// Copyright 2018 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.
//go:build gc && !purego
#include "textflag.h"
// This implementation of Poly1305 uses the vector facility (vx)
// to process up to 2 blocks (32 bytes) per iteration using an
// algorithm based on the one described in:
//
// NEON crypto, Daniel J. Bernstein & Peter Schwabe
// https://cryptojedi.org/papers/neoncrypto-20120320.pdf
//
// This algorithm uses 5 26-bit limbs to represent a 130-bit
// value. These limbs are, for the most part, zero extended and
// placed into 64-bit vector register elements. Each vector
// register is 128-bits wide and so holds 2 of these elements.
// Using 26-bit limbs allows us plenty of headroom to accommodate
// accumulations before and after multiplication without
// overflowing either 32-bits (before multiplication) or 64-bits
// (after multiplication).
//
// In order to parallelise the operations required to calculate
// the sum we use two separate accumulators and then sum those
// in an extra final step. For compatibility with the generic
// implementation we perform this summation at the end of every
// updateVX call.
//
// To use two accumulators we must multiply the message blocks
// by r² rather than r. Only the final message block should be
// multiplied by r.
//
// Example:
//
// We want to calculate the sum (h) for a 64 byte message (m):
//
// h = m[0:16]r⁴ + m[16:32]r³ + m[32:48]r² + m[48:64]r
//
// To do this we split the calculation into the even indices
// and odd indices of the message. These form our SIMD 'lanes':
//
// h = m[ 0:16]r⁴ + m[32:48]r² + <- lane 0
// m[16:32]r³ + m[48:64]r <- lane 1
//
// To calculate this iteratively we refactor so that both lanes
// are written in terms of r² and r:
//
// h = (m[ 0:16]r² + m[32:48])r² + <- lane 0
// (m[16:32]r² + m[48:64])r <- lane 1
// ^ ^
// | coefficients for second iteration
// coefficients for first iteration
//
// So in this case we would have two iterations. In the first
// both lanes are multiplied by r². In the second only the
// first lane is multiplied by r² and the second lane is
// instead multiplied by r. This gives use the odd and even
// powers of r that we need from the original equation.
//
// Notation:
//
// h - accumulator
// r - key
// m - message
//
// [a, b] - SIMD register holding two 64-bit values
// [a, b, c, d] - SIMD register holding four 32-bit values
// xᵢ[n] - limb n of variable x with bit width i
//
// Limbs are expressed in little endian order, so for 26-bit
// limbs x₂₆[4] will be the most significant limb and x₂₆[0]
// will be the least significant limb.
// masking constants
#define MOD24 V0 // [0x0000000000ffffff, 0x0000000000ffffff] - mask low 24-bits
#define MOD26 V1 // [0x0000000003ffffff, 0x0000000003ffffff] - mask low 26-bits
// expansion constants (see EXPAND macro)
#define EX0 V2
#define EX1 V3
#define EX2 V4
// key (r², r or 1 depending on context)
#define R_0 V5
#define R_1 V6
#define R_2 V7
#define R_3 V8
#define R_4 V9
// precalculated coefficients (5r², 5r or 0 depending on context)
#define R5_1 V10
#define R5_2 V11
#define R5_3 V12
#define R5_4 V13
// message block (m)
#define M_0 V14
#define M_1 V15
#define M_2 V16
#define M_3 V17
#define M_4 V18
// accumulator (h)
#define H_0 V19
#define H_1 V20
#define H_2 V21
#define H_3 V22
#define H_4 V23
// temporary registers (for short-lived values)
#define T_0 V24
#define T_1 V25
#define T_2 V26
#define T_3 V27
#define T_4 V28
GLOBL ·constants<>(SB), RODATA, $0x30
// EX0
DATA ·constants<>+0x00(SB)/8, $0x0006050403020100
DATA ·constants<>+0x08(SB)/8, $0x1016151413121110
// EX1
DATA ·constants<>+0x10(SB)/8, $0x060c0b0a09080706
DATA ·constants<>+0x18(SB)/8, $0x161c1b1a19181716
// EX2
DATA ·constants<>+0x20(SB)/8, $0x0d0d0d0d0d0f0e0d
DATA ·constants<>+0x28(SB)/8, $0x1d1d1d1d1d1f1e1d
// MULTIPLY multiplies each lane of f and g, partially reduced
// modulo 2¹³⁰ - 5. The result, h, consists of partial products
// in each lane that need to be reduced further to produce the
// final result.
