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modmult.c
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modmult.c
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/*
This file is part of Alpertron Calculators.
Copyright 2015 Dario Alejandro Alpern
Alpertron Calculators 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, either version 3 of the License, or
(at your option) any later version.
Alpertron Calculators 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 Alpertron Calculators. If not, see <http://www.gnu.org/licenses/>.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <stdint.h>
#include "bignbr.h"
limb MontgomeryR1[MAX_LEN];
limb TestNbr[MAX_LEN];
limb MontgomeryMultN[MAX_LEN];
limb MontgomeryMultR1[MAX_LEN];
limb MontgomeryMultR2[MAX_LEN];
int powerOf2Exponent;
static limb aux[MAX_LEN], aux2[MAX_LEN];
static limb aux3[MAX_LEN], aux4[MAX_LEN];
static limb aux5[MAX_LEN], aux6[MAX_LEN];
static limb resultModOdd[MAX_LEN], resultModPower2[MAX_LEN];
static int NumberLength2;
int NumberLength, NumberLengthR1;
long long lModularMult;
mmCback modmultCallback;
static limb U[MAX_LEN], V[MAX_LEN], R[MAX_LEN], S[MAX_LEN];
static limb Ubak[MAX_LEN], Vbak[MAX_LEN];
static BigInteger tmpDen, tmpNum, oddValue;
int getNbrLimbs(limb *bigNbr)
{
limb *ptrLimb = bigNbr + NumberLength;
while (ptrLimb > bigNbr)
{
if ((--ptrLimb)->x != 0)
{
return (int)(ptrLimb - &bigNbr[0] + 1);
}
}
return 1;
}
// Find the inverse of value mod 2^(NumberLength*BITS_PER_GROUP)
void ComputeInversePower2(limb *value, limb *result, limb *tmp)
{
int N, x, j;
limb Cy;
int currLen;
x = N = (int)value->x; // 2 least significant bits of inverse correct.
x = x * (2 - N * x); // 4 least significant bits of inverse correct.
x = x * (2 - N * x); // 8 least significant bits of inverse correct.
x = x * (2 - N * x); // 16 least significant bits of inverse correct.
x = x * (2 - N * x); // 32 least significant bits of inverse correct.
result->x = x & MAX_VALUE_LIMB;
for (currLen = 2; currLen <= NumberLength * 2; currLen <<= 1)
{
multiply(value, result, tmp, currLen, NULL); // tmp <- N * x
Cy.x = 2 - tmp[0].x;
tmp[0].x = Cy.x & MAX_VALUE_LIMB;
for (j = 1; j < currLen; j++)
{
Cy.x = (Cy.x >> BITS_PER_GROUP) - tmp[j].x;
tmp[j].x = Cy.x & MAX_VALUE_LIMB;
} // tmp <- 2 - N * x
multiply(result, tmp, result, currLen, NULL); // tmp <- x * (2 - N * x)
}
}
// Let R be a power of 2 of at least len limbs.
// Compute R1 = MontgomeryR1 and N = MontgomeryN using the formulas:
// R1 = R mod M
// N = -M^(-1) mod R
void GetMontgomeryParms(int len)
{
int j;
limb Cy;
int value;
TestNbr[len].x = 0;
NumberLength = len;
NumberLength2 = len + len;
if (NumberLength == 1)
{
MontgomeryMultR1[0].x = 1;
MontgomeryMultR2[0].x = 1;
NumberLengthR1 = 1;
return;
}
// Check whether TestNbr is a power of 2.
powerOf2Exponent = 0; // Indicate not power of 2 in advance.
for (j = 0; j < NumberLength-1; j++)
{
if (TestNbr[j].x != 0)
{
break;
}
}
if (j == NumberLength - 1)
{
value = TestNbr[NumberLength - 1].x;
for (j = 0; j < BITS_PER_GROUP; j++)
{
if (value == 1)
{
powerOf2Exponent = (NumberLength - 1)*BITS_PER_GROUP + j;
memset(MontgomeryMultR1, 0, NumberLength*sizeof(limb));
memset(MontgomeryMultR2, 0, NumberLength * sizeof(limb));
MontgomeryMultR1[0].x = 1;
MontgomeryMultR2[0].x = 1;
return;
}
value >>= 1;
}
}
// Compute MontgomeryMultN as -1/TestNbr (mod 2^k) using Newton method,
// which doubles the precision for each iteration.
