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Int.cpp
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Int.cpp
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/*
* This file is part of the BTCCollider distribution (https://github.com/JeanLucPons/BTCCollider).
* Copyright (c) 2020 Jean Luc PONS.
*
* 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, version 3.
*
* 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 <http://www.gnu.org/licenses/>.
*/
#include "Int.h"
#include "IntGroup.h"
#include <string.h>
#include <emmintrin.h>
#include "Timer.h"
#define MAX(x,y) (((x)>(y))?(x):(y))
#define MIN(x,y) (((x)<(y))?(x):(y))
Int _ONE(1);
// ------------------------------------------------
Int::Int() {
}
Int::Int(Int *a) {
if(a) Set(a);
else CLEAR();
}
Int::Int(int64_t i64) {
if (i64 < 0) {
CLEARFF();
} else {
CLEAR();
}
bits64[0] = i64;
}
// ------------------------------------------------
void Int::CLEAR() {
memset(bits64,0, NB64BLOCK*8);
}
void Int::CLEARFF() {
memset(bits64, 0xFF, NB64BLOCK * 8);
}
// ------------------------------------------------
void Int::Set(Int *a) {
for (int i = 0; i<NB64BLOCK; i++)
bits64[i] = a->bits64[i];
}
// ------------------------------------------------
void Int::Add(Int *a) {
unsigned char c = 0;
c = _addcarry_u64(c, bits64[0], a->bits64[0], bits64 +0);
c = _addcarry_u64(c, bits64[1], a->bits64[1], bits64 +1);
c = _addcarry_u64(c, bits64[2], a->bits64[2], bits64 +2);
c = _addcarry_u64(c, bits64[3], a->bits64[3], bits64 +3);
c = _addcarry_u64(c, bits64[4], a->bits64[4], bits64 +4);
#if NB64BLOCK > 5
c = _addcarry_u64(c, bits64[5], a->bits64[5], bits64 +5);
c = _addcarry_u64(c, bits64[6], a->bits64[6], bits64 +6);
c = _addcarry_u64(c, bits64[7], a->bits64[7], bits64 +7);
c = _addcarry_u64(c, bits64[8], a->bits64[8], bits64 +8);
#endif
}
// ------------------------------------------------
void Int::Add(uint64_t a) {
unsigned char c = 0;
c = _addcarry_u64(c, bits64[0], a, bits64 + 0);
c = _addcarry_u64(c, bits64[1], 0, bits64 + 1);
c = _addcarry_u64(c, bits64[2], 0, bits64 + 2);
c = _addcarry_u64(c, bits64[3], 0, bits64 + 3);
c = _addcarry_u64(c, bits64[4], 0, bits64 + 4);
#if NB64BLOCK > 5
c = _addcarry_u64(c, bits64[5], 0, bits64 + 5);
c = _addcarry_u64(c, bits64[6], 0, bits64 + 6);
c = _addcarry_u64(c, bits64[7], 0, bits64 + 7);
c = _addcarry_u64(c, bits64[8], 0, bits64 + 8);
#endif
}
// ------------------------------------------------
void Int::AddOne() {
unsigned char c = 0;
c = _addcarry_u64(c, bits64[0],1, bits64 +0);
c = _addcarry_u64(c, bits64[1],0, bits64 +1);
c = _addcarry_u64(c, bits64[2],0, bits64 +2);
c = _addcarry_u64(c, bits64[3],0, bits64 +3);
c = _addcarry_u64(c, bits64[4],0, bits64 +4);
#if NB64BLOCK > 5
c = _addcarry_u64(c, bits64[5],0, bits64 +5);
c = _addcarry_u64(c, bits64[6],0, bits64 +6);
c = _addcarry_u64(c, bits64[7],0, bits64 +7);
c = _addcarry_u64(c, bits64[8],0, bits64 +8);
#endif
}
// ------------------------------------------------
void Int::Add(Int *a,Int *b) {
unsigned char c = 0;
c = _addcarry_u64(c, b->bits64[0], a->bits64[0], bits64 +0);
