761 lines
26 KiB
PHP
761 lines
26 KiB
PHP
; mpint.inc - Multi precision integer procedures
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;
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; Copyright (C) 2015-2017 Jeffrey Amelynck
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;
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; This program is free software: you can redistribute it and/or modify
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; it under the terms of the GNU General Public License as published by
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; the Free Software Foundation, either version 3 of the License, or
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; (at your option) any later version.
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;
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; This program is distributed in the hope that it will be useful,
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; but WITHOUT ANY WARRANTY; without even the implied warranty of
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; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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; GNU General Public License for more details.
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;
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; You should have received a copy of the GNU General Public License
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; along with this program. If not, see <http://www.gnu.org/licenses/>.
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; Notes:
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;
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; These procedures work only with positive integers.
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; For compatibility reasons, the highest bit must always be 0.
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; However, leading 0 bytes MUST at all other times be omitted.
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;
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; You have been warned!
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MPINT_MAX_LEN = MAX_BITS/8
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;;===========================================================================;;
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proc mpint_to_little_endian uses esi edi ecx ;///////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Convert big endian MPINT to little endian MPINT. ;;
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;;---------------------------------------------------------------------------;;
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;> esi = pointer to big endian MPINT ;;
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;> edi = pointer to buffer for little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< eax = MPINT number length ;;
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;;===========================================================================;;
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; Load length dword
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lodsd
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; Convert to little endian
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bswap eax
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stosd
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test eax, eax
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jz .zero
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; Copy data, convert to little endian meanwhile
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push eax
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add esi, eax
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push esi
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dec esi
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mov ecx, eax
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std
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@@:
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lodsb
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mov byte[edi], al
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inc edi
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dec ecx
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jnz @r
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cld
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pop esi eax
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.zero:
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ret
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endp
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;;===========================================================================;;
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proc mpint_to_big_endian uses esi edi ecx ;//////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Convert little endian MPINT to big endian MPINT. ;;
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;;---------------------------------------------------------------------------;;
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;> esi = pointer to little endian MPINT ;;
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;> edi = pointer to buffer for big endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< eax = MPINT number length ;;
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;;===========================================================================;;
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; Load length dword
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lodsd
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test eax, eax
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jz .zero
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mov ecx, eax
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add esi, eax
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dec esi
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push eax ; we'll return length to the caller later
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bswap eax
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stosd
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; Copy data, convert to big endian meanwhile
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std
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@@:
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lodsb
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mov byte[edi], al
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inc edi
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dec ecx
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jnz @r
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cld
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pop eax
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ret
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.zero:
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stosd ; Number 0 has 0 data bytes
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ret
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endp
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;;===========================================================================;;
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proc mpint_print uses ecx esi eax, src ;/////////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Print MPINT to the debug board. ;;
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;;---------------------------------------------------------------------------;;
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;> src = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< - ;;
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;;===========================================================================;;
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DEBUGF 1, "0x"
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mov esi, [src]
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mov ecx, [esi]
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test ecx, ecx
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jz .zero
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lea esi, [esi + ecx + 4 - 1]
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pushf
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std
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.loop:
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lodsb
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DEBUGF 1, "%x", eax:2
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dec ecx
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jnz .loop
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DEBUGF 1, "\n"
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popf
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ret
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.zero:
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DEBUGF 1, "00\n"
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ret
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endp
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;;===========================================================================;;
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proc mpint_hob uses edi ecx eax, dst ;///////////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Return an index number giving the position of the highest order bit. ;;
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;;---------------------------------------------------------------------------;;
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;> src = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< eax = highest order bit number ;;
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;;===========================================================================;;
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mov edi, [dst]
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lodsd
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dec eax ; total length minus one
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mov cl, [edi+eax] ; load the highest order byte