// In the formula above: k = BITS_PER_GROUP * NumberLength.
if (NumberLength >= 8)
{
limb *ptrResult;
ComputeInversePower2(TestNbr, MontgomeryMultN, aux);
ptrResult = &MontgomeryMultN[0];
Cy.x = 0; // Change sign.
for (j = 0; j < NumberLength; j++)
{
Cy.x = (Cy.x >> BITS_PER_GROUP) - ptrResult->x;
ptrResult->x = Cy.x & MAX_VALUE_LIMB;
ptrResult++;
}
ptrResult->x = 0;
}
else
{
int x, N;
x = N = (int)TestNbr[0].x; // 2 least significant bits of inverse correct.
x = x * (2 - N * x); // 4 least significant bits of inverse correct.
x = x * (2 - N * x); // 8 least significant bits of inverse correct.
x = x * (2 - N * x); // 16 least significant bits of inverse correct.
x = x * (2 - N * x); // 32 least significant bits of inverse correct.
MontgomeryMultN[0].x = (-x) & MAX_VALUE_LIMB; // Change sign
}
// Compute MontgomeryMultR1 as 1 in Montgomery notation,
// this is 2^(NumberLength*BITS_PER_GROUP) % TestNbr.
j = NumberLength;
MontgomeryMultR1[j].x = 1;
do
{
MontgomeryMultR1[--j].x = 0;
} while (j > 0);
AdjustModN(MontgomeryMultR1, TestNbr, len);
MontgomeryMultR1[NumberLength].x = 0;
memcpy(MontgomeryMultR2, MontgomeryMultR1, (NumberLength+1)*sizeof(limb));
for (NumberLengthR1 = NumberLength; NumberLengthR1 > 0; NumberLengthR1--)
{
if (MontgomeryMultR1[NumberLengthR1 - 1].x != 0)
{
break;
}
}
// Compute MontgomeryMultR2 as 2^(2*NumberLength*BITS_PER_GROUP) % TestNbr.
for (j = NumberLength; j > 0; j--)
{
memmove(&MontgomeryMultR2[1], &MontgomeryMultR2[0], NumberLength*sizeof(limb));
MontgomeryMultR2[0].x = 0;
AdjustModN(MontgomeryMultR2, TestNbr, len);
}
}
// Compute Nbr <- Nbr mod Modulus.
// Modulus has NumberLength limbs.
void AdjustModN(limb *Nbr, limb *Modulus, int nbrLen)
{
int i, carry;
int TrialQuotient;
double dNbr, dModulus, dTrialQuotient;
double dAccumulator, dDelta;
double dVal = 1 / (double)LIMB_RANGE;
double dSquareLimb = (double)LIMB_RANGE * (double)LIMB_RANGE;
dModulus = getMantissa(Modulus+nbrLen, nbrLen);
dNbr = getMantissa(Nbr + nbrLen + 1, nbrLen + 1) * LIMB_RANGE;
TrialQuotient = (int)(unsigned int)floor(dNbr / dModulus + 0.5);
if ((unsigned int)TrialQuotient >= LIMB_RANGE)
{ // Maximum value for limb.
TrialQuotient = MAX_VALUE_LIMB;
}
// Compute Nbr <- Nbr - TrialQuotient * Modulus
dTrialQuotient = (double)TrialQuotient;
carry = 0;
dAccumulator = 0;
dDelta = 0;
for (i = 0; i <= nbrLen; i++)
{
int low = (Nbr[i].x - Modulus[i].x * TrialQuotient + carry) & MAX_INT_NBR;
// Subtract or add 0x20000000 so the multiplication by dVal is not nearly an integer.
// In that case, there would be an error of +/- 1.