//
// h₁₃₀ = (f₁₃₀g₁₃₀) % 2¹³⁰ + (5f₁₃₀g₁₃₀) / 2¹³⁰
//
// Note that the multiplication by 5 of the high bits is
// achieved by precalculating the multiplication of four of the
// g coefficients by 5. These are g51-g54.
#define MULTIPLY(f0, f1, f2, f3, f4, g0, g1, g2, g3, g4, g51, g52, g53, g54, h0, h1, h2, h3, h4) \
VMLOF f0, g0, h0 \
VMLOF f0, g3, h3 \
VMLOF f0, g1, h1 \
VMLOF f0, g4, h4 \
VMLOF f0, g2, h2 \
VMLOF f1, g54, T_0 \
VMLOF f1, g2, T_3 \
VMLOF f1, g0, T_1 \
VMLOF f1, g3, T_4 \
VMLOF f1, g1, T_2 \
VMALOF f2, g53, h0, h0 \
VMALOF f2, g1, h3, h3 \
VMALOF f2, g54, h1, h1 \
VMALOF f2, g2, h4, h4 \
VMALOF f2, g0, h2, h2 \
VMALOF f3, g52, T_0, T_0 \
VMALOF f3, g0, T_3, T_3 \
VMALOF f3, g53, T_1, T_1 \
VMALOF f3, g1, T_4, T_4 \
VMALOF f3, g54, T_2, T_2 \
VMALOF f4, g51, h0, h0 \
VMALOF f4, g54, h3, h3 \
VMALOF f4, g52, h1, h1 \
VMALOF f4, g0, h4, h4 \
VMALOF f4, g53, h2, h2 \
VAG T_0, h0, h0 \
VAG T_3, h3, h3 \
VAG T_1, h1, h1 \
VAG T_4, h4, h4 \
VAG T_2, h2, h2
// REDUCE performs the following carry operations in four
// stages, as specified in Bernstein & Schwabe:
//
// 1: h₂₆[0]->h₂₆[1] h₂₆[3]->h₂₆[4]
// 2: h₂₆[1]->h₂₆[2] h₂₆[4]->h₂₆[0]
// 3: h₂₆[0]->h₂₆[1] h₂₆[2]->h₂₆[3]
// 4: h₂₆[3]->h₂₆[4]
//
// The result is that all of the limbs are limited to 26-bits
// except for h₂₆[1] and h₂₆[4] which are limited to 27-bits.
//
// Note that although each limb is aligned at 26-bit intervals
// they may contain values that exceed 2²⁶ - 1, hence the need
// to carry the excess bits in each limb.
#define REDUCE(h0, h1, h2, h3, h4) \
VESRLG $26, h0, T_0 \
VESRLG $26, h3, T_1 \
VN MOD26, h0, h0 \
VN MOD26, h3, h3 \
VAG T_0, h1, h1 \
VAG T_1, h4, h4 \
VESRLG $26, h1, T_2 \
VESRLG $26, h4, T_3 \
VN MOD26, h1, h1 \
VN MOD26, h4, h4 \
VESLG $2, T_3, T_4 \
VAG T_3, T_4, T_4 \
VAG T_2, h2, h2 \
VAG T_4, h0, h0 \
VESRLG $26, h2, T_0 \
VESRLG $26, h0, T_1 \
VN MOD26, h2, h2 \
VN MOD26, h0, h0 \
VAG T_0, h3, h3 \
VAG T_1, h1, h1 \
VESRLG $26, h3, T_2 \
VN MOD26, h3, h3 \
VAG T_2, h4, h4
// EXPAND splits the 128-bit little-endian values in0 and in1
// into 26-bit big-endian limbs and places the results into
// the first and second lane of d₂₆[0:4] respectively.
