mirror of
https://github.com/CloverHackyColor/CloverBootloader.git
synced 2024-11-27 12:15:19 +01:00
620401dca6
Signed-off-by: Sergey Isakov <isakov-sl@bk.ru>
802 lines
22 KiB
C
802 lines
22 KiB
C
/**
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This library performs unsigned arbitrary precision arithmetic operations.
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All results are returned into caller-provided buffers. The caller is
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responsible to ensure the buffers can hold a value of the precision it
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desires. Too large results will be truncated without further notification for
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public APIs.
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https://github.com/kokke/tiny-bignum-c has served as a template for several
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algorithmic ideas.
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This code is not to be considered general-purpose but solely to support
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cryptographic operations such as RSA encryption. As such, there are arbitrary
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limitations, such as requirement of equal precision, to limit the complexity
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of the operations to the bare minimum required to support such use caes.
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SECURITY: Currently, no security measures have been taken. This code is
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vulnerable to both timing and side channel attacks for value
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leakage. However, its current purpose is the verification of public
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binaries with public certificates, for which this is perfectly
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acceptable, especially in regards to performance.
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Copyright (C) 2019, Download-Fritz. All rights reserved.
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This program and the accompanying materials
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are licensed and made available under the terms and conditions of the BSD License
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which accompanies this distribution. The full text of the license may be found at
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http://opensource.org/licenses/bsd-license.php
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THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
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WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
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**/
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#include <Base.h>
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#include <Library/BaseLib.h>
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#include <Library/BaseMemoryLib.h>
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#include <Library/DebugLib.h>
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#include <Library/MemoryAllocationLib.h>
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#include <Library/OcCryptoLib.h>
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#include <Library/OcGuardLib.h>
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#include "BigNumLibInternal.h"
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#define OC_BN_MAX_VAL ((OC_BN_WORD)0U - 1U)
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/*
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STATIC_ASSERT (
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OC_BN_WORD_SIZE == sizeof (UINT32) || OC_BN_WORD_SIZE == sizeof (UINT64),
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"OC_BN_WORD_SIZE and OC_BN_WORD_NUM_BITS usages must be adapted."
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);
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*/
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OC_BN_WORD
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BigNumSwapWord (
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IN OC_BN_WORD Word
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)
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{
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if (OC_BN_WORD_SIZE == sizeof (UINT32)) {
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return (OC_BN_WORD)SwapBytes32 ((UINT32)Word);
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}
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if (OC_BN_WORD_SIZE == sizeof (UINT64)) {
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return (OC_BN_WORD)SwapBytes64 ((UINT64)Word);
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}
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ASSERT (FALSE);
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}
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/**
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Shifts A left by Exponent Words.
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@param[in,out] Result The buffer to return the result into.
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@param[in] NumWordsResult The number of Words of Result.
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@param[in,out] A The number to be word-shifted.
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@param[in] NumWordsA The number of Words of A.
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@param[in] Exponent The Word shift exponent.
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**/
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STATIC
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VOID
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BigNumLeftShiftWords (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWordsResult,
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWordsA,
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IN UINTN Exponent
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)
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{
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ASSERT (Result != NULL);
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ASSERT (NumWordsResult > 0);
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ASSERT (A != NULL);
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ASSERT (NumWordsA > 0);
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ASSERT (Exponent < NumWordsResult);
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ASSERT (NumWordsResult - Exponent >= NumWordsA);
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CopyMem (&Result[Exponent], A, (NumWordsResult - Exponent) * OC_BN_WORD_SIZE);
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ZeroMem (Result, Exponent * OC_BN_WORD_SIZE);
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if (NumWordsResult - Exponent > NumWordsA) {
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ZeroMem (
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&Result[NumWordsA + Exponent],
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(NumWordsResult - Exponent - NumWordsA) * OC_BN_WORD_SIZE
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);
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}
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}
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/**
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Shifts A left by Exponent Bits for 0 < Exponent < #Bits(Word).
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Result must have the exact precision to carry the result.
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@param[in,out] Result The buffer to return the result into.
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@param[in] NumWordsResult The number of Words of Result.
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@param[in] A The base.
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@param[in] NumWordsA The number of Words of A.
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@param[in] NumWords The Word shift exponent.
