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GaussExpr.c
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GaussExpr.c
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//
// This file is part of Alpertron Calculators.
//
// Copyright 2016-2021 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 <stdlib.h>
#include <string.h>
#include <math.h>
#include "bignbr.h"
#include "factor.h"
#include "expression.h"
#define PAREN_STACK_SIZE 5000
#define COMPR_STACK_SIZE 1000000
#define TOKEN_PRIMORIAL 39
#define TOKEN_GCD 40
#define TOKEN_LCM 41
#define TOKEN_MODPOW 42
#define TOKEN_MODINV 43
#define TOKEN_NORM 44
#define TOKEN_RE 45
#define TOKEN_IM 46
#define TOKEN_ISPRIME 47
#define TOKEN_F 48
#define TOKEN_L 49
#define TOKEN_P 50
#define TOKEN_N 51
#define TOKEN_B 52
struct sFuncOperExpr stFuncOperGaussianExpr[] =
{
// First section: functions
{"ANS", TOKEN_ANS + NO_PARMS, 0},
{"GCD", TOKEN_GCD + MANY_PARMS, 0},
{"LCM", TOKEN_LCM + MANY_PARMS, 0},
{"MODPOW", TOKEN_MODPOW + THREE_PARMS, 0},
{"MODINV", TOKEN_MODINV + TWO_PARMS, 0},
{"NORM", TOKEN_NORM + ONE_PARM, 0},
{"RE", TOKEN_RE + ONE_PARM, 0},
{"IM", TOKEN_IM + ONE_PARM, 0},
{"ISPRIME", TOKEN_ISPRIME + ONE_PARM, 0},
{"F", TOKEN_F + ONE_PARM, 0},
{"L", TOKEN_L + ONE_PARM, 0},
{"P", TOKEN_P + ONE_PARM, 0},
{"N", TOKEN_N + ONE_PARM, 0},
{"B", TOKEN_B + ONE_PARM, 0},
{"RANDOM", TOKEN_RANDOM + TWO_PARMS, 0},
{NULL, 0, 0},
// Second section: functions written at right of argument.
{"#", TOKEN_PRIMORIAL, 0},
{NULL, 0, 0},
// Third section: unary operators.
{"-", OPER_UNARY_MINUS, 3},
{NULL, 0, 0},
// Fourth section: binary operators.
{"**", OPER_POWER, 1}, // This must be located before multiplication operator.
{"+", OPER_ADD, 4},
{"-", OPER_SUBT, 4},
{"*", OPER_MULTIPLY, 2},
{"%", OPER_REMAINDER, 2},
{"/", OPER_DIVIDE, 2},
{"^", OPER_POWER, 1},
{NULL, 0, 0},
};
static int comprStackValues[COMPR_STACK_SIZE];
static int comprStackOffset[PAREN_STACK_SIZE];
static int stackIndex;
#ifndef lang
bool lang;
#endif
char output[3000000];
limb Mult1[MAX_LEN];
limb Mult3[MAX_LEN];
limb Mult4[MAX_LEN];
int valueQ[MAX_LEN];
static void ComputeGCD(void);
static enum eExprErr ComputeLCM(void);
static enum eExprErr GaussianDivide(void);
static enum eExprErr GaussianMultiply(void);
static int Modulo(BigInteger* ReNum, BigInteger* ImNum,
const BigInteger* ReDen, const BigInteger* ImDen,
BigInteger* Result);
static enum eExprErr isPrime(void);
static enum eExprErr ComputeModPow(void);
static enum eExprErr ComputeModInv(void);
static enum eExprErr ComputePartition(void);
static enum eExprErr ComputePower(BigInteger* Re1, const BigInteger* Re2,
BigInteger* Im1, const BigInteger* Im2);
static enum eExprErr ModInv(const BigInteger* RealNbr, const BigInteger* ImagNbr,
const BigInteger* RealMod, const BigInteger* ImagMod,
BigInteger* Result);
static BigInteger curStackRe;
static BigInteger curStackIm;
static BigInteger curStack2Re;
static BigInteger curStack2Im;
static BigInteger curStack3Re;
static BigInteger curStack3Im;
static BigInteger curStackReBak;
static BigInteger curStackImBak;
static BigInteger curStack2ReBak;
static BigInteger curStack2ImBak;
static BigInteger curTmp;
