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fmpz.c
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fmpz.c
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/*============================================================================
This file is part of FLINT.
FLINT 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 2 of the License, or
(at your option) any later version.
FLINT 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 FLINT; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
===============================================================================*/
/****************************************************************************
fmpz.c: "flat" integer format
Copyright (C) 2007, William Hart and David Harvey
*****************************************************************************/
#include <gmp.h>
#include <stdio.h>
#include <stdlib.h>
#include "fmpz.h"
#include "flint.h"
#include "memory-manager.h"
#include "longlong_wrapper.h"
#include "longlong.h"
#include "mpn_extras.h"
#include "F_mpn_mul-tuning.h"
#include "long_extras.h"
#include "zn_poly/src/zn_poly.h"
#define SWAP_PTRS(x_dummy_p, y_dummy_p) \
do { \
fmpz_t swap_temp_p = x_dummy_p; \
x_dummy_p = y_dummy_p; \
y_dummy_p = swap_temp_p; \
} while(0);
void fmpz_check_normalisation(const fmpz_t x)
{
if ((x[0]) && (!x[ABS(x[0])]))
{
printf("Error: fmpz_t not normalised!\n");
abort();
}
}
void mpz_to_fmpz(fmpz_t res, const mpz_t x)
{
if (mpz_sgn(x))
{
size_t countp;
mpz_export(res + 1, &countp, -1, sizeof(mp_limb_t), 0, 0, x);
res[0] = ((long) mpz_sgn(x) > 0L) ? (long) countp : (long) -countp;
}
else
res[0] = 0L;
}
void fmpz_to_mpz(mpz_t res, const fmpz_t x)
{
long size = x[0];
if (size == 0)
mpz_set_ui(res, 0);
else
{
mpz_import(res, ABS(size), -1, sizeof(mp_limb_t), 0, 0, x + 1);
if (size < 0)
mpz_neg(res, res);
}
}
void fmpz_print(fmpz_t in)
{
mpz_t coeff;
mpz_init(coeff);
fmpz_to_mpz(coeff, in);
gmp_printf("%Zd", coeff);
mpz_clear(coeff);
}
/*
Generate a random fmpz_t with n limbs with longs strings of 1's and 0's
*/
void fmpz_random_limbs2(fmpz_t x, unsigned long n)
{
if (n == 0)
{
x[0] = 0L;
return;
}
mpn_random2(x + 1, n);
x[0] = n;
}
/*
Adds two fmpz's together
*/
void fmpz_add(fmpz_t coeffs_out, const fmpz_t in1, const fmpz_t in2)
{
fmpz_t coeffs1 = in1;
fmpz_t coeffs2 = in2;
long carry;
unsigned long size1 = ABS(coeffs1[0]);
unsigned long size2 = ABS(coeffs2[0]);
if (size1 < size2)
{
SWAP_PTRS(coeffs1, coeffs2);
size1 = ABS(coeffs1[0]);
size2 = ABS(coeffs2[0]);
}
if (!size1)
{
if (!size2) coeffs_out[0] = 0L;
else
{
if (coeffs_out != coeffs2) F_mpn_copy(coeffs_out, coeffs2, size2+1);
}
} else if (!size2)
{
if (coeffs_out != coeffs1) F_mpn_copy(coeffs_out, coeffs1, size1+1);
} else if ((long) (coeffs1[0] ^ coeffs2[0]) >= 0L)
{
coeffs_out[0] = coeffs1[0];
carry = mpn_add(coeffs_out+1, coeffs1+1, size1, coeffs2+1, size2);
if (carry)
{
coeffs_out[size1+1] = carry;
if ((long) coeffs_out[0] < 0L) coeffs_out[0]--;