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@param[in] NumBits The Bit shift exponent.
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**/
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STATIC
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VOID
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BigNumLeftShiftWordsAndBits (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWordsResult,
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWordsA,
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IN UINTN NumWords,
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IN UINT8 NumBits
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)
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{
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UINTN Index;
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ASSERT (Result != NULL);
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ASSERT (NumWordsResult > 0);
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ASSERT (A != NULL);
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ASSERT (NumWordsA > 0);
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ASSERT (NumWordsResult == NumWordsA + NumWords + 1);
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//
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// NumBits must not be 0 because a shift of a Word by its Bit width or
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// larger is Undefined Behaviour.
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//
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ASSERT (NumBits > 0);
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ASSERT (NumBits < OC_BN_WORD_NUM_BITS);
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//
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// This is not an algorithmic requirement, but BigNumLeftShiftWords shall be
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// called if TRUE.
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//
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ASSERT (NumWords > 0);
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for (Index = (NumWordsA - 1); Index > 0; --Index) {
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Result[Index + NumWords] = (A[Index] << NumBits) | (A[Index - 1] >> (OC_BN_WORD_NUM_BITS - NumBits));
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}
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//
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// Handle the edge-cases at the beginning and the end of the value.
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//
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Result[NumWords] = A[0] << NumBits;
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Result[NumWordsA + NumWords] = A[NumWordsA - 1] >> (OC_BN_WORD_NUM_BITS - NumBits);
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//
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// Zero everything outside of the previously set ranges.
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//
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ZeroMem (Result, NumWords * OC_BN_WORD_SIZE);
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}
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/**
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Calculates the left-shift of A by Exponent Bits.
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@param[in,out] Result The buffer to return the result into.
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@param[in] NumWordsResult The number of Words of Result.
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@param[in] A The number to shift.
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@param[in] NumWordsA The number of Words of A.
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@param[in] Exponent The amount of Bits to shift by.
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**/
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STATIC
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VOID
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BigNumLeftShift (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWordsResult,
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWordsA,
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IN UINTN Exponent
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)
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{
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UINTN NumWords;
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UINT8 NumBits;
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ASSERT (Result != NULL);
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ASSERT (NumWordsResult > 0);
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ASSERT (A != NULL);
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ASSERT (NumWordsA > 0);
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NumWords = Exponent / OC_BN_WORD_NUM_BITS;
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NumBits = Exponent % OC_BN_WORD_NUM_BITS;
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if (NumBits != 0) {
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BigNumLeftShiftWordsAndBits (
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Result,
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NumWordsResult,
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A,
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NumWordsA,
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NumWords,
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NumBits
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);
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} else {
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BigNumLeftShiftWords (Result, NumWordsResult, A, NumWordsA, NumWords);
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}
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}
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/**
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Shifts A right by Exponent Words.
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@param[in,out] Result The buffer to return the result into.
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@param[in] NumWordsResult The number of Words of Result.
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@param[in,out] A The number to be word-shifted.
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@param[in] NumWordsA The number of Words of A.
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@param[in] Exponent The Word shift exponent.
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**/
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STATIC
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VOID
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BigNumRightShiftWords (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWordsResult,
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWordsA,
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IN UINTN Exponent
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)
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{
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ASSERT (Result != NULL);
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ASSERT (NumWordsResult > 0);
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ASSERT (A != NULL);
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ASSERT (NumWordsA > 0);
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ASSERT (Exponent < NumWordsResult);
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ASSERT (NumWordsResult - Exponent >= NumWordsA);
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CopyMem (Result, &A[Exponent], (NumWordsResult - Exponent) * OC_BN_WORD_SIZE);
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ZeroMem (&Result[NumWordsResult - Exponent], Exponent * OC_BN_WORD_SIZE);
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}
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/**
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Shifts A right by Exponent Bits for 0 < Exponent < #Bits(Word).
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@param[in,out] A The base.
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@param[in] NumWords The number of Words of A.
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@param[in] Exponent The Bit shift exponent.
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**/
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STATIC
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VOID
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BigNumRightShiftBitsSmall (
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IN OUT OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWords,
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IN UINT8 Exponent
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)
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{
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UINTN Index;
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ASSERT (A != NULL);
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ASSERT (NumWords > 0);
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//
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// Exponent must not be 0 because a shift of a Word by its Bit width or
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// larger is Undefined Behaviour.