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shl eax, 3 ; multiply eax by 8 to get nr of bits
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; Now shift bits of the highest order byte right, until the byte reaches zero, counting bits meanwhile
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test cl, cl
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jz .end
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@@:
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inc eax
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shr cl, 1
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jnz @r
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.end:
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ret
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endp
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;;===========================================================================;;
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proc mpint_cmp uses esi edi ecx eax, dst, src ;//////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Compare two mpints. ;;
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;;---------------------------------------------------------------------------;;
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;> dst = pointer to little endian MPINT ;;
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;> src = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< flags are set as for single precision CMP instruction ;;
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;;===========================================================================;;
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; First, check if number of significant bytes is the same
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; If not, number with more bytes is bigger
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mov esi, [src]
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mov edi, [dst]
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mov ecx, [esi]
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cmp ecx, [edi]
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jne .got_answer
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; Numbers have equal amount of bytes, compare starting from the high order byte
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add edi, ecx
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add esi, ecx
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std
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.do_byte:
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test ecx, 11b
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jz .do_dword
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dec esi
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dec edi
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cmpsb
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jne .got_answer
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dec ecx
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jmp .do_byte
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.do_dword:
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shr ecx, 2
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jz .got_answer
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sub esi, 4
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sub edi, 4
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repe cmpsd
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.got_answer:
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cld
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ret
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endp
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;;===========================================================================;;
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proc mpint_mov uses esi edi ecx, dst, src ;//////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Copy mpint. ;;
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;;---------------------------------------------------------------------------;;
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;> dst = pointer to buffer for little endian MPINT ;;
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;> src = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< dst = src ;;
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;;===========================================================================;;
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mov esi, [src]
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mov edi, [dst]
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mov ecx, [esi]
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push ecx
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shr ecx, 2
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inc ecx ; for length dword
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rep movsd
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pop ecx
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and ecx, 11b
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jz @f
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rep movsb
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@@:
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ret
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endp
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;;===========================================================================;;
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proc mpint_shl1 uses esi ecx, dst ;//////////////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Shift little endian MPINT one bit to the left. ;;
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;;---------------------------------------------------------------------------;;
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;> dst = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< dst = dst SHL 1 ;;
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;;===========================================================================;;
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mov esi, [dst]
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mov ecx, [esi]
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test ecx, ecx
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jz .done
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; Test if high order byte will overflow
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; Remember: highest bit must never be set for positive numbers!
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test byte[esi+ecx+3], 11000000b
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jz @f
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; We must grow a byte in size!
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; TODO: check for overflow
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inc ecx
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mov [esi], ecx
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mov byte[esi+ecx+3], 0 ; Add the new MSB
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@@:
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add esi, 4
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; Do the lowest order byte first
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shl byte[esi], 1
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dec ecx
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jz .done
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; And the remaining bytes
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@@:
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inc esi
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rcl byte[esi], 1
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dec ecx
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jnz @r
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.done:
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ret
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endp
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;;===========================================================================;;
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proc mpint_shr1 uses edi ecx, dst ;//////////////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Shift little endian MPINT one bit to the right. ;;
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;;---------------------------------------------------------------------------;;
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;> dst = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< dst = dst SHR 1 ;;
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;;===========================================================================;;
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mov edi, [dst]
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mov ecx, [edi]
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test ecx, ecx
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jz .done
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; Do the highest order byte first
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dec ecx
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shr byte[edi+ecx+3], 1
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; Was it 0? If so, we must decrement total length
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jnz @f
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jc @f
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mov [edi], ecx
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@@:
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test ecx, ecx
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jz .done
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; Now do the trailing bytes
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add edi, 4
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add edi, ecx
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@@:
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dec edi
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rcr byte[edi], 1
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dec ecx ; does not affect carry flag, hooray!
