEL1
VL (1*16)(x_ptr), T0
VL (0*16)(x_ptr), T1
// First round
VPERM T1, T0, SEL1, RED2 // d1 d0 d1 d0
VPERM ZER, RED2, SEL2, RED1 // 0 d1 d0 0
VSQ RED1, RED2, RED2 // Guaranteed not to underflow
VSLDB $8, T1, T0, T0
VSLDB $8, T2, T1, T1
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, CAR2
VACQ T1, RED2, CAR1, T1
VAQ T2, CAR2, T2
// Second round
VPERM T1, T0, SEL1, RED2 // d1 d0 d1 d0
VPERM ZER, RED2, SEL2, RED1 // 0 d1 d0 0
VSQ RED1, RED2, RED2 // Guaranteed not to underflow
VSLDB $8, T1, T0, T0
VSLDB $8, T2, T1, T1
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, CAR2
VACQ T1, RED2, CAR1, T1
VAQ T2, CAR2, T2
// Third round
VPERM T1, T0, SEL1, RED2 // d1 d0 d1 d0
VPERM ZER, RED2, SEL2, RED1 // 0 d1 d0 0
VSQ RED1, RED2, RED2 // Guaranteed not to underflow
VSLDB $8, T1, T0, T0
VSLDB $8, T2, T1, T1
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, CAR2
VACQ T1, RED2, CAR1, T1
VAQ T2, CAR2, T2
// Last round
VPERM T1, T0, SEL1, RED2 // d1 d0 d1 d0
VPERM ZER, RED2, SEL2, RED1 // 0 d1 d0 0
VSQ RED1, RED2, RED2 // Guaranteed not to underflow
VSLDB $8, T1, T0, T0
VSLDB $8, T2, T1, T1
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, CAR2
VACQ T1, RED2, CAR1, T1
VAQ T2, CAR2, T2
// ---------------------------------------------------
VSCBIQ PL, T0, CAR1
VSQ PL, T0, TT0
VSBCBIQ T1, PH, CAR1, CAR2
VSBIQ T1, PH, CAR1, TT1
VSBIQ T2, ZER, CAR2, T2
// what output to use, TT1||TT0 or T1||T0?
VSEL T0, TT0, T2, T0
VSEL T1, TT1, T2, T1
VST T0, (1*16)(res_ptr)
VST T1, (0*16)(res_ptr)
RET
#undef res_ptr
#undef x_ptr
#undef CPOOL
#undef T0
#undef T1
#undef T2
#undef TT0
#undef TT1
#undef ZER
#undef SEL1
#undef SEL2
#undef CAR1
#undef CAR2
#undef RED1
#undef RED2
#undef PL
#undef PH
// ---------------------------------------
// func p256OrdMul(res, in1, in2 []byte)
#define res_ptr R1
#define x_ptr R2
#define y_ptr R3
#define X0 V0
#define X1 V1
#define Y0 V2
#define Y1 V3
#define M0 V4
#define M1 V5
#define T0 V6
#define T1 V7
#define T2 V8
#define YDIG V9
#define ADD1 V16
#define ADD1H V17
#define ADD2 V18
#define ADD2H V19
#define RED1 V20
#define RED1H V21
#define RED2 V22
#define RED2H V23
#define CAR1 V24
#define CAR1M V25
#define MK0 V30
#define K0 V31
TEXT ·p256OrdMul(SB), NOSPLIT, $0
MOVD res+0(FP), res_ptr
MOVD in1+24(FP), x_ptr
MOVD in2+48(FP), y_ptr
VZERO T2
MOVD $p256ordK0<>+0x00(SB), R4
// VLEF $3, 0(R4), K0
WORD $0xE7F40000
BYTE $0x38
BYTE $0x03
MOVD $p256ord<>+0x00(SB), R4
VL 16(R4), M0
VL 0(R4), M1
VL (1*16)(x_ptr), X0
VL (0*16)(x_ptr), X1
VL (1*16)(y_ptr), Y0
VL (0*16)(y_ptr), Y1
// ---------------------------------------------------------------------------/
VREPF $3, Y0, YDIG
VMLF X0, YDIG, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMLF X1, YDIG, ADD2
VMLHF X0, YDIG, ADD1H
VMLHF X1, YDIG, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
/* *
* ---+--------+--------+
* T2| T1 | T0 |
* ---+--------+--------+
* *(add)*
* +--------+--------+
* | X1 | X0 |
* +--------+--------+
* *(mul)*
* +--------+--------+
* | YDIG | YDIG |
* +--------+--------+
* *(add)*
* +--------+--------+
* | M1 | M0 |
* +--------+--------+
* *(mul)*
* +--------+--------+
* | MK0 | MK0 |
* +--------+--------+
*
* ---------------------
*
* +--------+--------+
* | ADD2 | ADD1 |
* +--------+--------+
* +--------+--------+
* | ADD2H | ADD1H |
* +--------+--------+
* +--------+--------+
* | RED2 | RED1 |
* +--------+--------+
* +--------+--------+
* | RED2H | RED1H |
* +--------+--------+
*/
VREPF $2, Y0, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VREPF $1, Y0, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VREPF $0, Y0, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VREPF $3, Y1, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VREPF $2, Y1, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VREPF $1, Y1, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VREPF $0, Y1, YDIG
VMALF X0, YDIG, T0, ADD1
VMLF ADD1, K0, MK0
VREPF $3, MK0, MK0
VMALF X1, YDIG, T1, ADD2
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF M0, MK0, ADD1, RED1
VMALHF M0, MK0, ADD1, RED1H
VMALF M1, MK0, ADD2, RED2
VMALHF M1, MK0, ADD2, RED2H
VSLDB $12, RED2, RED1, RED1
VSLDB $12, T2, RED2, RED2
VACCQ RED1, ADD1H, CAR1
VAQ RED1, ADD1H, T0
VACCQ RED1H, T0, CAR1M
VAQ RED1H, T0, T0
// << ready for next MK0
VACQ RED2, ADD2H, CAR1, T1
VACCCQ RED2, ADD2H, CAR1, CAR1
VACCCQ RED2H, T1, CAR1M, T2
VACQ RED2H, T1, CAR1M, T1
VAQ CAR1, T2, T2
// ---------------------------------------------------
VZERO RED1
VSCBIQ M0, T0, CAR1
VSQ M0, T0, ADD1
VSBCBIQ T1, M1, CAR1, CAR1M
VSBIQ T1, M1, CAR1, ADD2
VSBIQ T2, RED1, CAR1M, T2
// what output to use, ADD2||ADD1 or T1||T0?