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//
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ASSERT (Exponent > 0);
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ASSERT (Exponent < OC_BN_WORD_NUM_BITS);
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for (Index = 0; Index < (NumWords - 1U); ++Index) {
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A[Index] = (A[Index] >> Exponent) | (A[Index + 1] << (OC_BN_WORD_NUM_BITS - Exponent));
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}
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A[Index] >>= Exponent;
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}
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/**
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Shifts A right by Exponent Bits for 0 < Exponent < #Bits(Word).
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@param[in,out] Result The buffer to return the result into.
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@param[in] NumWordsResult The number of Words of Result.
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@param[in] A The base.
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@param[in] NumWordsA The number of Words of A.
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@param[in] NumWords The Word shift exponent.
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@param[in] NumBits The Bit shift exponent.
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**/
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STATIC
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VOID
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BigNumRightShiftWordsAndBits (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWordsResult,
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWordsA,
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IN UINTN NumWords,
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IN UINT8 NumBits
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)
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{
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UINTN Index;
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ASSERT (Result != NULL);
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ASSERT (NumWordsResult > 0);
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ASSERT (A != NULL);
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ASSERT (NumWordsA > 0);
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ASSERT (NumWordsA >= NumWords);
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//
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// NumBits must not be 0 because a shift of a Word by its Bit width or
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// larger is Undefined Behaviour.
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//
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ASSERT (NumBits > 0);
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ASSERT (NumBits < OC_BN_WORD_NUM_BITS);
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//
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// This, assuming below, is required to avoid overflows, which purely
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// internal calls should never produce.
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//
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ASSERT (NumWordsA - NumWords >= NumWordsResult);
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//
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// This is not an algorithmic requirement, but BigNumRightShiftWords shall be
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// called if FALSE.
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//
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//ASSERT (NumWords > 0);
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for (Index = NumWords; Index < (UINTN) (NumWordsA - 1); ++Index) {
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Result[Index - NumWords] = (A[Index] >> NumBits) | (A[Index + 1] << (OC_BN_WORD_NUM_BITS - NumBits));
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}
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//
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// Handle the edge-cases at the beginning and the end of the value.
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//
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Result[Index - NumWords] = (A[NumWordsA - 1] >> NumBits);
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//
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// Zero everything outside of the previously set ranges.
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//
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ZeroMem (&Result[Index - NumWords + 1], (NumWordsResult - (Index - NumWords + 1)) * OC_BN_WORD_SIZE);
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}
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/**
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Calculates the right-shift of A by Exponent Bits.
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@param[in,out] Result The buffer to return the result into.
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@param[in] NumWordsResult The number of Words of Result.
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@param[in] A The number to shift.
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@param[in] NumWordsA The number of Words of A.
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@param[in] Exponent The amount of Bits to shift by.
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**/
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STATIC
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VOID
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BigNumRightShift (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWordsResult,
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWordsA,
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IN UINTN Exponent
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)
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{
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UINTN NumWords;
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UINT8 NumBits;
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ASSERT (Result != NULL);
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ASSERT (NumWordsResult > 0);
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ASSERT (A != NULL);
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ASSERT (NumWordsA > 0);
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NumWords = Exponent / OC_BN_WORD_NUM_BITS;
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NumBits = Exponent % OC_BN_WORD_NUM_BITS;
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if (NumBits != 0) {
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BigNumRightShiftWordsAndBits (
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Result,
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NumWordsResult,
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A,
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NumWordsA,
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NumWords,
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NumBits
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);
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} else {
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BigNumRightShiftWords (Result, NumWordsResult, A, NumWordsA, NumWords);
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}
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}
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/**
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Calculates the product of A and B.
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@param[out] Hi Buffer in which the high Word of the result is returned.
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@param[in] A The multiplicant.
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@param[in] B The multiplier.
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@returns The low Word of the result.
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**/
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OC_BN_WORD
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BigNumWordMul (
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OUT OC_BN_WORD *Hi,
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IN OC_BN_WORD A,
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IN OC_BN_WORD B
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)
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{
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UINT64 Result64;
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ASSERT (Hi != NULL);
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if (OC_BN_WORD_SIZE == sizeof (UINT32)) {
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Result64 = (UINT64)A * B;
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//
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// FIXME: The subtraction in the shift is a dirty hack to shut up MSVC.
