#!/usr/bin/env perl # # Copyright (c) 2010-2011 Intel Corp. # Author: Vinodh.Gopal@intel.com # Jim Guilford # Erdinc.Ozturk@intel.com # Maxim.Perminov@intel.com # # More information about algorithm used can be found at: # http://www.cse.buffalo.edu/srds2009/escs2009_submission_Gopal.pdf # # ==================================================================== # Copyright (c) 2011 The OpenSSL Project. All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in # the documentation and/or other materials provided with the # distribution. # # 3. All advertising materials mentioning features or use of this # software must display the following acknowledgment: # "This product includes software developed by the OpenSSL Project # for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)" # # 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to # endorse or promote products derived from this software without # prior written permission. For written permission, please contact # licensing@OpenSSL.org. # # 5. Products derived from this software may not be called "OpenSSL" # nor may "OpenSSL" appear in their names without prior written # permission of the OpenSSL Project. # # 6. Redistributions of any form whatsoever must retain the following # acknowledgment: # "This product includes software developed by the OpenSSL Project # for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)" # # THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY # EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE # IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR # PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR # ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, # SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT # NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; # LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) # HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, # STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) # ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED # OF THE POSSIBILITY OF SUCH DAMAGE. # ==================================================================== $flavour = shift; $output = shift; if ($flavour =~ /\./) { $output = $flavour; undef $flavour; } my $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/); $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1; ( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or ( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or die "can't locate x86_64-xlate.pl"; open OUT,"| \"$^X\" $xlate $flavour $output"; *STDOUT=*OUT; use strict; my $code=".text\n\n"; my $m=0; # # Define x512 macros # #MULSTEP_512_ADD MACRO x7, x6, x5, x4, x3, x2, x1, x0, dst, src1, src2, add_src, tmp1, tmp2 # # uses rax, rdx, and args sub MULSTEP_512_ADD { my ($x, $DST, $SRC2, $ASRC, $OP, $TMP)=@_; my @X=@$x; # make a copy $code.=<<___; mov (+8*0)($SRC2), %rax mul $OP # rdx:rax = %OP * [0] mov ($ASRC), $X[0] add %rax, $X[0] adc \$0, %rdx mov $X[0], $DST ___ for(my $i=1;$i<8;$i++) { $code.=<<___; mov %rdx, $TMP mov (+8*$i)($SRC2), %rax mul $OP # rdx:rax = %OP * [$i] mov (+8*$i)($ASRC), $X[$i] add %rax, $X[$i] adc \$0, %rdx add $TMP, $X[$i] adc \$0, %rdx ___ } $code.=<<___; mov %rdx, $X[0] ___ } #MULSTEP_512 MACRO x7, x6, x5, x4, x3, x2, x1, x0, dst, src2, src1_val, tmp # # uses rax, rdx, and args sub MULSTEP_512 { my ($x, $DST, $SRC2, $OP, $TMP)=@_; my @X=@$x; # make a copy $code.=<<___; mov (+8*0)($SRC2), %rax mul $OP # rdx:rax = %OP * [0] add %rax, $X[0] adc \$0, %rdx mov $X[0], $DST ___ for(my $i=1;$i<8;$i++) { $code.=<<___; mov %rdx, $TMP mov (+8*$i)($SRC2), %rax mul $OP # rdx:rax = %OP * [$i] add %rax, $X[$i] adc \$0, %rdx add $TMP, $X[$i] adc \$0, %rdx ___ } $code.=<<___; mov %rdx, $X[0] ___ } # # Swizzle Macros # # macro to copy data from flat space to swizzled table #MACRO swizzle pDst, pSrc, tmp1, tmp2 # pDst and pSrc are modified sub swizzle { my ($pDst, $pSrc, $cnt, $d0)=@_; $code.