c = _addcarry_u64(c, b->bits64[1], a->bits64[1], bits64 +1);
c = _addcarry_u64(c, b->bits64[2], a->bits64[2], bits64 +2);
c = _addcarry_u64(c, b->bits64[3], a->bits64[3], bits64 +3);
c = _addcarry_u64(c, b->bits64[4], a->bits64[4], bits64 +4);
#if NB64BLOCK > 5
c = _addcarry_u64(c, b->bits64[5], a->bits64[5], bits64 +5);
c = _addcarry_u64(c, b->bits64[6], a->bits64[6], bits64 +6);
c = _addcarry_u64(c, b->bits64[7], a->bits64[7], bits64 +7);
c = _addcarry_u64(c, b->bits64[8], a->bits64[8], bits64 +8);
#endif
}
// ------------------------------------------------
bool Int::IsGreater(Int *a) {
int i;
for(i=NB64BLOCK-1;i>=0;) {
if( a->bits64[i]!= bits64[i] )
break;
i--;
}
if(i>=0) {
return bits64[i]>a->bits64[i];
} else {
return false;
}
}
// ------------------------------------------------
bool Int::IsLower(Int *a) {
int i;
for (i = NB64BLOCK - 1; i >= 0;) {
if (a->bits64[i] != bits64[i])
break;
i--;
}
if (i >= 0) {
return bits64[i]<a->bits64[i];
} else {
return false;
}
}
// ------------------------------------------------
bool Int::IsGreaterOrEqual(Int *a) {
Int p;
p.Sub(this,a);
return p.IsPositive();
}
// ------------------------------------------------
bool Int::IsLowerOrEqual(Int *a) {
int i = NB64BLOCK - 1;
while (i >= 0) {
if (a->bits64[i] != bits64[i])
break;
i--;
}
if (i >= 0) {
return bits64[i]<a->bits64[i];
} else {
return true;
}
}
bool Int::IsEqual(Int *a) {
return
#if NB64BLOCK > 5
(bits64[8] == a->bits64[8]) &&
(bits64[7] == a->bits64[7]) &&
(bits64[6] == a->bits64[6]) &&
(bits64[5] == a->bits64[5]) &&
#endif
(bits64[4] == a->bits64[4]) &&
(bits64[3] == a->bits64[3]) &&
(bits64[2] == a->bits64[2]) &&
(bits64[1] == a->bits64[1]) &&
(bits64[0] == a->bits64[0]);
}
bool Int::IsOne() {
return IsEqual(&_ONE);
}
bool Int::IsZero() {
#if NB64BLOCK > 5
return (bits64[8] | bits64[7] | bits64[6] | bits64[5] | bits64[4] | bits64[3] | bits64[2] | bits64[1] | bits64[0]) == 0;
#else
return (bits64[4] | bits64[3] | bits64[2] | bits64[1] | bits64[0]) == 0;
#endif
}
// ------------------------------------------------
void Int::SetInt32(uint32_t value) {
CLEAR();
bits[0]=value;
}
// ------------------------------------------------
uint32_t Int::GetInt32() {
return bits[0];
}
// ------------------------------------------------
unsigned char Int::GetByte(int n) {
unsigned char *bbPtr = (unsigned char *)bits;
return bbPtr[n];
}
void Int::Set32Bytes(unsigned char *bytes) {
CLEAR();
uint64_t *ptr = (uint64_t *)bytes;
bits64[3] = _byteswap_uint64(ptr[0]);
bits64[2] = _byteswap_uint64(ptr[1]);
bits64[1] = _byteswap_uint64(ptr[2]);
bits64[0] = _byteswap_uint64(ptr[3]);
}
void Int::Get32Bytes(unsigned char *buff) {
uint64_t *ptr = (uint64_t *)buff;
ptr[3] = _byteswap_uint64(bits64[0]);
ptr[2] = _byteswap_uint64(bits64[1]);
ptr[1] = _byteswap_uint64(bits64[2]);
ptr[0] = _byteswap_uint64(bits64[3]);
}
// ------------------------------------------------
void Int::SetByte(int n,unsigned char byte) {
unsigned char *bbPtr = (unsigned char *)bits;
bbPtr[n] = byte;
}
// ------------------------------------------------