//
// The EX0, EX1 and EX2 constants are arrays of byte indices
// for permutation. The permutation both reverses the bytes
// in the input and ensures the bytes are copied into the
// destination limb ready to be shifted into their final
// position.
#define EXPAND(in0, in1, d0, d1, d2, d3, d4) \
VPERM in0, in1, EX0, d0 \
VPERM in0, in1, EX1, d2 \
VPERM in0, in1, EX2, d4 \
VESRLG $26, d0, d1 \
VESRLG $30, d2, d3 \
VESRLG $4, d2, d2 \
VN MOD26, d0, d0 \ // [in0₂₆[0], in1₂₆[0]]
VN MOD26, d3, d3 \ // [in0₂₆[3], in1₂₆[3]]
VN MOD26, d1, d1 \ // [in0₂₆[1], in1₂₆[1]]
VN MOD24, d4, d4 \ // [in0₂₆[4], in1₂₆[4]]
VN MOD26, d2, d2 // [in0₂₆[2], in1₂₆[2]]
// func updateVX(state *macState, msg []byte)
TEXT ·updateVX(SB), NOSPLIT, $0
MOVD state+0(FP), R1
LMG msg+8(FP), R2, R3 // R2=msg_base, R3=msg_len
// load EX0, EX1 and EX2
MOVD $·constants<>(SB), R5
VLM (R5), EX0, EX2
// generate masks
VGMG $(64-24), $63, MOD24 // [0x00ffffff, 0x00ffffff]
VGMG $(64-26), $63, MOD26 // [0x03ffffff, 0x03ffffff]
// load h (accumulator) and r (key) from state
VZERO T_1 // [0, 0]
VL 0(R1), T_0 // [h₆₄[0], h₆₄[1]]
VLEG $0, 16(R1), T_1 // [h₆₄[2], 0]
VL 24(R1), T_2 // [r₆₄[0], r₆₄[1]]
VPDI $0, T_0, T_2, T_3 // [h₆₄[0], r₆₄[0]]
VPDI $5, T_0, T_2, T_4 // [h₆₄[1], r₆₄[1]]
// unpack h and r into 26-bit limbs
// note: h₆₄[2] may have the low 3 bits set, so h₂₆[4] is a 27-bit value
VN MOD26, T_3, H_0 // [h₂₆[0], r₂₆[0]]
VZERO H_1 // [0, 0]
VZERO H_3 // [0, 0]
VGMG $(64-12-14), $(63-12), T_0 // [0x03fff000, 0x03fff000] - 26-bit mask with low 12 bits masked out
VESLG $24, T_1, T_1 // [h₆₄[2]<<24, 0]
VERIMG $-26&63, T_3, MOD26, H_1 // [h₂₆[1], r₂₆[1]]
VESRLG $+52&63, T_3, H_2 // [h₂₆[2], r₂₆[2]] - low 12 bits only
VERIMG $-14&63, T_4, MOD26, H_3 // [h₂₆[1], r₂₆[1]]
VESRLG $40, T_4, H_4 // [h₂₆[4], r₂₆[4]] - low 24 bits only
VERIMG $+12&63, T_4, T_0, H_2 // [h₂₆[2], r₂₆[2]] - complete
VO T_1, H_4, H_4 // [h₂₆[4], r₂₆[4]] - complete
// replicate r across all 4 vector elements
VREPF $3, H_0, R_0 // [r₂₆[0], r₂₆[0], r₂₆[0], r₂₆[0]]
VREPF $3, H_1, R_1 // [r₂₆[1], r₂₆[1], r₂₆[1], r₂₆[1]]
VREPF $3, H_2, R_2 // [r₂₆[2], r₂₆[2], r₂₆[2], r₂₆[2]]
VREPF $3, H_3, R_3 // [r₂₆[3], r₂₆[3], r₂₆[3], r₂₆[3]]
VREPF $3, H_4, R_4 // [r₂₆[4], r₂₆[4], r₂₆[4], r₂₆[4]]
// zero out lane 1 of h
VLEIG $1, $0, H_0 // [h₂₆[0], 0]
VLEIG $1, $0, H_1 // [h₂₆[1], 0]
VLEIG $1, $0, H_2 // [h₂₆[2], 0]
VLEIG $1, $0, H_3 // [h₂₆[3], 0]