dAccumulator = Nbr[i].x - Modulus[i].x * dTrialQuotient + carry + dDelta;
dDelta = 0;
if (dAccumulator < 0)
{
dAccumulator += dSquareLimb;
dDelta = -(double)LIMB_RANGE;
}
if (low < HALF_INT_RANGE)
{
carry = (int)floor((dAccumulator + HALF_INT_RANGE / 2)*dVal);
}
else
{
carry = (int)floor((dAccumulator - HALF_INT_RANGE / 2)*dVal);
}
Nbr[i].x = low;
}
Nbr[i].x = carry & MAX_INT_NBR;
if ((Nbr[nbrLen].x & MAX_VALUE_LIMB) != 0)
{
unsigned int cy = 0;
for (i = 0; i < nbrLen; i++)
{
cy += (unsigned int)Nbr[i].x + (unsigned int)Modulus[i].x;
Nbr[i].x = (int)(cy & MAX_VALUE_LIMB);
cy >>= BITS_PER_GROUP;
}
Nbr[nbrLen].x = 0;
}
}
void AddBigNbrModN(limb *Nbr1, limb *Nbr2, limb *Sum, limb *mod, int nbrLen)
{
unsigned int carry;
int borrow;
int i;
carry = 0;
for (i = 0; i < nbrLen; i++)
{
carry = (carry >> BITS_PER_GROUP) +
(unsigned int)(Nbr1 + i)->x + (unsigned int)(Nbr2 + i)->x;
Sum[i].x = (int)(carry & MAX_VALUE_LIMB);
}
borrow = 0;
for (i = 0; i < nbrLen; i++)
{
borrow = (borrow >> BITS_PER_GROUP) +
(unsigned int)Sum[i].x - (mod + i)->x;
Sum[i].x = (int)(borrow & MAX_VALUE_LIMB);
}
if (carry < LIMB_RANGE && borrow < 0)
{
carry = 0;
for (i = 0; i < nbrLen; i++)
{
carry = (carry >> BITS_PER_GROUP) +
(unsigned int)(Sum+i)->x + (unsigned int)(mod+i)->x;
Sum[i].x = (int)(carry & MAX_VALUE_LIMB);
}
}
}
void AddBigNbrMod(limb *Nbr1, limb *Nbr2, limb *Sum)
{
AddBigNbrModN(Nbr1, Nbr2, Sum, TestNbr, NumberLength);
}
void SubtBigNbrModN(limb *Nbr1, limb *Nbr2, limb *Diff, limb *mod, int nbrLen)
{
int i;
int borrow = 0;
for (i = 0; i < nbrLen; i++)
{
borrow = (borrow >> BITS_PER_GROUP) + (Nbr1 + i)->x - (Nbr2 + i)->x;
Diff[i].x = (int)(borrow & MAX_VALUE_LIMB);
}
if (borrow < 0)
{
unsigned int carry = 0;
for (i = 0; i < nbrLen; i++)
{
carry = (carry >> BITS_PER_GROUP) +
(unsigned int)(Diff + i)->x + (unsigned int)(mod + i)->x;
Diff[i].x = (int)(carry & MAX_VALUE_LIMB);
}
}
}
void SubtBigNbrMod(limb *Nbr1, limb *Nbr2, limb *Sum)
{
SubtBigNbrModN(Nbr1, Nbr2, Sum, TestNbr, NumberLength);
}
static void smallmodmult(int factor1, int factor2, limb *product, int mod)
{
if (mod < SMALL_NUMBER_BOUND)
{
product->x = factor1 * factor2 % mod;
}
else
{ // TestNbr has one limb but it is not small.
#ifdef _USING64BITS_
product->x = (int64_t)factor1 * factor2 % mod;
#else
// Round up quotient.
int quotient = (int)floor((double)factor1 * (double)factor2 / (double)mod + 0.5);
int remainder = factor1 * factor2 - quotient * mod;
if (remainder < 0)
{ // Quotient was 1 more than expected. Adjust remainder.
remainder += mod;
}
product->x = remainder;
#endif
}
}
// Multiply two numbers in Montgomery notation.