=<<___; mov \$8, $cnt loop_$m: mov ($pSrc), $d0 mov $d0#w, ($pDst) shr \$16, $d0 mov $d0#w, (+64*1)($pDst) shr \$16, $d0 mov $d0#w, (+64*2)($pDst) shr \$16, $d0 mov $d0#w, (+64*3)($pDst) lea 8($pSrc), $pSrc lea 64*4($pDst), $pDst dec $cnt jnz loop_$m ___ $m++; } # macro to copy data from swizzled table to flat space #MACRO unswizzle pDst, pSrc, tmp*3 sub unswizzle { my ($pDst, $pSrc, $cnt, $d0, $d1)=@_; $code.=<<___; mov \$4, $cnt loop_$m: movzxw (+64*3+256*0)($pSrc), $d0 movzxw (+64*3+256*1)($pSrc), $d1 shl \$16, $d0 shl \$16, $d1 mov (+64*2+256*0)($pSrc), $d0#w mov (+64*2+256*1)($pSrc), $d1#w shl \$16, $d0 shl \$16, $d1 mov (+64*1+256*0)($pSrc), $d0#w mov (+64*1+256*1)($pSrc), $d1#w shl \$16, $d0 shl \$16, $d1 mov (+64*0+256*0)($pSrc), $d0#w mov (+64*0+256*1)($pSrc), $d1#w mov $d0, (+8*0)($pDst) mov $d1, (+8*1)($pDst) lea 256*2($pSrc), $pSrc lea 8*2($pDst), $pDst sub \$1, $cnt jnz loop_$m ___ $m++; } # # Data Structures # # Reduce Data # # # Offset Value # 0C0 Carries # 0B8 X2[10] # 0B0 X2[9] # 0A8 X2[8] # 0A0 X2[7] # 098 X2[6] # 090 X2[5] # 088 X2[4] # 080 X2[3] # 078 X2[2] # 070 X2[1] # 068 X2[0] # 060 X1[12] P[10] # 058 X1[11] P[9] Z[8] # 050 X1[10] P[8] Z[7] # 048 X1[9] P[7] Z[6] # 040 X1[8] P[6] Z[5] # 038 X1[7] P[5] Z[4] # 030 X1[6] P[4] Z[3] # 028 X1[5] P[3] Z[2] # 020 X1[4] P[2] Z[1] # 018 X1[3] P[1] Z[0] # 010 X1[2] P[0] Y[2] # 008 X1[1] Q[1] Y[1] # 000 X1[0] Q[0] Y[0] my $X1_offset = 0; # 13 qwords my $X2_offset = $X1_offset + 13*8; # 11 qwords my $Carries_offset = $X2_offset + 11*8; # 1 qword my $Q_offset = 0; # 2 qwords my $P_offset = $Q_offset + 2*8; # 11 qwords my $Y_offset = 0; # 3 qwords my $Z_offset = $Y_offset + 3*8; # 9 qwords my $Red_Data_Size = $Carries_offset + 1*8; # (25 qwords) # # Stack Frame # # # offset value # ... <old stack contents> # ... # 280 Garray # 278 tmp16[15] # ... ... # 200 tmp16[0] # 1F8 tmp[7] # ... ... # 1C0 tmp[0] # 1B8 GT[7] # ... ... # 180 GT[0] # 178 Reduce Data # ... ... # 0B8 Reduce Data # 0B0 reserved # 0A8 reserved # 0A0 reserved # 098 reserved # 090 reserved # 088 reduce result addr # 080 exp[8] # ... # 048 exp[1] # 040 exp[0] # 038 reserved # 030 loop_idx # 028 pg # 020 i # 018 pData ; arg 4 # 010 pG ; arg 2 # 008 pResult ; arg 1 # 000 rsp ; stack pointer before subtract my $rsp_offset = 0; my $pResult_offset = 8*1 + $rsp_offset; my $pG_offset = 8*1 + $pResult_offset; my $pData_offset = 8*1 + $pG_offset; my $i_offset = 8*1 + $pData_offset; my $pg_offset = 8*1 + $i_offset; my $loop_idx_offset = 8*1 + $pg_offset; my $reserved1_offset = 8*1 + $loop_idx_offset; my $exp_offset = 8*1 + $reserved1_offset; my $red_result_addr_offset= 8*9 + $exp_offset; my $reserved2_offset = 8*1 + $red_result_addr_offset; my $Reduce_Data_offset = 8*5 + $reserved2_offset; my $GT_offset = $Red_Data_Size + $Reduce_Data_offset; my $tmp_offset = 8*8 + $GT_offset; my $tmp16_offset = 8*8 + $tmp_offset; my $garray_offset = 8*16 + $tmp16_offset; my $mem_size = 8*8*32 + $garray_offset; # # Offsets within Reduce Data # # # struct MODF_2FOLD_MONT_512_C1_DATA { # UINT64 t[8][8]; # UINT64 m[8]; # UINT64 m1[8]; /* 2^768 % m */ # UINT64 m2[8]; /* 2^640 % m */ # UINT64 k1[2]; /* (- 1/m) % 2^128 */ # }; my $T = 0; my $M = 512; # = 8 * 8 * 8 my $M1 = 576; # = 8 * 8 * 9 /* += 8 * 8 */ my $M2 = 640; # = 8 * 8 * 10 /* += 8 * 8 */ my $K1 = 704; # = 8 * 8 * 11 /* += 8 * 8 */ # # FUNCTIONS # {{{ # # MULADD_128x512 : Function to multiply 128-bits (2 qwords) by 512-bits (8 qwords) # and add 512-bits (8 qwords) # to get 640 bits (10 qwords) # Input: 128-bit mul source: [rdi+8*1], rbp # 512-bit mul source: [rsi+8*n] # 512-bit add source: r15, r14, ..., r9, r8 # Output: r9, r8, r15, r14, r13, r12, r11, r10, [rcx+8*1], [rcx+8*0] # Clobbers all regs except: rcx, rsi, rdi $code.=<<___; .type MULADD_128x512,\@abi-omnipotent .align 16 MULADD_128x512: ___ &MULSTEP_512([map("%r$_",(8..15))], "(+8*0)(%rcx)", "%rsi", "%rbp", "%rbx"); $code.