VSEL T0, ADD1, T2, T0
VSEL T1, ADD2, T2, T1
VST T0, (1*16)(res_ptr)
VST T1, (0*16)(res_ptr)
RET
#undef res_ptr
#undef x_ptr
#undef y_ptr
#undef X0
#undef X1
#undef Y0
#undef Y1
#undef M0
#undef M1
#undef T0
#undef T1
#undef T2
#undef YDIG
#undef ADD1
#undef ADD1H
#undef ADD2
#undef ADD2H
#undef RED1
#undef RED1H
#undef RED2
#undef RED2H
#undef CAR1
#undef CAR1M
#undef MK0
#undef K0
// ---------------------------------------
// p256MulInternal
// V0-V3,V30,V31 - Not Modified
// V4-V15 - Volatile
#define CPOOL R4
// Parameters
#define X0 V0 // Not modified
#define X1 V1 // Not modified
#define Y0 V2 // Not modified
#define Y1 V3 // Not modified
#define T0 V4
#define T1 V5
#define P0 V30 // Not modified
#define P1 V31 // Not modified
// Temporaries
#define YDIG V6 // Overloaded with CAR2, ZER
#define ADD1H V7 // Overloaded with ADD3H
#define ADD2H V8 // Overloaded with ADD4H
#define ADD3 V9 // Overloaded with SEL2,SEL5
#define ADD4 V10 // Overloaded with SEL3,SEL6
#define RED1 V11 // Overloaded with CAR2
#define RED2 V12
#define RED3 V13 // Overloaded with SEL1
#define T2 V14
// Overloaded temporaries
#define ADD1 V4 // Overloaded with T0
#define ADD2 V5 // Overloaded with T1
#define ADD3H V7 // Overloaded with ADD1H
#define ADD4H V8 // Overloaded with ADD2H
#define ZER V6 // Overloaded with YDIG, CAR2
#define CAR1 V6 // Overloaded with YDIG, ZER
#define CAR2 V11 // Overloaded with RED1
// Constant Selects
#define SEL1 V13 // Overloaded with RED3
#define SEL2 V9 // Overloaded with ADD3,SEL5
#define SEL3 V10 // Overloaded with ADD4,SEL6
#define SEL4 V6 // Overloaded with YDIG,CAR2,ZER
#define SEL5 V9 // Overloaded with ADD3,SEL2
#define SEL6 V10 // Overloaded with ADD4,SEL3
/* *
* To follow the flow of bits, for your own sanity a stiff drink, need you shall.
* Of a single round, a 'helpful' picture, here is. Meaning, column position has.
* With you, SIMD be...
*
* +--------+--------+
* +--------| RED2 | RED1 |
* | +--------+--------+
* | ---+--------+--------+
* | +---- T2| T1 | T0 |--+
* | | ---+--------+--------+ |
* | | |
* | | ======================= |
* | | |
* | | +--------+--------+<-+
* | +-------| ADD2 | ADD1 |--|-----+
* | | +--------+--------+ | |
* | | +--------+--------+<---+ |
* | | | ADD2H | ADD1H |--+ |
* | | +--------+--------+ | |
* | | +--------+--------+<-+ |
* | | | ADD4 | ADD3 |--|-+ |
* | | +--------+--------+ | | |
* | | +--------+--------+<---+ | |
* | | | ADD4H | ADD3H |------|-+ |(+vzero)
* | | +--------+--------+ | | V
* | | ------------------------ | | +--------+
* | | | | | RED3 | [d0 0 0 d0]
* | | | | +--------+
* | +---->+--------+--------+ | | |
* (T2[1w]||ADD2[4w]||ADD1[3w]) +--------| T1 | T0 | | | |
* | +--------+--------+ | | |
* +---->---+--------+--------+ | | |
* T2| T1 | T0 |----+ | |
* ---+--------+--------+ | | |
* ---+--------+--------+<---+ | |
* +--- T2| T1 | T0 |----------+
* | ---+--------+--------+ | |
* | +--------+--------+<-------------+
* | | RED2 | RED1 |-----+ | | [0 d1 d0 d1] [d0 0 d1 d0]
* | +--------+--------+ | | |
* | +--------+<----------------------+
* | | RED3 |--------------+ | [0 0 d1 d0]
* | +--------+ | |
* +--->+--------+--------+ | |
* | T1 | T0 |--------+
* +--------+--------+ | |
* --------------------------- | |
* | |
* +--------+--------+<----+ |
* | RED2 | RED1 | |
* +--------+--------+ |
* ---+--------+--------+<-------+
* T2| T1 | T0 | (H1P-H1P-H00RRAY!)
* ---+--------+--------+
*
* *Mi obra de arte de siglo XXI @vpaprots
*
*
* First group is special, doesnt get the two inputs:
* +--------+--------+<-+
* +-------| ADD2 | ADD1 |--|-----+
* | +--------+--------+ | |
* | +--------+--------+<---+ |
* | | ADD2H | ADD1H |--+ |
* | +--------+--------+ | |
* | +--------+--------+<-+ |
* | | ADD4 | ADD3 |--|-+ |
* | +--------+--------+ | | |
* | +--------+--------+<---+ | |
* | | ADD4H | ADD3H |------|-+ |(+vzero)
* | +--------+--------+ | | V
* | ------------------------ | | +--------+
* | | | | RED3 | [d0 0 0 d0]
* | | | +--------+
* +---->+--------+--------+ | | |
* (T2[1w]||ADD2[4w]||ADD1[3w]) | T1 | T0 |----+ | |
* +--------+--------+ | | |
* ---+--------+--------+<---+ | |
* +--- T2| T1 | T0 |----------+
* | ---+--------+--------+ | |
* | +--------+--------+<-------------+
* | | RED2 | RED1 |-----+ | | [0 d1 d0 d1] [d0 0 d1 d0]
* | +--------+--------+ | | |
* | +--------+<----------------------+
* | | RED3 |--------------+ | [0 0 d1 d0]
* | +--------+ | |
* +--->+--------+--------+ | |
* | T1 | T0 |--------+
* +--------+--------+ | |
* --------------------------- | |
* | |
* +--------+--------+<----+ |
* | RED2 | RED1 | |
* +--------+--------+ |
* ---+--------+--------+<-------+
* T2| T1 | T0 | (H1P-H1P-H00RRAY!)