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//
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*Hi = (OC_BN_WORD)(RShiftU64 (Result64, OC_BN_WORD_NUM_BITS));
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return (OC_BN_WORD)Result64;
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}
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if (OC_BN_WORD_SIZE == sizeof (UINT64)) {
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return BigNumWordMul64 (Hi, A, B);
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}
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}
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VOID
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BigNumSub (
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IN OUT OC_BN_WORD *Result,
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IN OC_BN_NUM_WORDS NumWords,
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IN CONST OC_BN_WORD *A,
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IN CONST OC_BN_WORD *B
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)
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{
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OC_BN_WORD TmpResult;
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OC_BN_WORD Tmp1;
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OC_BN_WORD Tmp2;
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UINTN Index;
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UINT8 Borrow;
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ASSERT (Result != NULL);
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ASSERT (NumWords > 0);
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ASSERT (A != NULL);
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ASSERT (B != NULL);
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//
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// As only the same indices are ever accessed at a step, it is safe to call
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// this function with Result = A or Result = B.
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//
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Borrow = 0;
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for (Index = 0; Index < NumWords; ++Index) {
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Tmp1 = A[Index];
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Tmp2 = B[Index] + Borrow;
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TmpResult = (Tmp1 - Tmp2);
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//
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// When a subtraction wraps around, the result must be bigger than either
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// operand.
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//
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Borrow = (Tmp2 < Borrow) | (Tmp1 < TmpResult);
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Result[Index] = TmpResult;
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}
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}
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/**
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Returns the number of significant bits in a Word.
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@param[in] Word The word to gather the number of significant bits of.
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@returns The number of significant bits in Word.
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**/
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STATIC
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UINT8
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BigNumSignificantBitsWord (
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IN OC_BN_WORD Word
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)
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{
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UINT8 NumBits;
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OC_BN_WORD Mask;
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//
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// The values we are receiving are very likely large, thus this approach
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// should be reasonably fast.
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//
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NumBits = OC_BN_WORD_NUM_BITS;
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Mask = (OC_BN_WORD)1U << (OC_BN_WORD_NUM_BITS - 1);
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while (Mask != 0 && (Word & Mask) == 0) {
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--NumBits;
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Mask >>= 1U;
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}
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return NumBits;
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}
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/**
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Returns the most significant word index of A.
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@param[in] A The number to gather the most significant Word index of.
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@param[in] NumWords The number of Words of A.
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@returns The index of the most significant Word in A.
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**/
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STATIC
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OC_BN_NUM_WORDS
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BigNumMostSignificantWord (
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWords
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)