else coeffs_out[0]++;
}
} else
{
carry = 0;
if (size1 != size2) carry = 1;
else carry = mpn_cmp(coeffs1+1, coeffs2+1, size1);
if (carry == 0) coeffs_out[0] = 0L;
else if (carry > 0)
{
mpn_sub(coeffs_out+1, coeffs1+1, size1, coeffs2+1, size2);
coeffs_out[0] = coeffs1[0];
NORM(coeffs_out);
}
else
{
mpn_sub_n(coeffs_out+1, coeffs2+1, coeffs1+1, size1);
coeffs_out[0] = -coeffs1[0];
NORM(coeffs_out);
}
}
}
/*
Add an unsigned long to an fmpz, inplace
*/
void fmpz_add_ui_inplace(fmpz_t output, const unsigned long x)
{
unsigned long carry;
if (x)
{
if (!output[0])
{
output[1] = x;
output[0] = 1;
} else if ((long) output[0] > 0)
{
carry = mpn_add_1(output + 1, output + 1, output[0], x);
if (carry)
{
output[output[0]+1] = carry;
output[0]++;
}
} else if ((long) output[0] < -1L)
{
mpn_sub_1(output + 1, output + 1, ABS(output[0]), x);
NORM(output);
} else
{
if (x <= output[1])
{
output[1] -= x;
if (!output[1]) output[0] = 0;
} else
{
output[1] = x - output[1];
output[0] = 1;
}
}
}
}
/*
Add an unsigned long to an fmpz, inplace
*/
void fmpz_add_ui(fmpz_t output, const fmpz_t input, const unsigned long x)
{
unsigned long carry;
if (x)
{
if (!input[0])
{
output[1] = x;
output[0] = 1;
} else if ((long) input[0] > 0)
{
carry = mpn_add_1(output + 1, input + 1, input[0], x);
output[0] = input[0];
if (carry)
{
output[output[0]+1] = carry;
output[0]++;
}
} else if ((long) input[0] < -1L)
{
mpn_sub_1(output + 1, input + 1, ABS(input[0]), x);
output[0] = input[0];
NORM(output);
} else
{
if (x <= input[1])
{
output[1] = input[1] - x;
if (!output[1]) output[0] = 0L;
else output[0] = -1L;
} else
{
output[1] = x - input[1];
output[0] = 1L;
}
}
} else
{
fmpz_set(output, input);
}
}
/*
Add an unsigned long to a coefficient.
Assumes the output coefficient is non-negative.
*/
void __fmpz_add_ui_inplace(fmpz_t output, const unsigned long x)
{
unsigned long carry;
if (x)
{
if (!output[0])
{
output[1] = x;
output[0] = 1;
} else
{
carry = mpn_add_1(output + 1, output + 1, output[0], x);
if (carry)
{
output[output[0]+1] = carry;
output[0]++;
}
}
}
}
void fmpz_sub(fmpz_t coeffs_out, const fmpz_t in1, const fmpz_t in2)
{
fmpz_t coeffs1 = in1;
fmpz_t coeffs2 = in2;
long carry;
unsigned long size1 = ABS(coeffs1[0]);
unsigned long size2 = ABS(coeffs2[0]);
int in_order = 1;
if (size1 < size2)
{
SWAP_PTRS(coeffs1, coeffs2);
size1 = ABS(coeffs1[0]);
size2 = ABS(coeffs2[0]);
in_order = 0;
}
if (!size1)
{
if (!size2) coeffs_out[0] = 0L;
else
{
if (coeffs2 != coeffs_out) F_mpn_copy(coeffs_out, coeffs2, size2+1);
if (in_order) coeffs_out[0] = -coeffs_out[0];
}
} else if (!size2)
{
if (coeffs1 != coeffs_out) F_mpn_copy(coeffs_out, coeffs1, size1+1);
if (!in_order) coeffs_out[0] = -coeffs_out[0];
} else if ((long) (coeffs1[0] ^ coeffs2[0]) < 0)
{
if (in_order) coeffs_out[0] = coeffs1[0];
else coeffs_out[0] = -coeffs1[0];
carry = mpn_add(coeffs_out+1, coeffs1+1, size1, coeffs2+1, size2);
if (carry)
{
coeffs_out[size1+1] = carry;
if ((long) coeffs_out[0] < 0) coeffs_out[0]--;