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jnz @r
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.done:
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ret
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endp
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;;===========================================================================;;
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proc mpint_shl uses eax ebx ecx edx esi edi, dst, shift ;////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Left shift little endian MPINT by x bits. ;;
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;;---------------------------------------------------------------------------;;
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;> dst = pointer to little endian MPINT ;;
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;> shift = number of bits to shift the MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< - ;;
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;;===========================================================================;;
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mov ecx, [shift]
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shr ecx, 3 ; 8 bits in one byte
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cmp ecx, MPINT_MAX_LEN
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jge .zero
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mov esi, [dst]
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add esi, MPINT_MAX_LEN+4-4
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mov edi, esi
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and ecx, not 11b
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sub esi, ecx
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mov edx, MPINT_MAX_LEN/4-1
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shr ecx, 2 ; 4 bytes in one dword
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push ecx
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sub edx, ecx
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mov ecx, [shift]
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and ecx, 11111b
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std
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.loop:
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lodsd
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mov ebx, [esi]
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shld eax, ebx, cl
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stosd
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dec edx
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jnz .loop
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lodsd
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shl eax, cl
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stosd
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; fill the lsb bytes with zeros
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pop ecx
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test ecx, ecx
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jz @f
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xor eax, eax
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rep stosd
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@@:
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cld
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ret
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.zero:
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mov eax, [dst]
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mov dword[eax], 0
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ret
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endp
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;;===========================================================================;;
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proc mpint_shlmov uses eax ebx ecx edx esi edi, dst, src, shift ;////////////;;
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;;---------------------------------------------------------------------------;;
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;? Left shift by x bits and copy little endian MPINT. ;;
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;;---------------------------------------------------------------------------;;
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;> src = pointer to little endian MPINT ;;
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;> dst = pointer to little endian MPINT ;;
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;> shift = number of bits to shift the MPINT to the left ;;
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;;---------------------------------------------------------------------------;;
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;< dst = src SHL shift ;;
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;;===========================================================================;;
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mov ecx, [shift]
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shr ecx, 3 ; 8 bits in one byte
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cmp ecx, MPINT_MAX_LEN
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jge .zero
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mov esi, [src]
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add esi, MPINT_MAX_LEN+4-4
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mov edi, [dst]
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add edi, MPINT_MAX_LEN+4-4
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and ecx, not 11b
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sub esi, ecx
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mov edx, MPINT_MAX_LEN/4-1
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shr ecx, 2 ; 4 bytes in one dword
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push ecx
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sub edx, ecx
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mov ecx, [shift]
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and ecx, 11111b
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std
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.loop:
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lodsd
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mov ebx, [esi]
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shld eax, ebx, cl
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stosd
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dec edx
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jnz .loop
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lodsd
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shl eax, cl
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stosd
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; fill the lsb bytes with zeros
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pop ecx
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test ecx, ecx
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jz @f
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xor eax, eax
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rep stosd
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@@:
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cld
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ret
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.zero:
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mov eax, [dst]
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mov dword[eax], 0
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ret
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endp
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;;===========================================================================;;