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{
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OC_BN_NUM_WORDS Index;
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ASSERT (A != NULL);
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ASSERT (NumWords > 0);
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Index = NumWords;
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do {
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--Index;
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if (A[Index] != 0) {
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return Index;
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}
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} while (Index != 0);
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return 0;
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}
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OC_BN_NUM_BITS
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BigNumSignificantBits (
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IN CONST OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWords
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)
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{
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OC_BN_NUM_BITS Index;
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ASSERT (A != NULL);
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ASSERT (NumWords > 0);
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Index = BigNumMostSignificantWord (A, NumWords);
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return ((Index * OC_BN_WORD_NUM_BITS) + BigNumSignificantBitsWord (A[Index]));
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}
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VOID
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BigNumOrWord (
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IN OUT OC_BN_WORD *A,
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IN OC_BN_NUM_WORDS NumWords,
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IN OC_BN_WORD Value,
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IN UINTN Exponent
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)
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{
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UINTN WordIndex;
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UINT8 NumBits;
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ASSERT (A != NULL);
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ASSERT (NumWords > 0);
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ASSERT (Exponent / OC_BN_WORD_NUM_BITS < NumWords);
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WordIndex = Exponent / OC_BN_WORD_NUM_BITS;
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if (WordIndex < NumWords) {
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NumBits = Exponent % OC_BN_WORD_NUM_BITS;
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A[WordIndex] |= (Value << NumBits);
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}
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}
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INTN
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|
BigNumCmp (
|
|
IN CONST OC_BN_WORD *A,
|
|
IN OC_BN_NUM_WORDS NumWords,
|
|
IN CONST OC_BN_WORD *B
|
|
)
|
|
{
|
|
UINTN Index;
|
|
|
|
ASSERT (A != NULL);
|
|
ASSERT (NumWords > 0);
|
|
ASSERT (B != NULL);
|
|
|
|
Index = NumWords;
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|
do {
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|
--Index;
|
|
if (A[Index] > B[Index]) {
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|
return 1;
|
|
} else if (A[Index] < B[Index]) {
|
|
return -1;
|
|
}
|
|
} while (Index != 0);
|
|
|
|
return 0;
|
|
}
|
|
|
|
BOOLEAN
|
|
BigNumMod (
|
|
IN OUT OC_BN_WORD *Result,
|
|
IN OC_BN_NUM_WORDS NumWordsRest,
|
|
IN CONST OC_BN_WORD *A,
|
|
IN OC_BN_NUM_WORDS NumWordsA,
|
|
IN CONST OC_BN_WORD *B
|
|
)
|
|
{
|
|
INTN CmpResult;
|
|
|
|
VOID *Memory;
|
|
|
|
OC_BN_WORD *ModTmp;
|
|
OC_BN_NUM_BITS SigBitsModTmp;
|
|
OC_BN_NUM_WORDS SigWordsModTmp;
|
|
|
|
OC_BN_NUM_BITS BigDivExp;
|
|
OC_BN_WORD *BigDiv;
|
|
OC_BN_NUM_BITS SigBitsBigDiv;
|
|
OC_BN_NUM_WORDS SigWordsBigDiv;
|
|
|
|
OC_BN_NUM_BITS DeltaBits;
|
|
|
|
ASSERT (Result != NULL);
|
|
ASSERT (NumWordsRest > 0);
|
|
ASSERT (A != NULL);
|
|
ASSERT (NumWordsA > 0);
|
|
ASSERT (B != NULL);
|
|
ASSERT (NumWordsA >= NumWordsRest);
|
|
//
|
|
// SigBitsModTmp is calculated manually to avoid calculating SigWordsModTmp
|
|
// by modulo.
|
|
//
|
|
SigWordsModTmp = BigNumMostSignificantWord (A, NumWordsA);
|
|
SigBitsModTmp = SigWordsModTmp * OC_BN_WORD_NUM_BITS + BigNumSignificantBitsWord (A[SigWordsModTmp]);
|
|
++SigWordsModTmp;
|
|
/*
|
|
ASSERT (SigBitsModTmp == BigNumSignificantBits (A, SigWordsModTmp));
|
|
|
|
STATIC_ASSERT (
|
|
OC_BN_MAX_SIZE <= MAX_UINTN / 2,
|
|
"An overflow verification must be added"
|
|
);
|
|
*/
|
|
Memory = AllocatePool (2 * SigWordsModTmp * OC_BN_WORD_SIZE);
|
|
if (Memory == NULL) {
|
|
return FALSE;
|
|
}
|
|
|
|
ModTmp = Memory;
|
|
BigDiv = &ModTmp[SigWordsModTmp];
|
|
SigWordsBigDiv = SigWordsModTmp;
|
|
//
|
|
// Invariant: BigDiv > ModTmp / 2
|
|
// The invariant implies ModTmp / BigDiv <= 1 (latter in the strictest case).
|
|
//
|
|
// This loop iteratively subtracts multiples BigDiv of B from ModTmp := A [1],
|
|
// otherwise ModTmp is not modified. BigDiv is iteratively reduced such that
|
|
// ModTmp >= BigDiv [2]. The loop terminates once BigDiv < B yields true [3].
|
|
//
|
|
CopyMem (ModTmp, A, SigWordsModTmp * OC_BN_WORD_SIZE);
|
|
//
|
|
// Initialisation:
|
|
// A bit-shift by x is equal to multiplying the operand with 2^x.
|
|
// BigDiv := B << x so that its MSB is equal to the MSB of A implies:
|
|
// 2*BigDiv > A <=> BigDiv > ModTmp / 2 with ModTmp = A.