static BigInteger norm;
static BigInteger Result[2];
static BigInteger LastAnswerRe;
static BigInteger LastAnswerIm;
static int numLimbs(const int* pLen)
{
int nbrLimbs = *pLen;
if (nbrLimbs < 0)
{
nbrLimbs = -nbrLimbs;
}
return nbrLimbs;
}
static void getCurrentStackValue(BigInteger* pValueRe, BigInteger *pValueIm)
{
const int* ptrStackValue = &comprStackValues[comprStackOffset[2*stackIndex]];
NumberLength = numLimbs(ptrStackValue);
IntArray2BigInteger(ptrStackValue, pValueRe);
ptrStackValue = &comprStackValues[comprStackOffset[(2 * stackIndex) + 1]];
NumberLength = numLimbs(ptrStackValue);
IntArray2BigInteger(ptrStackValue, pValueIm);
}
static enum eExprErr setStackValue(const BigInteger* pValueRe, const BigInteger *pValueIm)
{
int currentOffset = comprStackOffset[2 * stackIndex];
if (currentOffset >= (COMPR_STACK_SIZE - ((int)sizeof(BigInteger) / (int)sizeof(limb))))
{
return EXPR_OUT_OF_MEMORY;
}
NumberLength = pValueRe->nbrLimbs;
BigInteger2IntArray(&comprStackValues[currentOffset], pValueRe);
currentOffset += pValueRe->nbrLimbs + 1;
comprStackOffset[(2 * stackIndex) + 1] = currentOffset;
NumberLength = pValueIm->nbrLimbs;
BigInteger2IntArray(&comprStackValues[currentOffset], pValueIm);
currentOffset += pValueIm->nbrLimbs + 1;
comprStackOffset[(2 * stackIndex) + 2] = currentOffset;
return EXPR_OK;
}
enum eExprErr ComputeGaussianExpression(const char *expr, BigInteger *ExpressionResult)
{
char* ptrRPNbuffer;
enum eExprErr retcode;
retcode = ConvertToReversePolishNotation(expr, &ptrRPNbuffer, stFuncOperGaussianExpr,
PARSE_EXPR_GAUSSIAN, NULL, NULL);
if (retcode != EXPR_OK)
{
return retcode;
}
stackIndex = -1;
comprStackOffset[0] = 0;
while (*ptrRPNbuffer != '\0')
{
char c = *ptrRPNbuffer;
int currentOffset;
int nbrLenBytes;
int len;
int nbrParameters;
switch (c)
{
case TOKEN_NUMBER:
ptrRPNbuffer++; // Skip token.
stackIndex++;
// Move number to compressed stack.
currentOffset = comprStackOffset[2 * stackIndex];
if (currentOffset >= (COMPR_STACK_SIZE - ((int)sizeof(BigInteger) / (int)sizeof(limb))))
{
return EXPR_OUT_OF_MEMORY;
}
len = ((int)(unsigned char)*ptrRPNbuffer * 256) + (int)(unsigned char)*(ptrRPNbuffer + 1);
comprStackValues[currentOffset] = len;
ptrRPNbuffer += 2; // Skip length.
nbrLenBytes = len * (int)sizeof(limb);
(void)memcpy(&comprStackValues[currentOffset + 1], ptrRPNbuffer, nbrLenBytes);
ptrRPNbuffer += nbrLenBytes;
currentOffset += 1 + len;
comprStackOffset[(2 * stackIndex) + 1] = currentOffset;
comprStackValues[currentOffset] = 1; // Imaginary part is zero.
comprStackValues[currentOffset + 1] = 0;
comprStackOffset[(2 * stackIndex) + 2] = currentOffset + 2;
break;
case TOKEN_VAR: // Push number i.
ptrRPNbuffer++; // Skip token.
stackIndex++;
currentOffset = comprStackOffset[2 * stackIndex];
comprStackValues[currentOffset] = 1; // Real part is zero.
comprStackValues[currentOffset + 1] = 0;
currentOffset += 2;
comprStackOffset[(2 * stackIndex) + 1] = currentOffset;
comprStackValues[currentOffset] = 1; // Imaginary part is one.
comprStackValues[currentOffset + 1] = 1;
comprStackOffset[(2 * stackIndex) + 2] = currentOffset + 2;
break;
case TOKEN_ANS: // Get last answer.