//
// For large numbers the REDC algorithm is:
// m <- ((T mod R)N') mod R
// t <- (T + mN) / R
// if t >= N then
// return t - N
// else
// return t
// end if
#ifdef _USING64BITS_
static void MontgomeryMult2(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1;
Prod0 = Prod1 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
for (i = 0; i<2; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr1 + 1) << BITS_PER_GROUP) || (Prod1 == TestNbr1 && Prod0 >= TestNbr0))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
}
static void MontgomeryMult3(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2;
Prod0 = Prod1 = Prod2 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
for (i = 0; i<3; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr2 + 1) << BITS_PER_GROUP)
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1 || (Prod1 == TestNbr1 && (Prod0 >= TestNbr0)))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
}
static void MontgomeryMult4(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3;
Prod0 = Prod1 = Prod2 = Prod3 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
for (i = 0; i<4; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr3 + 1) << BITS_PER_GROUP)
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1 || (Prod1 == TestNbr1 && (Prod0 >= TestNbr0)))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
}
static void MontgomeryMult5(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3, Prod4;
Prod0 = Prod1 = Prod2 = Prod3 = Prod4 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t TestNbr4 = TestNbr[4].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
uint32_t Nbr2_4 = (pNbr2 + 4)->x;
for (i = 0; i<5; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr4 + 1) << BITS_PER_GROUP)
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1 || (Prod1 == TestNbr1 && (Prod0 >= TestNbr0)))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
(pProd + 4)->x = Prod4;
}
static void MontgomeryMult6(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3, Prod4, Prod5;
Prod0 = Prod1 = Prod2 = Prod3 = Prod4 = Prod5 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t TestNbr4 = TestNbr[4].x;
uint32_t TestNbr5 = TestNbr[5].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
uint32_t Nbr2_4 = (pNbr2 + 4)->x;
uint32_t Nbr2_5 = (pNbr2 + 5)->x;
for (i = 0; i<6; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr5 + (uint64_t)Nbr * Nbr2_5 + (uint32_t)Prod5) & MAX_INT_NBR;
Prod5 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr5 + 1) << BITS_PER_GROUP)
|| (Prod5 == TestNbr5
&& (Prod4 > TestNbr4
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1
|| (Prod1 == TestNbr1
&& (Prod0 >= TestNbr0)))))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
Prod5 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod5 - (int32_t)TestNbr5) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
(pProd + 4)->x = Prod4;
(pProd + 5)->x = Prod5;
}
static void MontgomeryMult7(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
int Prod0, Prod1, Prod2, Prod3, Prod4, Prod5, Prod6;
Prod0 = Prod1 = Prod2 = Prod3 = Prod4 = Prod5 = Prod6 = 0;
int TestNbr0 = (int)TestNbr[0].x;
int TestNbr1 = (int)TestNbr[1].x;
int TestNbr2 = (int)TestNbr[2].x;
int TestNbr3 = (int)TestNbr[3].x;
int TestNbr4 = (int)TestNbr[4].x;
int TestNbr5 = (int)TestNbr[5].x;
int TestNbr6 = (int)TestNbr[6].x;
int Nbr2_0 = (int)pNbr2->x;
int Nbr2_1 = (int)(pNbr2 + 1)->x;
int Nbr2_2 = (int)(pNbr2 + 2)->x;
int Nbr2_3 = (int)(pNbr2 + 3)->x;
int Nbr2_4 = (int)(pNbr2 + 4)->x;
int Nbr2_5 = (int)(pNbr2 + 5)->x;
int Nbr2_6 = (int)(pNbr2 + 6)->x;
for (i = 0; i<7; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr5 + (uint64_t)Nbr * Nbr2_5 + (uint32_t)Prod5) & MAX_INT_NBR;
Prod5 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr6 + (uint64_t)Nbr * Nbr2_6 + (uint32_t)Prod6) & MAX_INT_NBR;