else coeffs_out[0]++;
}
} else
{
carry = 0;
if (size1 != size2) carry = 1;
else carry = mpn_cmp(coeffs1+1, coeffs2+1, size1);
if (carry == 0) coeffs_out[0] = 0L;
else if (carry > 0)
{
mpn_sub(coeffs_out+1, coeffs1+1, size1, coeffs2+1, size2);
if (in_order) coeffs_out[0] = coeffs1[0];
else coeffs_out[0] = -coeffs1[0];
NORM(coeffs_out);
}
else
{
mpn_sub_n(coeffs_out+1, coeffs2+1, coeffs1+1, size1);
if (in_order) coeffs_out[0] = -coeffs1[0];
else coeffs_out[0] = coeffs1[0];
NORM(coeffs_out);
}
}
}
void fmpz_sub_ui_inplace(fmpz_t output, const unsigned long x)
{
unsigned long carry;
if (x)
{
if (!output[0])
{
output[1] = x;
output[0] = -1L;
} else if ((long) output[0] < 0)
{
carry = mpn_add_1(output + 1, output + 1, ABS(output[0]), x);
if (carry)
{
output[ABS(output[0])+1] = carry;
output[0]--;
}
} else if ((long) output[0] > 1L)
{
mpn_sub_1(output + 1, output + 1, output[0], x);
NORM(output);
} else
{
if (x <= output[1])
{
output[1] -= x;
if (!output[1]) output[0] = 0;
} else
{
output[1] = x - output[1];
output[0] = -1L;
}
}
}
}
void fmpz_sub_ui(fmpz_t output, const fmpz_t input, const unsigned long x)
{
unsigned long carry;
if (x)
{
if (!input[0])
{
output[1] = x;
output[0] = -1L;
} else if ((long) input[0] < 0)
{
carry = mpn_add_1(output + 1, input + 1, ABS(input[0]), x);
output[0] = input[0];
if (carry)
{
output[ABS(output[0])+1] = carry;
output[0]--;
}
} else if ((long) input[0] > 1L)
{
mpn_sub_1(output + 1, input + 1, input[0], x);
output[0] = input[0];
NORM(output);
} else
{
if (x <= input[1])
{
output[1] = input[1] - x;
if (!output[1]) output[0] = 0;
else output[0] = 1L;
} else
{
output[1] = x - input[1];
output[0] = -1L;
}
}
} else
{
fmpz_set(output, input);
}
}
/*
Multiplies two fmpz's
Assumes no overlap
*/
void fmpz_mul(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if ((sizea == 0) || (sizeb == 0))
{
res[0] = 0;
} else if (sizea + sizeb < 100)
{
temp = (fmpz_t) flint_stack_alloc_small(sizea + sizeb + 1);
if (sizea > sizeb) mslimb = mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else if (sizea == sizeb)
{
mpn_mul_n(temp+1, a+1, b+1, sizeb);
mslimb = temp[2*sizeb];
}
else mslimb = mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
F_mpn_copy(res, temp, temp[0]+1);
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
flint_stack_release_small();
} else if (sizea + sizeb < 2*FLINT_FFT_LIMBS_CROSSOVER)
{
temp = (fmpz_t) flint_stack_alloc(sizea + sizeb + 1);
if (sizea > sizeb) mslimb = mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else if (sizea == sizeb)
{
mpn_mul_n(temp+1, a+1, b+1, sizeb);
mslimb = temp[2*sizeb];
}
else mslimb = mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
F_mpn_copy(res, temp, temp[0]+1);
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
flint_stack_release();
} else
{
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea+sizeb - (mslimb == 0);
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
}
}
/*
Used internally by fmpz_poly.