if (LastAnswerRe.nbrLimbs == 0)
{
intToBigInteger(&curStackRe, 0);
}
else
{
CopyBigInt(&curStackRe, &LastAnswerRe);
}
if (LastAnswerIm.nbrLimbs == 0)
{
intToBigInteger(&curStackIm, 0);
}
else
{
CopyBigInt(&curStackIm, &LastAnswerIm);
}
stackIndex++;
break;
case TOKEN_RE:
if (stackIndex < 0)
{
return EXPR_INTERNAL_ERROR;
}
getCurrentStackValue(&curStackRe, &curStackIm);
intToBigInteger(&curStackIm, 0);
break;
case TOKEN_IM:
if (stackIndex < 0)
{
return EXPR_INTERNAL_ERROR;
}
getCurrentStackValue(&curStackIm, &curStackRe);
intToBigInteger(&curStackIm, 0);
break;
case TOKEN_NORM:
if (stackIndex < 0)
{
return EXPR_INTERNAL_ERROR;
}
// norm = Re^2 + Im^2
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = BigIntMultiply(&curStackRe, &curStackRe, &curStack2Re);
if (retcode != EXPR_OK)
{
return retcode;
}
retcode = BigIntMultiply(&curStackIm, &curStackIm, &curStack2Im);
if (retcode != EXPR_OK)
{
return retcode;
}
BigIntAdd(&curStack2Re, &curStack2Im, &curStackRe);
intToBigInteger(&curStackIm, 0);
break;
case TOKEN_GCD:
ptrRPNbuffer++;
nbrParameters = (int)(unsigned char)*ptrRPNbuffer;
getCurrentStackValue(&curStackRe, &curStackIm);
for (int parmNbr = 1; parmNbr < nbrParameters; parmNbr++)
{
stackIndex--;
getCurrentStackValue(&curStack2Re, &curStack2Im);
ComputeGCD();
}
break;
case TOKEN_LCM:
ptrRPNbuffer++;
nbrParameters = (int)(unsigned char)*ptrRPNbuffer;
getCurrentStackValue(&curStackRe, &curStackIm);
for (int parmNbr = 1; parmNbr < nbrParameters; parmNbr++)
{
stackIndex--;
getCurrentStackValue(&curStack2Re, &curStack2Im);
retcode = ComputeLCM();
if (retcode != EXPR_OK)
{
return retcode;
}
}
break;
case TOKEN_MODPOW:
getCurrentStackValue(&curStack3Re, &curStack3Im);
stackIndex--;
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = ComputeModPow();
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_MODINV:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = ComputeModInv();
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_ISPRIME:
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = isPrime();
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_F:
getCurrentStackValue(&curStackRe, &curStackIm);
if (!BigIntIsZero(&curStackIm))
{ // Imaginary part of argument must be zero.
return EXPR_INVALID_PARAM;
}
retcode = ComputeFibLucas(0, &curStackRe);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_L:
getCurrentStackValue(&curStackRe, &curStackIm);
if (!BigIntIsZero(&curStackIm))
{ // Imaginary part of argument must be zero.
return EXPR_INVALID_PARAM;
}
retcode = ComputeFibLucas(2, &curStackRe);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_N:
getCurrentStackValue(&curStackRe, &curStackIm);
if (!BigIntIsZero(&curStackIm))
{ // Imaginary part of argument must be zero.
return EXPR_INVALID_PARAM;
}
retcode = ComputeNext(&curStackRe);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_B:
getCurrentStackValue(&curStackRe, &curStackIm);
if (!BigIntIsZero(&curStackIm))
{ // Imaginary part of argument must be zero.
return EXPR_INVALID_PARAM;
}
retcode = ComputeBack(&curStackRe);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_P:
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = ComputePartition();
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_RANDOM:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
BigIntRandom(&curStackRe, &curStack2Re, &curStackRe);
BigIntRandom(&curStackIm, &curStack2Im, &curStackIm);
break;
case TOKEN_FACTORIAL:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
if (!BigIntIsZero(&curStackIm) || (curStackRe.sign == SIGN_NEGATIVE))
{ // Imaginary part must be zero.
return EXPR_INVALID_PARAM;
}
retcode = factorial(&curStackRe, curStackRe.limbs[0].x, curStack2Re.limbs[0].x);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case TOKEN_PRIMORIAL:
getCurrentStackValue(&curStackRe, &curStackIm);
if (!BigIntIsZero(&curStackIm) || (curStackRe.sign == SIGN_NEGATIVE))
{ // Imaginary part must be zero.