* ---+--------+--------+
*
* Last 'group' needs to RED2||RED1 shifted less
*/
TEXT p256MulInternal<>(SB), NOSPLIT, $0-0
VL 32(CPOOL), SEL1
VL 48(CPOOL), SEL2
VL 64(CPOOL), SEL3
VL 80(CPOOL), SEL4
// ---------------------------------------------------
VREPF $3, Y0, YDIG
VMLHF X0, YDIG, ADD1H
VMLHF X1, YDIG, ADD2H
VMLF X0, YDIG, ADD1
VMLF X1, YDIG, ADD2
VREPF $2, Y0, YDIG
VMALF X0, YDIG, ADD1H, ADD3
VMALF X1, YDIG, ADD2H, ADD4
VMALHF X0, YDIG, ADD1H, ADD3H // ADD1H Free
VMALHF X1, YDIG, ADD2H, ADD4H // ADD2H Free
VZERO ZER
VL 32(CPOOL), SEL1
VPERM ZER, ADD1, SEL1, RED3 // [d0 0 0 d0]
VSLDB $12, ADD2, ADD1, T0 // ADD1 Free
VSLDB $12, ZER, ADD2, T1 // ADD2 Free
VACCQ T0, ADD3, CAR1
VAQ T0, ADD3, T0 // ADD3 Free
VACCCQ T1, ADD4, CAR1, T2
VACQ T1, ADD4, CAR1, T1 // ADD4 Free
VL 48(CPOOL), SEL2
VL 64(CPOOL), SEL3
VL 80(CPOOL), SEL4
VPERM RED3, T0, SEL2, RED1 // [d0 0 d1 d0]
VPERM RED3, T0, SEL3, RED2 // [ 0 d1 d0 d1]
VPERM RED3, T0, SEL4, RED3 // [ 0 0 d1 d0]
VSQ RED3, RED2, RED2 // Guaranteed not to underflow
VSLDB $12, T1, T0, T0
VSLDB $12, T2, T1, T1
VACCQ T0, ADD3H, CAR1
VAQ T0, ADD3H, T0
VACCCQ T1, ADD4H, CAR1, T2
VACQ T1, ADD4H, CAR1, T1
// ---------------------------------------------------
VREPF $1, Y0, YDIG
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF X0, YDIG, T0, ADD1 // T0 Free->ADD1
VMALF X1, YDIG, T1, ADD2 // T1 Free->ADD2
VREPF $0, Y0, YDIG
VMALF X0, YDIG, ADD1H, ADD3
VMALF X1, YDIG, ADD2H, ADD4
VMALHF X0, YDIG, ADD1H, ADD3H // ADD1H Free->ADD3H
VMALHF X1, YDIG, ADD2H, ADD4H // ADD2H Free->ADD4H , YDIG Free->ZER
VZERO ZER
VL 32(CPOOL), SEL1
VPERM ZER, ADD1, SEL1, RED3 // [d0 0 0 d0]
VSLDB $12, ADD2, ADD1, T0 // ADD1 Free->T0
VSLDB $12, T2, ADD2, T1 // ADD2 Free->T1, T2 Free
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, T2
VACQ T1, RED2, CAR1, T1
VACCQ T0, ADD3, CAR1
VAQ T0, ADD3, T0
VACCCQ T1, ADD4, CAR1, CAR2
VACQ T1, ADD4, CAR1, T1
VAQ T2, CAR2, T2
VL 48(CPOOL), SEL2
VL 64(CPOOL), SEL3
VL 80(CPOOL), SEL4
VPERM RED3, T0, SEL2, RED1 // [d0 0 d1 d0]
VPERM RED3, T0, SEL3, RED2 // [ 0 d1 d0 d1]
VPERM RED3, T0, SEL4, RED3 // [ 0 0 d1 d0]
VSQ RED3, RED2, RED2 // Guaranteed not to underflow
VSLDB $12, T1, T0, T0
VSLDB $12, T2, T1, T1
VACCQ T0, ADD3H, CAR1
VAQ T0, ADD3H, T0
VACCCQ T1, ADD4H, CAR1, T2
VACQ T1, ADD4H, CAR1, T1
// ---------------------------------------------------
VREPF $3, Y1, YDIG
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF X0, YDIG, T0, ADD1
VMALF X1, YDIG, T1, ADD2
VREPF $2, Y1, YDIG
VMALF X0, YDIG, ADD1H, ADD3
VMALF X1, YDIG, ADD2H, ADD4
VMALHF X0, YDIG, ADD1H, ADD3H // ADD1H Free
VMALHF X1, YDIG, ADD2H, ADD4H // ADD2H Free
VZERO ZER
VL 32(CPOOL), SEL1
VPERM ZER, ADD1, SEL1, RED3 // [d0 0 0 d0]
VSLDB $12, ADD2, ADD1, T0 // ADD1 Free
VSLDB $12, T2, ADD2, T1 // ADD2 Free
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, T2
VACQ T1, RED2, CAR1, T1
VACCQ T0, ADD3, CAR1
VAQ T0, ADD3, T0
VACCCQ T1, ADD4, CAR1, CAR2
VACQ T1, ADD4, CAR1, T1
VAQ T2, CAR2, T2
VL 48(CPOOL), SEL2
VL 64(CPOOL), SEL3
VL 80(CPOOL), SEL4
VPERM RED3, T0, SEL2, RED1 // [d0 0 d1 d0]
VPERM RED3, T0, SEL3, RED2 // [ 0 d1 d0 d1]
VPERM RED3, T0, SEL4, RED3 // [ 0 0 d1 d0]
VSQ RED3, RED2, RED2 // Guaranteed not to underflow
VSLDB $12, T1, T0, T0
VSLDB $12, T2, T1, T1
VACCQ T0, ADD3H, CAR1
VAQ T0, ADD3H, T0
VACCCQ T1, ADD4H, CAR1, T2
VACQ T1, ADD4H, CAR1, T1
// ---------------------------------------------------
VREPF $1, Y1, YDIG
VMALHF X0, YDIG, T0, ADD1H
VMALHF X1, YDIG, T1, ADD2H
VMALF X0, YDIG, T0, ADD1
VMALF X1, YDIG, T1, ADD2
VREPF $0, Y1, YDIG
VMALF X0, YDIG, ADD1H, ADD3
VMALF X1, YDIG, ADD2H, ADD4
VMALHF X0, YDIG, ADD1H, ADD3H
VMALHF X1, YDIG, ADD2H, ADD4H
VZERO ZER
VL 32(CPOOL), SEL1
VPERM ZER, ADD1, SEL1, RED3 // [d0 0 0 d0]
VSLDB $12, ADD2, ADD1, T0
VSLDB $12, T2, ADD2, T1
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, T2
VACQ T1, RED2, CAR1, T1
VACCQ T0, ADD3, CAR1
VAQ T0, ADD3, T0
VACCCQ T1, ADD4, CAR1, CAR2
VACQ T1, ADD4, CAR1, T1
VAQ T2, CAR2, T2
VL 96(CPOOL), SEL5
VL 112(CPOOL), SEL6
VPERM T0, RED3, SEL5, RED2 // [d1 d0 d1 d0]
VPERM T0, RED3, SEL6, RED1 // [ 0 d1 d0 0]
VSQ RED1, RED2, RED2 // Guaranteed not to underflow
VSLDB $12, T1, T0, T0
VSLDB $12, T2, T1, T1
VACCQ T0, ADD3H, CAR1
VAQ T0, ADD3H, T0
VACCCQ T1, ADD4H, CAR1, T2
VACQ T1, ADD4H, CAR1, T1
VACCQ T0, RED1, CAR1
VAQ T0, RED1, T0
VACCCQ T1, RED2, CAR1, CAR2
VACQ T1, RED2, CAR1, T1
VAQ T2, CAR2, T2
// ---------------------------------------------------
VZERO RED3
VSCBIQ P0, T0, CAR1
VSQ P0, T0, ADD1H
VSBCBIQ T1, P1, CAR1, CAR2
VSBIQ T1, P1, CAR1, ADD2H
VSBIQ T2, RED3, CAR2, T2
// what output to use, ADD2H||ADD1H or T1||T0?