VLEIG $1, $0, H_4 // [h₂₆[4], 0]
// calculate 5r (ignore least significant limb)
VREPIF $5, T_0
VMLF T_0, R_1, R5_1 // [5r₂₆[1], 5r₂₆[1], 5r₂₆[1], 5r₂₆[1]]
VMLF T_0, R_2, R5_2 // [5r₂₆[2], 5r₂₆[2], 5r₂₆[2], 5r₂₆[2]]
VMLF T_0, R_3, R5_3 // [5r₂₆[3], 5r₂₆[3], 5r₂₆[3], 5r₂₆[3]]
VMLF T_0, R_4, R5_4 // [5r₂₆[4], 5r₂₆[4], 5r₂₆[4], 5r₂₆[4]]
// skip r² calculation if we are only calculating one block
CMPBLE R3, $16, skip
// calculate r²
MULTIPLY(R_0, R_1, R_2, R_3, R_4, R_0, R_1, R_2, R_3, R_4, R5_1, R5_2, R5_3, R5_4, M_0, M_1, M_2, M_3, M_4)
REDUCE(M_0, M_1, M_2, M_3, M_4)
VGBM $0x0f0f, T_0
VERIMG $0, M_0, T_0, R_0 // [r₂₆[0], r²₂₆[0], r₂₆[0], r²₂₆[0]]
VERIMG $0, M_1, T_0, R_1 // [r₂₆[1], r²₂₆[1], r₂₆[1], r²₂₆[1]]
VERIMG $0, M_2, T_0, R_2 // [r₂₆[2], r²₂₆[2], r₂₆[2], r²₂₆[2]]
VERIMG $0, M_3, T_0, R_3 // [r₂₆[3], r²₂₆[3], r₂₆[3], r²₂₆[3]]
VERIMG $0, M_4, T_0, R_4 // [r₂₆[4], r²₂₆[4], r₂₆[4], r²₂₆[4]]
// calculate 5r² (ignore least significant limb)
VREPIF $5, T_0
VMLF T_0, R_1, R5_1 // [5r₂₆[1], 5r²₂₆[1], 5r₂₆[1], 5r²₂₆[1]]
VMLF T_0, R_2, R5_2 // [5r₂₆[2], 5r²₂₆[2], 5r₂₆[2], 5r²₂₆[2]]
VMLF T_0, R_3, R5_3 // [5r₂₆[3], 5r²₂₆[3], 5r₂₆[3], 5r²₂₆[3]]
VMLF T_0, R_4, R5_4 // [5r₂₆[4], 5r²₂₆[4], 5r₂₆[4], 5r²₂₆[4]]
loop:
CMPBLE R3, $32, b2 // 2 or fewer blocks remaining, need to change key coefficients
// load next 2 blocks from message
VLM (R2), T_0, T_1
// update message slice
SUB $32, R3
MOVD $32(R2), R2
// unpack message blocks into 26-bit big-endian limbs
EXPAND(T_0, T_1, M_0, M_1, M_2, M_3, M_4)
// add 2¹²⁸ to each message block value
VLEIB $4, $1, M_4
VLEIB $12, $1, M_4
multiply:
// accumulate the incoming message
VAG H_0, M_0, M_0
VAG H_3, M_3, M_3
VAG H_1, M_1, M_1
VAG H_4, M_4, M_4
VAG H_2, M_2, M_2
// multiply the accumulator by the key coefficient
MULTIPLY(M_0, M_1, M_2, M_3, M_4, R_0, R_1, R_2, R_3, R_4, R5_1, R5_2, R5_3, R5_4, H_0, H_1, H_2, H_3, H_4)
// carry and partially reduce the partial products
REDUCE(H_0, H_1, H_2, H_3, H_4)
CMPBNE R3, $0, loop
finish:
// sum lane 0 and lane 1 and put the result in lane 1
VZERO T_0
VSUMQG H_0, T_0, H_0
VSUMQG H_3, T_0, H_3
VSUMQG H_1, T_0, H_1
VSUMQG H_4, T_0, H_4
VSUMQG H_2, T_0, H_2
// reduce again after summation
// TODO(mundaym): there might be a more efficient way to do this
// now that we only have 1 active lane. For example, we could
// simultaneously pack the values as we reduce them.