void Int::SetDWord(int n,uint32_t b) {
bits[n] = b;
}
// ------------------------------------------------
void Int::SetQWord(int n, uint64_t b) {
bits64[n] = b;
}
// ------------------------------------------------
void Int::Sub(Int *a) {
unsigned char c = 0;
c = _subborrow_u64(c, bits64[0], a->bits64[0], bits64 +0);
c = _subborrow_u64(c, bits64[1], a->bits64[1], bits64 +1);
c = _subborrow_u64(c, bits64[2], a->bits64[2], bits64 +2);
c = _subborrow_u64(c, bits64[3], a->bits64[3], bits64 +3);
c = _subborrow_u64(c, bits64[4], a->bits64[4], bits64 +4);
#if NB64BLOCK > 5
c = _subborrow_u64(c, bits64[5], a->bits64[5], bits64 +5);
c = _subborrow_u64(c, bits64[6], a->bits64[6], bits64 +6);
c = _subborrow_u64(c, bits64[7], a->bits64[7], bits64 +7);
c = _subborrow_u64(c, bits64[8], a->bits64[8], bits64 +8);
#endif
}
// ------------------------------------------------
void Int::Sub(Int *a,Int *b) {
unsigned char c = 0;
c = _subborrow_u64(c, a->bits64[0], b->bits64[0], bits64 + 0);
c = _subborrow_u64(c, a->bits64[1], b->bits64[1], bits64 + 1);
c = _subborrow_u64(c, a->bits64[2], b->bits64[2], bits64 + 2);
c = _subborrow_u64(c, a->bits64[3], b->bits64[3], bits64 + 3);
c = _subborrow_u64(c, a->bits64[4], b->bits64[4], bits64 + 4);
#if NB64BLOCK > 5
c = _subborrow_u64(c, a->bits64[5], b->bits64[5], bits64 + 5);
c = _subborrow_u64(c, a->bits64[6], b->bits64[6], bits64 + 6);
c = _subborrow_u64(c, a->bits64[7], b->bits64[7], bits64 + 7);
c = _subborrow_u64(c, a->bits64[8], b->bits64[8], bits64 + 8);
#endif
}
void Int::Sub(uint64_t a) {
unsigned char c = 0;
c = _subborrow_u64(c, bits64[0], a, bits64 + 0);
c = _subborrow_u64(c, bits64[1], 0, bits64 + 1);
c = _subborrow_u64(c, bits64[2], 0, bits64 + 2);
c = _subborrow_u64(c, bits64[3], 0, bits64 + 3);
c = _subborrow_u64(c, bits64[4], 0, bits64 + 4);
#if NB64BLOCK > 5
c = _subborrow_u64(c, bits64[5], 0, bits64 + 5);
c = _subborrow_u64(c, bits64[6], 0, bits64 + 6);
c = _subborrow_u64(c, bits64[7], 0, bits64 + 7);
c = _subborrow_u64(c, bits64[8], 0, bits64 + 8);
#endif
}
void Int::SubOne() {
unsigned char c = 0;
c = _subborrow_u64(c, bits64[0], 1, bits64 + 0);
c = _subborrow_u64(c, bits64[1], 0, bits64 + 1);
c = _subborrow_u64(c, bits64[2], 0, bits64 + 2);
c = _subborrow_u64(c, bits64[3], 0, bits64 + 3);
c = _subborrow_u64(c, bits64[4], 0, bits64 + 4);
#if NB64BLOCK > 5
c = _subborrow_u64(c, bits64[5], 0, bits64 + 5);
c = _subborrow_u64(c, bits64[6], 0, bits64 + 6);
c = _subborrow_u64(c, bits64[7], 0, bits64 + 7);
c = _subborrow_u64(c, bits64[8], 0, bits64 + 8);
#endif
}
// ------------------------------------------------
bool Int::IsPositive() {
return (int64_t)(bits64[NB64BLOCK - 1])>=0;
}
// ------------------------------------------------
bool Int::IsNegative() {
return (int64_t)(bits64[NB64BLOCK - 1])<0;
}
// ------------------------------------------------
bool Int::IsStrictPositive() {
if( IsPositive() )
return !IsZero();
else
return false;
}
// ------------------------------------------------
bool Int::IsEven() {
return (bits[0] & 0x1) == 0;
}