return EXPR_INVALID_PARAM;
}
if ((curStackRe.nbrLimbs > 1) || (curStackRe.limbs[0].x > 46049))
{
return EXPR_INTERM_TOO_HIGH;
}
retcode = primorial(&curStackRe, curStackRe.limbs[0].x);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case OPER_ADD:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
BigIntAdd(&curStackRe, &curStack2Re, &curStackRe);
BigIntAdd(&curStackIm, &curStack2Im, &curStackIm);
break;
case OPER_SUBT:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
BigIntSubt(&curStackRe, &curStack2Re, &curStackRe);
BigIntSubt(&curStackIm, &curStack2Im, &curStackIm);
break;
case OPER_UNARY_MINUS:
getCurrentStackValue(&curStackRe, &curStackIm);
BigIntChSign(&curStackRe);
BigIntChSign(&curStackIm);
break;
case OPER_MULTIPLY:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = GaussianMultiply();
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case OPER_DIVIDE:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = GaussianDivide();
if (retcode != EXPR_OK)
{
return retcode;
}
break;
case OPER_REMAINDER:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = Modulo(&curStackRe, &curStackIm, &curStack2Re, &curStack2Im, Result);
if (retcode != EXPR_OK)
{
return retcode;
}
CopyBigInt(&curStackRe, &Result[0]);
CopyBigInt(&curStackIm, &Result[1]);
break;
case TOKEN_END_EXPON:
getCurrentStackValue(&curStack2Re, &curStack2Im);
stackIndex--;
getCurrentStackValue(&curStackRe, &curStackIm);
retcode = ComputePower(&curStackRe, &curStack2Re, &curStackIm, &curStack2Im);
if (retcode != EXPR_OK)
{
return retcode;
}
break;
default:
break;
}
if ((c != TOKEN_NUMBER) && (c != TOKEN_VAR))
{
if (c != TOKEN_START_EXPON)
{
retcode = setStackValue(&curStackRe, &curStackIm);
if (retcode != EXPR_OK)
{
return retcode;
}
}
ptrRPNbuffer++; // Skip token.
}
}
getCurrentStackValue(ExpressionResult, ExpressionResult + 1);
if ((ExpressionResult->nbrLimbs > 2215) && // 10000/log_10(32768)
((ExpressionResult+1)->nbrLimbs > 2215))
{
return EXPR_NUMBER_TOO_HIGH;
}
CopyBigInt(&LastAnswerRe, ExpressionResult);
CopyBigInt(&LastAnswerIm, ExpressionResult + 1);
return EXPR_OK;
}
static enum eExprErr isPrime(void)
{
if (BigIntIsZero(&curStackRe))
{
if ((curStackIm.limbs[0].x % 4) != 3)
{
intToBigInteger(&curStackRe, 0); // Number not prime.
intToBigInteger(&curStackIm, 0);
return EXPR_OK;
}
CopyBigInt(&curStack2Re, &curStackIm);
}
else if (BigIntIsZero(&curStackIm))
{
if ((curStackRe.limbs[0].x % 4) != 3)
{
intToBigInteger(&curStackRe, 0); // Number not prime.
intToBigInteger(&curStackIm, 0);
return EXPR_OK;
}
CopyBigInt(&curStack2Re, &curStackRe);
}
else
{
enum eExprErr retcode;
retcode = BigIntMultiply(&curStackRe, &curStackRe, &curStack2Re);
if (retcode != EXPR_OK)
{
return retcode;
}
retcode = BigIntMultiply(&curStackIm, &curStackIm, &curStack2Im);
if (retcode != EXPR_OK)
{
return retcode;
}
BigIntAdd(&curStack2Re, &curStack2Im, &curStack2Re);
}
#ifdef FACTORIZATION_APP
if (BpswPrimalityTest(&curStack2Re, NULL) == 0)
#else
if (BpswPrimalityTest(&curStack2Re) == 0)
#endif
{ // Argument is a probable prime.
intToBigInteger(&curStackRe, -1);
}
else
{ // Argument is not a probable prime.
intToBigInteger(&curStackRe, 0);
}
intToBigInteger(&curStackIm, 0);
return EXPR_OK;
}
static enum eExprErr ComputePartition(void)
{
int val;
if (!BigIntIsZero(&curStackIm))
{ // Imaginary part must be zero.
return EXPR_INVALID_PARAM;
}
if (curStackRe.sign == SIGN_NEGATIVE)
{
return EXPR_INVALID_PARAM;
}
if (curStackRe.nbrLimbs > 1)
{
return EXPR_INTERM_TOO_HIGH;
}
val = curStackRe.limbs[0].x;
if (val > 100000)
{
return EXPR_INVALID_PARAM;
}
partition(val, &curStackRe);
return EXPR_OK;
}
// Replace dividend by the remainder.
