diff options
Diffstat (limited to 'src/VBox/Runtime/common/math/bignum.cpp')
| -rw-r--r-- | src/VBox/Runtime/common/math/bignum.cpp | 2877 |
1 files changed, 2877 insertions, 0 deletions
diff --git a/src/VBox/Runtime/common/math/bignum.cpp b/src/VBox/Runtime/common/math/bignum.cpp new file mode 100644 index 00000000..efa67644 --- /dev/null +++ b/src/VBox/Runtime/common/math/bignum.cpp @@ -0,0 +1,2877 @@ +/* $Id: bignum.cpp $ */ +/** @file + * IPRT - Big Integer Numbers. + */ + +/* + * Copyright (C) 2006-2023 Oracle and/or its affiliates. + * + * This file is part of VirtualBox base platform packages, as + * available from https://www.virtualbox.org. + * + * This program is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation, in version 3 of the + * License. + * + * This program is distributed in the hope that it will be useful, but + * WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + * General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, see <https://www.gnu.org/licenses>. + * + * The contents of this file may alternatively be used under the terms + * of the Common Development and Distribution License Version 1.0 + * (CDDL), a copy of it is provided in the "COPYING.CDDL" file included + * in the VirtualBox distribution, in which case the provisions of the + * CDDL are applicable instead of those of the GPL. + * + * You may elect to license modified versions of this file under the + * terms and conditions of either the GPL or the CDDL or both. + * + * SPDX-License-Identifier: GPL-3.0-only OR CDDL-1.0 + */ + + +/********************************************************************************************************************************* +* Header Files * +*********************************************************************************************************************************/ +/*#ifdef IN_RING3 +# define RTMEM_WRAP_TO_EF_APIS +#endif*/ +#include "internal/iprt.h" +#include <iprt/bignum.h> + +#include <iprt/asm.h> +#include <iprt/asm-math.h> +#include <iprt/err.h> +#include <iprt/mem.h> +#include <iprt/memsafer.h> +#include <iprt/string.h> +#if RTBIGNUM_ELEMENT_BITS == 64 +# include <iprt/uint128.h> +#endif + + +/********************************************************************************************************************************* +* Defined Constants And Macros * +*********************************************************************************************************************************/ +/** Allocation alignment in elements. */ +#ifndef RTMEM_WRAP_TO_EF_APIS +# define RTBIGNUM_ALIGNMENT 4U +#else +# define RTBIGNUM_ALIGNMENT 1U +#endif + +/** The max size (in bytes) of an elements array. */ +#define RTBIGNUM_MAX_SIZE _4M + + +/** Assert the validity of a big number structure pointer in strict builds. */ +#ifdef RT_STRICT +# define RTBIGNUM_ASSERT_VALID(a_pBigNum) \ + do { \ + AssertPtr(a_pBigNum); \ + Assert(!(a_pBigNum)->fCurScrambled); \ + Assert( (a_pBigNum)->cUsed == (a_pBigNum)->cAllocated \ + || ASMMemIsZero(&(a_pBigNum)->pauElements[(a_pBigNum)->cUsed], \ + ((a_pBigNum)->cAllocated - (a_pBigNum)->cUsed) * RTBIGNUM_ELEMENT_SIZE)); \ + } while (0) +#else +# define RTBIGNUM_ASSERT_VALID(a_pBigNum) do {} while (0) +#endif + + +/** Enable assembly optimizations. */ +#if defined(RT_ARCH_AMD64) || defined(RT_ARCH_X86) +# define IPRT_BIGINT_WITH_ASM +#endif + + +/** @def RTBIGNUM_ZERO_ALIGN + * For calculating the rtBigNumEnsureExtraZeroElements argument from cUsed. + * This has to do with 64-bit assembly instruction operating as RTBIGNUMELEMENT + * was 64-bit on some hosts. + */ +#if defined(IPRT_BIGINT_WITH_ASM) && ARCH_BITS == 64 && RTBIGNUM_ELEMENT_SIZE == 4 && defined(RT_LITTLE_ENDIAN) +# define RTBIGNUM_ZERO_ALIGN(a_cUsed) RT_ALIGN_32(a_cUsed, 2) +#elif defined(IPRT_BIGINT_WITH_ASM) +# define RTBIGNUM_ZERO_ALIGN(a_cUsed) (a_cUsed) +#else +# define RTBIGNUM_ZERO_ALIGN(a_cUsed) (a_cUsed) +#endif + +#define RTBIGNUMELEMENT_HALF_MASK ( ((RTBIGNUMELEMENT)1 << (RTBIGNUM_ELEMENT_BITS / 2)) - (RTBIGNUMELEMENT)1) +#define RTBIGNUMELEMENT_LO_HALF(a_uElement) ( (RTBIGNUMELEMENT_HALF_MASK) & (a_uElement) ) +#define RTBIGNUMELEMENT_HI_HALF(a_uElement) ( (a_uElement) >> (RTBIGNUM_ELEMENT_BITS / 2) ) + + +/********************************************************************************************************************************* +* Structures and Typedefs * +*********************************************************************************************************************************/ +/** Type the size of two elements. */ +#if RTBIGNUM_ELEMENT_BITS == 64 +typedef RTUINT128U RTBIGNUMELEMENT2X; +#else +typedef RTUINT64U RTBIGNUMELEMENT2X; +#endif + + +/********************************************************************************************************************************* +* Internal Functions * +*********************************************************************************************************************************/ +DECLINLINE(int) rtBigNumSetUsed(PRTBIGNUM pBigNum, uint32_t cNewUsed); + +#ifdef IPRT_BIGINT_WITH_ASM +/* bignum-amd64-x86.asm: */ +DECLASM(void) rtBigNumMagnitudeSubAssemblyWorker(RTBIGNUMELEMENT *pauResult, RTBIGNUMELEMENT const *pauMinuend, + RTBIGNUMELEMENT const *pauSubtrahend, uint32_t cUsed); +DECLASM(void) rtBigNumMagnitudeSubThisAssemblyWorker(RTBIGNUMELEMENT *pauMinuendResult, RTBIGNUMELEMENT const *pauSubtrahend, + uint32_t cUsed); +DECLASM(RTBIGNUMELEMENT) rtBigNumMagnitudeShiftLeftOneAssemblyWorker(RTBIGNUMELEMENT *pauElements, uint32_t cUsed, + RTBIGNUMELEMENT uCarry); +DECLASM(void) rtBigNumElement2xDiv2xBy1x(RTBIGNUMELEMENT2X *puQuotient, RTBIGNUMELEMENT *puRemainder, + RTBIGNUMELEMENT uDividendHi, RTBIGNUMELEMENT uDividendLo, RTBIGNUMELEMENT uDivisor); +DECLASM(void) rtBigNumMagnitudeMultiplyAssemblyWorker(PRTBIGNUMELEMENT pauResult, + PCRTBIGNUMELEMENT pauMultiplier, uint32_t cMultiplier, + PCRTBIGNUMELEMENT pauMultiplicand, uint32_t cMultiplicand); +#endif + + + + + +/** @name Functions working on one element. + * @{ */ + +DECLINLINE(uint32_t) rtBigNumElementBitCount(RTBIGNUMELEMENT uElement) +{ +#if RTBIGNUM_ELEMENT_SIZE == 8 + if (uElement >> 32) + return ASMBitLastSetU32((uint32_t)(uElement >> 32)) + 32; + return ASMBitLastSetU32((uint32_t)uElement); +#elif RTBIGNUM_ELEMENT_SIZE == 4 + return ASMBitLastSetU32(uElement); +#else +# error "Bad RTBIGNUM_ELEMENT_SIZE value" +#endif +} + + +/** + * Does addition with carry. + * + * This is a candidate for inline assembly on some platforms. + * + * @returns The result (the sum) + * @param uAugend What to add to. + * @param uAddend What to add to it. + * @param pfCarry Where to read the input carry and return the output + * carry. + */ +DECLINLINE(RTBIGNUMELEMENT) rtBigNumElementAddWithCarry(RTBIGNUMELEMENT uAugend, RTBIGNUMELEMENT uAddend, + RTBIGNUMELEMENT *pfCarry) +{ + RTBIGNUMELEMENT uRet = uAugend + uAddend; + if (!*pfCarry) + *pfCarry = uRet < uAugend; + else + { + uRet += 1; + *pfCarry = uRet <= uAugend; + } + return uRet; +} + + +#if !defined(IPRT_BIGINT_WITH_ASM) || defined(RT_STRICT) +/** + * Does addition with borrow. + * + * This is a candidate for inline assembly on some platforms. + * + * @returns The result (the sum) + * @param uMinuend What to subtract from. + * @param uSubtrahend What to subtract. + * @param pfBorrow Where to read the input borrow and return the output + * borrow. + */ +DECLINLINE(RTBIGNUMELEMENT) rtBigNumElementSubWithBorrow(RTBIGNUMELEMENT uMinuend, RTBIGNUMELEMENT uSubtrahend, + RTBIGNUMELEMENT *pfBorrow) +{ + RTBIGNUMELEMENT uRet = uMinuend - uSubtrahend - *pfBorrow; + + /* Figure out if we borrowed. */ + *pfBorrow = !*pfBorrow ? uMinuend < uSubtrahend : uMinuend <= uSubtrahend; + return uRet; +} +#endif + +/** @} */ + + + + +/** @name Double element primitives. + * @{ */ + +static int rtBigNumElement2xCopyToMagnitude(RTBIGNUMELEMENT2X const *pValue2x, PRTBIGNUM pDst) +{ + int rc; + if (pValue2x->s.Hi) + { + rc = rtBigNumSetUsed(pDst, 2); + if (RT_SUCCESS(rc)) + { + pDst->pauElements[0] = pValue2x->s.Lo; + pDst->pauElements[1] = pValue2x->s.Hi; + } + } + else if (pValue2x->s.Lo) + { + rc = rtBigNumSetUsed(pDst, 1); + if (RT_SUCCESS(rc)) + pDst->pauElements[0] = pValue2x->s.Lo; + } + else + rc = rtBigNumSetUsed(pDst, 0); + return rc; +} + +static void rtBigNumElement2xDiv(RTBIGNUMELEMENT2X *puQuotient, RTBIGNUMELEMENT2X *puRemainder, + RTBIGNUMELEMENT uDividendHi, RTBIGNUMELEMENT uDividendLo, + RTBIGNUMELEMENT uDivisorHi, RTBIGNUMELEMENT uDivisorLo) +{ + RTBIGNUMELEMENT2X uDividend; + uDividend.s.Lo = uDividendLo; + uDividend.s.Hi = uDividendHi; + + RTBIGNUMELEMENT2X uDivisor; + uDivisor.s.Lo = uDivisorLo; + uDivisor.s.Hi = uDivisorHi; + +#if RTBIGNUM_ELEMENT_BITS == 64 + RTUInt128DivRem(puQuotient, puRemainder, &uDividend, &uDivisor); +#else + puQuotient->u = uDividend.u / uDivisor.u; + puRemainder->u = uDividend.u % uDivisor.u; +#endif +} + +#ifndef IPRT_BIGINT_WITH_ASM +static void rtBigNumElement2xDiv2xBy1x(RTBIGNUMELEMENT2X *puQuotient, RTBIGNUMELEMENT *puRemainder, + RTBIGNUMELEMENT uDividendHi, RTBIGNUMELEMENT uDividendLo, RTBIGNUMELEMENT uDivisor) +{ + RTBIGNUMELEMENT2X uDividend; + uDividend.s.Lo = uDividendLo; + uDividend.s.Hi = uDividendHi; + +# if RTBIGNUM_ELEMENT_BITS == 64 + RTBIGNUMELEMENT2X uRemainder2x; + RTBIGNUMELEMENT2X uDivisor2x; + uDivisor2x.s.Hi = 0; + uDivisor2x.s.Lo = uDivisor; + /** @todo optimize this. */ + RTUInt128DivRem(puQuotient, &uRemainder2x, &uDividend, &uDivisor2x); + *puRemainder = uRemainder2x.s.Lo; +# else + puQuotient->u = uDividend.u / uDivisor; + puRemainder->u = uDividend.u % uDivisor; +# endif +} +#endif + +DECLINLINE(void) rtBigNumElement2xDec(RTBIGNUMELEMENT2X *puValue) +{ +#if RTBIGNUM_ELEMENT_BITS == 64 + if (puValue->s.Lo-- == 0) + puValue->s.Hi--; +#else + puValue->u -= 1; +#endif +} + +#if 0 /* unused */ +DECLINLINE(void) rtBigNumElement2xAdd1x(RTBIGNUMELEMENT2X *puValue, RTBIGNUMELEMENT uAdd) +{ +#if RTBIGNUM_ELEMENT_BITS == 64 + RTUInt128AssignAddU64(puValue, uAdd); +#else + puValue->u += uAdd; +#endif +} +#endif /* unused */ + +/** @} */ + + + + + +/** + * Scrambles a big number if required. + * + * @param pBigNum The big number. + */ +DECLINLINE(void) rtBigNumScramble(PRTBIGNUM pBigNum) +{ + if (pBigNum->fSensitive) + { + AssertReturnVoid(!pBigNum->fCurScrambled); + if (pBigNum->pauElements) + { + int rc = RTMemSaferScramble(pBigNum->pauElements, pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); AssertRC(rc); + pBigNum->fCurScrambled = RT_SUCCESS(rc); + } + else + pBigNum->fCurScrambled = true; + } +} + + +/** + * Unscrambles a big number if required. + * + * @returns IPRT status code. + * @param pBigNum The big number. + */ +DECLINLINE(int) rtBigNumUnscramble(PRTBIGNUM pBigNum) +{ + if (pBigNum->fSensitive) + { + AssertReturn(pBigNum->fCurScrambled, VERR_INTERNAL_ERROR_2); + if (pBigNum->pauElements) + { + int rc = RTMemSaferUnscramble(pBigNum->pauElements, pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); AssertRC(rc); + pBigNum->fCurScrambled = !RT_SUCCESS(rc); + return rc; + } + else + pBigNum->fCurScrambled = false; + } + return VINF_SUCCESS; +} + + +/** + * Getter function for pauElements which extends the array to infinity. + * + * @returns The element value. + * @param pBigNum The big number. + * @param iElement The element index. + */ +DECLINLINE(RTBIGNUMELEMENT) rtBigNumGetElement(PCRTBIGNUM pBigNum, uint32_t iElement) +{ + if (iElement < pBigNum->cUsed) + return pBigNum->pauElements[iElement]; + return 0; +} + + +/** + * Grows the pauElements array so it can fit at least @a cNewUsed entries. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param cNewUsed The new cUsed value. + * @param cMinElements The minimum number of elements. + */ +static int rtBigNumGrow(PRTBIGNUM pBigNum, uint32_t cNewUsed, uint32_t cMinElements) +{ + Assert(cMinElements >= cNewUsed); + uint32_t const cbOld = pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE; + uint32_t const cNew = RT_ALIGN_32(cMinElements, RTBIGNUM_ALIGNMENT); + uint32_t const cbNew = cNew * RTBIGNUM_ELEMENT_SIZE; + Assert(cbNew > cbOld); + if (cbNew <= RTBIGNUM_MAX_SIZE && cbNew > cbOld) + { + void *pvNew; + if (pBigNum->fSensitive) + pvNew = RTMemSaferReallocZ(cbOld, pBigNum->pauElements, cbNew); + else + pvNew = RTMemRealloc(pBigNum->pauElements, cbNew); + if (RT_LIKELY(pvNew)) + { + if (cbNew > cbOld) + RT_BZERO((char *)pvNew + cbOld, cbNew - cbOld); + if (pBigNum->cUsed > cNewUsed) + RT_BZERO((RTBIGNUMELEMENT *)pvNew + cNewUsed, (pBigNum->cUsed - cNewUsed) * RTBIGNUM_ELEMENT_SIZE); + + pBigNum->pauElements = (RTBIGNUMELEMENT *)pvNew; + pBigNum->cUsed = cNewUsed; + pBigNum->cAllocated = cNew; + return VINF_SUCCESS; + } + return VERR_NO_MEMORY; + } + return VERR_OUT_OF_RANGE; +} + + +/** + * Changes the cUsed member, growing the pauElements array if necessary. + * + * Any elements added to the array will be initialized to zero. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param cNewUsed The new cUsed value. + */ +DECLINLINE(int) rtBigNumSetUsed(PRTBIGNUM pBigNum, uint32_t cNewUsed) +{ + if (pBigNum->cAllocated >= cNewUsed) + { + if (pBigNum->cUsed > cNewUsed) + RT_BZERO(&pBigNum->pauElements[cNewUsed], (pBigNum->cUsed - cNewUsed) * RTBIGNUM_ELEMENT_SIZE); +#ifdef RT_STRICT + else if (pBigNum->cUsed != cNewUsed) + Assert(ASMMemIsZero(&pBigNum->pauElements[pBigNum->cUsed], (cNewUsed - pBigNum->cUsed) * RTBIGNUM_ELEMENT_SIZE)); +#endif + pBigNum->cUsed = cNewUsed; + return VINF_SUCCESS; + } + return rtBigNumGrow(pBigNum, cNewUsed, cNewUsed); +} + + +/** + * Extended version of rtBigNumSetUsed that also allow specifying the number of + * zero elements required. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param cNewUsed The new cUsed value. + * @param cMinElements The minimum number of elements allocated. The + * difference between @a cNewUsed and @a cMinElements + * is initialized to zero because all free elements are + * zero. + */ +DECLINLINE(int) rtBigNumSetUsedEx(PRTBIGNUM pBigNum, uint32_t cNewUsed, uint32_t cMinElements) +{ + if (pBigNum->cAllocated >= cMinElements) + { + if (pBigNum->cUsed > cNewUsed) + RT_BZERO(&pBigNum->pauElements[cNewUsed], (pBigNum->cUsed - cNewUsed) * RTBIGNUM_ELEMENT_SIZE); +#ifdef RT_STRICT + else if (pBigNum->cUsed != cNewUsed) + Assert(ASMMemIsZero(&pBigNum->pauElements[pBigNum->cUsed], (cNewUsed - pBigNum->cUsed) * RTBIGNUM_ELEMENT_SIZE)); +#endif + pBigNum->cUsed = cNewUsed; + return VINF_SUCCESS; + } + return rtBigNumGrow(pBigNum, cNewUsed, cMinElements); +} + + +/** + * For ensuring zero padding of pauElements for sub/add with carry assembly + * operations. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param cElements The number of elements that must be in the elements + * array array, where those after pBigNum->cUsed must + * be zero. + */ +DECLINLINE(int) rtBigNumEnsureExtraZeroElements(PRTBIGNUM pBigNum, uint32_t cElements) +{ + if (pBigNum->cAllocated >= cElements) + { + Assert( pBigNum->cAllocated == pBigNum->cUsed + || ASMMemIsZero(&pBigNum->pauElements[pBigNum->cUsed], + (pBigNum->cAllocated - pBigNum->cUsed) * RTBIGNUM_ELEMENT_SIZE)); + return VINF_SUCCESS; + } + return rtBigNumGrow(pBigNum, pBigNum->cUsed, cElements); +} + + +/** + * The slow part of rtBigNumEnsureElementPresent where we need to do actual zero + * extending. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param iElement The element we wish to access. + */ +static int rtBigNumEnsureElementPresentSlow(PRTBIGNUM pBigNum, uint32_t iElement) +{ + uint32_t const cOldUsed = pBigNum->cUsed; + int rc = rtBigNumSetUsed(pBigNum, iElement + 1); + if (RT_SUCCESS(rc)) + { + RT_BZERO(&pBigNum->pauElements[cOldUsed], (iElement + 1 - cOldUsed) * RTBIGNUM_ELEMENT_SIZE); + return VINF_SUCCESS; + } + return rc; +} + + +/** + * Zero extends the element array to make sure a the specified element index is + * accessible. + * + * This is typically used with bit operations and self modifying methods. Any + * new elements added will be initialized to zero. The caller is responsible + * for there not being any trailing zero elements. + * + * The number must be unscrambled. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param iElement The element we wish to access. + */ +DECLINLINE(int) rtBigNumEnsureElementPresent(PRTBIGNUM pBigNum, uint32_t iElement) +{ + if (iElement < pBigNum->cUsed) + return VINF_SUCCESS; + return rtBigNumEnsureElementPresentSlow(pBigNum, iElement); +} + + +/** + * Strips zero elements from the magnitude value. + * + * @param pBigNum The big number to strip. + */ +static void rtBigNumStripTrailingZeros(PRTBIGNUM pBigNum) +{ + uint32_t i = pBigNum->cUsed; + while (i > 0 && pBigNum->pauElements[i - 1] == 0) + i--; + pBigNum->cUsed = i; +} + + +/** + * Initialize the big number to zero. + * + * @returns @a pBigNum + * @param pBigNum The big number. + * @param fFlags The flags. + * @internal + */ +DECLINLINE(PRTBIGNUM) rtBigNumInitZeroInternal(PRTBIGNUM pBigNum, uint32_t fFlags) +{ + RT_ZERO(*pBigNum); + pBigNum->fSensitive = RT_BOOL(fFlags & RTBIGNUMINIT_F_SENSITIVE); + return pBigNum; +} + + +/** + * Initialize the big number to zero from a template variable. + * + * @returns @a pBigNum + * @param pBigNum The big number. + * @param pTemplate The template big number. + * @internal + */ +DECLINLINE(PRTBIGNUM) rtBigNumInitZeroTemplate(PRTBIGNUM pBigNum, PCRTBIGNUM pTemplate) +{ + RT_ZERO(*pBigNum); + pBigNum->fSensitive = pTemplate->fSensitive; + return pBigNum; +} + + +RTDECL(int) RTBigNumInit(PRTBIGNUM pBigNum, uint32_t fFlags, void const *pvRaw, size_t cbRaw) +{ + /* + * Validate input. + */ + AssertPtrReturn(pBigNum, VERR_INVALID_POINTER); + AssertReturn(RT_BOOL(fFlags & RTBIGNUMINIT_F_ENDIAN_BIG) ^ RT_BOOL(fFlags & RTBIGNUMINIT_F_ENDIAN_LITTLE), + VERR_INVALID_PARAMETER); + AssertReturn(RT_BOOL(fFlags & RTBIGNUMINIT_F_UNSIGNED) ^ RT_BOOL(fFlags & RTBIGNUMINIT_F_SIGNED), VERR_INVALID_PARAMETER); + if (cbRaw) + AssertPtrReturn(pvRaw, VERR_INVALID_POINTER); + + /* + * Initalize the big number to zero. + */ + rtBigNumInitZeroInternal(pBigNum, fFlags); + + /* + * Strip the input and figure the sign flag. + */ + uint8_t const *pb = (uint8_t const *)pvRaw; + if (cbRaw) + { + if (fFlags & RTBIGNUMINIT_F_ENDIAN_LITTLE) + { + if (fFlags & RTBIGNUMINIT_F_UNSIGNED) + { + while (cbRaw > 0 && pb[cbRaw - 1] == 0) + cbRaw--; + } + else + { + if (pb[cbRaw - 1] >> 7) + { + pBigNum->fNegative = 1; + while (cbRaw > 1 && pb[cbRaw - 1] == 0xff) + cbRaw--; + } + else + while (cbRaw > 0 && pb[cbRaw - 1] == 0) + cbRaw--; + } + } + else + { + if (fFlags & RTBIGNUMINIT_F_UNSIGNED) + { + while (cbRaw > 0 && *pb == 0) + pb++, cbRaw--; + } + else + { + if (*pb >> 7) + { + pBigNum->fNegative = 1; + while (cbRaw > 1 && *pb == 0xff) + pb++, cbRaw--; + } + else + while (cbRaw > 0 && *pb == 0) + pb++, cbRaw--; + } + } + } + + /* + * Allocate memory for the elements. + */ + size_t cbAligned = RT_ALIGN_Z(cbRaw, RTBIGNUM_ELEMENT_SIZE); + if (RT_UNLIKELY(cbAligned >= RTBIGNUM_MAX_SIZE)) + return VERR_OUT_OF_RANGE; + pBigNum->cUsed = (uint32_t)cbAligned / RTBIGNUM_ELEMENT_SIZE; + if (pBigNum->cUsed) + { + pBigNum->cAllocated = RT_ALIGN_32(pBigNum->cUsed, RTBIGNUM_ALIGNMENT); + if (pBigNum->fSensitive) + pBigNum->pauElements = (RTBIGNUMELEMENT *)RTMemSaferAllocZ(pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); + else + pBigNum->pauElements = (RTBIGNUMELEMENT *)RTMemAlloc(pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); + if (RT_UNLIKELY(!pBigNum->pauElements)) + return VERR_NO_MEMORY; + + /* + * Initialize the array. + */ + uint32_t i = 0; + if (fFlags & RTBIGNUMINIT_F_ENDIAN_LITTLE) + { + while (cbRaw >= RTBIGNUM_ELEMENT_SIZE) + { +#if RTBIGNUM_ELEMENT_SIZE == 8 + pBigNum->pauElements[i] = RT_MAKE_U64_FROM_U8(pb[0], pb[1], pb[2], pb[3], pb[4], pb[5], pb[6], pb[7]); +#elif RTBIGNUM_ELEMENT_SIZE == 4 + pBigNum->pauElements[i] = RT_MAKE_U32_FROM_U8(pb[0], pb[1], pb[2], pb[3]); +#else +# error "Bad RTBIGNUM_ELEMENT_SIZE value" +#endif + i++; + pb += RTBIGNUM_ELEMENT_SIZE; + cbRaw -= RTBIGNUM_ELEMENT_SIZE; + } + + if (cbRaw > 0) + { + RTBIGNUMELEMENT uLast = pBigNum->fNegative ? ~(RTBIGNUMELEMENT)0 : 0; + switch (cbRaw) + { + default: AssertFailed(); +#if RTBIGNUM_ELEMENT_SIZE == 8 + RT_FALL_THRU(); + case 7: uLast = (uLast << 8) | pb[6]; RT_FALL_THRU(); + case 6: uLast = (uLast << 8) | pb[5]; RT_FALL_THRU(); + case 5: uLast = (uLast << 8) | pb[4]; RT_FALL_THRU(); + case 4: uLast = (uLast << 8) | pb[3]; +#endif + RT_FALL_THRU(); + case 3: uLast = (uLast << 8) | pb[2]; RT_FALL_THRU(); + case 2: uLast = (uLast << 8) | pb[1]; RT_FALL_THRU(); + case 1: uLast = (uLast << 8) | pb[0]; + } + pBigNum->pauElements[i] = uLast; + } + } + else + { + pb += cbRaw; + while (cbRaw >= RTBIGNUM_ELEMENT_SIZE) + { + pb -= RTBIGNUM_ELEMENT_SIZE; +#if RTBIGNUM_ELEMENT_SIZE == 8 + pBigNum->pauElements[i] = RT_MAKE_U64_FROM_U8(pb[7], pb[6], pb[5], pb[4], pb[3], pb[2], pb[1], pb[0]); +#elif RTBIGNUM_ELEMENT_SIZE == 4 + pBigNum->pauElements[i] = RT_MAKE_U32_FROM_U8(pb[3], pb[2], pb[1], pb[0]); +#else +# error "Bad RTBIGNUM_ELEMENT_SIZE value" +#endif + i++; + cbRaw -= RTBIGNUM_ELEMENT_SIZE; + } + + if (cbRaw > 0) + { + RTBIGNUMELEMENT uLast = pBigNum->fNegative ? ~(RTBIGNUMELEMENT)0 : 0; + pb -= cbRaw; + switch (cbRaw) + { + default: AssertFailed(); +#if RTBIGNUM_ELEMENT_SIZE == 8 + RT_FALL_THRU(); + case 7: uLast = (uLast << 8) | *pb++; RT_FALL_THRU(); + case 6: uLast = (uLast << 8) | *pb++; RT_FALL_THRU(); + case 5: uLast = (uLast << 8) | *pb++; RT_FALL_THRU(); + case 4: uLast = (uLast << 8) | *pb++; +#endif + RT_FALL_THRU(); + case 3: uLast = (uLast << 8) | *pb++; RT_FALL_THRU(); + case 2: uLast = (uLast << 8) | *pb++; RT_FALL_THRU(); + case 1: uLast = (uLast << 8) | *pb++; + } + pBigNum->pauElements[i] = uLast; + } + } + + /* + * If negative, negate it so we get a positive magnitude value in pauElements. + */ + if (pBigNum->fNegative) + { + pBigNum->pauElements[0] = 0U - pBigNum->pauElements[0]; + for (i = 1; i < pBigNum->cUsed; i++) + pBigNum->pauElements[i] = 0U - pBigNum->pauElements[i] - 1U; + } + + /* + * Clear unused elements. + */ + if (pBigNum->cUsed != pBigNum->cAllocated) + { + RTBIGNUMELEMENT *puUnused = &pBigNum->pauElements[pBigNum->cUsed]; + AssertCompile(RTBIGNUM_ALIGNMENT <= 4); + switch (pBigNum->cAllocated - pBigNum->cUsed) + { + default: AssertFailed(); RT_FALL_THRU(); + case 3: *puUnused++ = 0; RT_FALL_THRU(); + case 2: *puUnused++ = 0; RT_FALL_THRU(); + case 1: *puUnused++ = 0; + } + } + RTBIGNUM_ASSERT_VALID(pBigNum); + } + + rtBigNumScramble(pBigNum); + return VINF_SUCCESS; +} + + +RTDECL(int) RTBigNumInitZero(PRTBIGNUM pBigNum, uint32_t fFlags) +{ + AssertReturn(!(fFlags & ~RTBIGNUMINIT_F_SENSITIVE), VERR_INVALID_PARAMETER); + AssertPtrReturn(pBigNum, VERR_INVALID_POINTER); + + rtBigNumInitZeroInternal(pBigNum, fFlags); + rtBigNumScramble(pBigNum); + return VINF_SUCCESS; +} + + +/** + * Internal clone function that assumes the caller takes care of scrambling. + * + * @returns IPRT status code. + * @param pBigNum The target number. + * @param pSrc The source number. + */ +static int rtBigNumCloneInternal(PRTBIGNUM pBigNum, PCRTBIGNUM pSrc) +{ + Assert(!pSrc->fCurScrambled); + int rc = VINF_SUCCESS; + + /* + * Copy over the data. + */ + RT_ZERO(*pBigNum); + pBigNum->fNegative = pSrc->fNegative; + pBigNum->fSensitive = pSrc->fSensitive; + pBigNum->cUsed = pSrc->cUsed; + if (pSrc->cUsed) + { + /* Duplicate the element array. */ + pBigNum->cAllocated = RT_ALIGN_32(pBigNum->cUsed, RTBIGNUM_ALIGNMENT); + if (pBigNum->fSensitive) + pBigNum->pauElements = (RTBIGNUMELEMENT *)RTMemSaferAllocZ(pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); + else + pBigNum->pauElements = (RTBIGNUMELEMENT *)RTMemAlloc(pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); + if (RT_LIKELY(pBigNum->pauElements)) + { + memcpy(pBigNum->pauElements, pSrc->pauElements, pBigNum->cUsed * RTBIGNUM_ELEMENT_SIZE); + if (pBigNum->cUsed != pBigNum->cAllocated) + RT_BZERO(&pBigNum->pauElements[pBigNum->cUsed], (pBigNum->cAllocated - pBigNum->cUsed) * RTBIGNUM_ELEMENT_SIZE); + } + else + { + RT_ZERO(*pBigNum); + rc = VERR_NO_MEMORY; + } + } + return rc; +} + + +RTDECL(int) RTBigNumClone(PRTBIGNUM pBigNum, PCRTBIGNUM pSrc) +{ + int rc = rtBigNumUnscramble((PRTBIGNUM)pSrc); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pSrc); + rc = rtBigNumCloneInternal(pBigNum, pSrc); + if (RT_SUCCESS(rc)) + rtBigNumScramble(pBigNum); + rtBigNumScramble((PRTBIGNUM)pSrc); + } + return rc; +} + + +RTDECL(int) RTBigNumDestroy(PRTBIGNUM pBigNum) +{ + if (pBigNum) + { + if (pBigNum->pauElements) + { + Assert(pBigNum->cAllocated > 0); + if (!pBigNum->fSensitive) + RTMemFree(pBigNum->pauElements); + else + { + RTMemSaferFree(pBigNum->pauElements, pBigNum->cAllocated * RTBIGNUM_ELEMENT_SIZE); + RT_ZERO(*pBigNum); + } + pBigNum->pauElements = NULL; + } + } + return VINF_SUCCESS; +} + + +RTDECL(int) RTBigNumAssign(PRTBIGNUM pDst, PCRTBIGNUM pSrc) +{ + AssertReturn(pDst->fSensitive >= pSrc->fSensitive, VERR_BIGNUM_SENSITIVE_INPUT); + int rc = rtBigNumUnscramble(pDst); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pDst); + rc = rtBigNumUnscramble((PRTBIGNUM)pSrc); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pSrc); + if ( pDst->fSensitive == pSrc->fSensitive + || pDst->fSensitive) + { + if (pDst->cAllocated >= pSrc->cUsed) + { + if (pDst->cUsed > pSrc->cUsed) + RT_BZERO(&pDst->pauElements[pSrc->cUsed], (pDst->cUsed - pSrc->cUsed) * RTBIGNUM_ELEMENT_SIZE); + pDst->cUsed = pSrc->cUsed; + pDst->fNegative = pSrc->fNegative; + memcpy(pDst->pauElements, pSrc->pauElements, pSrc->cUsed * RTBIGNUM_ELEMENT_SIZE); + } + else + { + rc = rtBigNumGrow(pDst, pSrc->cUsed, pSrc->cUsed); + if (RT_SUCCESS(rc)) + { + pDst->fNegative = pSrc->fNegative; + memcpy(pDst->pauElements, pSrc->pauElements, pSrc->cUsed * RTBIGNUM_ELEMENT_SIZE); + } + } + } + else + rc = VERR_BIGNUM_SENSITIVE_INPUT; + rtBigNumScramble((PRTBIGNUM)pSrc); + } + rtBigNumScramble(pDst); + } + return rc; +} + + +/** + * Same as RTBigNumBitWidth, except that it ignore the signed bit. + * + * The number must be unscrambled. + * + * @returns The effective width of the magnitude, in bits. Returns 0 if the + * value is zero. + * @param pBigNum The bit number. + */ +static uint32_t rtBigNumMagnitudeBitWidth(PCRTBIGNUM pBigNum) +{ + uint32_t idxLast = pBigNum->cUsed; + if (idxLast) + { + idxLast--; + RTBIGNUMELEMENT uLast = pBigNum->pauElements[idxLast]; Assert(uLast); + return rtBigNumElementBitCount(uLast) + idxLast * RTBIGNUM_ELEMENT_BITS; + } + return 0; +} + + +RTDECL(uint32_t) RTBigNumBitWidth(PCRTBIGNUM pBigNum) +{ + uint32_t idxLast = pBigNum->cUsed; + if (idxLast) + { + idxLast--; + rtBigNumUnscramble((PRTBIGNUM)pBigNum); + RTBIGNUMELEMENT uLast = pBigNum->pauElements[idxLast]; Assert(uLast); + rtBigNumScramble((PRTBIGNUM)pBigNum); + return rtBigNumElementBitCount(uLast) + idxLast * RTBIGNUM_ELEMENT_BITS + pBigNum->fNegative; + } + return 0; +} + + +RTDECL(uint32_t) RTBigNumByteWidth(PCRTBIGNUM pBigNum) +{ + uint32_t cBits = RTBigNumBitWidth(pBigNum); + return (cBits + 7) / 8; +} + + +RTDECL(int) RTBigNumToBytesBigEndian(PCRTBIGNUM pBigNum, void *pvBuf, size_t cbWanted) +{ + AssertPtrReturn(pvBuf, VERR_INVALID_POINTER); + AssertReturn(cbWanted > 0, VERR_INVALID_PARAMETER); + + int rc = rtBigNumUnscramble((PRTBIGNUM)pBigNum); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pBigNum); + rc = VINF_SUCCESS; + if (pBigNum->cUsed != 0) + { + uint8_t *pbDst = (uint8_t *)pvBuf; + pbDst += cbWanted - 1; + for (uint32_t i = 0; i < pBigNum->cUsed; i++) + { + RTBIGNUMELEMENT uElement = pBigNum->pauElements[i]; + if (pBigNum->fNegative) + uElement = (RTBIGNUMELEMENT)0 - uElement - (i > 0); + if (cbWanted >= sizeof(uElement)) + { + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; +#if RTBIGNUM_ELEMENT_SIZE == 8 + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + *pbDst-- = (uint8_t)uElement; +#elif RTBIGNUM_ELEMENT_SIZE != 4 +# error "Bad RTBIGNUM_ELEMENT_SIZE value" +#endif + cbWanted -= sizeof(uElement); + } + else + { + + uint32_t cBitsLeft = RTBIGNUM_ELEMENT_BITS; + while (cbWanted > 0) + { + *pbDst-- = (uint8_t)uElement; + uElement >>= 8; + cBitsLeft -= 8; + cbWanted--; + } + Assert(cBitsLeft > 0); Assert(cBitsLeft < RTBIGNUM_ELEMENT_BITS); + if ( i + 1 < pBigNum->cUsed + || ( !pBigNum->fNegative + ? uElement != 0 + : uElement != ((RTBIGNUMELEMENT)1 << cBitsLeft) - 1U ) ) + rc = VERR_BUFFER_OVERFLOW; + break; + } + } + + /* Sign extend the number to the desired output size. */ + if (cbWanted > 0) + memset(pbDst - cbWanted, pBigNum->fNegative ? 0 : 0xff, cbWanted); + } + else + RT_BZERO(pvBuf, cbWanted); + rtBigNumScramble((PRTBIGNUM)pBigNum); + } + return rc; +} + + +RTDECL(int) RTBigNumCompare(PRTBIGNUM pLeft, PRTBIGNUM pRight) +{ + int rc = rtBigNumUnscramble(pLeft); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pLeft); + rc = rtBigNumUnscramble(pRight); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pRight); + if (pLeft->fNegative == pRight->fNegative) + { + if (pLeft->cUsed == pRight->cUsed) + { + rc = 0; + uint32_t i = pLeft->cUsed; + while (i-- > 0) + if (pLeft->pauElements[i] != pRight->pauElements[i]) + { + rc = pLeft->pauElements[i] < pRight->pauElements[i] ? -1 : 1; + break; + } + if (pLeft->fNegative) + rc = -rc; + } + else + rc = !pLeft->fNegative + ? pLeft->cUsed < pRight->cUsed ? -1 : 1 + : pLeft->cUsed < pRight->cUsed ? 1 : -1; + } + else + rc = pLeft->fNegative ? -1 : 1; + + rtBigNumScramble(pRight); + } + rtBigNumScramble(pLeft); + } + return rc; +} + + +RTDECL(int) RTBigNumCompareWithU64(PRTBIGNUM pLeft, uint64_t uRight) +{ + int rc = rtBigNumUnscramble(pLeft); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pLeft); + if (!pLeft->fNegative) + { + if (pLeft->cUsed * RTBIGNUM_ELEMENT_SIZE <= sizeof(uRight)) + { + if (pLeft->cUsed == 0) + rc = uRight == 0 ? 