Prod6 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr6 + 1) << BITS_PER_GROUP)
|| (Prod6 == TestNbr6
&& (Prod5 > TestNbr5
|| (Prod5 == TestNbr5
&& (Prod4 > TestNbr4
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1
|| (Prod1 == TestNbr1
&& (Prod0 >= TestNbr0)))))))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
Prod5 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod5 - (int32_t)TestNbr5) & MAX_INT_NBR;
Prod6 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod6 - (int32_t)TestNbr6) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
(pProd + 4)->x = Prod4;
(pProd + 5)->x = Prod5;
(pProd + 6)->x = Prod6;
}
static void MontgomeryMult8(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3, Prod4, Prod5, Prod6, Prod7;
Prod0 = Prod1 = Prod2 = Prod3 = Prod4 = Prod5 = Prod6 = Prod7 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t TestNbr4 = TestNbr[4].x;
uint32_t TestNbr5 = TestNbr[5].x;
uint32_t TestNbr6 = TestNbr[6].x;
uint32_t TestNbr7 = TestNbr[7].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
uint32_t Nbr2_4 = (pNbr2 + 4)->x;
uint32_t Nbr2_5 = (pNbr2 + 5)->x;
uint32_t Nbr2_6 = (pNbr2 + 6)->x;
uint32_t Nbr2_7 = (pNbr2 + 7)->x;
for (i = 0; i<8; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr5 + (uint64_t)Nbr * Nbr2_5 + (uint32_t)Prod5) & MAX_INT_NBR;
Prod5 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr6 + (uint64_t)Nbr * Nbr2_6 + (uint32_t)Prod6) & MAX_INT_NBR;
Prod6 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr7 + (uint64_t)Nbr * Nbr2_7 + (uint32_t)Prod7) & MAX_INT_NBR;
Prod7 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr7 + 1) << BITS_PER_GROUP)
|| (Prod7 == TestNbr7
&& (Prod6 > TestNbr6
|| (Prod6 == TestNbr6
&& (Prod5 > TestNbr5
|| (Prod5 == TestNbr5
&& (Prod4 > TestNbr4
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1
|| (Prod1 == TestNbr1
&& (Prod0 >= TestNbr0)))))))))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
Prod5 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod5 - (int32_t)TestNbr5) & MAX_INT_NBR;
Prod6 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod6 - (int32_t)TestNbr6) & MAX_INT_NBR;
Prod7 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod7 - (int32_t)TestNbr7) & MAX_INT_NBR;
}
pProd->x = (int)Prod0;
(pProd + 1)->x = (int)Prod1;
(pProd + 2)->x = (int)Prod2;
(pProd + 3)->x = (int)Prod3;
(pProd + 4)->x = (int)Prod4;
(pProd + 5)->x = (int)Prod5;
(pProd + 6)->x = (int)Prod6;
(pProd + 7)->x = (int)Prod7;
}
static void MontgomeryMult9(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3, Prod4, Prod5, Prod6, Prod7, Prod8;
Prod0 =
Prod1 = Prod2 = Prod3 = Prod4 = Prod5 = Prod6 = Prod7 = Prod8 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t TestNbr4 = TestNbr[4].x;
uint32_t TestNbr5 = TestNbr[5].x;
uint32_t TestNbr6 = TestNbr[6].x;
uint32_t TestNbr7 = TestNbr[7].x;
uint32_t TestNbr8 = TestNbr[8].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
uint32_t Nbr2_4 = (pNbr2 + 4)->x;
uint32_t Nbr2_5 = (pNbr2 + 5)->x;
uint32_t Nbr2_6 = (pNbr2 + 6)->x;
uint32_t Nbr2_7 = (pNbr2 + 7)->x;
uint32_t Nbr2_8 = (pNbr2 + 8)->x;
for (i = 0; i<9; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr5 + (uint64_t)Nbr * Nbr2_5 + (uint32_t)Prod5) & MAX_INT_NBR;
Prod5 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr6 + (uint64_t)Nbr * Nbr2_6 + (uint32_t)Prod6) & MAX_INT_NBR;
Prod6 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr7 + (uint64_t)Nbr * Nbr2_7 + (uint32_t)Prod7) & MAX_INT_NBR;
Prod7 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr8 + (uint64_t)Nbr * Nbr2_8 + (uint32_t)Prod8) & MAX_INT_NBR;
Prod8 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr8 + 1) << BITS_PER_GROUP)
|| (Prod8 == TestNbr8
&& (Prod7 > TestNbr7
|| (Prod7 == TestNbr7