VSEL T0, ADD1H, T2, T0
VSEL T1, ADD2H, T2, T1
RET
#undef CPOOL
#undef X0
#undef X1
#undef Y0
#undef Y1
#undef T0
#undef T1
#undef P0
#undef P1
#undef SEL1
#undef SEL2
#undef SEL3
#undef SEL4
#undef SEL5
#undef SEL6
#undef YDIG
#undef ADD1H
#undef ADD2H
#undef ADD3
#undef ADD4
#undef RED1
#undef RED2
#undef RED3
#undef T2
#undef ADD1
#undef ADD2
#undef ADD3H
#undef ADD4H
#undef ZER
#undef CAR1
#undef CAR2
#define p256SubInternal(T1, T0, X1, X0, Y1, Y0) \
VZERO ZER \
VSCBIQ Y0, X0, CAR1 \
VSQ Y0, X0, T0 \
VSBCBIQ X1, Y1, CAR1, SEL1 \
VSBIQ X1, Y1, CAR1, T1 \
VSQ SEL1, ZER, SEL1 \
\
VACCQ T0, PL, CAR1 \
VAQ T0, PL, TT0 \
VACQ T1, PH, CAR1, TT1 \
\
VSEL T0, TT0, SEL1, T0 \
VSEL T1, TT1, SEL1, T1 \
#define p256AddInternal(T1, T0, X1, X0, Y1, Y0) \
VACCQ X0, Y0, CAR1 \
VAQ X0, Y0, T0 \
VACCCQ X1, Y1, CAR1, T2 \
VACQ X1, Y1, CAR1, T1 \
\
VZERO ZER \
VSCBIQ PL, T0, CAR1 \
VSQ PL, T0, TT0 \
VSBCBIQ T1, PH, CAR1, CAR2 \
VSBIQ T1, PH, CAR1, TT1 \
VSBIQ T2, ZER, CAR2, SEL1 \
\
VSEL T0, TT0, SEL1, T0 \
VSEL T1, TT1, SEL1, T1
#define p256HalfInternal(T1, T0, X1, X0) \
VZERO ZER \
VSBIQ ZER, ZER, X0, SEL1 \
\
VACCQ X0, PL, CAR1 \
VAQ X0, PL, T0 \
VACCCQ X1, PH, CAR1, T2 \
VACQ X1, PH, CAR1, T1 \
\
VSEL X0, T0, SEL1, T0 \
VSEL X1, T1, SEL1, T1 \
VSEL ZER, T2, SEL1, T2 \
\
VSLDB $15, T2, ZER, TT1 \
VSLDB $15, T1, ZER, TT0 \
VREPIB $1, SEL1 \
VSRL SEL1, T0, T0 \
VSRL SEL1, T1, T1 \
VREPIB $7, SEL1 \
VSL SEL1, TT0, TT0 \
VSL SEL1, TT1, TT1 \
VO T0, TT0, T0 \
VO T1, TT1, T1
// ---------------------------------------
// func p256MulAsm(res, in1, in2 []byte)
#define res_ptr R1
#define x_ptr R2
#define y_ptr R3
#define CPOOL R4
// Parameters
#define X0 V0
#define X1 V1
#define Y0 V2
#define Y1 V3
#define T0 V4
#define T1 V5
// Constants
#define P0 V30
#define P1 V31
TEXT ·p256MulAsm(SB), NOSPLIT, $0
MOVD res+0(FP), res_ptr
MOVD in1+24(FP), x_ptr
MOVD in2+48(FP), y_ptr
VL (1*16)(x_ptr), X0
VL (0*16)(x_ptr), X1
VL (1*16)(y_ptr), Y0
VL (0*16)(y_ptr), Y1
MOVD $p256mul<>+0x00(SB), CPOOL
VL 16(CPOOL), P0
VL 0(CPOOL), P1
CALL p256MulInternal<>(SB)
VST T0, (1*16)(res_ptr)
VST T1, (0*16)(res_ptr)
RET
#undef res_ptr
#undef x_ptr
#undef y_ptr
#undef CPOOL
#undef X0
#undef X1
#undef Y0
#undef Y1
#undef T0
#undef T1
#undef P0
#undef P1
// Point add with P2 being affine point
// If sign == 1 -> P2 = -P2
// If sel == 0 -> P3 = P1
// if zero == 0 -> P3 = P2
// p256PointAddAffineAsm(P3, P1, P2 *p256Point, sign, sel, zero int)
#define P3ptr R1
#define P1ptr R2
#define P2ptr R3
#define CPOOL R4
// Temporaries in REGs
#define Y2L V15
#define Y2H V16
#define T1L V17
#define T1H V18
#define T2L V19
#define T2H V20
#define T3L V21
#define T3H V22
#define T4L V23
#define T4H V24
// Temps for Sub and Add
#define TT0 V11
#define TT1 V12
#define T2 V13
// p256MulAsm Parameters
#define X0 V0
#define X1 V1
#define Y0 V2
#define Y1 V3
#define T0 V4
#define T1 V5
#define PL V30
#define PH V31
// Names for zero/sel selects
#define X1L V0
#define X1H V1
#define Y1L V2 // p256MulAsmParmY
#define Y1H V3 // p256MulAsmParmY
#define Z1L V4
#define Z1H V5
#define X2L V0
#define X2H V1
#define Z2L V4
#define Z2H V5
#define X3L V17 // T1L
#define X3H V18 // T1H
#define Y3L V21 // T3L
#define Y3H V22 // T3H
#define Z3L V28
#define Z3H V29
#define ZER V6
#define SEL1 V7
#define CAR1 V8
#define CAR2 V9
/* *
* Three operand formula:
* Source: 2004 Hankerson–Menezes–Vanstone, page 91.