0 : -1; + else + { +#if RTBIGNUM_ELEMENT_SIZE == 8 + uint64_t uLeft = rtBigNumGetElement(pLeft, 0); + if (uLeft < uRight) + rc = -1; + else + rc = uLeft == uRight ? 0 : 1; +#elif RTBIGNUM_ELEMENT_SIZE == 4 + uint32_t uSubLeft = rtBigNumGetElement(pLeft, 1); + uint32_t uSubRight = uRight >> 32; + if (uSubLeft == uSubRight) + { + uSubLeft = rtBigNumGetElement(pLeft, 0); + uSubRight = (uint32_t)uRight; + } + if (uSubLeft < uSubRight) + rc = -1; + else + rc = uSubLeft == uSubRight ? 0 : 1; +#else +# error "Bad RTBIGNUM_ELEMENT_SIZE value" +#endif + } + } + else + rc = 1; + } + else + rc = -1; + rtBigNumScramble(pLeft); + } + return rc; +} + + +RTDECL(int) RTBigNumCompareWithS64(PRTBIGNUM pLeft, int64_t iRight) +{ + int rc = rtBigNumUnscramble(pLeft); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pLeft); + if (pLeft->fNegative == (unsigned)(iRight < 0)) /* (unsigned cast is for MSC weirdness) */ + { + AssertCompile(RTBIGNUM_ELEMENT_SIZE <= sizeof(iRight)); + if (pLeft->cUsed * RTBIGNUM_ELEMENT_SIZE <= sizeof(iRight)) + { + uint64_t uRightMagn = !pLeft->fNegative ? (uint64_t)iRight : (uint64_t)-iRight; +#if RTBIGNUM_ELEMENT_SIZE == 8 + uint64_t uLeft = rtBigNumGetElement(pLeft, 0); + if (uLeft < uRightMagn) + rc = -1; + else + rc = uLeft == (uint64_t)uRightMagn ? 0 : 1; +#elif RTBIGNUM_ELEMENT_SIZE == 4 + uint32_t uSubLeft = rtBigNumGetElement(pLeft, 1); + uint32_t uSubRight = uRightMagn >> 32; + if (uSubLeft == uSubRight) + { + uSubLeft = rtBigNumGetElement(pLeft, 0); + uSubRight = (uint32_t)uRightMagn; + } + if (uSubLeft < uSubRight) + rc = -1; + else + rc = uSubLeft == uSubRight ? 0 : 1; +#else +# error "Bad RTBIGNUM_ELEMENT_SIZE value" +#endif + if (pLeft->fNegative) + rc = -rc; + } + else + rc = pLeft->fNegative ? -1 : 1; + } + else + rc = pLeft->fNegative ? -1 : 1; + rtBigNumScramble(pLeft); + } + return rc; +} + + +/** + * Compares the magnitude values of two big numbers. + * + * @retval -1 if pLeft is smaller than pRight. + * @retval 0 if pLeft is equal to pRight. + * @retval 1 if pLeft is larger than pRight. + * @param pLeft The left side number. + * @param pRight The right side number. + */ +static int rtBigNumMagnitudeCompare(PCRTBIGNUM pLeft, PCRTBIGNUM pRight) +{ + Assert(!pLeft->fCurScrambled); Assert(!pRight->fCurScrambled); + int rc; + uint32_t i = pLeft->cUsed; + if (i == pRight->cUsed) + { + rc = 0; + while (i-- > 0) + if (pLeft->pauElements[i] != pRight->pauElements[i]) + { + rc = pLeft->pauElements[i] < pRight->pauElements[i] ? -1 : 1; + break; + } + } + else + rc = i < pRight->cUsed ? -1 : 1; + return rc; +} + + +/** + * Copies the magnitude of on number (@a pSrc) to another (@a pBigNum). + * + * The variables must be unscrambled. The sign flag is not considered nor + * touched. + * + * @returns IPRT status code. + * @param pDst The destination number. + * @param pSrc The source number. + */ +DECLINLINE(int) rtBigNumMagnitudeCopy(PRTBIGNUM pDst, PCRTBIGNUM pSrc) +{ + int rc = rtBigNumSetUsed(pDst, pSrc->cUsed); + if (RT_SUCCESS(rc)) + memcpy(pDst->pauElements, pSrc->pauElements, pSrc->cUsed * RTBIGNUM_ELEMENT_SIZE); + return rc; +} + + + +/** + * Adds two magnitudes and stores them into a third. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched. + * + * @returns IPRT status code. + * @param pResult The resultant. + * @param pAugend To whom it shall be addede. + * @param pAddend The nombre to addede. + */ +static int rtBigNumMagnitudeAdd(PRTBIGNUM pResult, PCRTBIGNUM pAugend, PCRTBIGNUM pAddend) +{ + Assert(!pResult->fCurScrambled); Assert(!pAugend->fCurScrambled); Assert(!pAddend->fCurScrambled); + Assert(pResult != pAugend); Assert(pResult != pAddend); + + uint32_t cElements = RT_MAX(pAugend->cUsed, pAddend->cUsed); + int rc = rtBigNumSetUsed(pResult, cElements); + if (RT_SUCCESS(rc)) + { + /* + * The primitive way, requires at least two additions for each entry + * without machine code help. + */ + RTBIGNUMELEMENT fCarry = 0; + for (uint32_t i = 0; i < cElements; i++) + pResult->pauElements[i] = rtBigNumElementAddWithCarry(rtBigNumGetElement(pAugend, i), + rtBigNumGetElement(pAddend, i), + &fCarry); + if (fCarry) + { + rc = rtBigNumSetUsed(pResult, cElements + 1); + if (RT_SUCCESS(rc)) + pResult->pauElements[cElements++] = 1; + } + Assert(pResult->cUsed == cElements || RT_FAILURE_NP(rc)); + } + + return rc; +} + + +/** + * Substracts a smaller (or equal) magnitude from another one and stores it into + * a third. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched. For this reason, the @a pMinuend must be larger or equal to @a + * pSubtrahend. + * + * @returns IPRT status code. + * @param pResult There to store the result. + * @param pMinuend What to subtract from. + * @param pSubtrahend What to subtract. + */ +static int rtBigNumMagnitudeSub(PRTBIGNUM pResult, PCRTBIGNUM pMinuend, PCRTBIGNUM pSubtrahend) +{ + Assert(!pResult->fCurScrambled); Assert(!pMinuend->fCurScrambled); Assert(!pSubtrahend->fCurScrambled); + Assert(pResult != pMinuend); Assert(pResult != pSubtrahend); + Assert(pMinuend->cUsed >= pSubtrahend->cUsed); + + int rc; + if (pSubtrahend->cUsed) + { + /* + * Resize the result. In the assembly case, ensure that all three arrays + * has the same number of used entries, possibly with an extra zero + * element on 64-bit systems. + */ + rc = rtBigNumSetUsedEx(pResult, pMinuend->cUsed, RTBIGNUM_ZERO_ALIGN(pMinuend->cUsed)); +#ifdef IPRT_BIGINT_WITH_ASM + if (RT_SUCCESS(rc)) + rc = rtBigNumEnsureExtraZeroElements((PRTBIGNUM)pMinuend, RTBIGNUM_ZERO_ALIGN(pMinuend->cUsed)); + if (RT_SUCCESS(rc)) + rc = rtBigNumEnsureExtraZeroElements((PRTBIGNUM)pSubtrahend, RTBIGNUM_ZERO_ALIGN(pMinuend->cUsed)); +#endif + if (RT_SUCCESS(rc)) + { +#ifdef IPRT_BIGINT_WITH_ASM + /* + * Call assembly to do the work. + */ + rtBigNumMagnitudeSubAssemblyWorker(pResult->pauElements, pMinuend->pauElements, + pSubtrahend->pauElements, pMinuend->cUsed); +# ifdef RT_STRICT + RTBIGNUMELEMENT fBorrow = 0; + for (uint32_t i = 0; i < pMinuend->cUsed; i++) + { + RTBIGNUMELEMENT uCorrect = rtBigNumElementSubWithBorrow(pMinuend->pauElements[i], rtBigNumGetElement(pSubtrahend, i), &fBorrow); + AssertMsg(pResult->pauElements[i] == uCorrect, ("[%u]=%#x, expected %#x\n", i, pResult->pauElements[i], uCorrect)); + } +# endif +#else + /* + * The primitive C way. + */ + RTBIGNUMELEMENT fBorrow = 0; + for (uint32_t i = 0; i < pMinuend->cUsed; i++) + pResult->pauElements[i] = rtBigNumElementSubWithBorrow(pMinuend->pauElements[i], + rtBigNumGetElement(pSubtrahend, i), + &fBorrow); + Assert(fBorrow == 0); +#endif + + /* + * Trim the result. + */ + rtBigNumStripTrailingZeros(pResult); + } + } + /* + * Special case: Subtrahend is zero. + */ + else + rc = rtBigNumMagnitudeCopy(pResult, pMinuend); + + return rc; +} + + +/** + * Substracts a smaller (or equal) magnitude from another one and stores the + * result into the first. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched. For this reason, the @a pMinuendResult must be larger or equal to + * @a pSubtrahend. + * + * @returns IPRT status code (memory alloc error). + * @param pMinuendResult What to subtract from and return as result. + * @param pSubtrahend What to subtract. + */ +static int rtBigNumMagnitudeSubThis(PRTBIGNUM pMinuendResult, PCRTBIGNUM pSubtrahend) +{ + Assert(!pMinuendResult->fCurScrambled); Assert(!pSubtrahend->fCurScrambled); + Assert(pMinuendResult != pSubtrahend); + Assert(pMinuendResult->cUsed >= pSubtrahend->cUsed); + +#ifdef IPRT_BIGINT_WITH_ASM + /* + * Use the assembly worker. Requires same sized element arrays, so zero extend them. + */ + int rc = rtBigNumEnsureExtraZeroElements(pMinuendResult, RTBIGNUM_ZERO_ALIGN(pMinuendResult->cUsed)); + if (RT_SUCCESS(rc)) + rc = rtBigNumEnsureExtraZeroElements((PRTBIGNUM)pSubtrahend, RTBIGNUM_ZERO_ALIGN(pMinuendResult->cUsed)); + if (RT_FAILURE(rc)) + return rc; + rtBigNumMagnitudeSubThisAssemblyWorker(pMinuendResult->pauElements, pSubtrahend->pauElements, pMinuendResult->cUsed); +#else + /* + * The primitive way, as usual. + */ + RTBIGNUMELEMENT fBorrow = 0; + for (uint32_t i = 0; i < pMinuendResult->cUsed; i++) + pMinuendResult->pauElements[i] = rtBigNumElementSubWithBorrow(pMinuendResult->pauElements[i], + rtBigNumGetElement(pSubtrahend, i), + &fBorrow); + Assert(fBorrow == 0); +#endif + + /* + * Trim the result. + */ + rtBigNumStripTrailingZeros(pMinuendResult); + + return VINF_SUCCESS; +} + + +RTDECL(int) RTBigNumAdd(PRTBIGNUM pResult, PCRTBIGNUM pAugend, PCRTBIGNUM pAddend) +{ + Assert(pResult != pAugend); Assert(pResult != pAddend); + AssertReturn(pResult->fSensitive >= (pAugend->fSensitive | pAddend->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + rc = rtBigNumUnscramble((PRTBIGNUM)pAugend); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pAugend); + rc = rtBigNumUnscramble((PRTBIGNUM)pAddend); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pAddend); + + /* + * Same sign: Add magnitude, keep sign. + * 1 + 1 = 2 + * (-1) + (-1) = -2 + */ + if (pAugend->fNegative == pAddend->fNegative) + { + pResult->fNegative = pAugend->fNegative; + rc = rtBigNumMagnitudeAdd(pResult, pAugend, pAddend); + } + /* + * Different sign: Subtract smaller from larger, keep sign of larger. + * (-5) + 3 = -2 + * 5 + (-3) = 2 + * (-1) + 3 = 2 + * 1 + (-3) = -2 + */ + else if (rtBigNumMagnitudeCompare(pAugend, pAddend) >= 0) + { + pResult->fNegative = pAugend->fNegative; + rc = rtBigNumMagnitudeSub(pResult, pAugend, pAddend); + if (!pResult->cUsed) + pResult->fNegative = 0; + } + else + { + pResult->fNegative = pAddend->fNegative; + rc = rtBigNumMagnitudeSub(pResult, pAddend, pAugend); + } + rtBigNumScramble((PRTBIGNUM)pAddend); + } + rtBigNumScramble((PRTBIGNUM)pAugend); + } + rtBigNumScramble(pResult); + } + return rc; +} + + +RTDECL(int) RTBigNumSubtract(PRTBIGNUM pResult, PCRTBIGNUM pMinuend, PCRTBIGNUM pSubtrahend) +{ + Assert(pResult != pMinuend); Assert(pResult != pSubtrahend); + AssertReturn(pResult->fSensitive >= (pMinuend->fSensitive | pSubtrahend->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + if (pMinuend != pSubtrahend) + { + rc = rtBigNumUnscramble((PRTBIGNUM)pMinuend); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pMinuend); + rc = rtBigNumUnscramble((PRTBIGNUM)pSubtrahend); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pSubtrahend); + + /* + * Different sign: Add magnitude, keep sign of first. + * 1 - (-2) == 3 + * -1 - 2 == -3 + */ + if (pMinuend->fNegative != pSubtrahend->fNegative) + { + pResult->fNegative = pMinuend->fNegative; + rc = rtBigNumMagnitudeAdd(pResult, pMinuend, pSubtrahend); + } + /* + * Same sign, minuend has greater or equal absolute value: Subtract, keep sign of first. + * 10 - 7 = 3 + */ + else if (rtBigNumMagnitudeCompare(pMinuend, pSubtrahend) >= 0) + { + pResult->fNegative = pMinuend->fNegative; + rc = rtBigNumMagnitudeSub(pResult, pMinuend, pSubtrahend); + } + /* + * Same sign, subtrahend is larger: Reverse and subtract, invert sign of first. + * 7 - 10 = -3 + * -1 - (-3) = 2 + */ + else + { + pResult->fNegative = !pMinuend->fNegative; + rc = rtBigNumMagnitudeSub(pResult, pSubtrahend, pMinuend); + } + rtBigNumScramble((PRTBIGNUM)pSubtrahend); + } + rtBigNumScramble((PRTBIGNUM)pMinuend); + } + } + else + { + /* zero. */ + pResult->fNegative = 0; + rtBigNumSetUsed(pResult, 0); + } + rtBigNumScramble(pResult); + } + return rc; +} + + +RTDECL(int) RTBigNumNegateThis(PRTBIGNUM pThis) +{ + pThis->fNegative = !pThis->fNegative; + return VINF_SUCCESS; +} + + +RTDECL(int) RTBigNumNegate(PRTBIGNUM pResult, PCRTBIGNUM pBigNum) +{ + int rc = RTBigNumAssign(pResult, pBigNum); + if (RT_SUCCESS(rc)) + rc = RTBigNumNegateThis(pResult); + return rc; +} + + +/** + * Multiplies the magnitudes of two values, letting the caller care about the + * sign bit. + * + * @returns IPRT status code. + * @param pResult Where to store the result. + * @param pMultiplicand The first value. + * @param pMultiplier The second value. + */ +static int rtBigNumMagnitudeMultiply(PRTBIGNUM pResult, PCRTBIGNUM pMultiplicand, PCRTBIGNUM pMultiplier) +{ + Assert(pResult != pMultiplicand); Assert(pResult != pMultiplier); + Assert(!pResult->fCurScrambled); Assert(!pMultiplicand->fCurScrambled); Assert(!pMultiplier->fCurScrambled); + + /* + * Multiplication involving zero is zero. + */ + if (!pMultiplicand->cUsed || !pMultiplier->cUsed) + { + pResult->fNegative = 0; + rtBigNumSetUsed(pResult, 0); + return VINF_SUCCESS; + } + + /* + * Allocate a result array that is the sum of the two factors, initialize + * it to zero. + */ + uint32_t cMax = pMultiplicand->cUsed + pMultiplier->cUsed; + int rc = rtBigNumSetUsed(pResult, cMax); + if (RT_SUCCESS(rc)) + { + RT_BZERO(pResult->pauElements, pResult->cUsed * RTBIGNUM_ELEMENT_SIZE); + +#ifdef IPRT_BIGINT_WITH_ASM + rtBigNumMagnitudeMultiplyAssemblyWorker(pResult->pauElements, + pMultiplier->pauElements, pMultiplier->cUsed, + pMultiplicand->pauElements, pMultiplicand->cUsed); +#else + for (uint32_t i = 0; i < pMultiplier->cUsed; i++) + { + RTBIGNUMELEMENT uMultiplier = pMultiplier->pauElements[i]; + for (uint32_t j = 0; j < pMultiplicand->cUsed; j++) + { + RTBIGNUMELEMENT uHi; + RTBIGNUMELEMENT uLo; +#if RTBIGNUM_ELEMENT_SIZE == 4 + uint64_t u64 = ASMMult2xU32RetU64(pMultiplicand->pauElements[j], uMultiplier); + uLo = (uint32_t)u64; + uHi = u64 >> 32; +#elif RTBIGNUM_ELEMENT_SIZE == 8 + uLo = ASMMult2xU64Ret2xU64(pMultiplicand->pauElements[j], uMultiplier, &uHi); +#else +# error "Invalid RTBIGNUM_ELEMENT_SIZE value" +#endif + RTBIGNUMELEMENT fCarry = 0; + uint64_t k = i + j; + pResult->pauElements[k] = rtBigNumElementAddWithCarry(pResult->pauElements[k], uLo, &fCarry); + k++; + pResult->pauElements[k] = rtBigNumElementAddWithCarry(pResult->pauElements[k], uHi, &fCarry); + while (fCarry) + { + k++; + pResult->pauElements[k] = rtBigNumElementAddWithCarry(pResult->pauElements[k], 0, &fCarry); + } + Assert(k < cMax); + } + } +#endif + + /* It's possible we overestimated the output size by 1 element. */ + rtBigNumStripTrailingZeros(pResult); + } + return rc; +} + + +RTDECL(int) RTBigNumMultiply(PRTBIGNUM pResult, PCRTBIGNUM pMultiplicand, PCRTBIGNUM pMultiplier) +{ + Assert(pResult != pMultiplicand); Assert(pResult != pMultiplier); + AssertReturn(pResult->fSensitive >= (pMultiplicand->fSensitive | pMultiplier->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + rc = rtBigNumUnscramble((PRTBIGNUM)pMultiplicand); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pMultiplicand); + rc = rtBigNumUnscramble((PRTBIGNUM)pMultiplier); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pMultiplier); + + /* + * The sign values follow XOR rules: + * -1 * 1 = -1; 1 ^ 0 = 1 + * 1 * -1 = -1; 1 ^ 0 = 1 + * -1 * -1 = 1; 1 ^ 1 = 0 + * 1 * 1 = 1; 0 ^ 0 = 0 + */ + pResult->fNegative = pMultiplicand->fNegative ^ pMultiplier->fNegative; + rc = rtBigNumMagnitudeMultiply(pResult, pMultiplicand, pMultiplier); + + rtBigNumScramble((PRTBIGNUM)pMultiplier); + } + rtBigNumScramble((PRTBIGNUM)pMultiplicand); + } + rtBigNumScramble(pResult); + } + return rc; +} + + +#if 0 /* unused */ +/** + * Clears a bit in the magnitude of @a pBigNum. + * + * The variables must be unscrambled. + * + * @param pBigNum The big number. + * @param iBit The bit to clear (0-based). + */ +DECLINLINE(void) rtBigNumMagnitudeClearBit(PRTBIGNUM pBigNum, uint32_t iBit) +{ + uint32_t iElement = iBit / RTBIGNUM_ELEMENT_BITS; + if (iElement < pBigNum->cUsed) + { + iBit &= RTBIGNUM_ELEMENT_BITS - 1; + pBigNum->pauElements[iElement] &= ~RTBIGNUM_ELEMENT_BIT(iBit); + if (iElement + 1 == pBigNum->cUsed && !pBigNum->pauElements[iElement]) + rtBigNumStripTrailingZeros(pBigNum); + } +} +#endif /* unused */ + + +/** + * Sets a bit in the magnitude of @a pBigNum. + * + * The variables must be unscrambled. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param iBit The bit to clear (0-based). + */ +DECLINLINE(int) rtBigNumMagnitudeSetBit(PRTBIGNUM pBigNum, uint32_t iBit) +{ + uint32_t iElement = iBit / RTBIGNUM_ELEMENT_BITS; + int rc = rtBigNumEnsureElementPresent(pBigNum, iElement); + if (RT_SUCCESS(rc)) + { + iBit &= RTBIGNUM_ELEMENT_BITS - 1; + pBigNum->pauElements[iElement] |= RTBIGNUM_ELEMENT_BIT(iBit); + return VINF_SUCCESS; + } + return rc; +} + + +#if 0 /* unused */ +/** + * Writes a bit in the magnitude of @a pBigNum. + * + * The variables must be unscrambled. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param iBit The bit to write (0-based). + * @param fValue The bit value. + */ +DECLINLINE(int) rtBigNumMagnitudeWriteBit(PRTBIGNUM pBigNum, uint32_t iBit, bool fValue) +{ + if (fValue) + return rtBigNumMagnitudeSetBit(pBigNum, iBit); + rtBigNumMagnitudeClearBit(pBigNum, iBit); + return VINF_SUCCESS; +} +#endif + + +/** + * Returns the given magnitude bit. + * + * The variables must be unscrambled. + * + * @returns The bit value (1 or 0). + * @param pBigNum The big number. + * @param iBit The bit to return (0-based). + */ +DECLINLINE(RTBIGNUMELEMENT) rtBigNumMagnitudeGetBit(PCRTBIGNUM pBigNum, uint32_t iBit) +{ + uint32_t iElement = iBit / RTBIGNUM_ELEMENT_BITS; + if (iElement < pBigNum->cUsed) + { + iBit &= RTBIGNUM_ELEMENT_BITS - 1; + return (pBigNum->pauElements[iElement] >> iBit) & 1; + } + return 0; +} + + +/** + * Shifts the magnitude left by one. + * + * The variables must be unscrambled. + * + * @returns IPRT status code. + * @param pBigNum The big number. + * @param uCarry The value to shift in at the bottom. + */ +DECLINLINE(int) rtBigNumMagnitudeShiftLeftOne(PRTBIGNUM pBigNum, RTBIGNUMELEMENT uCarry) +{ + Assert(uCarry <= 1); + + /* Do the shifting. */ + uint32_t cUsed = pBigNum->cUsed; +#ifdef IPRT_BIGINT_WITH_ASM + uCarry = rtBigNumMagnitudeShiftLeftOneAssemblyWorker(pBigNum->pauElements, cUsed, uCarry); +#else + for (uint32_t i = 0; i < cUsed; i++) + { + RTBIGNUMELEMENT uTmp = pBigNum->pauElements[i]; + pBigNum->pauElements[i] = (uTmp << 1) | uCarry; + uCarry = uTmp >> (RTBIGNUM_ELEMENT_BITS - 1); + } +#endif + + /* If we still carry a bit, we need to increase the size. */ + if (uCarry) + { + int rc = rtBigNumSetUsed(pBigNum, cUsed + 1); + AssertRCReturn(rc, rc); + pBigNum->pauElements[cUsed] = uCarry; + } + + return VINF_SUCCESS; +} + + +/** + * Shifts the magnitude left by @a cBits. + * + * The variables must be unscrambled. + * + * @returns IPRT status code. + * @param pResult Where to store the result. + * @param pValue The value to shift. + * @param cBits The shift count. + */ +static int rtBigNumMagnitudeShiftLeft(PRTBIGNUM pResult, PCRTBIGNUM pValue, uint32_t cBits) +{ + int rc; + if (cBits) + { + uint32_t cBitsNew = rtBigNumMagnitudeBitWidth(pValue); + if (cBitsNew > 0) + { + if (cBitsNew + cBits > cBitsNew) + { + cBitsNew += cBits; + rc = rtBigNumSetUsedEx(pResult, 0, RT_ALIGN_32(cBitsNew, RTBIGNUM_ELEMENT_BITS) / RTBIGNUM_ELEMENT_BITS); + if (RT_SUCCESS(rc)) + rc = rtBigNumSetUsed(pResult, RT_ALIGN_32(cBitsNew, RTBIGNUM_ELEMENT_BITS) / RTBIGNUM_ELEMENT_BITS); + if (RT_SUCCESS(rc)) + { + uint32_t const cLeft = pValue->cUsed; + PCRTBIGNUMELEMENT pauSrc = pValue->pauElements; + PRTBIGNUMELEMENT pauDst = pResult->pauElements; + + Assert(ASMMemIsZero(pauDst, (cBits / RTBIGNUM_ELEMENT_BITS) * RTBIGNUM_ELEMENT_SIZE)); + pauDst += cBits / RTBIGNUM_ELEMENT_BITS; + + cBits &= RTBIGNUM_ELEMENT_BITS - 1; + if (cBits) + { + RTBIGNUMELEMENT uPrev = 0; + for (uint32_t i = 0; i < cLeft; i++) + { + RTBIGNUMELEMENT uCur = pauSrc[i]; + pauDst[i] = (uCur << cBits) | (uPrev >> (RTBIGNUM_ELEMENT_BITS - cBits)); + uPrev = uCur; + } + uPrev >>= RTBIGNUM_ELEMENT_BITS - cBits; + if (uPrev) + pauDst[pValue->cUsed] = uPrev; + } + else + memcpy(pauDst, pauSrc, cLeft * RTBIGNUM_ELEMENT_SIZE); + } + } + else + rc = VERR_OUT_OF_RANGE; + } + /* Shifting zero always yields a zero result. */ + else + rc = rtBigNumSetUsed(pResult, 0); + } + else + rc = rtBigNumMagnitudeCopy(pResult, pValue); + return