&& (Prod6 > TestNbr6
|| (Prod6 == TestNbr6
&& (Prod5 > TestNbr5
|| (Prod5 == TestNbr5
&& (Prod4 > TestNbr4
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1
|| (Prod1 == TestNbr1
&& (Prod0 >= TestNbr0)))))))))))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
Prod5 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod5 - (int32_t)TestNbr5) & MAX_INT_NBR;
Prod6 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod6 - (int32_t)TestNbr6) & MAX_INT_NBR;
Prod7 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod7 - (int32_t)TestNbr7) & MAX_INT_NBR;
Prod8 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod8 - (int32_t)TestNbr8) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
(pProd + 4)->x = Prod4;
(pProd + 5)->x = Prod5;
(pProd + 6)->x = Prod6;
(pProd + 7)->x = Prod7;
(pProd + 8)->x = Prod8;
}
static void MontgomeryMult10(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3, Prod4, Prod5, Prod6, Prod7, Prod8,
Prod9;
Prod0 = Prod1 =
Prod2 = Prod3 = Prod4 = Prod5 = Prod6 = Prod7 = Prod8 = Prod9 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t TestNbr4 = TestNbr[4].x;
uint32_t TestNbr5 = TestNbr[5].x;
uint32_t TestNbr6 = TestNbr[6].x;
uint32_t TestNbr7 = TestNbr[7].x;
uint32_t TestNbr8 = TestNbr[8].x;
uint32_t TestNbr9 = TestNbr[9].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
uint32_t Nbr2_4 = (pNbr2 + 4)->x;
uint32_t Nbr2_5 = (pNbr2 + 5)->x;
uint32_t Nbr2_6 = (pNbr2 + 6)->x;
uint32_t Nbr2_7 = (pNbr2 + 7)->x;
uint32_t Nbr2_8 = (pNbr2 + 8)->x;
uint32_t Nbr2_9 = (pNbr2 + 9)->x;
for (i = 0; i<10; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr5 + (uint64_t)Nbr * Nbr2_5 + (uint32_t)Prod5) & MAX_INT_NBR;
Prod5 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr6 + (uint64_t)Nbr * Nbr2_6 + (uint32_t)Prod6) & MAX_INT_NBR;
Prod6 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr7 + (uint64_t)Nbr * Nbr2_7 + (uint32_t)Prod7) & MAX_INT_NBR;
Prod7 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr8 + (uint64_t)Nbr * Nbr2_8 + (uint32_t)Prod8) & MAX_INT_NBR;
Prod8 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr9 + (uint64_t)Nbr * Nbr2_9 + (uint32_t)Prod9) & MAX_INT_NBR;
Prod9 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr9 + 1) << BITS_PER_GROUP)
|| (Prod9 == TestNbr9
&& (Prod8 > TestNbr8
|| (Prod8 == TestNbr8
&& (Prod7 > TestNbr7
|| (Prod7 == TestNbr7
&& (Prod6 > TestNbr6
|| (Prod6 == TestNbr6
&& (Prod5 > TestNbr5
|| (Prod5 == TestNbr5
&& (Prod4 > TestNbr4
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1
|| (Prod1 == TestNbr1
&& (Prod0 >= TestNbr0)))))))))))))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
Prod5 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod5 - (int32_t)TestNbr5) & MAX_INT_NBR;
Prod6 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod6 - (int32_t)TestNbr6) & MAX_INT_NBR;
Prod7 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod7 - (int32_t)TestNbr7) & MAX_INT_NBR;
Prod8 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod8 - (int32_t)TestNbr8) & MAX_INT_NBR;
Prod9 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod9 - (int32_t)TestNbr9) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
(pProd + 4)->x = Prod4;
(pProd + 5)->x = Prod5;
(pProd + 6)->x = Prod6;
(pProd + 7)->x = Prod7;
(pProd + 8)->x = Prod8;
(pProd + 9)->x = Prod9;
}
static void MontgomeryMult11(limb *pNbr1, limb *pNbr2, limb *pProd)
{
int i;
uint64_t Pr;
int32_t borrow;
uint32_t Nbr, MontDig;
uint32_t Prod0, Prod1, Prod2, Prod3, Prod4, Prod5, Prod6, Prod7, Prod8,
Prod9, Prod10;
Prod0 = Prod1 = Prod2 = Prod3 =
Prod4 = Prod5 = Prod6 = Prod7 = Prod8 = Prod9 = Prod10 = 0;
uint32_t TestNbr0 = TestNbr[0].x;
uint32_t TestNbr1 = TestNbr[1].x;
uint32_t TestNbr2 = TestNbr[2].x;
uint32_t TestNbr3 = TestNbr[3].x;
uint32_t TestNbr4 = TestNbr[4].x;