* T1 = Z1²
* T2 = T1*Z1
* T1 = T1*X2
* T2 = T2*Y2
* T1 = T1-X1
* T2 = T2-Y1
* Z3 = Z1*T1
* T3 = T1²
* T4 = T3*T1
* T3 = T3*X1
* T1 = 2*T3
* X3 = T2²
* X3 = X3-T1
* X3 = X3-T4
* T3 = T3-X3
* T3 = T3*T2
* T4 = T4*Y1
* Y3 = T3-T4
* Three operand formulas, but with MulInternal X,Y used to store temps
X=Z1; Y=Z1; MUL;T- // T1 = Z1² T1
X=T ; Y- ; MUL;T2=T // T2 = T1*Z1 T1 T2
X- ; Y=X2; MUL;T1=T // T1 = T1*X2 T1 T2
X=T2; Y=Y2; MUL;T- // T2 = T2*Y2 T1 T2
SUB(T2<T-Y1) // T2 = T2-Y1 T1 T2
SUB(Y<T1-X1) // T1 = T1-X1 T1 T2
X=Z1; Y- ; MUL;Z3:=T// Z3 = Z1*T1 T2
X=Y; Y- ; MUL;X=T // T3 = T1*T1 T2
X- ; Y- ; MUL;T4=T // T4 = T3*T1 T2 T4
X- ; Y=X1; MUL;T3=T // T3 = T3*X1 T2 T3 T4
ADD(T1<T+T) // T1 = T3+T3 T1 T2 T3 T4
X=T2; Y=T2; MUL;T- // X3 = T2*T2 T1 T2 T3 T4
SUB(T<T-T1) // X3 = X3-T1 T1 T2 T3 T4
SUB(T<T-T4) X3:=T // X3 = X3-T4 T2 T3 T4
SUB(X<T3-T) // T3 = T3-X3 T2 T3 T4
X- ; Y- ; MUL;T3=T // T3 = T3*T2 T2 T3 T4
X=T4; Y=Y1; MUL;T- // T4 = T4*Y1 T3 T4
SUB(T<T3-T) Y3:=T // Y3 = T3-T4 T3 T4
*/
TEXT ·p256PointAddAffineAsm(SB), NOSPLIT, $0
MOVD P3+0(FP), P3ptr
MOVD P1+8(FP), P1ptr
MOVD P2+16(FP), P2ptr
MOVD $p256mul<>+0x00(SB), CPOOL
VL 16(CPOOL), PL
VL 0(CPOOL), PH
// if (sign == 1) {
// Y2 = fromBig(new(big.Int).Mod(new(big.Int).Sub(p256.P, new(big.Int).SetBytes(Y2)), p256.P)) // Y2 = P-Y2
// }
VL 32(P2ptr), Y2H
VL 48(P2ptr), Y2L
VLREPG sign+24(FP), SEL1
VZERO ZER
VCEQG SEL1, ZER, SEL1
VSCBIQ Y2L, PL, CAR1
VSQ Y2L, PL, T1L
VSBIQ PH, Y2H, CAR1, T1H
VSEL Y2L, T1L, SEL1, Y2L
VSEL Y2H, T1H, SEL1, Y2H
/* *
* Three operand formula:
* Source: 2004 Hankerson–Menezes–Vanstone, page 91.
*/
// X=Z1; Y=Z1; MUL; T- // T1 = Z1² T1
VL 64(P1ptr), X1 // Z1H
VL 80(P1ptr), X0 // Z1L
VLR X0, Y0
VLR X1, Y1
CALL p256MulInternal<>(SB)
// X=T ; Y- ; MUL; T2=T // T2 = T1*Z1 T1 T2
VLR T0, X0
VLR T1, X1
CALL p256MulInternal<>(SB)
VLR T0, T2L
VLR T1, T2H
// X- ; Y=X2; MUL; T1=T // T1 = T1*X2 T1 T2
VL 0(P2ptr), Y1 // X2H
VL 16(P2ptr), Y0 // X2L
CALL p256MulInternal<>(SB)
VLR T0, T1L
VLR T1, T1H
// X=T2; Y=Y2; MUL; T- // T2 = T2*Y2 T1 T2
VLR T2L, X0
VLR T2H, X1
VLR Y2L, Y0
VLR Y2H, Y1
CALL p256MulInternal<>(SB)
// SUB(T2<T-Y1) // T2 = T2-Y1 T1 T2
VL 32(P1ptr), Y1H
VL 48(P1ptr), Y1L
p256SubInternal(T2H,T2L,T1,T0,Y1H,Y1L)
// SUB(Y<T1-X1) // T1 = T1-X1 T1 T2
VL 0(P1ptr), X1H
VL 16(P1ptr), X1L
p256SubInternal(Y1,Y0,T1H,T1L,X1H,X1L)
// X=Z1; Y- ; MUL; Z3:=T// Z3 = Z1*T1 T2
VL 64(P1ptr), X1 // Z1H
VL 80(P1ptr), X0 // Z1L
CALL p256MulInternal<>(SB)
// VST T1, 64(P3ptr)
// VST T0, 80(P3ptr)
VLR T0, Z3L
VLR T1, Z3H
// X=Y; Y- ; MUL; X=T // T3 = T1*T1 T2
VLR Y0, X0
VLR Y1, X1
CALL p256MulInternal<>(SB)
VLR T0, X0
VLR T1, X1
// X- ; Y- ; MUL; T4=T // T4 = T3*T1 T2 T4
CALL p256MulInternal<>(SB)
VLR T0, T4L
VLR T1, T4H
// X- ; Y=X1; MUL; T3=T // T3 = T3*X1 T2 T3 T4
VL 0(P1ptr), Y1 // X1H
VL 16(P1ptr), Y0 // X1L
CALL p256MulInternal<>(SB)
VLR T0, T3L
VLR T1, T3H
// ADD(T1<T+T) // T1 = T3+T3 T1 T2 T3 T4
p256AddInternal(T1H,T1L, T1,T0,T1,T0)
// X=T2; Y=T2; MUL; T- // X3 = T2*T2 T1 T2 T3 T4
VLR T2L, X0
VLR T2H, X1
VLR T2L, Y0
VLR T2H, Y1
CALL p256MulInternal<>(SB)
// SUB(T<T-T1) // X3 = X3-T1 T1 T2 T3 T4 (T1 = X3)
p256SubInternal(T1,T0,T1,T0,T1H,T1L)
// SUB(T<T-T4) X3:=T // X3 = X3-T4 T2 T3 T4