=<<___; mov (+8*1)(%rdi), %rbp ___ &MULSTEP_512([map("%r$_",(9..15,8))], "(+8*1)(%rcx)", "%rsi", "%rbp", "%rbx"); $code.=<<___; ret .size MULADD_128x512,.-MULADD_128x512 ___ }}} {{{ #MULADD_256x512 MACRO pDst, pA, pB, OP, TMP, X7, X6, X5, X4, X3, X2, X1, X0 # # Inputs: pDst: Destination (768 bits, 12 qwords) # pA: Multiplicand (1024 bits, 16 qwords) # pB: Multiplicand (512 bits, 8 qwords) # Dst = Ah * B + Al # where Ah is (in qwords) A[15:12] (256 bits) and Al is A[7:0] (512 bits) # Results in X3 X2 X1 X0 X7 X6 X5 X4 Dst[3:0] # Uses registers: arguments, RAX, RDX sub MULADD_256x512 { my ($pDst, $pA, $pB, $OP, $TMP, $X)=@_; $code.=<<___; mov (+8*12)($pA), $OP ___ &MULSTEP_512_ADD($X, "(+8*0)($pDst)", $pB, $pA, $OP, $TMP); push(@$X,shift(@$X)); $code.=<<___; mov (+8*13)($pA), $OP ___ &MULSTEP_512($X, "(+8*1)($pDst)", $pB, $OP, $TMP); push(@$X,shift(@$X)); $code.=<<___; mov (+8*14)($pA), $OP ___ &MULSTEP_512($X, "(+8*2)($pDst)", $pB, $OP, $TMP); push(@$X,shift(@$X)); $code.=<<___; mov (+8*15)($pA), $OP ___ &MULSTEP_512($X, "(+8*3)($pDst)", $pB, $OP, $TMP); push(@$X,shift(@$X)); } # # mont_reduce(UINT64 *x, /* 1024 bits, 16 qwords */ # UINT64 *m, /* 512 bits, 8 qwords */ # MODF_2FOLD_MONT_512_C1_DATA *data, # UINT64 *r) /* 512 bits, 8 qwords */ # Input: x (number to be reduced): tmp16 (Implicit) # m (modulus): [pM] (Implicit) # data (reduce data): [pData] (Implicit) # Output: r (result): Address in [red_res_addr] # result also in: r9, r8, r15, r14, r13, r12, r11, r10 my @X=map("%r$_",(8..15)); $code.=<<___; .type mont_reduce,\@abi-omnipotent .align 16 mont_reduce: ___ my $STACK_DEPTH = 8; # # X1 = Xh * M1 + Xl $code.=<<___; lea (+$Reduce_Data_offset+$X1_offset+$STACK_DEPTH)(%rsp), %rdi # pX1 (Dst) 769 bits, 13 qwords mov (+$pData_offset+$STACK_DEPTH)(%rsp), %rsi # pM1 (Bsrc) 512 bits, 8 qwords add \$$M1, %rsi lea (+$tmp16_offset+$STACK_DEPTH)(%rsp), %rcx # X (Asrc) 1024 bits, 16 qwords ___ &MULADD_256x512("%rdi", "%rcx", "%rsi", "%rbp", "%rbx", \@X); # rotates @X 4 times # results in r11, r10, r9, r8, r15, r14, r13, r12, X1[3:0] $code.=<<___; xor %rax, %rax # X1 += xl add (+8*8)(%rcx), $X[4] adc (+8*9)(%rcx), $X[5] adc (+8*10)(%rcx), $X[6] adc (+8*11)(%rcx), $X[7] adc \$0, %rax # X1 is now rax, r11-r8, r15-r12, tmp16[3:0] # # check for carry ;; carry stored in rax mov $X[4], (+8*8)(%rdi) # rdi points to X1 mov $X[5], (+8*9)(%rdi) mov $X[6], %rbp mov $X[7], (+8*11)(%rdi) mov %rax, (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp) mov (+8*0)(%rdi), $X[4] mov (+8*1)(%rdi), $X[5] mov (+8*2)(%rdi), $X[6] mov (+8*3)(%rdi), $X[7] # X1 is now stored in: X1[11], rbp, X1[9:8], r15-r8 # rdi -> X1 # rsi -> M1 # # X2 = Xh * M2 + Xl # do first part (X2 = Xh * M2) add \$8*10, %rdi # rdi -> pXh ; 128 bits, 2 qwords # Xh is actually { [rdi+8*1], rbp } add \$`$M2-$M1`, %rsi # rsi -> M2 lea (+$Reduce_Data_offset+$X2_offset+$STACK_DEPTH)(%rsp), %rcx # rcx -> pX2 ; 641 bits, 11 qwords ___ unshift(@X,pop(@X)); unshift(@X,pop(@X)); $code.=<<___; call MULADD_128x512 # args in rcx, rdi / rbp, rsi, r15-r8 # result in r9, r8, r15, r14, r13, r12, r11, r10, X2[1:0] mov (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp), %rax # X2 += Xl add (+8*8-8*10)(%rdi), $X[6] # (-8*10) is to adjust rdi -> Xh to Xl adc (+8*9-8*10)(%rdi), $X[7] mov $X[6], (+8*8)(%rcx) mov $X[7], (+8*9)(%rcx) adc %rax, %rax mov %rax, (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp) lea (+$Reduce_Data_offset+$Q_offset+$STACK_DEPTH)(%rsp), %rdi # rdi -> pQ ; 128 bits, 2 qwords add \$`$K1-$M2`, %rsi # rsi -> pK1 ; 128 bits, 2 qwords # MUL_128x128t128 rdi, rcx, rsi ; Q = X2 * K1 (bottom half) # B1:B0 = rsi[1:0] = K1[1:0] # A1:A0 = rcx[1:0] = X2[1:0] # Result = rdi[1],rbp = Q[1],rbp mov (%rsi), %r8 # B0 mov (+8*1)(%rsi), %rbx # B1 mov (%rcx), %rax # A0 mul %r8 # B0 mov %rax, %rbp mov %rdx, %r9 mov (+8*1)(%rcx), %rax # A1 mul %r8 # B0 add %rax, %r9 mov (%rcx), %rax # A0 mul %rbx # B1 add %rax, %r9 