uint32_t TestNbr5 = TestNbr[5].x;
uint32_t TestNbr6 = TestNbr[6].x;
uint32_t TestNbr7 = TestNbr[7].x;
uint32_t TestNbr8 = TestNbr[8].x;
uint32_t TestNbr9 = TestNbr[9].x;
uint32_t TestNbr10 = TestNbr[10].x;
uint32_t Nbr2_0 = pNbr2->x;
uint32_t Nbr2_1 = (pNbr2 + 1)->x;
uint32_t Nbr2_2 = (pNbr2 + 2)->x;
uint32_t Nbr2_3 = (pNbr2 + 3)->x;
uint32_t Nbr2_4 = (pNbr2 + 4)->x;
uint32_t Nbr2_5 = (pNbr2 + 5)->x;
uint32_t Nbr2_6 = (pNbr2 + 6)->x;
uint32_t Nbr2_7 = (pNbr2 + 7)->x;
uint32_t Nbr2_8 = (pNbr2 + 8)->x;
uint32_t Nbr2_9 = (pNbr2 + 9)->x;
uint32_t Nbr2_10 = (pNbr2 + 10)->x;
for (i = 0; i<11; i++)
{
Pr = (Nbr = (pNbr1 + i)->x) * (uint64_t)Nbr2_0 + (uint32_t)Prod0;
MontDig = ((uint32_t)Pr * MontgomeryMultN[0].x) & MAX_INT_NBR;
Prod0 = (Pr = (((uint64_t)MontDig * TestNbr0 + Pr) >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr1 + (uint64_t)Nbr * Nbr2_1 + (uint32_t)Prod1) & MAX_INT_NBR;
Prod1 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr2 + (uint64_t)Nbr * Nbr2_2 + (uint32_t)Prod2) & MAX_INT_NBR;
Prod2 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr3 + (uint64_t)Nbr * Nbr2_3 + (uint32_t)Prod3) & MAX_INT_NBR;
Prod3 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr4 + (uint64_t)Nbr * Nbr2_4 + (uint32_t)Prod4) & MAX_INT_NBR;
Prod4 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr5 + (uint64_t)Nbr * Nbr2_5 + (uint32_t)Prod5) & MAX_INT_NBR;
Prod5 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr6 + (uint64_t)Nbr * Nbr2_6 + (uint32_t)Prod6) & MAX_INT_NBR;
Prod6 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr7 + (uint64_t)Nbr * Nbr2_7 + (uint32_t)Prod7) & MAX_INT_NBR;
Prod7 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr8 + (uint64_t)Nbr * Nbr2_8 + (uint32_t)Prod8) & MAX_INT_NBR;
Prod8 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr9 + (uint64_t)Nbr * Nbr2_9 + (uint32_t)Prod9) & MAX_INT_NBR;
Prod9 = (Pr = (Pr >> BITS_PER_GROUP) +
(uint64_t)MontDig * TestNbr10 + (uint64_t)Nbr * Nbr2_10 + (uint32_t)Prod10) & MAX_INT_NBR;
Prod10 = (uint32_t)(Pr >> BITS_PER_GROUP);
}
if (Pr >= ((uint64_t)(TestNbr10 + 1) << BITS_PER_GROUP)
|| (Prod10 == TestNbr10
&& (Prod9 > TestNbr9
|| (Prod9 == TestNbr9
&& (Prod8 > TestNbr8
|| (Prod8 == TestNbr8
&& (Prod7 > TestNbr7
|| (Prod7 == TestNbr7
&& (Prod6 > TestNbr6
|| (Prod6 == TestNbr6
&& (Prod5 > TestNbr5
|| (Prod5 == TestNbr5
&& (Prod4 > TestNbr4
|| (Prod4 == TestNbr4
&& (Prod3 > TestNbr3
|| (Prod3 == TestNbr3
&& (Prod2 > TestNbr2
|| (Prod2 == TestNbr2
&& (Prod1 > TestNbr1
|| (Prod1 == TestNbr1
&& (Prod0 >= TestNbr0)))))))))))))))))))))
{
Prod0 = (borrow = (int32_t)Prod0 - (int32_t)TestNbr0) & MAX_INT_NBR;
Prod1 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod1 - (int32_t)TestNbr1) & MAX_INT_NBR;
Prod2 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod2 - (int32_t)TestNbr2) & MAX_INT_NBR;
Prod3 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod3 - (int32_t)TestNbr3) & MAX_INT_NBR;
Prod4 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod4 - (int32_t)TestNbr4) & MAX_INT_NBR;
Prod5 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod5 - (int32_t)TestNbr5) & MAX_INT_NBR;
Prod6 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod6 - (int32_t)TestNbr6) & MAX_INT_NBR;
Prod7 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod7 - (int32_t)TestNbr7) & MAX_INT_NBR;
Prod8 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod8 - (int32_t)TestNbr8) & MAX_INT_NBR;
Prod9 = (borrow = (borrow >> BITS_PER_GROUP) + (int32_t)Prod9 - (int32_t)TestNbr9) & MAX_INT_NBR;
Prod10 = ((borrow >> BITS_PER_GROUP) + (int32_t)Prod10 - (int32_t)TestNbr10) & MAX_INT_NBR;
}
pProd->x = Prod0;
(pProd + 1)->x = Prod1;
(pProd + 2)->x = Prod2;
(pProd + 3)->x = Prod3;
(pProd + 4)->x = Prod4;
(pProd + 5)->x = Prod5;
(pProd + 6)->x = Prod6;