p256SubInternal(T1,T0,T1,T0,T4H,T4L)
VLR T0, X3L
VLR T1, X3H
// SUB(X<T3-T) // T3 = T3-X3 T2 T3 T4
p256SubInternal(X1,X0,T3H,T3L,T1,T0)
// X- ; Y- ; MUL; T3=T // T3 = T3*T2 T2 T3 T4
CALL p256MulInternal<>(SB)
VLR T0, T3L
VLR T1, T3H
// X=T4; Y=Y1; MUL; T- // T4 = T4*Y1 T3 T4
VLR T4L, X0
VLR T4H, X1
VL 32(P1ptr), Y1 // Y1H
VL 48(P1ptr), Y0 // Y1L
CALL p256MulInternal<>(SB)
// SUB(T<T3-T) Y3:=T // Y3 = T3-T4 T3 T4 (T3 = Y3)
p256SubInternal(Y3H,Y3L,T3H,T3L,T1,T0)
// if (sel == 0) {
// copy(P3.x[:], X1)
// copy(P3.y[:], Y1)
// copy(P3.z[:], Z1)
// }
VL 0(P1ptr), X1H
VL 16(P1ptr), X1L
// Y1 already loaded, left over from addition
VL 64(P1ptr), Z1H
VL 80(P1ptr), Z1L
VLREPG sel+32(FP), SEL1
VZERO ZER
VCEQG SEL1, ZER, SEL1
VSEL X1L, X3L, SEL1, X3L
VSEL X1H, X3H, SEL1, X3H
VSEL Y1L, Y3L, SEL1, Y3L
VSEL Y1H, Y3H, SEL1, Y3H
VSEL Z1L, Z3L, SEL1, Z3L
VSEL Z1H, Z3H, SEL1, Z3H
// if (zero == 0) {
// copy(P3.x[:], X2)
// copy(P3.y[:], Y2)
// copy(P3.z[:], []byte{0x00, 0x00, 0x00, 0x00, 0xff, 0xff, 0xff, 0xfe, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
// 0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x01}) //(p256.z*2^256)%p
// }
VL 0(P2ptr), X2H
VL 16(P2ptr), X2L
// Y2 already loaded
VL 128(CPOOL), Z2H
VL 144(CPOOL), Z2L
VLREPG zero+40(FP), SEL1
VZERO ZER
VCEQG SEL1, ZER, SEL1
VSEL X2L, X3L, SEL1, X3L
VSEL X2H, X3H, SEL1, X3H
VSEL Y2L, Y3L, SEL1, Y3L
VSEL Y2H, Y3H, SEL1, Y3H
VSEL Z2L, Z3L, SEL1, Z3L
VSEL Z2H, Z3H, SEL1, Z3H
// All done, store out the result!!!
VST X3H, 0(P3ptr)
VST X3L, 16(P3ptr)
VST Y3H, 32(P3ptr)
VST Y3L, 48(P3ptr)
VST Z3H, 64(P3ptr)
VST Z3L, 80(P3ptr)
RET
#undef P3ptr
#undef P1ptr
#undef P2ptr
#undef CPOOL
#undef Y2L
#undef Y2H
#undef T1L
#undef T1H
#undef T2L
#undef T2H
#undef T3L
#undef T3H
#undef T4L
#undef T4H
#undef TT0
#undef TT1
#undef T2
#undef X0
#undef X1
#undef Y0
#undef Y1
#undef T0
#undef T1
#undef PL
#undef PH
#undef X1L
#undef X1H
#undef Y1L
#undef Y1H
#undef Z1L
#undef Z1H
#undef X2L
#undef X2H
#undef Z2L
#undef Z2H
#undef X3L
#undef X3H
#undef Y3L
#undef Y3H
#undef Z3L
#undef Z3H
#undef ZER
#undef SEL1
#undef CAR1
#undef CAR2
// p256PointDoubleAsm(P3, P1 *p256Point)
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian.html#doubling-dbl-2007-bl
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw.html
// http://www.hyperelliptic.org/EFD/g1p/auto-shortw-projective-3.html
#define P3ptr R1
#define P1ptr R2
#define CPOOL R4
// Temporaries in REGs
#define X3L V15
#define X3H V16
#define Y3L V17
#define Y3H V18
#define T1L V19
#define T1H V20
#define T2L V21
#define T2H V22
#define T3L V23
#define T3H V24
#define X1L V6
#define X1H V7
#define Y1L V8
#define Y1H V9
#define Z1L V10
#define Z1H V11
// Temps for Sub and Add
#define TT0 V11
#define TT1 V12
#define T2 V13
// p256MulAsm Parameters
#define X0 V0
#define X1 V1
#define Y0 V2
#define Y1 V3
#define T0 V4
#define T1 V5
#define PL V30
#define PH V31
#define Z3L V23
#define Z3H V24
#define ZER V26
#define SEL1 V27
#define CAR1 V28
#define CAR2 V29
/*
* http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2004-hmv
* Cost: 4M + 4S + 1*half + 5add + 2*2 + 1*3.
* Source: 2004 Hankerson–Menezes–Vanstone, page 91.