// Back-up sign of dividend and then divide positive by positive (divisor is always positive).
static void GetRemainder(const BigInteger *Norm, BigInteger *ReDividend, BigInteger *ImDividend,
const BigInteger *ReDivisor, const BigInteger *ImDivisor,
BigInteger *Re, BigInteger *Im)
{
BigInteger ReTmp;
BigInteger ImTmp;
int signBak;
// Compute Re as ((Re1*Re2+Im1*Im2)*2/norm+1)/2
(void)BigIntMultiply(ReDividend, ReDivisor, &ReTmp);
(void)BigIntMultiply(ImDividend, ImDivisor, &ImTmp);
BigIntAdd(&ReTmp, &ImTmp, &ReTmp);
multint(&ReTmp, &ReTmp, 2);
signBak = ReTmp.sign;
ReTmp.sign = SIGN_POSITIVE;
(void)BigIntDivide(&ReTmp, Norm, Re);
subtractdivide(Re, -1, 2);
if (!BigIntIsZero(Re))
{
Re->sign = signBak;
}
// Compute Im as ((Im1*Re2-Re1*Im2)*2/norm+1)/2
(void)BigIntMultiply(ImDividend, ReDivisor, &ReTmp);
(void)BigIntMultiply(ReDividend, ImDivisor, &ImTmp);
BigIntSubt(&ReTmp, &ImTmp, &ImTmp);
multint(&ImTmp, &ImTmp, 2);
signBak = ImTmp.sign;
ImTmp.sign = SIGN_POSITIVE;
(void)BigIntDivide(&ImTmp, Norm, Im);
subtractdivide(Im, -1, 2);
if (!BigIntIsZero(Im))
{
Im->sign = signBak;
}
// Compute Re1 as Re1 - Re*Re2 + Im*Im2.
(void)BigIntMultiply(Re, ReDivisor, &ReTmp);
BigIntSubt(ReDividend, &ReTmp, ReDividend);
(void)BigIntMultiply(Im, ImDivisor, &ReTmp);
BigIntAdd(ReDividend, &ReTmp, ReDividend);
// Compute Im1 as Im1 - Im*Re2 - Re*Im2.
(void)BigIntMultiply(Im, ReDivisor, &ReTmp);
BigIntSubt(ImDividend, &ReTmp, ImDividend);
(void)BigIntMultiply(Re, ImDivisor, &ReTmp);
BigIntSubt(ImDividend, &ReTmp, ImDividend);
}
// Compute curStack as gcd(curStack, curStack2)
static void ComputeGCD(void)
{
BigInteger ReTmp;
BigInteger ImTmp;
GaussianGCD(&curStackRe, &curStackIm, &curStack2Re, &curStack2Im,
&curStack3Re, &curStack3Im, &ReTmp, &ImTmp);
CopyBigInt(&curStackRe, &curStack3Re);
CopyBigInt(&curStackIm, &curStack3Im);
while ((curStackRe.sign == SIGN_NEGATIVE) || (curStackIm.sign == SIGN_NEGATIVE))
{ // Multiply by i until number is in first quadrant.
CopyBigInt(&curStack3Re, &curStackRe);
BigIntNegate(&curStackIm, &curStackRe);
CopyBigInt(&curStackIm, &curStack3Re);
}
}
static enum eExprErr ComputeLCM(void)
{
enum eExprErr retcode;
if ((BigIntIsZero(&curStackRe) && BigIntIsZero(&curStackIm)) ||
(BigIntIsZero(&curStack2Re) && BigIntIsZero(&curStack2Im)))
{ // If any of the arguments is zero, the LCM is zero.
intToBigInteger(&curStackRe, 0);
intToBigInteger(&curStackIm, 0);
return EXPR_OK;
}
// Save both parameters because ComputeGCD will overwrite them.
CopyBigInt(&curStackReBak, &curStackRe);
CopyBigInt(&curStackImBak, &curStackIm);
CopyBigInt(&curStack2ReBak, &curStack2Re);
CopyBigInt(&curStack2ImBak, &curStack2Im);
ComputeGCD(); // curStackRe + i*curStackIm = GCD.
// Divide first parameter by GCD.