REDUCE(H_0, H_1, H_2, H_3, H_4)
// carry h[1] through to h[4] so that only h[4] can exceed 2²⁶ - 1
// TODO(mundaym): in testing this final carry was unnecessary.
// Needs a proof before it can be removed though.
VESRLG $26, H_1, T_1
VN MOD26, H_1, H_1
VAQ T_1, H_2, H_2
VESRLG $26, H_2, T_2
VN MOD26, H_2, H_2
VAQ T_2, H_3, H_3
VESRLG $26, H_3, T_3
VN MOD26, H_3, H_3
VAQ T_3, H_4, H_4
// h is now < 2(2¹³⁰ - 5)
// Pack each lane in h₂₆[0:4] into h₁₂₈[0:1].
VESLG $26, H_1, H_1
VESLG $26, H_3, H_3
VO H_0, H_1, H_0
VO H_2, H_3, H_2
VESLG $4, H_2, H_2
VLEIB $7, $48, H_1
VSLB H_1, H_2, H_2
VO H_0, H_2, H_0
VLEIB $7, $104, H_1
VSLB H_1, H_4, H_3
VO H_3, H_0, H_0
VLEIB $7, $24, H_1
VSRLB H_1, H_4, H_1
// update state
VSTEG $1, H_0, 0(R1)
VSTEG $0, H_0, 8(R1)
VSTEG $1, H_1, 16(R1)
RET
b2: // 2 or fewer blocks remaining
CMPBLE R3, $16, b1
// Load the 2 remaining blocks (17-32 bytes remaining).
MOVD $-17(R3), R0 // index of final byte to load modulo 16
VL (R2), T_0 // load full 16 byte block
VLL R0, 16(R2), T_1 // load final (possibly partial) block and pad with zeros to 16 bytes
// The Poly1305 algorithm requires that a 1 bit be appended to
// each message block. If the final block is less than 16 bytes
// long then it is easiest to insert the 1 before the message
// block is split into 26-bit limbs. If, on the other hand, the
// final message block is 16 bytes long then we append the 1 bit
// after expansion as normal.
MOVBZ $1, R0
MOVD $-16(R3), R3 // index of byte in last block to insert 1 at (could be 16)
CMPBEQ R3, $16, 2(PC) // skip the insertion if the final block is 16 bytes long
VLVGB R3, R0, T_1 // insert 1 into the byte at index R3
// Split both blocks into 26-bit limbs in the appropriate lanes.
EXPAND(T_0, T_1, M_0, M_1, M_2, M_3, M_4)
// Append a 1 byte to the end of the second to last block.
VLEIB $4, $1, M_4
// Append a 1 byte to the end of the last block only if it is a
// full 16 byte block.
CMPBNE R3, $16, 2(PC)
VLEIB $12, $1, M_4
// Finally, set up the coefficients for the final multiplication.
// We have previously saved r and 5r in the 32-bit even indexes
// of the R_[0-4] and R5_[1-4] coefficient registers.
//
// We want lane 0 to be multiplied by r² so that can be kept the
// same. We want lane 1 to be multiplied by r so we need to move
// the saved r value into the 32-bit odd index in lane 1 by
// rotating the 64-bit lane by 32.