* A = 3(X₁-Z₁²)×(X₁+Z₁²)
* B = 2Y₁
* Z₃ = B×Z₁
* C = B²
* D = C×X₁
* X₃ = A²-2D
* Y₃ = (D-X₃)×A-C²/2
*
* Three-operand formula:
* T1 = Z1²
* T2 = X1-T1
* T1 = X1+T1
* T2 = T2*T1
* T2 = 3*T2
* Y3 = 2*Y1
* Z3 = Y3*Z1
* Y3 = Y3²
* T3 = Y3*X1
* Y3 = Y3²
* Y3 = half*Y3
* X3 = T2²
* T1 = 2*T3
* X3 = X3-T1
* T1 = T3-X3
* T1 = T1*T2
* Y3 = T1-Y3
*/
TEXT ·p256PointDoubleAsm(SB), NOSPLIT, $0
MOVD P3+0(FP), P3ptr
MOVD P1+8(FP), P1ptr
MOVD $p256mul<>+0x00(SB), CPOOL
VL 16(CPOOL), PL
VL 0(CPOOL), PH
// X=Z1; Y=Z1; MUL; T- // T1 = Z1²
VL 64(P1ptr), X1 // Z1H
VL 80(P1ptr), X0 // Z1L
VLR X0, Y0
VLR X1, Y1
CALL p256MulInternal<>(SB)
// SUB(X<X1-T) // T2 = X1-T1
VL 0(P1ptr), X1H
VL 16(P1ptr), X1L
p256SubInternal(X1,X0,X1H,X1L,T1,T0)
// ADD(Y<X1+T) // T1 = X1+T1
p256AddInternal(Y1,Y0,X1H,X1L,T1,T0)
// X- ; Y- ; MUL; T- // T2 = T2*T1
CALL p256MulInternal<>(SB)
// ADD(T2<T+T); ADD(T2<T2+T) // T2 = 3*T2
p256AddInternal(T2H,T2L,T1,T0,T1,T0)
p256AddInternal(T2H,T2L,T2H,T2L,T1,T0)
// ADD(X<Y1+Y1) // Y3 = 2*Y1
VL 32(P1ptr), Y1H
VL 48(P1ptr), Y1L
p256AddInternal(X1,X0,Y1H,Y1L,Y1H,Y1L)
// X- ; Y=Z1; MUL; Z3:=T // Z3 = Y3*Z1
VL 64(P1ptr), Y1 // Z1H
VL 80(P1ptr), Y0 // Z1L
CALL p256MulInternal<>(SB)
VST T1, 64(P3ptr)
VST T0, 80(P3ptr)
// X- ; Y=X ; MUL; T- // Y3 = Y3²
VLR X0, Y0
VLR X1, Y1
CALL p256MulInternal<>(SB)
// X=T ; Y=X1; MUL; T3=T // T3 = Y3*X1
VLR T0, X0
VLR T1, X1
VL 0(P1ptr), Y1
VL 16(P1ptr), Y0
CALL p256MulInternal<>(SB)
VLR T0, T3L
VLR T1, T3H
// X- ; Y=X ; MUL; T- // Y3 = Y3²
VLR X0, Y0
VLR X1, Y1
CALL p256MulInternal<>(SB)
// HAL(Y3<T) // Y3 = half*Y3
p256HalfInternal(Y3H,Y3L, T1,T0)
// X=T2; Y=T2; MUL; T- // X3 = T2²
VLR T2L, X0
VLR T2H, X1
VLR T2L, Y0
VLR T2H, Y1
CALL p256MulInternal<>(SB)
// ADD(T1<T3+T3) // T1 = 2*T3
p256AddInternal(T1H,T1L,T3H,T3L,T3H,T3L)
// SUB(X3<T-T1) X3:=X3 // X3 = X3-T1
p256SubInternal(X3H,X3L,T1,T0,T1H,T1L)
VST X3H, 0(P3ptr)
VST X3L, 16(P3ptr)
// SUB(X<T3-X3) // T1 = T3-X3
p256SubInternal(X1,X0,T3H,T3L,X3H,X3L)
// X- ; Y- ; MUL; T- // T1 = T1*T2
CALL p256MulInternal<>(SB)
// SUB(Y3<T-Y3) // Y3 = T1-Y3
p256SubInternal(Y3H,Y3L,T1,T0,Y3H,Y3L)
VST Y3H, 32(P3ptr)
VST Y3L, 48(P3ptr)
RET
#undef P3ptr
#undef P1ptr
#undef CPOOL
#undef X3L
#undef X3H
#undef Y3L
#undef Y3H
#undef T1L
#undef T1H
#undef T2L
#undef T2H
#undef T3L
#undef T3H
#undef X1L
#undef X1H
#undef Y1L
#undef Y1H
#undef Z1L
#undef Z1H
#undef TT0
#undef TT1
#undef T2
#undef X0
#undef X1
#undef Y0
#undef Y1
#undef T0
#undef T1
#undef PL
#undef PH
#undef Z3L
#undef Z3H
#undef ZER
#undef SEL1
#undef CAR1
#undef CAR2
// p256PointAddAsm(P3, P1, P2 *p256Point)
#define P3ptr R1
#define P1ptr R2
#define P2ptr R3
#define CPOOL R4
// Temporaries in REGs
#define T1L V16
#define T1H V17
#define T2L V18
#define T2H V19
#define U1L V20
#define U1H V21
#define S1L V22
#define S1H V23
#define HL V24
#define HH V25
#define RL V26
#define RH V27
// Temps for Sub and Add
#define ZER V6
#define SEL1 V7
#define CAR1 V8
#define CAR2 V9
#define TT0 V11
#define TT1 V12
#define T2 V13
// p256MulAsm Parameters
#define X0 V0
#define X1 V1
#define Y0 V2
#define Y1 V3
#define T0 V4
#define T1 V5
#define PL V30
#define PH V31
/*
* https://choucroutage.com/Papers/SideChannelAttacks/ctrsa-2011-brown.pdf "Software Implementation of the NIST Elliptic Curves Over Prime Fields"
*
* A = X₁×Z₂²
* B = Y₁×Z₂³
* C = X₂×Z₁²-A
* D = Y₂×Z₁³-B
* X₃ = D² - 2A×C² - C³
* Y₃ = D×(A×C² - X₃) - B×C³
* Z₃ = Z₁×Z₂×C
*
* Three-operand formula (adopted): http://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2
* Temp storage: T1,T2,U1,H,Z3=X3=Y3,S1,R
*
* T1 = Z1*Z1
* T2 = Z2*Z2
* U1 = X1*T2
* H = X2*T1
* H = H-U1
* Z3 = Z1*Z2
* Z3 = Z3*H << store-out Z3 result reg.. could override Z1, if slices have same backing array
*
* S1 = Z2*T2
* S1 = Y1*S1
* R = Z1*T1
* R = Y2*R
* R = R-S1
*
* T1 = H*H
* T2 = H*T1
* U1 = U1*T1
*
* X3 = R*R