CopyBigInt(&curStack2Re, &curStackRe); // Divisor
CopyBigInt(&curStack2Im, &curStackIm);
CopyBigInt(&curStackRe, &curStackReBak); // Dividend
CopyBigInt(&curStackIm, &curStackImBak);
retcode = GaussianDivide();
if (retcode != EXPR_OK)
{
return retcode;
}
// Multiply the quotient by the second parameter.
CopyBigInt(&curStack2Re, &curStack2ReBak);
CopyBigInt(&curStack2Im, &curStack2ImBak);
return GaussianMultiply();
}
static int ComputePower(BigInteger *Re1, const BigInteger *Re2,
BigInteger *Im1, const BigInteger *Im2)
{
unsigned int expon;
double logNorm;
bool performPower = false;
BigInteger ReTmp;
BigInteger ImTmp;
BigInteger Re;
BigInteger Im;
if (!BigIntIsZero(Im2) || (Re2->sign == SIGN_NEGATIVE))
{ // Exponent must be positive or zero.
return EXPR_INVALID_PARAM;
}
if (Re2->nbrLimbs > 2)
{
return EXPR_INTERM_TOO_HIGH;
}
expon = (unsigned int)Re2->limbs[0].x;
if (Re2->nbrLimbs == 2)
{
expon += (unsigned int)Re2->limbs[1].x << BITS_PER_GROUP;
}
(void)BigIntMultiply(Re1, Re1, &ReTmp);
(void)BigIntMultiply(Im1, Im1, &ImTmp);
BigIntAdd(&ReTmp, &ImTmp, &norm); // norm <- re1^2 + im1^2.
logNorm = logLimbs(norm.limbs, norm.nbrLimbs); // Get logarithm of norm.
if (logNorm*(double)expon > 23026.0)
{ // More than 20000 digits. 23026 = log(10^10000) (norm is already squared).
return EXPR_INTERM_TOO_HIGH;
}
/* Compute actual power */
Re.limbs[0].x = 1; // Initialize Re <- 1, Im <- 0.
Im.limbs[0].x = 0;
Re.nbrLimbs = 1;
Im.nbrLimbs = 1;
Re.sign = SIGN_POSITIVE;
Im.sign = SIGN_POSITIVE;
for (unsigned int mask = HALF_INT_RANGE_U; mask != 0U; mask >>= 1)
{
if ((expon & mask) != 0U)
{
performPower = true;
}
if (performPower)
{
(void)BigIntMultiply(&Re, &Re, &ReTmp); // ReTmp <- re*re - im*im.
(void)BigIntMultiply(&Im, &Im, &ImTmp);
BigIntSubt(&ReTmp, &ImTmp, &ReTmp);
(void)BigIntMultiply(&Re, &Im, &Im); // Im <- 2*re*im
BigIntAdd(&Im, &Im, &Im);
CopyBigInt(&Re, &ReTmp);
if ((expon & mask) != 0U)
{
(void)BigIntMultiply(Re1, &Re, &ReTmp); // Re2 <- re1*re - im1*im.
(void)BigIntMultiply(Im1, &Im, &ImTmp);
BigIntSubt(&ReTmp, &ImTmp, &curTmp);
(void)BigIntMultiply(Re1, &Im, &ReTmp); // Im <- re1*im + im1*re.
(void)BigIntMultiply(Im1, &Re, &ImTmp);
BigIntAdd(&ReTmp, &ImTmp, &Im);
CopyBigInt(&Re, &curTmp);
}
}
}
CopyBigInt(Re1, &Re);
CopyBigInt(Im1, &Im);
return EXPR_OK;
}
static enum eExprErr ComputeModPow(void)
{
static BigInteger ReTmp;
static BigInteger ImTmp;
static BigInteger ReBase;
static BigInteger ImBase;
static BigInteger ReExp;
static BigInteger ImExp;
static BigInteger ReMod;
static BigInteger ImMod;
static BigInteger Re;
static BigInteger Im;
CopyBigInt(&ReBase, &curStackRe);
CopyBigInt(&ImBase, &curStackIm);
CopyBigInt(&ReExp, &curStack2Re);
CopyBigInt(&ImExp, &curStack2Im);
CopyBigInt(&ReMod, &curStack3Re);
CopyBigInt(&ImMod, &curStack3Im);
if (!BigIntIsZero(&ImExp))
{ // Imaginary part must be zero.