|
|
//
|
|
SigBitsBigDiv = BigNumSignificantBits (B, NumWordsRest);
|
|
ASSERT (SigBitsModTmp >= SigBitsBigDiv);
|
|
BigDivExp = SigBitsModTmp - SigBitsBigDiv;
|
|
|
|
BigNumLeftShift (BigDiv, SigWordsBigDiv, B, NumWordsRest, BigDivExp);
|
|
SigBitsBigDiv = SigBitsModTmp;
|
|
ASSERT (SigBitsBigDiv == BigNumSignificantBits (BigDiv, SigWordsBigDiv));
|
|
|
|
while (TRUE) {
|
|
//
|
|
// Because the invariant is maintained optimally, the MSB of BigDiv is
|
|
// either the MSB of ModTmp or one below. SigWords* are maintained
|
|
// precisely during the loop's execution, so when SigWordsModTmp is larger
|
|
// than SigWordsBigDiv, ModTmp is larger than BigDiv.
|
|
//
|
|
ASSERT (SigWordsModTmp == SigWordsBigDiv || SigWordsModTmp == SigWordsBigDiv + 1);
|
|
if (SigWordsModTmp > SigWordsBigDiv) {
|
|
ASSERT (ModTmp[SigWordsModTmp - 1] != 0);
|
|
CmpResult = 1;
|
|
} else {
|
|
CmpResult = BigNumCmp (ModTmp, SigWordsBigDiv, BigDiv);
|
|
}
|
|
|
|
if (CmpResult >= 0) {
|
|
//
|
|
// Iteration 1: [1] ModTmp >= BigDiv means ModTmp is reduced.
|
|
//
|
|
// Subtract SigWordsModTmp words because the current divisor value may be
|
|
// shorter than the current modulus value. As both reside in buffers of
|
|
// equal length and no high word is stripped without being set to 0, this
|
|
// is safe.
|
|
//
|
|
BigNumSub (ModTmp, SigWordsModTmp, ModTmp, BigDiv);
|
|
|
|
if (BigDivExp == 0) {
|
|
//
|
|
// Iteration 1: [3] BigDiv = B implies BigDiv < B would yield true
|
|
// after executing the reduction below.
|
|
//
|
|
ASSERT (BigNumCmp (BigDiv, SigWordsBigDiv, B) == 0);
|
|
break;
|
|
}
|
|
//
|
|
// SigBitsModTmp is calculated manually to avoid calculating
|
|
// SigWordsModTmp by modulo.
|
|
//
|
|
SigWordsModTmp = BigNumMostSignificantWord (ModTmp, SigWordsModTmp);
|
|
SigBitsModTmp = SigWordsModTmp * OC_BN_WORD_NUM_BITS + BigNumSignificantBitsWord (ModTmp[SigWordsModTmp]);
|
|
++SigWordsModTmp;
|
|
ASSERT (SigBitsModTmp == BigNumSignificantBits (ModTmp, SigWordsModTmp));
|
|
|
|
ASSERT (SigBitsBigDiv >= SigBitsModTmp);
|
|
DeltaBits = SigBitsBigDiv - SigBitsModTmp;
|
|
if (DeltaBits > BigDivExp) {
|
|
//
|
|
// Iteration 1: [3] This implies BigDiv < B would yield true after
|
|
// executing the reduction below.
|
|
//
|
|
break;
|
|
}
|
|
//
|
|
// Iteration 1: [2] Please refer to Initialisation.
|
|
//
|
|
BigNumRightShift (BigDiv, SigWordsBigDiv, BigDiv, SigWordsBigDiv, DeltaBits);
|
|
|
|
SigWordsBigDiv = (OC_BN_NUM_WORDS) ((SigBitsModTmp + (OC_BN_WORD_NUM_BITS - 1U)) / OC_BN_WORD_NUM_BITS);
|
|
SigBitsBigDiv = SigBitsModTmp;
|
|
|
|
BigDivExp -= DeltaBits;
|
|
} else {
|
|
//
|
|
// Iteration 2: [1] BigDiv > ModTmp means ModTmp will be reduced next
|
|
// iteration.
|
|
//
|
|
if (BigDivExp == 0) {
|
|
//
|
|
// Iteration 2: [3] BigDiv = B implies BigDiv < B would yield true
|
|
// after executing the reduction below.