// ------------------------------------------------
bool Int::IsOdd() {
return (bits[0] & 0x1) == 1;
}
// ------------------------------------------------
void Int::Neg() {
volatile unsigned char c=0;
c = _subborrow_u64(c, 0, bits64[0], bits64 + 0);
c = _subborrow_u64(c, 0, bits64[1], bits64 + 1);
c = _subborrow_u64(c, 0, bits64[2], bits64 + 2);
c = _subborrow_u64(c, 0, bits64[3], bits64 + 3);
c = _subborrow_u64(c, 0, bits64[4], bits64 + 4);
#if NB64BLOCK > 5
c = _subborrow_u64(c, 0, bits64[5], bits64 + 5);
c = _subborrow_u64(c, 0, bits64[6], bits64 + 6);
c = _subborrow_u64(c, 0, bits64[7], bits64 + 7);
c = _subborrow_u64(c, 0, bits64[8], bits64 + 8);
#endif
}
// ------------------------------------------------
void Int::ShiftL32Bit() {
for(int i=NB32BLOCK-1;i>0;i--) {
bits[i]=bits[i-1];
}
bits[0]=0;
}
// ------------------------------------------------
void Int::ShiftL64Bit() {
for (int i = NB64BLOCK-1 ; i>0; i--) {
bits64[i] = bits64[i - 1];
}
bits64[0] = 0;
}
// ------------------------------------------------
void Int::ShiftL32BitAndSub(Int *a,int n) {
Int b;
int i=NB32BLOCK-1;
for(;i>=n;i--)
b.bits[i] = ~a->bits[i-n];
for(;i>=0;i--)
b.bits[i] = 0xFFFFFFFF;
Add(&b);
AddOne();
}
// ------------------------------------------------
void Int::ShiftL(uint32_t n) {
if( n<64 ) {
shiftL((unsigned char)n, bits64);
} else {
uint32_t nb64 = n/64;
uint32_t nb = n%64;
for(uint32_t i=0;i<nb64;i++) ShiftL64Bit();
shiftL((unsigned char)nb, bits64);
}
}
// ------------------------------------------------
void Int::ShiftR32Bit() {
for(int i=0;i<NB32BLOCK-1;i++) {
bits[i]=bits[i+1];
}
if(((int32_t)bits[NB32BLOCK-2])<0)
bits[NB32BLOCK-1] = 0xFFFFFFFF;
else
bits[NB32BLOCK-1]=0;
}
// ------------------------------------------------
void Int::ShiftR64Bit() {
for (int i = 0; i<NB64BLOCK - 1; i++) {
bits64[i] = bits64[i + 1];
}
if (((int64_t)bits64[NB64BLOCK - 2])<0)
bits64[NB64BLOCK - 1] = 0xFFFFFFFFFFFFFFFF;
else
bits64[NB64BLOCK - 1] = 0;
}
// ---------------------------------D---------------
void Int::ShiftR(uint32_t n) {
if( n<64 ) {
shiftR((unsigned char)n, bits64);
} else {
uint32_t nb64 = n/64;
uint32_t nb = n%64;
for(uint32_t i=0;i<nb64;i++) ShiftR64Bit();
shiftR((unsigned char)nb, bits64);
}
}
// ------------------------------------------------
void Int::Mult(Int *a) {
Int b(this);
Mult(a,&b);
}
// ------------------------------------------------
void Int::IMult(int64_t a) {
// Make a positive
if (a < 0LL) {
a = -a;
Neg();
}
imm_mul(bits64, a, bits64);
}
// ------------------------------------------------
void Int::Mult(uint64_t a) {
imm_mul(bits64, a, bits64);
}
// ------------------------------------------------
void Int::IMult(Int *a, int64_t b) {
Set(a);
// Make b positive
if (b < 0LL) {
Neg();
b = -b;
}
imm_mul(bits64, b, bits64);
}
// ------------------------------------------------
void Int::Mult(Int *a, uint64_t b) {
imm_mul(a->bits64, b, bits64);
}
// ------------------------------------------------
void Int::Mult(Int *a,Int *b) {
unsigned char c = 0;
uint64_t h;
uint64_t pr = 0;
uint64_t carryh = 0;
uint64_t carryl = 0;