rc; +} + + +RTDECL(int) RTBigNumShiftLeft(PRTBIGNUM pResult, PCRTBIGNUM pValue, uint32_t cBits) +{ + Assert(pResult != pValue); + AssertReturn(pResult->fSensitive >= pValue->fSensitive, VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + rc = rtBigNumUnscramble((PRTBIGNUM)pValue); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pValue); + + pResult->fNegative = pValue->fNegative; + rc = rtBigNumMagnitudeShiftLeft(pResult, pValue, cBits); + + rtBigNumScramble((PRTBIGNUM)pValue); + } + rtBigNumScramble(pResult); + } + return rc; +} + + +/** + * Shifts the magnitude right by @a cBits. + * + * The variables must be unscrambled. + * + * @returns IPRT status code. + * @param pResult Where to store the result. + * @param pValue The value to shift. + * @param cBits The shift count. + */ +static int rtBigNumMagnitudeShiftRight(PRTBIGNUM pResult, PCRTBIGNUM pValue, uint32_t cBits) +{ + int rc; + if (cBits) + { + uint32_t cBitsNew = rtBigNumMagnitudeBitWidth(pValue); + if (cBitsNew > cBits) + { + cBitsNew -= cBits; + uint32_t cElementsNew = RT_ALIGN_32(cBitsNew, RTBIGNUM_ELEMENT_BITS) / RTBIGNUM_ELEMENT_BITS; + rc = rtBigNumSetUsed(pResult, cElementsNew); + if (RT_SUCCESS(rc)) + { + uint32_t i = cElementsNew; + PCRTBIGNUMELEMENT pauSrc = pValue->pauElements; + PRTBIGNUMELEMENT pauDst = pResult->pauElements; + + pauSrc += cBits / RTBIGNUM_ELEMENT_BITS; + + cBits &= RTBIGNUM_ELEMENT_BITS - 1; + if (cBits) + { + RTBIGNUMELEMENT uPrev = &pauSrc[i] == &pValue->pauElements[pValue->cUsed] ? 0 : pauSrc[i]; + while (i-- > 0) + { + RTBIGNUMELEMENT uCur = pauSrc[i]; + pauDst[i] = (uCur >> cBits) | (uPrev << (RTBIGNUM_ELEMENT_BITS - cBits)); + uPrev = uCur; + } + } + else + memcpy(pauDst, pauSrc, i * RTBIGNUM_ELEMENT_SIZE); + } + } + else + rc = rtBigNumSetUsed(pResult, 0); + } + else + rc = rtBigNumMagnitudeCopy(pResult, pValue); + return rc; +} + + +RTDECL(int) RTBigNumShiftRight(PRTBIGNUM pResult, PCRTBIGNUM pValue, uint32_t cBits) +{ + Assert(pResult != pValue); + AssertReturn(pResult->fSensitive >= pValue->fSensitive, VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + rc = rtBigNumUnscramble((PRTBIGNUM)pValue); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pValue); + + pResult->fNegative = pValue->fNegative; + rc = rtBigNumMagnitudeShiftRight(pResult, pValue, cBits); + if (!pResult->cUsed) + pResult->fNegative = 0; + + rtBigNumScramble((PRTBIGNUM)pValue); + } + rtBigNumScramble(pResult); + } + return rc; +} + + +/** + * Implements the D3 test for Qhat decrementation. + * + * @returns True if Qhat should be decremented. + * @param puQhat Pointer to Qhat. + * @param uRhat The remainder. + * @param uDivisorY The penultimate divisor element. + * @param uDividendJMinus2 The j-2 dividend element. + */ +DECLINLINE(bool) rtBigNumKnuthD3_ShouldDecrementQhat(RTBIGNUMELEMENT2X const *puQhat, RTBIGNUMELEMENT uRhat, + RTBIGNUMELEMENT uDivisorY, RTBIGNUMELEMENT uDividendJMinus2) +{ + if (puQhat->s.Lo == RTBIGNUM_ELEMENT_MAX && puQhat->s.Hi == 0) + return true; +#if RTBIGNUM_ELEMENT_BITS == 64 + RTBIGNUMELEMENT2X TmpLeft; + RTUInt128MulByU64(&TmpLeft, puQhat, uDivisorY); + + RTBIGNUMELEMENT2X TmpRight; + TmpRight.s.Lo = 0; + TmpRight.s.Hi = uRhat; + RTUInt128AssignAddU64(&TmpRight, uDividendJMinus2); + + if (RTUInt128Compare(&TmpLeft, &TmpRight) > 0) + return true; +#else + if (puQhat->u * uDivisorY > ((uint64_t)uRhat << 32) + uDividendJMinus2) + return true; +#endif + return false; +} + + +/** + * C implementation of the D3 step of Knuth's division algorithm. + * + * This estimates a value Qhat that will be used as quotient "digit" (element) + * at the current level of the division (j). + * + * @returns The Qhat value we've estimated. + * @param pauDividendJN Pointer to the j+n (normalized) dividend element. + * Will access up to two elements prior to this. + * @param uDivZ The last element in the (normalized) divisor. + * @param uDivY The penultimate element in the (normalized) divisor. + */ +DECLINLINE(RTBIGNUMELEMENT) rtBigNumKnuthD3_EstimateQhat(PCRTBIGNUMELEMENT pauDividendJN, + RTBIGNUMELEMENT uDivZ, RTBIGNUMELEMENT uDivY) +{ + RTBIGNUMELEMENT2X uQhat; + RTBIGNUMELEMENT uRhat; + RTBIGNUMELEMENT uDividendJN = pauDividendJN[0]; + Assert(uDividendJN <= uDivZ); + if (uDividendJN != uDivZ) + rtBigNumElement2xDiv2xBy1x(&uQhat, &uRhat, uDividendJN, pauDividendJN[-1], uDivZ); + else + { + /* + * This is the case where we end up with an initial Qhat that's all Fs. + */ + /* Calc the remainder for max Qhat value. */ + RTBIGNUMELEMENT2X uTmp1; /* (v[j+n] << bits) + v[J+N-1] */ + uTmp1.s.Hi = uDivZ; + uTmp1.s.Lo = pauDividendJN[-1]; + + RTBIGNUMELEMENT2X uTmp2; /* uQhat * uDividendJN */ + uTmp2.s.Hi = uDivZ - 1; + uTmp2.s.Lo = 0 - uDivZ; +#if RTBIGNUM_ELEMENT_BITS == 64 + RTUInt128AssignSub(&uTmp1, &uTmp2); +#else + uTmp1.u -= uTmp2.u; +#endif + /* If we overflowed the remainder, don't bother trying to adjust. */ + if (uTmp1.s.Hi) + return RTBIGNUM_ELEMENT_MAX; + + uRhat = uTmp1.s.Lo; + uQhat.s.Lo = RTBIGNUM_ELEMENT_MAX; + uQhat.s.Hi = 0; + } + + /* + * Adjust Q to eliminate all cases where it's two to large and most cases + * where it's one too large. + */ + while (rtBigNumKnuthD3_ShouldDecrementQhat(&uQhat, uRhat, uDivY, pauDividendJN[-2])) + { + rtBigNumElement2xDec(&uQhat); + uRhat += uDivZ; + if (uRhat < uDivZ /* overflow */ || uRhat == RTBIGNUM_ELEMENT_MAX) + break; + } + + return uQhat.s.Lo; +} + + +#ifdef IPRT_BIGINT_WITH_ASM +DECLASM(bool) rtBigNumKnuthD4_MulSub(PRTBIGNUMELEMENT pauDividendJ, PRTBIGNUMELEMENT pauDivisor, + uint32_t cDivisor, RTBIGNUMELEMENT uQhat); +#else +/** + * C implementation of the D4 step of Knuth's division algorithm. + * + * This subtracts Divisor * Qhat from the dividend at the current J index. + * + * @returns true if negative result (unlikely), false if positive. + * @param pauDividendJ Pointer to the j-th (normalized) dividend element. + * Will access up to two elements prior to this. + * @param uDivZ The last element in the (normalized) divisor. + * @param uDivY The penultimate element in the (normalized) divisor. + */ +DECLINLINE(bool) rtBigNumKnuthD4_MulSub(PRTBIGNUMELEMENT pauDividendJ, PRTBIGNUMELEMENT pauDivisor, + uint32_t cDivisor, RTBIGNUMELEMENT uQhat) +{ + uint32_t i; + bool fBorrow = false; + RTBIGNUMELEMENT uMulCarry = 0; + for (i = 0; i < cDivisor; i++) + { + RTBIGNUMELEMENT2X uSub; +# if RTBIGNUM_ELEMENT_BITS == 64 + RTUInt128MulU64ByU64(&uSub, uQhat, pauDivisor[i]); + RTUInt128AssignAddU64(&uSub, uMulCarry); +# else + uSub.u = (uint64_t)uQhat * pauDivisor[i] + uMulCarry; +# endif + uMulCarry = uSub.s.Hi; + + RTBIGNUMELEMENT uDividendI = pauDividendJ[i]; + if (!fBorrow) + { + fBorrow = uDividendI < uSub.s.Lo; + uDividendI -= uSub.s.Lo; + } + else + { + fBorrow = uDividendI <= uSub.s.Lo; + uDividendI -= uSub.s.Lo + 1; + } + pauDividendJ[i] = uDividendI; + } + + /* Carry and borrow into the final dividend element. */ + RTBIGNUMELEMENT uDividendI = pauDividendJ[i]; + if (!fBorrow) + { + fBorrow = uDividendI < uMulCarry; + pauDividendJ[i] = uDividendI - uMulCarry; + } + else + { + fBorrow = uDividendI <= uMulCarry; + pauDividendJ[i] = uDividendI - uMulCarry - 1; + } + + return fBorrow; +} +#endif /* !IPRT_BIGINT_WITH_ASM */ + + +/** + * C implementation of the D6 step of Knuth's division algorithm. + * + * This adds the divisor to the dividend to undo the negative value step D4 + * produced. This is not very frequent occurence. + * + * @param pauDividendJ Pointer to the j-th (normalized) dividend element. + * Will access up to two elements prior to this. + * @param pauDivisor The last element in the (normalized) divisor. + * @param cDivisor The penultimate element in the (normalized) divisor. + */ +DECLINLINE(void) rtBigNumKnuthD6_AddBack(PRTBIGNUMELEMENT pauDividendJ, PRTBIGNUMELEMENT pauDivisor, uint32_t cDivisor) +{ + RTBIGNUMELEMENT2X uTmp; + uTmp.s.Lo = 0; + + uint32_t i; + for (i = 0; i < cDivisor; i++) + { + uTmp.s.Hi = 0; +#if RTBIGNUM_ELEMENT_BITS == 64 + RTUInt128AssignAddU64(&uTmp, pauDivisor[i]); + RTUInt128AssignAddU64(&uTmp, pauDividendJ[i]); +#else + uTmp.u += pauDivisor[i]; + uTmp.u += pauDividendJ[i]; +#endif + pauDividendJ[i] = uTmp.s.Lo; + uTmp.s.Lo = uTmp.s.Hi; + } + + /* The final dividend entry. */ + Assert(pauDividendJ[i] + uTmp.s.Lo < uTmp.s.Lo); + pauDividendJ[i] += uTmp.s.Lo; +} + + +/** + * Knuth's division (core). + * + * @returns IPRT status code. + * @param pQuotient Where to return the quotient. Can be NULL. + * @param pRemainder Where to return the remainder. + * @param pDividend What to divide. + * @param pDivisor What to divide by. + */ +static int rtBigNumMagnitudeDivideKnuth(PRTBIGNUM pQuotient, PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor) +{ + Assert(pDivisor->cUsed > 1); + uint32_t const cDivisor = pDivisor->cUsed; + Assert(pDividend->cUsed >= cDivisor); + + /* + * Make sure we've got enough space in the quotient, so we can build it + * without any trouble come step D5. + */ + int rc; + if (pQuotient) + { + rc = rtBigNumSetUsedEx(pQuotient, 0, pDividend->cUsed - cDivisor + 1); + if (RT_SUCCESS(rc)) + rc = rtBigNumSetUsed(pQuotient, pDividend->cUsed - cDivisor + 1); + if (RT_FAILURE(rc)) + return rc; + } + + /* + * D1. Normalize. The goal here is to make sure the last element in the + * divisor is greater than RTBIGNUMELEMENTS_MAX/2. We must also make sure + * we can access element pDividend->cUsed of the normalized dividend. + */ + RTBIGNUM NormDividend; + RTBIGNUM NormDivisor; + PCRTBIGNUM pNormDivisor = &NormDivisor; + rtBigNumInitZeroTemplate(&NormDivisor, pDividend); + + uint32_t cNormShift = (RTBIGNUM_ELEMENT_BITS - rtBigNumMagnitudeBitWidth(pDivisor)) & (RTBIGNUM_ELEMENT_BITS - 1); + if (cNormShift) + { + rtBigNumInitZeroTemplate(&NormDividend, pDividend); + rc = rtBigNumMagnitudeShiftLeft(&NormDividend, pDividend, cNormShift); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeShiftLeft(&NormDivisor, pDivisor, cNormShift); + } + else + { + pNormDivisor = pDivisor; + rc = rtBigNumCloneInternal(&NormDividend, pDividend); + } + if (RT_SUCCESS(rc) && pDividend->cUsed == NormDividend.cUsed) + rc = rtBigNumEnsureExtraZeroElements(&NormDividend, NormDividend.cUsed + 1); + if (RT_SUCCESS(rc)) + { + /* + * D2. Initialize the j index so we can loop thru the elements in the + * dividend that makes it larger than the divisor. + */ + uint32_t j = pDividend->cUsed - cDivisor; + + RTBIGNUMELEMENT const DivZ = pNormDivisor->pauElements[cDivisor - 1]; + RTBIGNUMELEMENT const DivY = pNormDivisor->pauElements[cDivisor - 2]; + for (;;) + { + /* + * D3. Estimate a Q' by dividing the j and j-1 dividen elements by + * the last divisor element, then adjust against the next elements. + */ + RTBIGNUMELEMENT uQhat = rtBigNumKnuthD3_EstimateQhat(&NormDividend.pauElements[j + cDivisor], DivZ, DivY); + + /* + * D4. Multiply and subtract. + */ + bool fNegative = rtBigNumKnuthD4_MulSub(&NormDividend.pauElements[j], pNormDivisor->pauElements, cDivisor, uQhat); + + /* + * D5. Test remainder. + * D6. Add back. + */ + if (fNegative) + { +//__debugbreak(); + rtBigNumKnuthD6_AddBack(&NormDividend.pauElements[j], pNormDivisor->pauElements, cDivisor); + uQhat--; + } + + if (pQuotient) + pQuotient->pauElements[j] = uQhat; + + /* + * D7. Loop on j. + */ + if (j == 0) + break; + j--; + } + + /* + * D8. Unnormalize the remainder. + */ + rtBigNumStripTrailingZeros(&NormDividend); + if (cNormShift) + rc = rtBigNumMagnitudeShiftRight(pRemainder, &NormDividend, cNormShift); + else + rc = rtBigNumMagnitudeCopy(pRemainder, &NormDividend); + if (pQuotient) + rtBigNumStripTrailingZeros(pQuotient); + } + + /* + * Delete temporary variables. + */ + RTBigNumDestroy(&NormDividend); + if (pNormDivisor == &NormDivisor) + RTBigNumDestroy(&NormDivisor); + return rc; +} + + +static int rtBigNumMagnitudeDivideSlowLong(PRTBIGNUM pQuotient, PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor) +{ + /* + * Do very simple long division. This ain't fast, but it does the trick. + */ + int rc = VINF_SUCCESS; + uint32_t iBit = rtBigNumMagnitudeBitWidth(pDividend); + while (iBit-- > 0) + { + rc = rtBigNumMagnitudeShiftLeftOne(pRemainder, rtBigNumMagnitudeGetBit(pDividend, iBit)); + AssertRCBreak(rc); + int iDiff = rtBigNumMagnitudeCompare(pRemainder, pDivisor); + if (iDiff >= 0) + { + if (iDiff != 0) + { + rc = rtBigNumMagnitudeSubThis(pRemainder, pDivisor); + AssertRCBreak(rc); + } + else + rtBigNumSetUsed(pRemainder, 0); + rc = rtBigNumMagnitudeSetBit(pQuotient, iBit); + AssertRCBreak(rc); + } + } + + /* This shouldn't be necessary. */ + rtBigNumStripTrailingZeros(pQuotient); + rtBigNumStripTrailingZeros(pRemainder); + + return rc; +} + + +/** + * Divides the magnitudes of two values, letting the caller care about the sign + * bit. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched, this means the caller have to check for zero outputs. + * + * @returns IPRT status code. + * @param pQuotient Where to return the quotient. + * @param pRemainder Where to return the remainder. + * @param pDividend What to divide. + * @param pDivisor What to divide by. + * @param fForceLong Force long division. + */ +static int rtBigNumMagnitudeDivide(PRTBIGNUM pQuotient, PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor, + bool fForceLong) +{ + Assert(pQuotient != pDividend); Assert(pQuotient != pDivisor); Assert(pRemainder != pDividend); Assert(pRemainder != pDivisor); Assert(pRemainder != pQuotient); + Assert(!pQuotient->fCurScrambled); Assert(!pRemainder->fCurScrambled); Assert(!pDividend->fCurScrambled); Assert(!pDivisor->fCurScrambled); + + /* + * Just set both output values to zero as that's the return for several + * special case and the initial state of the general case. + */ + rtBigNumSetUsed(pQuotient, 0); + rtBigNumSetUsed(pRemainder, 0); + + /* + * Dividing something by zero is undefined. + * Diving zero by something is zero, unless the divsor is also zero. + */ + if (!pDivisor->cUsed || !pDividend->cUsed) + return pDivisor->cUsed ? VINF_SUCCESS : VERR_BIGNUM_DIV_BY_ZERO; + + /* + * Dividing by one? Quotient = dividend, no remainder. + */ + if (pDivisor->cUsed == 1 && pDivisor->pauElements[0] == 1) + return rtBigNumMagnitudeCopy(pQuotient, pDividend); + + /* + * Dividend smaller than the divisor. Zero quotient, all divisor. + */ + int iDiff = rtBigNumMagnitudeCompare(pDividend, pDivisor); + if (iDiff < 0) + return rtBigNumMagnitudeCopy(pRemainder, pDividend); + + /* + * Since we already have done the compare, check if the two values are the + * same. The result is 1 and no remainder then. + */ + if (iDiff == 0) + { + int rc = rtBigNumSetUsed(pQuotient, 1); + if (RT_SUCCESS(rc)) + pQuotient->pauElements[0] = 1; + return rc; + } + + /* + * Sort out special cases before going to the preferred or select algorithm. + */ + int rc; + if (pDividend->cUsed <= 2 && !fForceLong) + { + if (pDividend->cUsed < 2) + { + /* + * Single element division. + */ + RTBIGNUMELEMENT uQ = pDividend->pauElements[0] / pDivisor->pauElements[0]; + RTBIGNUMELEMENT uR = pDividend->pauElements[0] % pDivisor->pauElements[0]; + rc = VINF_SUCCESS; + if (uQ) + { + rc = rtBigNumSetUsed(pQuotient, 1); + if (RT_SUCCESS(rc)) + pQuotient->pauElements[0] = uQ; + } + if (uR && RT_SUCCESS(rc)) + { + rc = rtBigNumSetUsed(pRemainder, 1); + if (RT_SUCCESS(rc)) + pRemainder->pauElements[0] = uR; + } + } + else + { + /* + * Two elements dividend by a one or two element divisor. + */ + RTBIGNUMELEMENT2X uQ, uR; + if (pDivisor->cUsed == 1) + { + rtBigNumElement2xDiv2xBy1x(&uQ, &uR.s.Lo, pDividend->pauElements[1], pDividend->pauElements[0], + pDivisor->pauElements[0]); + uR.s.Hi = 0; + } + else + rtBigNumElement2xDiv(&uQ, &uR, pDividend->pauElements[1], pDividend->pauElements[0], + pDivisor->pauElements[1], pDivisor->pauElements[0]); + rc = rtBigNumElement2xCopyToMagnitude(&uQ, pQuotient); + if (RT_SUCCESS(rc)) + rc = rtBigNumElement2xCopyToMagnitude(&uR, pRemainder); + } + } + /* + * Decide upon which algorithm to use. Knuth requires a divisor that's at + * least 2 elements big. + */ + else if (pDivisor->cUsed < 2 || fForceLong) + rc = rtBigNumMagnitudeDivideSlowLong(pQuotient, pRemainder, pDividend, pDivisor); + else + rc = rtBigNumMagnitudeDivideKnuth(pQuotient, pRemainder, pDividend, pDivisor); + return rc; +} + + +static int rtBigNumDivideCommon(PRTBIGNUM pQuotient, PRTBIGNUM pRemainder, + PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor, bool fForceLong) +{ + Assert(pQuotient != pDividend); Assert(pQuotient != pDivisor); Assert(pRemainder != pDividend); Assert(pRemainder != pDivisor); Assert(pRemainder != pQuotient); + AssertReturn(pQuotient->fSensitive >= (pDividend->fSensitive | pDivisor->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + AssertReturn(pRemainder->fSensitive >= (pDividend->fSensitive | pDivisor->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pQuotient); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pQuotient); + rc = rtBigNumUnscramble(pRemainder); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pRemainder); + rc = rtBigNumUnscramble((PRTBIGNUM)pDividend); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pDividend); + rc = rtBigNumUnscramble((PRTBIGNUM)pDivisor); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pDivisor); + + /* + * The sign value of the remainder is the same as the dividend. + * The sign values of the quotient follow XOR rules, just like multiplication: + * -3 / 2 = -1; r=-1; 1 ^ 0 = 1 + * 3 / -2 = -1; r= 1; 1 ^ 0 = 1 + * -3 / -2 = 1; r=-1; 1 ^ 1 = 0 + * 3 / 2 = 1; r= 1; 0 ^ 0 = 0 + */ + pQuotient->fNegative = pDividend->fNegative ^ pDivisor->fNegative; + pRemainder->fNegative = pDividend->fNegative; + + rc = rtBigNumMagnitudeDivide(pQuotient, pRemainder, pDividend, pDivisor, fForceLong); + + if (pQuotient->cUsed == 0) + pQuotient->fNegative = 0; + if (pRemainder->cUsed == 0) + pRemainder->fNegative = 0; + + rtBigNumScramble((PRTBIGNUM)pDivisor); + } + rtBigNumScramble((PRTBIGNUM)pDividend); + } + rtBigNumScramble(pRemainder); + } + rtBigNumScramble(pQuotient); + } + return rc; +} + + +RTDECL(int) RTBigNumDivide(PRTBIGNUM pQuotient, PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor) +{ + return rtBigNumDivideCommon(pQuotient, pRemainder, pDividend, pDivisor, false /*fForceLong*/); +} + + +RTDECL(int) RTBigNumDivideLong(PRTBIGNUM pQuotient, PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor) +{ + return rtBigNumDivideCommon(pQuotient, pRemainder, pDividend, pDivisor, true /*fForceLong*/); +} + + +/** + * Calculates the modulus of a magnitude value, leaving the sign bit to the + * caller. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched, this means the caller have to check for zero outputs. + * + * @returns IPRT status code. + * @param pRemainder Where to return the remainder. + * @param pDividend What to divide. + * @param pDivisor What to divide by. + */ +static int rtBigNumMagnitudeModulo(PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor) +{ + Assert(pRemainder != pDividend); Assert(pRemainder != pDivisor); + Assert(!pRemainder->fCurScrambled); Assert(!pDividend->fCurScrambled); Assert(!pDivisor->fCurScrambled); + + /* + * Just set the output value to zero as that's the return for several + * special case and the initial state of the general case. + */ + rtBigNumSetUsed(pRemainder, 0); + + /* + * Dividing something by zero is undefined. + * Diving zero by something is zero, unless the divsor is also zero. + */ + if (!pDivisor->cUsed || !pDividend->cUsed) + return pDivisor->cUsed ? VINF_SUCCESS : VERR_BIGNUM_DIV_BY_ZERO; + + /* + * Dividing by one? Quotient = dividend, no remainder. + */ + if (pDivisor->cUsed == 1 && pDivisor->pauElements[0] == 1) + return VINF_SUCCESS; + + /* + * Dividend smaller than the divisor. Zero quotient, all divisor. + */ + int iDiff = rtBigNumMagnitudeCompare(pDividend, pDivisor); + if (iDiff < 0) + return rtBigNumMagnitudeCopy(pRemainder, pDividend); + + /* + * Since we already have done the compare, check if the two values are the + * same. The result is 1 and no remainder then. + */ + if (iDiff == 0) + return VINF_SUCCESS; + + /** @todo optimize small numbers. */ + int rc = VINF_SUCCESS; + if (pDivisor->cUsed < 2) + { + /* + * Do very simple long division. This ain't fast, but it does the trick. + */ + uint32_t iBit = rtBigNumMagnitudeBitWidth(pDividend); + while (iBit-- > 0) + { + rc = rtBigNumMagnitudeShiftLeftOne(pRemainder, rtBigNumMagnitudeGetBit(pDividend, iBit)); + AssertRCBreak(rc); + iDiff = rtBigNumMagnitudeCompare(pRemainder, pDivisor); + if (iDiff >= 0) + { + if (iDiff != 0) + { + rc = rtBigNumMagnitudeSubThis(pRemainder, pDivisor); + AssertRCBreak(rc); + } + else + rtBigNumSetUsed(pRemainder, 0); + } + } + } + else + { + /* + * Join paths with division. + */ + rc = rtBigNumMagnitudeDivideKnuth(NULL, pRemainder, pDividend, pDivisor); + } + + /* This shouldn't be necessary. */ + rtBigNumStripTrailingZeros(pRemainder); + return rc; +} + + +RTDECL(int) RTBigNumModulo(PRTBIGNUM pRemainder, PCRTBIGNUM pDividend, PCRTBIGNUM pDivisor) +{ + Assert(pRemainder != pDividend); Assert(pRemainder != pDivisor); + AssertReturn(pRemainder->fSensitive >= (pDividend->fSensitive | pDivisor->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pRemainder); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pRemainder); + rc = rtBigNumUnscramble((PRTBIGNUM)pDividend); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pDividend); + rc = rtBigNumUnscramble((PRTBIGNUM)pDivisor); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pDivisor); + + /* + * The sign value of the remainder is the same as the dividend. + */ + pRemainder->fNegative = pDividend->fNegative; + + rc = rtBigNumMagnitudeModulo(pRemainder, pDividend, pDivisor); + + if (pRemainder->cUsed == 0) + pRemainder->fNegative = 0; + + rtBigNumScramble((PRTBIGNUM)pDivisor); + } + rtBigNumScramble((PRTBIGNUM)pDividend); + } + rtBigNumScramble(pRemainder); + } + return rc; +} + + + +/** + * Exponentiate the magnitude. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched, this means the caller have to reject negative exponents. + * + * @returns IPRT status code. + * @param pResult Where to return power. + * @param pBase The base value. + * @param pExponent The exponent (assumed positive or zero). + */ +static int rtBigNumMagnitudeExponentiate(PRTBIGNUM pResult, PCRTBIGNUM pBase, PCRTBIGNUM pExponent) +{ + Assert(pResult != pBase); Assert(pResult != pExponent); + Assert(!pResult->fCurScrambled); Assert(!pBase->fCurScrambled); Assert(!pExponent->fCurScrambled); + + /* + * A couple of special cases. + */ + int rc; + /* base ^ 0 => 1. */ + if (pExponent->cUsed == 0) + { + rc = rtBigNumSetUsed(pResult, 1); + if (RT_SUCCESS(rc)) + pResult->pauElements[0] = 1; + return rc; + } + + /* base ^ 1 => base. */ + if (pExponent->cUsed == 1 && pExponent->pauElements[0] == 1) + return rtBigNumMagnitudeCopy(pResult, pBase); + + /* + * Set up. + */ + /* Init temporary power-of-two variable to base. */ + RTBIGNUM Pow2; + rc = rtBigNumCloneInternal(&Pow2, pBase); + if (RT_SUCCESS(rc)) + { + /* Init result to 1. */ + rc = rtBigNumSetUsed(pResult, 1); + if (RT_SUCCESS(rc)) + { + pResult->pauElements[0] = 1; + + /* Make a temporary variable that we can use for temporary storage of the result. */ + RTBIGNUM TmpMultiplicand; + rc = rtBigNumCloneInternal(&TmpMultiplicand, pResult); + if (RT_SUCCESS(rc)) + { + /* + * Exponentiation by squaring. Reduces the number of + * multiplications to: NumBitsSet(Exponent) + BitWidth(Exponent). + */ + uint32_t const cExpBits = rtBigNumMagnitudeBitWidth(pExponent); + uint32_t iBit = 0; + for (;;) + { + if (rtBigNumMagnitudeGetBit(pExponent, iBit) != 0) + { + rc = rtBigNumMagnitudeCopy(&TmpMultiplicand, pResult); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeMultiply(pResult, &TmpMultiplicand, &Pow2); + if (RT_FAILURE(rc)) + break; + } + + /* Done? */ + iBit++; + if (iBit >= cExpBits) + break; + + /* Not done yet, square the base again. */ + rc = rtBigNumMagnitudeCopy(&TmpMultiplicand, &Pow2); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeMultiply(&Pow2, &TmpMultiplicand, &TmpMultiplicand); + if (RT_FAILURE(rc)) + break; + } + + RTBigNumDestroy(&TmpMultiplicand); + } + } + RTBigNumDestroy(&Pow2); + } + return rc; +} + + +RTDECL(int) RTBigNumExponentiate(PRTBIGNUM pResult, PCRTBIGNUM pBase, PCRTBIGNUM pExponent) +{ + Assert(pResult != pBase); Assert(pResult != pExponent); + AssertReturn(pResult->fSensitive >= (pBase->fSensitive | pExponent->fSensitive), VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + rc = rtBigNumUnscramble((PRTBIGNUM)pBase); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pBase); + rc = rtBigNumUnscramble((PRTBIGNUM)pExponent); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pExponent); + if (!pExponent->fNegative) + { + pResult->fNegative = pBase->fNegative; /* sign unchanged. */ + rc = rtBigNumMagnitudeExponentiate(pResult, pBase, pExponent); + } + else + rc = VERR_BIGNUM_NEGATIVE_EXPONENT; + + rtBigNumScramble((PRTBIGNUM)pExponent); + } + rtBigNumScramble((PRTBIGNUM)pBase); + } + rtBigNumScramble(pResult); + } + return rc; +} + + +/** + * Modular exponentiation, magnitudes only. + * + * All variables must be unscrambled. The sign flag is not considered nor + * touched, this means the caller have to reject negative exponents and do any + * other necessary sign bit fiddling. + * + * @returns IPRT status code. + * @param pResult Where to return the remainder of the power. + * @param pBase The base value. + * @param pExponent The exponent (assumed positive or zero). + * @param pModulus The modulus value (or divisor if you like). + */ +static int rtBigNumMagnitudeModExp(PRTBIGNUM pResult, PRTBIGNUM pBase, PRTBIGNUM pExponent, PRTBIGNUM pModulus) +{ + Assert(pResult != pBase); Assert(pResult != pBase); Assert(pResult != pExponent); Assert(pResult != pModulus); + Assert(!pResult->fCurScrambled); Assert(!pBase->fCurScrambled); Assert(!pExponent->fCurScrambled); Assert(!pModulus->fCurScrambled); + int rc; + + /* + * Check some special cases to get them out of the way. + */ + /* Div by 0 => invalid. */ + if (pModulus->cUsed == 0) + return VERR_BIGNUM_DIV_BY_ZERO; + + /* Div by 1 => no remainder. */ + if (pModulus->cUsed == 1 && pModulus->pauElements[0] == 1) + { + rtBigNumSetUsed(pResult, 0); + return VINF_SUCCESS; + } + + /* base ^ 0 => 1. */ + if (pExponent->cUsed == 0) + { + rc = rtBigNumSetUsed(pResult, 1); + if (RT_SUCCESS(rc)) + pResult->pauElements[0] = 1; + return rc; + } + + /* base ^ 1 => base. */ + if (pExponent->cUsed == 1 && pExponent->pauElements[0] == 1) + return rtBigNumMagnitudeModulo(pResult, pBase, pModulus); + + /* + * Set up. + */ + /* Result = 1; preallocate space for the result while at it. */ + rc = rtBigNumSetUsed(pResult, pModulus->cUsed + 1); + if (RT_SUCCESS(rc)) + rc = rtBigNumSetUsed(pResult, 1); + if (RT_SUCCESS(rc)) + { + pResult->pauElements[0] = 1; + + /* ModBase = pBase or pBase % pModulus depending on the difference in size. */ + RTBIGNUM Pow2; + if (pBase->cUsed <= pModulus->cUsed + pModulus->cUsed / 2) + rc = rtBigNumCloneInternal(&Pow2, pBase); + else + rc = rtBigNumMagnitudeModulo(rtBigNumInitZeroTemplate(&Pow2, pBase), pBase, pModulus); + + /* Need a couple of temporary variables. */ + RTBIGNUM TmpMultiplicand; + rtBigNumInitZeroTemplate(&TmpMultiplicand, pResult); + + RTBIGNUM TmpProduct; + rtBigNumInitZeroTemplate(&TmpProduct, pResult); + + /* + * We combine the exponentiation by squaring with the fact that: + * (a*b) mod n = ( (a mod n) * (b mod n) ) mod n + * + * Thus, we can reduce the size of intermediate results by mod'ing them + * in each step. + */ + uint32_t const cExpBits = rtBigNumMagnitudeBitWidth(pExponent); + uint32_t iBit = 0; + for (;;) + { + if (rtBigNumMagnitudeGetBit(pExponent, iBit) != 0) + { + rc = rtBigNumMagnitudeCopy(&TmpMultiplicand, pResult); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeMultiply(&TmpProduct, &TmpMultiplicand, &Pow2); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeModulo(pResult, &TmpProduct, pModulus); + if (RT_FAILURE(rc)) + break; + } + + /* Done? */ + iBit++; + if (iBit >= cExpBits) + break; + + /* Not done yet, square and mod the base again. */ + rc = rtBigNumMagnitudeCopy(&TmpMultiplicand, &Pow2); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeMultiply(&TmpProduct, &TmpMultiplicand, &TmpMultiplicand); + if (RT_SUCCESS(rc)) + rc = rtBigNumMagnitudeModulo(&Pow2, &TmpProduct, pModulus); + if (RT_FAILURE(rc)) + break; + } + + RTBigNumDestroy(&TmpMultiplicand); + RTBigNumDestroy(&TmpProduct); + RTBigNumDestroy(&Pow2); + } + return rc; +} + + +RTDECL(int) RTBigNumModExp(PRTBIGNUM pResult, PRTBIGNUM pBase, PRTBIGNUM pExponent, PRTBIGNUM pModulus) +{ + Assert(pResult != pBase); Assert(pResult != pBase); Assert(pResult != pExponent); Assert(pResult != pModulus); + AssertReturn(pResult->fSensitive >= (pBase->fSensitive | pExponent->fSensitive | pModulus->fSensitive), + VERR_BIGNUM_SENSITIVE_INPUT); + + int rc = rtBigNumUnscramble(pResult); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pResult); + rc = rtBigNumUnscramble((PRTBIGNUM)pBase); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pBase); + rc = rtBigNumUnscramble((PRTBIGNUM)pExponent); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pExponent); + rc = rtBigNumUnscramble((PRTBIGNUM)pModulus); + if (RT_SUCCESS(rc)) + { + RTBIGNUM_ASSERT_VALID(pModulus); + if (!pExponent->fNegative) + { + pResult->fNegative = pModulus->fNegative; /* pBase ^ pExponent / pModulus; result = remainder. */ + rc = rtBigNumMagnitudeModExp(pResult, pBase, pExponent, pModulus); + } + else + rc = VERR_BIGNUM_NEGATIVE_EXPONENT; + rtBigNumScramble((PRTBIGNUM)pModulus); + } + rtBigNumScramble((PRTBIGNUM)pExponent); + } + rtBigNumScramble((PRTBIGNUM)pBase); + } + rtBigNumScramble(pResult); + } + return rc; +} + |