return EXPR_INVALID_PARAM;
}
if (ReExp.sign == SIGN_NEGATIVE)
{
enum eExprErr retcode;
BigIntNegate(&ReExp, &ReExp);
retcode = ModInv(&ReBase, &ImBase, &ReMod, &ImMod, Result);
if (retcode != EXPR_OK)
{
return retcode;
}
ReBase = Result[0];
ImBase = Result[1];
}
// Re <- 1, Im <- 0
Re.limbs[0].x = 1;
Im.limbs[0].x = 0;
Re.nbrLimbs = 1;
Im.nbrLimbs = 1;
Re.sign = SIGN_POSITIVE;
Im.sign = SIGN_POSITIVE;
if (BigIntIsZero(&ReMod) && BigIntIsZero(&ImMod))
{ /* Modulus is zero */
(void)ComputePower(&ReBase, &ReExp, &ImBase, &ImExp);
CopyBigInt(&curStackRe, &ReBase);
CopyBigInt(&curStackIm, &ImBase);
}
else
{ /* Modulus is not zero */
(void)BigIntMultiply(&ReMod, &ReMod, &ReTmp);
(void)BigIntMultiply(&ImMod, &ImMod, &ImTmp);
BigIntAdd(&ReTmp, &ImTmp, &norm);
for (int index = ReExp.nbrLimbs - 1; index >= 0; index--)
{
int groupExp = ReExp.limbs[index].x;
for (unsigned int mask = HALF_INT_RANGE_U; mask > 0U; mask >>= 1)
{
// Let Re + i*Im <- (Re + i*Im)^2
(void)BigIntMultiply(&Re, &Re, &ReTmp);
(void)BigIntMultiply(&Im, &Im, &ImTmp);
BigIntSubt(&ReTmp, &ImTmp, &ReTmp);
(void)BigIntMultiply(&Re, &Im, &ImTmp);
BigIntAdd(&ImTmp, &ImTmp, &Im);
CopyBigInt(&Re, &ReTmp);
// Replace (Re + i*Im) by the remainder of
// (ReTmp + i*ImTmp) / (ReMod + i*ImMod)
// ReTmp and ImTmp are used as temporary values.
GetRemainder(&norm, &Re, &Im, &ReMod, &ImMod, &ReTmp, &ImTmp);
if (((unsigned int)groupExp & mask) != 0U)
{
// Let Re + i*Im <- (Re + i*Im)*(ReBase + i*ImBase)
(void)BigIntMultiply(&ReBase, &Re, &ReTmp);
(void)BigIntMultiply(&ImBase, &Im, &ImTmp);
BigIntSubt(&ReTmp, &ImTmp, &ReTmp);
(void)BigIntMultiply(&ImBase, &Re, &ImTmp);
(void)BigIntMultiply(&ReBase, &Im, &Re);
BigIntAdd(&Re, &ImTmp, &Im);
CopyBigInt(&Re, &ReTmp);
// Replace (Re + i*Im) by the remainder of
// (ReTmp + i*ImTmp) / (ReMod + i*ImMod)
// ReTmp and ImTmp are used as temporary values.
GetRemainder(&norm, &Re, &Im, &ReMod, &ImMod, &ReTmp, &ImTmp);
}
}
}
(void)Modulo(&Re, &Im, &ReMod, &ImMod, Result);
CopyBigInt(&curStackRe, &Result[0]);
CopyBigInt(&curStackIm, &Result[1]);
return EXPR_OK;
}
return EXPR_OK;
}
static enum eExprErr ComputeModInv(void)
{
enum eExprErr retcode = ModInv(&curStackRe, &curStackIm,
&curStack2Re, &curStack2Im, Result);
if (retcode != EXPR_OK)
{
return retcode;
}
CopyBigInt(&curStackRe, &Result[0]);
CopyBigInt(&curStackIm, &Result[1]);
return EXPR_OK;
}
static enum eExprErr ModInv(const BigInteger *RealNbr, const BigInteger *ImagNbr,
const BigInteger *RealMod, const BigInteger *ImagMod,
BigInteger *result)
{
static BigInteger ReG0;
static BigInteger ReG1;
static BigInteger ImG0;
static BigInteger ImG1;
static BigInteger ReU0;
static BigInteger ReU1;
static BigInteger ImU0;
static BigInteger ImU1;
static BigInteger Re;
static BigInteger Im;
static BigInteger Tmp;
if (BigIntIsZero(RealMod) && BigIntIsZero(ImagMod))
{ // Argument is zero.
return EXPR_INVALID_PARAM;
}
CopyBigInt(&ReG0, RealNbr);
CopyBigInt(&ImG0, ImagNbr);
CopyBigInt(&ReG1, RealMod);
CopyBigInt(&ImG1, ImagMod);
// Initialize U0 <- 1, U1 <- 0.