mov %r9, (+8*1)(%rdi) # end MUL_128x128t128 sub \$`$K1-$M`, %rsi mov (%rcx), $X[6] mov (+8*1)(%rcx), $X[7] # r9:r8 = X2[1:0] call MULADD_128x512 # args in rcx, rdi / rbp, rsi, r15-r8 # result in r9, r8, r15, r14, r13, r12, r11, r10, X2[1:0] # load first half of m to rdx, rdi, rbx, rax # moved this here for efficiency mov (+8*0)(%rsi), %rax mov (+8*1)(%rsi), %rbx mov (+8*2)(%rsi), %rdi mov (+8*3)(%rsi), %rdx # continue with reduction mov (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp), %rbp add (+8*8)(%rcx), $X[6] adc (+8*9)(%rcx), $X[7] #accumulate the final carry to rbp adc %rbp, %rbp # Add in overflow corrections: R = (X2>>128) += T[overflow] # R = {r9, r8, r15, r14, ..., r10} shl \$3, %rbp mov (+$pData_offset+$STACK_DEPTH)(%rsp), %rcx # rsi -> Data (and points to T) add %rcx, %rbp # pT ; 512 bits, 8 qwords, spread out # rsi will be used to generate a mask after the addition xor %rsi, %rsi add (+8*8*0)(%rbp), $X[0] adc (+8*8*1)(%rbp), $X[1] adc (+8*8*2)(%rbp), $X[2] adc (+8*8*3)(%rbp), $X[3] adc (+8*8*4)(%rbp), $X[4] adc (+8*8*5)(%rbp), $X[5] adc (+8*8*6)(%rbp), $X[6] adc (+8*8*7)(%rbp), $X[7] # if there is a carry: rsi = 0xFFFFFFFFFFFFFFFF # if carry is clear: rsi = 0x0000000000000000 sbb \$0, %rsi # if carry is clear, subtract 0. Otherwise, subtract 256 bits of m and %rsi, %rax and %rsi, %rbx and %rsi, %rdi and %rsi, %rdx mov \$1, %rbp sub %rax, $X[0] sbb %rbx, $X[1] sbb %rdi, $X[2] sbb %rdx, $X[3] # if there is a borrow: rbp = 0 # if there is no borrow: rbp = 1 # this is used to save the borrows in between the first half and the 2nd half of the subtraction of m sbb \$0, %rbp #load second half of m to rdx, rdi, rbx, rax add \$$M, %rcx mov (+8*4)(%rcx), %rax mov (+8*5)(%rcx), %rbx mov (+8*6)(%rcx), %rdi mov (+8*7)(%rcx), %rdx # use the rsi mask as before # if carry is clear, subtract 0. Otherwise, subtract 256 bits of m and %rsi, %rax and %rsi, %rbx and %rsi, %rdi and %rsi, %rdx # if rbp = 0, there was a borrow before, it is moved to the carry flag # if rbp = 1, there was not a borrow before, carry flag is cleared sub \$1, %rbp sbb %rax, $X[4] sbb %rbx, $X[5] sbb %rdi, $X[6] sbb %rdx, $X[7] # write R back to memory mov (+$red_result_addr_offset+$STACK_DEPTH)(%rsp), %rsi mov $X[0], (+8*0)(%rsi) mov $X[1], (+8*1)(%rsi) mov $X[2], (+8*2)(%rsi) mov $X[3], (+8*3)(%rsi) mov $X[4], (+8*4)(%rsi) mov $X[5], (+8*5)(%rsi) mov $X[6], (+8*6)(%rsi) mov $X[7], (+8*7)(%rsi) ret .size mont_reduce,.-mont_reduce ___ }}} {{{ #MUL_512x512 MACRO pDst, pA, pB, x7, x6, x5, x4, x3, x2, x1, x0, tmp*2 # # Inputs: pDst: Destination (1024 bits, 16 qwords) # pA: Multiplicand (512 bits, 8 qwords) # pB: Multiplicand (512 bits, 8 qwords) # Uses registers rax, rdx, args # B operand in [pB] and also in x7...x0 sub MUL_512x512 { my ($pDst, $pA, $pB, $x, $OP, $TMP, $pDst_o)=@_; my ($pDst, $pDst_o) = ($pDst =~ m/([^+]*)\+?(.*)?/); my @X=@$x; # make a copy $code.=<<___; mov (+8*0)($pA), $OP mov $X[0], %rax mul $OP # rdx:rax = %OP * [0] mov %rax, (+$pDst_o+8*0)($pDst) mov %rdx, $X[0] ___ for(my $i=1;$i<8;$i++) { $code.=<<___; mov $X[$i], %rax mul $OP # rdx:rax = %OP * [$i] add %rax, $X[$i-1] adc \$0, %rdx mov %rdx, $X[$i] ___ } for(my $i=1;$i<8;$i++) { $code.=<<___; mov (+8*$i)($pA), $OP ___ &MULSTEP_512(\@X, "(+$pDst_o+8*$i)($pDst)", $pB, $OP, $TMP); push(@X,shift(@X)); } $code.=<<___; mov $X[0], (+$pDst_o+8*8)($pDst) mov $X[1], (+$pDst_o+8*9)($pDst) mov $X[2], (+$pDst_o+8*10)($pDst) mov $X[3], (+$pDst_o+8*11)($pDst) mov $X[4], (+$pDst_o+8*12)($pDst) mov $X[5], (+$pDst_o+8*13)($pDst) mov $X[6], (+$pDst_o+8*14)($pDst) mov $X[7], (+$pDst_o+8*15)($pDst) ___ } # # mont_mul_a3b : subroutine to compute (Src1 * Src2) % M (all 512-bits) # Input: src1: Address of source 1: rdi # src2: Address of source 2: rsi # Output: dst: Address of destination: [red_res_addr] # src2 and result also in: r9, r8, r15, r14, r13, r12, r11, r10 # Temp: Clobbers [tmp16], all registers $code.