|
|
//
|
|
ASSERT (BigNumCmp (BigDiv, SigWordsBigDiv, B) == 0);
|
|
break;
|
|
}
|
|
//
|
|
// Iteration 2: [2] BigDiv > ModTmp means BigDiv is reduced to more
|
|
// strictly maintain the invariant BigDiv / 2 > ModTmp.
|
|
//
|
|
BigNumRightShiftBitsSmall (BigDiv, SigWordsBigDiv, 1);
|
|
|
|
--SigBitsBigDiv;
|
|
--BigDivExp;
|
|
|
|
if (SigBitsBigDiv % OC_BN_WORD_NUM_BITS == 0) {
|
|
//
|
|
// Every time the subtraction by 1 yields a multiplie of the word
|
|
// length, the most significant Byte has become zero and is stripped.
|
|
//
|
|
ASSERT (BigDiv[SigWordsBigDiv - 1] == 0);
|
|
--SigWordsBigDiv;
|
|
}
|
|
}
|
|
//
|
|
// ASSERT both branches maintain SigBitsBigDiv correctly.
|
|
//
|
|
ASSERT (SigBitsBigDiv == BigNumSignificantBits (BigDiv, SigWordsBigDiv));
|
|
}
|
|
//
|
|
// Termination:
|
|
// Because BigDiv = B and, by invariant, BigDiv > ModTmp / 2 are true in the
|
|
// last iteration, B > ModTmp / 2 <=> 2 * B > ModTmp is true and thus
|
|
// conditionally subtracting B from ModTmp once more yields B > ModTmp, at
|
|
// which point ModTmp must carry the modulus of A / B. The final reduction
|
|
// of BigDiv yields BigDiv < B and thus the loop is terminated without
|
|
// further effects.
|
|
//
|
|
|
|
//
|
|
// Assuming correctness, the modulus cannot be larger than the divisor.
|
|
//
|
|
ASSERT (BigNumMostSignificantWord (ModTmp, SigWordsModTmp) + 1 <= NumWordsRest);
|
|
CopyMem (Result, ModTmp, NumWordsRest * OC_BN_WORD_SIZE);
|
|
|
|
FreePool (Memory);
|
|
return TRUE;
|
|
}
|
|
|
|
VOID
|
|
BigNumParseBuffer (
|
|
IN OUT OC_BN_WORD *Result,
|
|
IN OC_BN_NUM_WORDS NumWords,
|
|
IN CONST UINT8 *Buffer,
|
|
IN UINTN BufferSize
|
|
)
|
|
{
|
|
UINTN Index;
|
|
OC_BN_WORD Tmp;
|
|
|
|
ASSERT (Result != NULL);
|
|
ASSERT (NumWords * OC_BN_WORD_SIZE == BufferSize);
|
|
ASSERT (Buffer != NULL);
|
|
ASSERT (BufferSize > 0);
|
|
ASSERT ((BufferSize % OC_BN_WORD_SIZE) == 0);
|
|
|
|
for (Index = OC_BN_WORD_SIZE; Index <= BufferSize; Index += OC_BN_WORD_SIZE) {
|
|
if (OC_BN_WORD_SIZE == sizeof (UINT32)) {
|
|
Tmp = (OC_BN_WORD)(
|
|
((UINT32)Buffer[(BufferSize - Index) + 0] << 24U) |
|
|
((UINT32)Buffer[(BufferSize - Index) + 1] << 16U) |
|
|
((UINT32)Buffer[(BufferSize - Index) + 2] << 8U) |
|
|
((UINT32)Buffer[(BufferSize - Index) + 3] << 0U));
|
|
} else if (OC_BN_WORD_SIZE == sizeof (UINT64)) {
|
|
Tmp = (OC_BN_WORD)(
|
|
((UINT64)Buffer[(BufferSize - Index) + 0] << 56U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 1] << 48U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 2] << 40U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 3] << 32U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 4] << 24U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 5] << 16U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 6] << 8U) |
|
|
((UINT64)Buffer[(BufferSize - Index) + 7] << 0U));
|
|
}
|
|
|
|
Result[(Index / OC_BN_WORD_SIZE) - 1] = Tmp;
|
|
}
|
|
}
|