* X3 = X3-T2
* T1 = 2*U1
* X3 = X3-T1 << store-out X3 result reg
*
* T2 = S1*T2
* Y3 = U1-X3
* Y3 = R*Y3
* Y3 = Y3-T2 << store-out Y3 result reg
// X=Z1; Y=Z1; MUL; T- // T1 = Z1*Z1
// X- ; Y=T ; MUL; R=T // R = Z1*T1
// X=X2; Y- ; MUL; H=T // H = X2*T1
// X=Z2; Y=Z2; MUL; T- // T2 = Z2*Z2
// X- ; Y=T ; MUL; S1=T // S1 = Z2*T2
// X=X1; Y- ; MUL; U1=T // U1 = X1*T2
// SUB(H<H-T) // H = H-U1
// X=Z1; Y=Z2; MUL; T- // Z3 = Z1*Z2
// X=T ; Y=H ; MUL; Z3:=T// Z3 = Z3*H << store-out Z3 result reg.. could override Z1, if slices have same backing array
// X=Y1; Y=S1; MUL; S1=T // S1 = Y1*S1
// X=Y2; Y=R ; MUL; T- // R = Y2*R
// SUB(R<T-S1) // R = R-S1
// X=H ; Y=H ; MUL; T- // T1 = H*H
// X- ; Y=T ; MUL; T2=T // T2 = H*T1
// X=U1; Y- ; MUL; U1=T // U1 = U1*T1
// X=R ; Y=R ; MUL; T- // X3 = R*R
// SUB(T<T-T2) // X3 = X3-T2
// ADD(X<U1+U1) // T1 = 2*U1
// SUB(T<T-X) X3:=T // X3 = X3-T1 << store-out X3 result reg
// SUB(Y<U1-T) // Y3 = U1-X3
// X=R ; Y- ; MUL; U1=T // Y3 = R*Y3
// X=S1; Y=T2; MUL; T- // T2 = S1*T2
// SUB(T<U1-T); Y3:=T // Y3 = Y3-T2 << store-out Y3 result reg
*/
TEXT ·p256PointAddAsm(SB), NOSPLIT, $0
MOVD P3+0(FP), P3ptr
MOVD P1+8(FP), P1ptr
MOVD P2+16(FP), P2ptr
MOVD $p256mul<>+0x00(SB), CPOOL
VL 16(CPOOL), PL
VL 0(CPOOL), PH
// X=Z1; Y=Z1; MUL; T- // T1 = Z1*Z1
VL 64(P1ptr), X1 // Z1H
VL 80(P1ptr), X0 // Z1L
VLR X0, Y0
VLR X1, Y1
CALL p256MulInternal<>(SB)
// X- ; Y=T ; MUL; R=T // R = Z1*T1
VLR T0, Y0
VLR T1, Y1
CALL p256MulInternal<>(SB)
VLR T0, RL
VLR T1, RH
// X=X2; Y- ; MUL; H=T // H = X2*T1
VL 0(P2ptr), X1 // X2H
VL 16(P2ptr), X0 // X2L
CALL p256MulInternal<>(SB)
VLR T0, HL
VLR T1, HH
// X=Z2; Y=Z2; MUL; T- // T2 = Z2*Z2
VL 64(P2ptr), X1 // Z2H
VL 80(P2ptr), X0 // Z2L
VLR X0, Y0
VLR X1, Y1
CALL p256MulInternal<>(SB)
// X- ; Y=T ; MUL; S1=T // S1 = Z2*T2
VLR T0, Y0
VLR T1, Y1
CALL p256MulInternal<>(SB)
VLR T0, S1L
VLR T1, S1H
// X=X1; Y- ; MUL; U1=T // U1 = X1*T2
VL 0(P1ptr), X1 // X1H
VL 16(P1ptr), X0 // X1L
CALL p256MulInternal<>(SB)
VLR T0, U1L
VLR T1, U1H
// SUB(H<H-T) // H = H-U1
p256SubInternal(HH,HL,HH,HL,T1,T0)
// X=Z1; Y=Z2; MUL; T- // Z3 = Z1*Z2
VL 64(P1ptr), X1 // Z1H
VL 80(P1ptr), X0 // Z1L
VL 64(P2ptr), Y1 // Z2H
VL 80(P2ptr), Y0 // Z2L
CALL p256MulInternal<>(SB)
// X=T ; Y=H ; MUL; Z3:=T// Z3 = Z3*H
VLR T0, X0
VLR T1, X1
VLR HL, Y0
VLR HH, Y1
CALL p256MulInternal<>(SB)
VST T1, 64(P3ptr)
VST T0, 80(P3ptr)
// X=Y1; Y=S1; MUL; S1=T // S1 = Y1*S1
VL 32(P1ptr), X1
VL 48(P1ptr), X0
VLR S1L, Y0
VLR S1H, Y1
CALL p256MulInternal<>(SB)
VLR T0, S1L
VLR T1, S1H
// X=Y2; Y=R ; MUL; T- // R = Y2*R
VL 32(P2ptr), X1
VL 48(P2ptr), X0
VLR RL, Y0
VLR RH, Y1
CALL p256MulInternal<>(SB)
// SUB(R<T-S1) // R = T-S1
p256SubInternal(RH,RL,T1,T0,S1H,S1L)
// X=H ; Y=H ; MUL; T- // T1 = H*H
VLR HL, X0
VLR HH, X1
VLR HL, Y0
VLR HH, Y1
CALL p256MulInternal<>(SB)
// X- ; Y=T ; MUL; T2=T // T2 = H*T1
VLR T0, Y0
VLR T1, Y1
CALL p256MulInternal<>(SB)
VLR T0, T2L
VLR T1, T2H
// X=U1; Y- ; MUL; U1=T // U1 = U1*T1
VLR U1L, X0
VLR U1H, X1
CALL p256MulInternal<>(SB)
VLR T0, U1L
VLR T1, U1H
// X=R ; Y=R ; MUL; T- // X3 = R*R
VLR RL, X0
VLR RH, X1
VLR RL, Y0
VLR RH, Y1
CALL p256MulInternal<>(SB)
// SUB(T<T-T2) // X3 = X3-T2
p256SubInternal(T1,T0,T1,T0,T2H,T2L)
// ADD(X<U1+U1) // T1 = 2*U1
p256AddInternal(X1,X0,U1H,U1L,U1H,U1L)
// SUB(T<T-X) X3:=T // X3 = X3-T1 << store-out X3 result reg
p256SubInternal(T1,T0,T1,T0,X1,X0)
VST T1, 0(P3ptr)
VST T0, 16(P3ptr)
// SUB(Y<U1-T) // Y3 = U1-X3
p256SubInternal(Y1,Y0,U1H,U1L,T1,T0)
// X=R ; Y- ; MUL; U1=T // Y3 = R*Y3
VLR RL, X0
VLR RH, X1
CALL p256MulInternal<>(SB)
VLR T0, U1L
VLR T1, U1H
// X=S1; Y=T2; MUL; T- // T2 = S1*T2
VLR S1L, X0
VLR S1H, X1
VLR T2L, Y0
VLR T2H, Y1
CALL p256MulInternal<>(SB)
// SUB(T<U1-T); Y3:=T // Y3 = Y3-T2 << store-out Y3 result reg
p256SubInternal(T1,T0,U1H,U1L,T1,T0)
VST T1, 32(P3ptr)
VST T0, 48(P3ptr)
RET