=<<___; .type mont_mul_a3b,\@abi-omnipotent .align 16 mont_mul_a3b: # # multiply tmp = src1 * src2 # For multiply: dst = rcx, src1 = rdi, src2 = rsi # stack depth is extra 8 from call ___ &MUL_512x512("%rsp+$tmp16_offset+8", "%rdi", "%rsi", [map("%r$_",(10..15,8..9))], "%rbp", "%rbx"); $code.=<<___; # # Dst = tmp % m # Call reduce(tmp, m, data, dst) # tail recursion optimization: jmp to mont_reduce and return from there jmp mont_reduce # call mont_reduce # ret .size mont_mul_a3b,.-mont_mul_a3b ___ }}} {{{ #SQR_512 MACRO pDest, pA, x7, x6, x5, x4, x3, x2, x1, x0, tmp*4 # # Input in memory [pA] and also in x7...x0 # Uses all argument registers plus rax and rdx # # This version computes all of the off-diagonal terms into memory, # and then it adds in the diagonal terms sub SQR_512 { my ($pDst, $pA, $x, $A, $tmp, $x7, $x6, $pDst_o)=@_; my ($pDst, $pDst_o) = ($pDst =~ m/([^+]*)\+?(.*)?/); my @X=@$x; # make a copy $code.=<<___; # ------------------ # first pass 01...07 # ------------------ mov $X[0], $A mov $X[1],%rax mul $A mov %rax, (+$pDst_o+8*1)($pDst) ___ for(my $i=2;$i<8;$i++) { $code.=<<___; mov %rdx, $X[$i-2] mov $X[$i],%rax mul $A add %rax, $X[$i-2] adc \$0, %rdx ___ } $code.=<<___; mov %rdx, $x7 mov $X[0], (+$pDst_o+8*2)($pDst) # ------------------ # second pass 12...17 # ------------------ mov (+8*1)($pA), $A mov (+8*2)($pA),%rax mul $A add %rax, $X[1] adc \$0, %rdx mov $X[1], (+$pDst_o+8*3)($pDst) mov %rdx, $X[0] mov (+8*3)($pA),%rax mul $A add %rax, $X[2] adc \$0, %rdx add $X[0], $X[2] adc \$0, %rdx mov $X[2], (+$pDst_o+8*4)($pDst) mov %rdx, $X[0] mov (+8*4)($pA),%rax mul $A add %rax, $X[3] adc \$0, %rdx add $X[0], $X[3] adc \$0, %rdx mov %rdx, $X[0] mov (+8*5)($pA),%rax mul $A add %rax, $X[4] adc \$0, %rdx add $X[0], $X[4] adc \$0, %rdx mov %rdx, $X[0] mov $X[6],%rax mul $A add %rax, $X[5] adc \$0, %rdx add $X[0], $X[5] adc \$0, %rdx mov %rdx, $X[0] mov $X[7],%rax mul $A add %rax, $x7 adc \$0, %rdx add $X[0], $x7 adc \$0, %rdx mov %rdx, $X[1] # ------------------ # third pass 23...27 # ------------------ mov (+8*2)($pA), $A mov (+8*3)($pA),%rax mul $A add %rax, $X[3] adc \$0, %rdx mov $X[3], (+$pDst_o+8*5)($pDst) mov %rdx, $X[0] mov (+8*4)($pA),%rax mul $A add %rax, $X[4] adc \$0, %rdx add $X[0], $X[4] adc \$0, %rdx mov $X[4], (+$pDst_o+8*6)($pDst) mov %rdx, $X[0] mov (+8*5)($pA),%rax mul $A add %rax, $X[5] adc \$0, %rdx add $X[0], $X[5] adc \$0, %rdx mov %rdx, $X[0] mov $X[6],%rax mul $A add %rax, $x7 adc \$0, %rdx add $X[0], $x7 adc \$0, %rdx mov %rdx, $X[0] mov $X[7],%rax mul $A add %rax, $X[1] adc \$0, %rdx add $X[0], $X[1] adc \$0, %rdx mov %rdx, $X[2] # ------------------ # fourth pass 34...37 # ------------------ mov (+8*3)($pA), $A mov (+8*4)($pA),%rax mul $A add %rax, $X[5] adc \$0, %rdx mov $X[5], (+$pDst_o+8*7)($pDst) mov %rdx, $X[0] mov (+8*5)($pA),%rax mul $A add %rax, $x7 adc \$0, %rdx add $X[0], $x7 adc \$0, %rdx mov $x7, (+$pDst_o+8*8)($pDst) mov %rdx, $X[0] mov $X[6],%rax mul $A add %rax, $X[1] adc \$0, %rdx add $X[0], $X[1] adc \$0, %rdx mov %rdx, $X[0] mov $X[7],%rax mul $A add %rax, $X[2] adc \$0, %rdx add $X[0], $X[2] adc \$0, %rdx mov %rdx, $X[5] # ------------------ # fifth pass 45...47 # ------------------ mov (+8*4)($pA), $A mov (+8*5)($pA),%rax mul $A add %rax, $X[1] adc \$0, %rdx mov $X[1], (+$pDst_o+8*9)($pDst) mov %rdx, $X[0] mov $X[6],%rax mul $A add %rax, $X[2] adc \$0, %rdx add $X[0], $X[2] adc \$0, %rdx mov $X[2], (+$pDst_o+8*10)($pDst) mov %rdx, $X[0] mov $X[7],%rax mul $A add %rax, $X[5] adc \$0, %rdx add $X[0], $X[5] adc \$0, %rdx mov %rdx, $X[1] # ------------------ # sixth pass 56...57 # ------------------ mov (+8*5)($pA), $A mov $X[6],%rax mul $A add %rax, $X[5] adc \$0, %rdx mov $X[5], (+$pDst_o+8*11)($pDst) mov %rdx, $X[0] mov $X[7],%rax mul $A add %rax, $X[1] adc \$0, %rdx add $X[0], $X[1] adc \$0, %rdx mov $X[1], (+$pDst_o+8*12)($pDst) mov %rdx, $X[2] # ------------------ # seventh pass 67 # ------------------ mov $X[6], $A mov $X[7],%rax mul $A add %rax, $X[2] adc \$0, %rdx mov $X[2], (+$pDst_o+8*13)($pDst) mov %rdx, (+$pDst_o+8*14)($pDst) # start finalize (add in squares, and double off-terms) mov (+$pDst_o+8*1)($pDst), $X[0] mov (+$pDst_o+8*2)($pDst), $X[1] mov (+$pDst_o+8*3)($pDst), $X[2] mov (+$pDst_o+8*4)($pDst), $X[3] mov (+$pDst_o+8*5)($pDst), $X[4] mov (+$pDst_o+8*6)($pDst), $X[5] mov (+8*3)($pA), %rax mul %rax mov %rax, $x6 mov %rdx, $X[6] add $X[0], $X[0] adc $X[1], $X[1] adc $X[2], $X[2] adc $X[3], $X[3] adc $X[4], $X[4] adc $X[5], $X[5] adc \$0, $X[6] mov (+8*0)($pA), %rax mul %rax mov %rax, (+$pDst_o+8*0)($pDst) mov %rdx, $A mov (+8*1)($pA), %rax mul %rax add $A, $X[0] adc %rax, $X[1] adc \$0, %rdx mov %rdx, $A mov $X[0], (+$pDst_o+8*1)($pDst) mov $X[1], (+$pDst_o+8*2)($pDst) mov (+8*2)($pA), %rax mul %rax add $A, $X[2] adc %rax, $X[3] adc \$0, %rdx mov %rdx, $A mov $X[2], (+$pDst_o+8*3)($pDst) mov $X[3], (+$pDst_o+8*4)($pDst) xor $tmp, $tmp add $A, $X[4] adc $x6, $X[5] adc \$0, $tmp mov $X[4], (+$pDst_o+8*5)($pDst) mov $X[5], (+$pDst_o+8*6)($pDst) # %%tmp has 0/1 in column 7 # %%A6 has a full value in column 7 mov (+$pDst_o+8*7)($pDst), $X[0] mov (+$pDst_o+8*8)($pDst), $X[1] mov (+$pDst_o+8*9)($pDst), $X[2] mov (+$pDst_o+8*10)($pDst), $X[3] mov (+$pDst_o+8*11)($pDst), $X[4] mov (+$pDst_o+8*12)($pDst), $X[5] mov (+$pDst_o+8*13)($pDst), $x6 mov (+$pDst_o+8*14)($pDst), $x7 mov $X[7], %rax mul %rax mov %rax, $X[7] mov %rdx, $A add $X[0], $X[0] adc $X[1], $X[1] adc $X[2], $X[2] adc $X[3], $X[3] adc $X[4], $X[4] adc $X[5], $X[5] adc $x6, $x6 adc $x7, $x7 adc \$0, $A add $tmp, $X[0] mov (+8*4)($pA), %rax mul %rax add $X[6], $X[0] adc %rax, $X[1] adc \$0, %rdx mov %rdx, $tmp mov $X[0], (+$pDst_o+8*7)($pDst) mov $X[1], (+$pDst_o+8*8)($pDst) mov (+8*5)($pA), %rax mul %rax add $tmp, $X[2] adc %rax, $X[3] adc \$0, %rdx mov %rdx, $tmp mov $X[2], (+$pDst_o+8*9)($pDst) mov $X[3], (+$pDst_o+8*10)($pDst) mov (+8*6)($pA), %rax mul %rax add $tmp, $X[4] adc %rax, $X[5] adc \$0, %rdx mov $X[4], (+$pDst_o+8*11)($pDst) mov $X[5], (+$pDst_o+8*12)($pDst) add %rdx, $x6 adc $X[7], $x7 adc \$0, $A mov $x6, (+$pDst_o+8*13)($pDst) mov $x7, (+$pDst_o+8*14)($pDst) mov $A, (+$pDst_o+8*15)($pDst) ___ } # # sqr_reduce: subroutine to compute Result = reduce(Result * Result) # # input and result also in: r9, r8, r15, r14, r13, r12, r11, r10 # $code.=<<___; .type sqr_reduce,\@abi-omnipotent .align 16 sqr_reduce: mov (+$pResult_offset+8)(%rsp), %rcx ___ &SQR_512("%rsp+$tmp16_offset+8", "%rcx", [map("%r$_",(10..15,8..9))], "%rbx", "%rbp", "%rsi", "%rdi"); $code.=<<___; # tail recursion optimization: jmp to mont_reduce and return from there jmp mont_reduce # call mont_reduce # ret .size sqr_reduce,.-sqr_reduce ___ }}} # # MAIN FUNCTION # #mod_exp_512(UINT64 *result, /* 512 bits, 8 qwords */ # UINT64 *g, /* 512 bits, 8 qwords */ # UINT64 *exp, /* 512 bits, 8 qwords */ # struct mod_ctx_512 *data) # window size = 5 # table size = 2^5 = 32 #table_entries equ 32 #table_size equ table_entries * 8 $code.=<<___; .globl mod_exp_512 .type mod_exp_512,\@function,4 mod_exp_512: push %rbp push %rbx push %r12 push %r13 push %r14 push %r15 # adjust stack down and then align it with cache boundary mov %rsp, %r8 sub \$$mem_size, %rsp and \$-64, %rsp # store previous stack pointer and arguments mov %r8, (+$rsp_offset)(%rsp) mov %rdi, (+$pResult_offset)(%rsp) mov %rsi, (+$pG_offset)(%rsp) mov %rcx, (+$pData_offset)(%rsp) .Lbody: # transform g into montgomery space # GT = reduce(g * C2) = reduce(g * (2^256)) # reduce expects to have the input in [tmp16] pxor %xmm4, %xmm4 movdqu (+16*0)(%rsi), %xmm0 movdqu (+16*1)(%rsi), %xmm1 movdqu (+16*2)(%rsi), %xmm2 movdqu (+16*3)(%rsi), %xmm3 movdqa %xmm4, (+$tmp16_offset+16*0)(%rsp) movdqa %xmm4, (+$tmp16_offset+16*1)(%rsp) movdqa %xmm4, (+$tmp16_offset+16*6)(%rsp) movdqa %xmm4, (+$tmp16_offset+16*7)(%rsp) movdqa %xmm0, (+$tmp16_offset+16*2)(%rsp) movdqa %xmm1, (+$tmp16_offset+16*3)(%rsp) movdqa %xmm2, (+$tmp16_offset+16*4)(%rsp) movdqa %xmm3, (+$tmp16_offset+16*5)(%rsp) # load pExp before rdx gets blown away movdqu (+16*0)(%rdx), %xmm0 movdqu (+16*1)(%rdx), %xmm1 movdqu (+16*2)(%rdx), %xmm2 movdqu (+16*3)(%rdx), %xmm3 lea (+$GT_offset)(%rsp), %rbx mov %rbx, (+$red_result_addr_offset)(%rsp) call mont_reduce # Initialize tmp = C lea (+$tmp_offset)(%rsp), %rcx xor %rax, %rax mov %rax, (+8*0)(%rcx) mov %rax, (+8*1)(%rcx) mov %rax, (+8*3)(%rcx) mov %rax, (+8*4)(%rcx) mov %rax, (+8*5)(%rcx) mov %rax, (+8*6)(%rcx) mov %rax, (+8*7)(%rcx) mov %rax, (+$exp_offset+8*8)(%rsp) movq \$1, (+8*2)(%rcx) lea (+$garray_offset)(%rsp), %rbp mov %rcx, %rsi # pTmp mov %rbp, %rdi # Garray[][0] ___ &swizzle("%rdi", "%rcx", "%rax", "%rbx"); # for (rax = 31; rax != 0; rax--) { # tmp = reduce(tmp * G) # swizzle(pg, tmp); # pg += 2; } $code.=<<___; mov \$31, %rax mov %rax, (+$i_offset)(%rsp) mov %rbp, (+$pg_offset)(%rsp) # rsi -> pTmp mov %rsi, (+$red_result_addr_offset)(%rsp) mov (+8*0)(%rsi), %r10 mov (+8*1)(%rsi), %r11 mov (+8*2)(%rsi), %r12 mov (+8*3)(%rsi), %r13 mov (+8*4)(%rsi), %r14 mov (+8*5)(%rsi), %r15 mov (+8*6)(%rsi), %r8 mov (+8*7)(%rsi), %r9 init_loop: lea (+$GT_offset)(%rsp), %rdi call mont_mul_a3b lea (+$tmp_offset)(%rsp), %rsi mov (+$pg_offset)(%rsp), %rbp add \$2, %rbp mov %rbp, (+$pg_offset)(%rsp) mov %rsi, %rcx # rcx = rsi = addr of tmp ___ &swizzle("%rbp", "%rcx", "%rax", "%rbx"); $code.=<<___; mov (+$i_offset)(%rsp), %rax sub \$1, %rax mov %rax, (+$i_offset)(%rsp) jne init_loop # # Copy exponent onto stack movdqa %xmm0, (+$exp_offset+16*0)(%rsp) movdqa %xmm1, (+$exp_offset+16*1)(%rsp) movdqa %xmm2, (+$exp_offset+16*2)(%rsp) movdqa %xmm3, (+$exp_offset+16*3)(%rsp) # # Do exponentiation # Initialize result to G[exp{511:507}] mov (+$exp_offset+62)(%rsp), %eax mov %rax, %rdx shr \$11, %rax and \$0x07FF, %edx mov %edx, (+$exp_offset+62)(%rsp) lea (+$garray_offset)(%rsp,%rax,2), %rsi mov (+$pResult_offset)(%rsp), %rdx ___ &unswizzle("%rdx", "%rsi", "%rbp", "%rbx", "%rax"); # # Loop variables # rcx = [loop_idx] = index: 510-5 to 0 by 5 $code.=<<___; movq \$505, (+$loop_idx_offset)(%rsp) mov (+$pResult_offset)(%rsp), %rcx mov %rcx, (+$red_result_addr_offset)(%rsp) mov (+8*0)(%rcx), %r10 mov (+8*1)(%rcx), %r11 mov (+8*2)(%rcx), %r12 mov (+8*3)(%rcx), %r13 mov (+8*4)(%rcx), %r14 mov (+8*5)(%rcx), %r15 mov (+8*6)(%rcx), %r8 mov (+8*7)(%rcx), %r9 jmp sqr_2 main_loop_a3b: call sqr_reduce call sqr_reduce call sqr_reduce sqr_2: call sqr_reduce call sqr_reduce # # Do multiply, first look up proper value in Garray mov (+$loop_idx_offset)(%rsp), %rcx # bit index mov %rcx, %rax shr \$4, %rax # rax is word pointer mov (+$exp_offset)(%rsp,%rax,2), %edx and \$15, %rcx shrq %cl, %rdx and \$0x1F, %rdx lea (+$garray_offset)(%rsp,%rdx,2), %rsi lea (+$tmp_offset)(%rsp), %rdx mov %rdx, %rdi ___ &unswizzle("%rdx", "%rsi", "%rbp", "%rbx", "%rax"); # rdi = tmp = pG # # Call mod_mul_a1(pDst, pSrc1, pSrc2, pM, pData) # result result pG M Data $code.=<<___; mov (+$pResult_offset)(%rsp), %rsi call mont_mul_a3b # # finish loop mov (+$loop_idx_offset)(%rsp), %rcx sub \$5, %rcx mov %rcx, (+$loop_idx_offset)(%rsp) jge main_loop_a3b # end_main_loop_a3b: # transform result out of Montgomery space # result = reduce(result) mov (+$pResult_offset)(%rsp), %rdx pxor %xmm4, %xmm4 movdqu (+16*0)(%rdx), %xmm0 movdqu (+16*1)(%rdx), %xmm1 movdqu (+16*2)(%rdx), %xmm2 movdqu (+16*3)(%rdx), %xmm3 movdqa %xmm4, (+$tmp16_offset+16*4)(%rsp) movdqa %xmm4, (+$tmp16_offset+16*5)(%rsp) movdqa %xmm4, (+$tmp16_offset+16*6)(%rsp) movdqa %xmm4, (+$tmp16_offset+16*7)(%rsp) movdqa %xmm0, (+$tmp16_offset+16*0)(%rsp) movdqa %xmm1, (+$tmp16_offset+16*1)(%rsp) movdqa %xmm2, (+$tmp16_offset+16*2)(%rsp) movdqa %xmm3, (+$tmp16_offset+16*3)(%rsp) call mont_reduce # If result > m, subract m # load result into r15:r8 mov (+$pResult_offset)(%rsp), %rax mov (+8*0)(%rax), %r8 mov (+8*1)(%rax), %r9 mov (+8*2)(%rax), %r10 mov (+8*3)(%rax), %r11 mov (+8*4)(%rax), %r12 mov (+8*5)(%rax), %r13 mov (+8*6)(%rax), %r14 mov (+8*7)(%rax), %r15 # subtract m mov (+$pData_offset)(%rsp), %rbx add \$$M, %rbx sub (+8*0)(%rbx), %r8 sbb (+8*1)(%rbx), %r9 sbb (+8*2)(%rbx), %r10 sbb (+8*3)(%rbx), %r11 sbb (+8*4)(%rbx), %r12 sbb (+8*5)(%rbx), %r13 sbb (+8*6)(%rbx), %r14 sbb (+8*7)(%rbx), %r15 # if Carry is clear, replace result with difference mov (+8*0)(%rax), %rsi mov (+8*1)(%rax), %rdi mov (+8*2)(%rax), %rcx mov (+8*3)(%rax), %rdx cmovnc %r8, %rsi cmovnc %r9, %rdi cmovnc %r10, %rcx cmovnc %r11, %rdx mov %rsi, (+8*0)(%rax) mov %rdi, (+8*1)(%rax) mov %rcx, (+8*2)(%rax) mov %rdx, (+8*3)(%rax) mov (+8*4)(%rax), %rsi mov (+8*5)(%rax), %rdi mov (+8*6)(%rax), %rcx mov (+8*7)(%rax), %rdx cmovnc %r12, %rsi cmovnc %r13, %rdi cmovnc %r14, %rcx cmovnc %r15, %rdx mov %rsi, (+8*4)(%rax) mov %rdi, (+8*5)(%rax) mov %rcx, (+8*6)(%rax) mov %rdx, (+8*7)(%rax) mov (+$rsp_offset)(%rsp), %rsi mov 0(%rsi),%r15 mov 8(%rsi),%r14 mov 16(%rsi),%r13 mov 24(%rsi),%r12 mov 32(%rsi),%rbx mov 40(%rsi),%rbp lea 48(%rsi),%rsp .Lepilogue: ret .size mod_exp_512, . - mod_exp_512 ___ if ($win64) { # EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame, # CONTEXT *context,DISPATCHER_CONTEXT *disp) my $rec="%rcx"; my $frame="%rdx"; my $context="%r8"; my $disp="%r9"; $code.=<<___; .extern __imp_RtlVirtualUnwind .type mod_exp_512_se_handler,\@abi-omnipotent .align 16 mod_exp_512_se_handler: push %rsi push %rdi push %rbx push %rbp push %r12 push %r13 push %r14 push %r15 pushfq sub \$64,%rsp mov 120($context),%rax # pull context->Rax mov 248($context),%rbx # pull context->Rip lea .Lbody(%rip),%r10 cmp %r10,%rbx # context->Rip<prologue label jb .Lin_prologue mov 152($context),%rax # pull context->Rsp lea .Lepilogue(%rip),%r10 cmp %r10,%rbx # context->Rip>=epilogue label jae .Lin_prologue mov $rsp_offset(%rax),%rax # pull saved Rsp mov 32(%rax),%rbx mov 40(%rax),%rbp mov 24(%rax),%r12 mov 16(%rax),%r13 mov 8(%rax),%r14 mov 0(%rax),%r15 lea 48(%rax),%rax mov %rbx,144($context) # restore context->Rbx mov %rbp,160($context) # restore context->Rbp mov %r12,216($context) # restore context->R12 mov %r13,224($context) # restore context->R13 mov %r14,232($context) # restore context->R14 mov %r15,240($context) # restore context->R15 .Lin_prologue: mov 8(%rax),%rdi mov 16(%rax),%rsi mov %rax,152($context) # restore context->Rsp mov %rsi,168($context) # restore context->Rsi mov %rdi,176($context) # restore context->Rdi mov 40($disp),%rdi # disp->ContextRecord mov $context,%rsi # context mov \$154,%ecx # sizeof(CONTEXT) .long 0xa548f3fc # cld; rep movsq mov $disp,%rsi xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER mov 8(%rsi),%rdx # arg2, disp->ImageBase mov 0(%rsi),%r8 # arg3, disp->ControlPc mov 16(%rsi),%r9 # arg4, disp->FunctionEntry mov 40(%rsi),%r10 # disp->ContextRecord lea 56(%rsi),%r11 # &disp->HandlerData lea 24(%rsi),%r12 # &disp->EstablisherFrame mov %r10,32(%rsp) # arg5 mov %r11,40(%rsp) # arg6 mov %r12,48(%rsp) # arg7 mov %rcx,56(%rsp) # arg8, (NULL) call *__imp_RtlVirtualUnwind(%rip) mov \$1,%eax # ExceptionContinueSearch add \$64,%rsp popfq pop %r15 pop %r14 pop %r13 pop %r12 pop %rbp pop %rbx pop %rdi pop %rsi ret .size mod_exp_512_se_handler,.-mod_exp_512_se_handler .section .pdata .align 4 .rva .LSEH_begin_mod_exp_512 .rva .LSEH_end_mod_exp_512 .rva .LSEH_info_mod_exp_512 .section .xdata .align 8 .LSEH_info_mod_exp_512: .byte 9,0,0,0 .rva mod_exp_512_se_handler ___ } sub reg_part { my ($reg,$conv)=@_; if ($reg =~ /%r[0-9]+/) { $reg .= $conv; } elsif ($conv eq "b") { $reg =~ s/%[er]([^x]+)x?/%$1l/; } elsif ($conv eq "w") { $reg =~ s/%[er](.+)/%$1/; } elsif ($conv eq "d") { $reg =~ s/%[er](.+)/%e$1/; } return $reg; } $code =~ s/(%[a-z0-9]+)#([bwd])/reg_part($1,$2)/gem; $code =~ s/\`([^\`]*)\`/eval $1/gem; $code =~ s/(\(\+[^)]+\))/eval $1/gem; print $code; close STDOUT;