VGBM $0x00ff, T_0 // [0, 0xffffffffffffffff] - mask lane 1 only
VERIMG $32, R_0, T_0, R_0 // [_, r²₂₆[0], _, r₂₆[0]]
VERIMG $32, R_1, T_0, R_1 // [_, r²₂₆[1], _, r₂₆[1]]
VERIMG $32, R_2, T_0, R_2 // [_, r²₂₆[2], _, r₂₆[2]]
VERIMG $32, R_3, T_0, R_3 // [_, r²₂₆[3], _, r₂₆[3]]
VERIMG $32, R_4, T_0, R_4 // [_, r²₂₆[4], _, r₂₆[4]]
VERIMG $32, R5_1, T_0, R5_1 // [_, 5r²₂₆[1], _, 5r₂₆[1]]
VERIMG $32, R5_2, T_0, R5_2 // [_, 5r²₂₆[2], _, 5r₂₆[2]]
VERIMG $32, R5_3, T_0, R5_3 // [_, 5r²₂₆[3], _, 5r₂₆[3]]
VERIMG $32, R5_4, T_0, R5_4 // [_, 5r²₂₆[4], _, 5r₂₆[4]]
MOVD $0, R3
BR multiply
skip:
CMPBEQ R3, $0, finish
b1: // 1 block remaining
// Load the final block (1-16 bytes). This will be placed into
// lane 0.
MOVD $-1(R3), R0
VLL R0, (R2), T_0 // pad to 16 bytes with zeros
// The Poly1305 algorithm requires that a 1 bit be appended to
// each message block. If the final block is less than 16 bytes
// long then it is easiest to insert the 1 before the message
// block is split into 26-bit limbs. If, on the other hand, the
// final message block is 16 bytes long then we append the 1 bit
// after expansion as normal.
MOVBZ $1, R0
CMPBEQ R3, $16, 2(PC)
VLVGB R3, R0, T_0
// Set the message block in lane 1 to the value 0 so that it
// can be accumulated without affecting the final result.
VZERO T_1
// Split the final message block into 26-bit limbs in lane 0.
// Lane 1 will be contain 0.
EXPAND(T_0, T_1, M_0, M_1, M_2, M_3, M_4)
// Append a 1 byte to the end of the last block only if it is a
// full 16 byte block.
CMPBNE R3, $16, 2(PC)
VLEIB $4, $1, M_4
// We have previously saved r and 5r in the 32-bit even indexes
// of the R_[0-4] and R5_[1-4] coefficient registers.
//
// We want lane 0 to be multiplied by r so we need to move the
// saved r value into the 32-bit odd index in lane 0. We want
// lane 1 to be set to the value 1. This makes multiplication
// a no-op. We do this by setting lane 1 in every register to 0
// and then just setting the 32-bit index 3 in R_0 to 1.
VZERO T_0
MOVD $0, R0
MOVD $0x10111213, R12
VLVGP R12, R0, T_1 // [_, 0x10111213, _, 0x00000000]
VPERM T_0, R_0, T_1, R_0 // [_, r₂₆[0], _, 0]
VPERM T_0, R_1, T_1, R_1 // [_, r₂₆[1], _, 0]
VPERM T_0, R_2, T_1, R_2 // [_, r₂₆[2], _, 0]
VPERM T_0, R_3, T_1, R_3 // [_, r₂₆[3], _, 0]
VPERM T_0, R_4, T_1, R_4 // [_, r₂₆[4], _, 0]
VPERM T_0, R5_1, T_1, R5_1 // [_, 5r₂₆[1], _, 0]
VPERM T_0, R5_2, T_1, R5_2 // [_, 5r₂₆[2], _, 0]
VPERM T_0, R5_3, T_1, R5_3 // [_, 5r₂₆[3], _, 0]
VPERM T_0, R5_4, T_1, R5_4 // [_, 5r₂₆[4], _, 0]
// Set the value of lane 1 to be 1.
VLEIF $3, $1, R_0 // [_, r₂₆[0], _, 1]
MOVD $0, R3
BR multiply
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