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proc mpint_add uses esi edi ecx eax, dst, src ;//////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Add a little endian MPINT to another little endian MPINT. ;;
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;;---------------------------------------------------------------------------;;
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;> src = pointer to little endian MPINT ;;
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;> dst = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< dst = dst + src ;;
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;;===========================================================================;;
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mov esi, [src]
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mov edi, [dst]
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mov ecx, [esi] ; source number length
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sub ecx, [dst]
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jbe .length_ok
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; Length of the destination is currently smaller then the source, pad with 0 bytes
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add edi, [edi]
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add edi, 4
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mov al, 0
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rep stosb
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.length_ok:
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mov ecx, [esi]
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mov edi, [dst]
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add esi, 4
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add edi, 4
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; Add the first byte
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lodsb
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add byte[edi], al
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dec ecx
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jz .done
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; Add the other bytes
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@@:
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inc edi
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lodsb
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adc byte[edi], al
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dec ecx
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jnz @r
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.done:
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; check if highest bit OR carry flag is set
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; if so, add a byte if we have the buffer space
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; TODO: check if we have the buffer space
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jc .carry
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cmp byte[edi], 0x80
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jnz .high_bit_set
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ret
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.carry:
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inc edi
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mov byte[edi], 1
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mov eax, [dst]
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inc dword[eax]
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ret
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.high_bit_set:
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inc edi
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mov byte[edi], 0
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mov eax, [dst]
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inc dword[eax]
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ret
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endp
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;;===========================================================================;;
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proc mpint_sub uses eax esi edi ecx, dst, src ;//////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Subtract a little endian MPINT to another little endian MPINT. ;;
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;;---------------------------------------------------------------------------;;
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;> src = pointer to little endian MPINT ;;
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;> dst = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< dst = dst - src ;;
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;;===========================================================================;;
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mov esi, [src]
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mov edi, [dst]
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mov ecx, [esi] ; destination number length
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cmp ecx, [edi]
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ja .overflow
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add esi, 4
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add edi, 4
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; Subtract the first byte
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lodsb
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sub byte[edi], al
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dec ecx
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jz .done
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; Subtract the other bytes
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@@:
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inc edi
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lodsb
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sbb byte[edi], al
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dec ecx
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jnz @r
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.done:
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stdcall mpint_shrink, [dst]
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ret
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.overflow:
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mov dword[edi], 0
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stc
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ret
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endp
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;;===========================================================================;;
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proc mpint_shrink uses eax edi ecx, dst ;////////////////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Get rid of leading zeroes on a little endian MPINT. ;;
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;;---------------------------------------------------------------------------;;
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;> src = pointer to little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< ;;
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;;===========================================================================;;
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mov edi, [dst]
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lodsd
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std
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mov ecx, eax
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dec eax ; total length minus one
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add edi, eax