bits64[0] = _umul128(a->bits64[0], b->bits64[0], &pr);
for (int i = 1; i < NB64BLOCK; i++) {
for (int j = 0; j <= i; j++) {
c = _addcarry_u64(c, _umul128(a->bits64[j], b->bits64[i - j], &h), pr, &pr);
c = _addcarry_u64(c, carryl, h, &carryl);
c = _addcarry_u64(c, carryh, 0, &carryh);
}
bits64[i] = pr;
pr = carryl;
carryl = carryh;
carryh = 0;
}
}
// ------------------------------------------------
void Int::Mult(Int *a,uint32_t b) {
imm_mul(a->bits64, (uint64_t)b, bits64);
}
// ------------------------------------------------
static uint32_t bitLength(uint32_t dw) {
uint32_t mask = 0x80000000;
uint32_t b=0;
while(b<32 && (mask & dw)==0) {
b++;
mask >>= 1;
}
return b;
}
// ------------------------------------------------
int Int::GetBitLength() {
Int t(this);
if(IsNegative())
t.Neg();
int i=NB32BLOCK-1;
while(i>=0 && t.bits[i]==0) i--;
if(i<0) return 0;
return (32-bitLength(t.bits[i])) + i*32;
}
// ------------------------------------------------
int Int::GetSize() {
int i=NB32BLOCK-1;
while(i>0 && bits[i]==0) i--;
return i+1;
}
// ------------------------------------------------
void Int::MultModN(Int *a,Int *b,Int *n) {
Int r;
Mult(a,b);
Div(n,&r);
Set(&r);
}
// ------------------------------------------------
void Int::Mod(Int *n) {
Int r;
Div(n,&r);
Set(&r);
}
// ------------------------------------------------
int Int::GetLowestBit() {
// Assume this!=0
int b=0;
while(GetBit(b)==0) b++;
return b;
}
// ------------------------------------------------
void Int::MaskByte(int n) {
for (int i = n; i < NB32BLOCK; i++)
bits[i] = 0;
}
// ------------------------------------------------
void Int::Abs() {
if (IsNegative())
Neg();
}
// ------------------------------------------------
void Int::Rand(int nbit) {
CLEAR();
uint32_t nb = nbit/32;
uint32_t leftBit = nbit%32;
uint32_t mask = 1;
mask = (mask << leftBit) - 1;
uint32_t i=0;
for(;i<nb;i++)
bits[i]=rndl();
bits[i]=rndl()&mask;
}
// ------------------------------------------------
void Int::Div(Int *a,Int *mod) {
if(a->IsGreater(this)) {
if(mod) mod->Set(this);
CLEAR();
return;
}
if(a->IsZero()) {
printf("Divide by 0!\n");
return;
}
if(IsEqual(a)) {
if(mod) mod->CLEAR();
Set(&_ONE);
return;
}
//Division algorithm D (Knuth section 4.3.1)
Int rem(this);
Int d(a);
Int dq;
CLEAR();
// Size
uint32_t dSize = d.GetSize();
uint32_t tSize = rem.GetSize();
uint32_t qSize = tSize - dSize + 1;
// D1 normalize the divisor
uint32_t shift = bitLength(d.bits[dSize-1]);
if (shift > 0) {
d.ShiftL(shift);
rem.ShiftL(shift);
}
uint32_t _dh = d.bits[dSize-1];
uint64_t dhLong = _dh;
uint32_t _dl = (dSize>1)?d.bits[dSize-2]:0;
int sb = tSize-1;
// D2 Initialize j
for(int j=0; j<(int)qSize; j++) {
// D3 Estimate qhat
uint32_t qhat = 0;
uint32_t qrem = 0;
int skipCorrection = false;
uint32_t nh = rem.bits[sb-j+1];
uint32_t nm = rem.bits[sb-j];
if (nh == _dh) {
qhat = ~0;
qrem = nh + nm;
skipCorrection = qrem < nh;
} else {
uint64_t nChunk = ((uint64_t)nh << 32) | (uint64_t)nm;
qhat = (uint32_t) (nChunk / dhLong);
qrem = (uint32_t) (nChunk % dhLong);
}
if (qhat == 0)
continue;