ReU0.limbs[0].x = 1;
ReU0.nbrLimbs = 1;
ReU0.sign = SIGN_POSITIVE;
ReU1.limbs[0].x = 0;
ImU0.limbs[0].x = 0;
ImU1.limbs[0].x = 0;
ReU1.nbrLimbs = 1;
ImU0.nbrLimbs = 1;
ImU1.nbrLimbs = 1;
ReU1.sign = SIGN_POSITIVE;
ImU0.sign = SIGN_POSITIVE;
ImU1.sign = SIGN_POSITIVE;
while (!BigIntIsZero(&ReG1) || !BigIntIsZero(&ImG1))
{ // G1 is not zero.
(void)BigIntMultiply(&ReG1, &ReG1, &Re);
(void)BigIntMultiply(&ImG1, &ImG1, &Im);
BigIntAdd(&Re, &Im, &norm);
// Replace G0 by the remainder of G0/G1.
GetRemainder(&norm, &ReG0, &ImG0, &ReG1, &ImG1, &Re, &Im);
// Exchange G0 and G1.
CopyBigInt(&Tmp, &ReG0);
CopyBigInt(&ReG0, &ReG1);
CopyBigInt(&ReG1, &Tmp);
CopyBigInt(&Tmp, &ImG0);
CopyBigInt(&ImG0, &ImG1);
CopyBigInt(&ImG1, &Tmp);
(void)BigIntMultiply(&Re, &ReU1, &Tmp);
BigIntSubt(&ReU0, &Tmp, &ReU0);
(void)BigIntMultiply(&Im, &ImU1, &Tmp);
BigIntAdd(&ReU0, &Tmp, &ReU0);
(void)BigIntMultiply(&Im, &ReU1, &Tmp);
BigIntSubt(&ImU0, &Tmp, &ImU0);
(void)BigIntMultiply(&Re, &ImU1, &Tmp);
BigIntSubt(&ImU0, &Tmp, &ImU0);
// Exchange U0 and U1.
CopyBigInt(&Tmp, &ReU0);
CopyBigInt(&ReU0, &ReU1);
CopyBigInt(&ReU1, &Tmp);
CopyBigInt(&Tmp, &ImU0);
CopyBigInt(&ImU0, &ImU1);
CopyBigInt(&ImU1, &Tmp);
}
for (;;)
{
CopyBigInt(&Tmp, &ImG0);
Tmp.sign = SIGN_POSITIVE; // Tmp <- abs(Tmp)
BigIntSubt(&ReG0, &Tmp, &Tmp);
if (Tmp.sign == SIGN_POSITIVE)
{
break;
}
// Multiply G0 and U0 by i.
CopyBigInt(&Tmp, &ReG0);
BigIntNegate(&ImG0, &ReG0);
CopyBigInt(&ImG0, &Tmp);
CopyBigInt(&Tmp, &ReU0);
BigIntNegate(&ImU0, &ReU0);
CopyBigInt(&ImU0, &Tmp);
}
if ((ReG0.nbrLimbs != 1) || (ReG0.limbs[0].x != 1) || !BigIntIsZero(&ImG0))
{ // G0 is not 1.
return EXPR_INVALID_PARAM;
}
return Modulo(&ReU0, &ImU0, RealMod, ImagMod, result);
}
static int Modulo(BigInteger *ReNum, BigInteger *ImNum,
const BigInteger *ReDen, const BigInteger *ImDen,
BigInteger *result)
{
BigInteger Re;
BigInteger Im;
BigInteger ReMin;
BigInteger ImMin;
BigInteger Tmp;
BigInteger normmin;
if (BigIntIsZero(ReDen) && BigIntIsZero(ImDen))
{ // Denominator is zero.
CopyBigInt(result, ReNum);
CopyBigInt(result+1, ImNum);
return 0;
}
ReMin.limbs[0].x = 0;
ImMin.limbs[0].x = 0;
ReMin.nbrLimbs = 1;
ImMin.nbrLimbs = 1;
ReMin.sign = SIGN_POSITIVE;
ImMin.sign = SIGN_POSITIVE;
(void)BigIntMultiply(ReDen, ReDen, &norm);
(void)BigIntMultiply(ImDen, ImDen, &Tmp);