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xor al, al
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repe cmpsb
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inc ecx
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mov edi, [dst]
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mov [edi], ecx
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cld
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ret
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endp
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;;===========================================================================;;
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proc mpint_mul uses esi edi ecx ebx eax, dst, A, B ;/////////////////////////;;
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;;---------------------------------------------------------------------------;;
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;? Multiply to little endian MPINTS and store them in a new one. ;;
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;;---------------------------------------------------------------------------;;
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;> A = pointer to little endian MPINT ;;
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;> B = pointer to little endian MPINT ;;
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;> dst = pointer to buffer for little endian MPINT ;;
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;;---------------------------------------------------------------------------;;
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;< dst = A * B ;;
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;;===========================================================================;;
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; Set result to zero
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mov eax, [dst]
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mov dword[eax], 0
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; first, find the byte in A containing the highest order bit
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mov edi, [A]
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mov eax, [edi]
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test eax, eax
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jz .zero
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add edi, eax
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mov al, [edi+1]
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mov esi, edi
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mov bl, 8
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@@:
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shl al, 1
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jc .first_hit
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dec bl
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jnz @r
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; Then, starting from this byte, iterate through the bits in A,
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; starting from the highest order bit down to the lowest order bit.
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.next_byte:
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mov al, [edi]
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dec edi
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mov bl, 8
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.next_bit:
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stdcall mpint_shl1, [dst]
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shl al, 1
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jnc .zero_bit
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.first_hit:
|
|
stdcall mpint_add, [dst], [B]
|
|
.zero_bit:
|
|
dec bl
|
|
jnz .next_bit
|
|
dec ecx
|
|
jnz .next_byte
|
|
.zero:
|
|
ret
|
|
|
|
endp
|
|
|
|
;;===========================================================================;;
|
|
proc mpint_mod uses eax ebx ecx, dst, mod ;//////////////////////////////////;;
|
|
;;---------------------------------------------------------------------------;;
|
|
;? Find the modulo (remainder after division) of dst by mod. ;;
|
|
;;---------------------------------------------------------------------------;;
|
|
;> dst = pointer to little endian MPINT ;;
|
|
;> mod = pointer to little endian MPINT ;;
|
|
;;---------------------------------------------------------------------------;;
|
|
;< dst = dst MOD mod ;;
|
|
;;===========================================================================;;
|
|
|
|
locals
|
|
mpint_tmp rb MPINT_MAX_LEN+4
|
|
endl
|
|
|
|
; if mod is zero, return
|
|
mov eax, [mod]
|
|
cmp dword[eax], 0
|
|
je .zero
|
|
|
|
stdcall mpint_cmp, eax, [dst]
|
|
jb .done ; if dst < mod, dst = dst
|
|
je .zero ; if dst == mod, dst = 0
|
|
|
|
lea ebx, [mpint_tmp]
|
|
|
|
; left shift mod until the high order bits of mod and dst are aligned
|
|
stdcall mpint_hob, [dst]
|
|
mov ecx, eax
|
|
stdcall mpint_hob, [mod]
|
|
sub ecx, eax
|
|
stdcall mpint_shlmov, ebx, [mod], ecx
|
|
inc ecx
|
|
|
|
; For every bit in dst (starting from the high order bit):
|
|
.loop:
|
|
; determine if dst is bigger than mpint_tmp
|
|
stdcall mpint_cmp, [dst], ebx
|
|
ja @f
|
|
; if so, subtract mpint_tmp from dst
|
|
stdcall mpint_sub, [dst], ebx
|
|
@@:
|
|
dec ecx
|
|
jz .done
|
|
; shift mpint_tmp right by 1
|
|
stdcall mpint_shr1, ebx
|
|
jmp .loop
|
|
|
|
.zero:
|
|
mov eax, [dst]
|
|
mov dword[eax], 0
|
|
.done:
|
|
ret
|
|
|
|
endp
|
|
|
|
;;===========================================================================;;
|
|
proc mpint_modexp uses edi eax ebx ecx edx, dst, base, exp, mod ;////////////;;
|
|
;;---------------------------------------------------------------------------;;
|
|
;? Find the modulo (remainder after division) of dst by mod. ;;
|
|
;;---------------------------------------------------------------------------;;
|
|
;> dst = pointer to buffer for little endian MPINT ;;
|
|
;> base = pointer to little endian MPINT ;;
|
|
;> exp = pointer to little endian MPINT ;;
|
|
;> mod = pointer to little endian MPINT ;;
|
|
;;---------------------------------------------------------------------------;;
|
|
;< dst = base ** exp MOD mod ;;
|
|
;;===========================================================================;;
|
|
|
|
locals
|
|
mpint_tmp rb MPINT_MAX_LEN+4
|
|
endl
|
|
|
|
; If mod is zero, return
|
|
mov eax, [mod]
|
|
cmp dword[eax], 0
|
|
je .mod_zero
|
|
|
|
; Find the highest order byte in exponent
|
|
mov edi, [exp]
|
|
mov ecx, [edi]
|
|
lea edi, [edi + 4 + ecx - 1]
|
|
; Find the highest order bit in this byte
|
|
mov al, [edi]
|
|
test al, al
|
|
jz .invalid
|
|
mov bl, 9
|
|
@@:
|
|
dec bl
|
|
shl al, 1
|
|
jnc @r
|
|
|
|
lea edx, [mpint_tmp]
|
|
; Initialise result to base, to take care of the highest order bit
|
|
stdcall mpint_mov, [dst], [base]
|
|
dec bl
|
|
jz .next_byte
|
|
.bit_loop:
|
|
; For each bit, square result
|
|
stdcall mpint_mov, edx, [dst]
|
|
stdcall mpint_mul, [dst], edx, edx
|
|
stdcall mpint_mod, [dst], [mod]
|
|
|
|
; If the bit is set, multiply result by the base
|
|
shl al, 1
|
|
jnc .next_bit
|
|
stdcall mpint_mov, edx, [dst]
|
|
stdcall mpint_mul, [dst], [base], edx
|
|
stdcall mpint_mod, [dst], [mod]
|
|
.next_bit:
|
|
dec bl
|
|
jnz .bit_loop
|
|
.next_byte:
|
|
dec ecx
|
|
jz .done
|
|
dec edi
|
|
mov al, [edi]
|
|
mov bl, 8
|
|
jmp .bit_loop
|
|
.done:
|
|
ret
|
|
|
|
.mod_zero:
|
|
DEBUGF 3, "modexp with modulo 0\n"
|
|
; if mod is zero, result = 0
|
|
mov eax, [dst]
|
|
mov dword[eax], 0
|
|
ret
|
|
|
|
.exp_zero:
|
|
DEBUGF 3, "modexp with exponent 0\n"
|
|
; if exponent is zero, result = 1
|
|
mov eax, [dst]
|
|
mov dword[eax], 1
|
|
mov byte[eax+4], 1
|
|
ret
|
|
|
|
.invalid:
|
|
DEBUGF 3, "modexp: Invalid input!\n"
|
|
ret
|
|
|
|
endp |