if (!skipCorrection) {
// Correct qhat
uint64_t nl = (uint64_t)rem.bits[sb-j-1];
uint64_t rs = ((uint64_t)qrem << 32) | nl;
uint64_t estProduct = (uint64_t)_dl * (uint64_t)(qhat);
if (estProduct>rs) {
qhat--;
qrem = (uint32_t)(qrem + (uint32_t)dhLong);
if ((uint64_t)qrem >= dhLong) {
estProduct = (uint64_t)_dl * (uint64_t)(qhat);
rs = ((uint64_t)qrem << 32) | nl;
if(estProduct>rs)
qhat--;
}
}
}
// D4 Multiply and subtract
dq.Mult(&d,qhat);
rem.ShiftL32BitAndSub(&dq,qSize-j-1);
if( rem.IsNegative() ) {
// Overflow
rem.Add(&d);
qhat--;
}
bits[qSize-j-1] = qhat;
}
if( mod ) {
// Unnormalize remainder
rem.ShiftR(shift);
mod->Set(&rem);
}
}
// ------------------------------------------------
void Int::GCD(Int *a) {
uint32_t k;
uint32_t b;
Int U(this);
Int V(a);
Int T;
if(U.IsZero()) {
Set(&V);
return;
}
if(V.IsZero()) {
Set(&U);
return;
}
if(U.IsNegative()) U.Neg();
if(V.IsNegative()) V.Neg();
k = 0;
while (U.GetBit(k)==0 && V.GetBit(k)==0)
k++;
U.ShiftR(k);
V.ShiftR(k);
if (U.GetBit(0)==1) {
T.Set(&V);
T.Neg();
} else {
T.Set(&U);
}
do {
if( T.IsNegative() ) {
T.Neg();
b=0;while(T.GetBit(b)==0) b++;
T.ShiftR(b);
V.Set(&T);
T.Set(&U);
} else {
b=0;while(T.GetBit(b)==0) b++;
T.ShiftR(b);
U.Set(&T);
}
T.Sub(&V);
} while (!T.IsZero());
// Store gcd
Set(&U);
ShiftL(k);
}
// ------------------------------------------------
void Int::SetBase10(char *value) {
CLEAR();
Int pw(1);
Int c;
int lgth = (int)strlen(value);
for(int i=lgth-1;i>=0;i--) {
uint32_t id = (uint32_t)(value[i]-'0');
c.Set(&pw);
c.Mult(id);
Add(&c);
pw.Mult(10);
}
}
// ------------------------------------------------
void Int::SetBase16(char *value) {
SetBaseN(16,"0123456789ABCDEF",value);
}
// ------------------------------------------------
std::string Int::GetBase10() {
return GetBaseN(10,"0123456789");
}
// ------------------------------------------------
std::string Int::GetBase16() {
return GetBaseN(16,"0123456789ABCDEF");
}
// ------------------------------------------------
std::string Int::GetBlockStr() {
char tmp[256];
char bStr[256];
tmp[0] = 0;
for (int i = NB32BLOCK-3; i>=0 ; i--) {
sprintf(bStr, "%08X", bits[i]);
strcat(tmp, bStr);
if(i!=0) strcat(tmp, " ");
}
return std::string(tmp);
}
// ------------------------------------------------
std::string Int::GetC64Str(int nbDigit) {
char tmp[256];
char bStr[256];
tmp[0] = '{';
tmp[1] = 0;
for (int i = 0; i< nbDigit; i++) {
if (bits64[i] != 0) {
#ifdef WIN64
sprintf(bStr, "0x%016I64XULL", bits64[i]);
#else
sprintf(bStr, "0x%" PRIx64 "ULL", bits64[i]);
#endif
} else {
sprintf(bStr, "0ULL");
}
strcat(tmp, bStr);
if (i != nbDigit -1) strcat(tmp, ",");
}
strcat(tmp,"}");
return std::string(tmp);
}
// ------------------------------------------------
void Int::SetBaseN(int n,char *charset,char *value) {
CLEAR();
Int pw((uint32_t)1);
Int nb((int32_t)n);
Int c;
int lgth = (int)strlen(value);
for(int i=lgth-1;i>=0;i--) {
char *p = strchr(charset,toupper(value[i]));
if(!p) {
printf("Invalid charset !!\n");
return;
}
int id = (int)(p-charset);
c.SetInt32(id);
c.Mult(&pw);
Add(&c);
pw.Mult(&nb);
}
}