Multiplies two fmpz's but assumes res has enough space to contain the
number of limbs in _a_ plus the number of limbs of _b_, whenever
this sum is less than 2*FLINT_FFT_LIMBS_CROSSOVER
Assumes no overlap
*/
void __fmpz_mul(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if ((sizea == 0) || (sizeb == 0))
{
res[0] = 0;
}
else if (sizea + sizeb < 100)
{
if (sizea >= sizeb) mslimb = mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea + sizeb - (mslimb == 0);
if ((long) (a[0] ^ b[0]) < 0) res[0] = -res[0];
} else
{
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea+sizeb - (mslimb == 0);
if ((long) (a[0] ^ b[0]) < 0) res[0] = -res[0];
}
}
void fmpz_mul_ui(fmpz_t output, const fmpz_t input, const unsigned long x)
{
if (x == 0)
{
output[0] = 0;
return;
}
mp_limb_t mslimb;
if (output[0] = input[0]) // This isn't a typo
{
mslimb = mpn_mul_1(output+1, input+1, FLINT_ABS(input[0]), x);
if (mslimb)
{
output[FLINT_ABS(input[0])+1] = mslimb;
if ((long) output[0] > 0) output[0]++;
else output[0]--;
}
}
}
/*
Sets res to res+a*b
Assumes no overlap
*/
void fmpz_addmul(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
fmpz_t temp;
mp_limb_t mslimb;
if (sizea && sizeb)
{
if (sizea + sizeb < 100)
{
temp = (fmpz_t) flint_stack_alloc_small(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else mslimb = mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
if ((long) (a[0] ^ b[0]) < 0) temp[0] = -temp[0];
fmpz_add(res, res, temp);
flint_stack_release_small();
} else
{
temp = (fmpz_t) flint_stack_alloc(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = F_mpn_mul(temp+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(temp+1, b+1, sizeb, a+1, sizea);
temp[0] = sizea + sizeb - (mslimb == 0);
if ((long) (a[0] ^ b[0]) < 0) temp[0] = -temp[0];
fmpz_add(res, res, temp);
flint_stack_release();
}
}
}
/*
Sets res to a / b
Assumes no overlap
Rounding occurs towards zero
*/
void fmpz_tdiv(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea < sizeb) // Todo: make this deal with sizea == sizeb but a < b
{
res[0] = 0;
} else
{
temp = (fmpz_t) flint_stack_alloc(sizeb);
mpn_tdiv_qr(res+1, temp, 0, a+1, sizea, b+1, sizeb);
res[0] = sizea - sizeb + 1;
if ((long) (a0 ^ b0) < 0) res[0] = -res[0];
flint_stack_release();
}
NORM(res);
}
/*
Sets res to a / b
Assumes no overlap
Rounding occurs towards minus infinity
*/
void fmpz_fdiv(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea < sizeb) // Todo: make this deal with sizea == sizeb but a < b
{
if (((long) (a0 ^ b0) < 0L) && (a0))
{
res[0] = -1L;
res[1] = 1;
} else res[0] = 0;
return;
} else
{
temp = (fmpz_t) flint_stack_alloc(sizeb);
mpn_tdiv_qr(res+1, temp, 0, a+1, sizea, b+1, sizeb);
res[0] = sizea - sizeb + 1;
if ((long) (a0 ^ b0) < 0L) res[0] = -res[0];
NORM(res);
if ((long) (a0 ^ b0) < 0L)
{
unsigned long i = 0;
for (; i < sizeb; i++)
{
if (temp[i]) break;
}
if (i < sizeb)
{
fmpz_sub_ui_inplace(res, 1UL);
}
}
flint_stack_release();
}
}
/*
Reduce a mod b, assuming b is positive
*/
void fmpz_mod(fmpz_t res, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = b0;
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
mp_limb_t mslimb;
fmpz_t temp, temp2;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea < sizeb)
{
if ((long) a0 < 0L)
{
temp = (fmpz_t) flint_stack_alloc(sizeb + 2);
fmpz_add(temp, a, b);
fmpz_set(res, temp);
flint_stack_release();
} else fmpz_set(res, a);
return;
} else if ((sizea == sizeb) && (fmpz_cmpabs(a, b) < 0L))
{
if (fmpz_sgn(a) < 0) fmpz_add(res, a, b);
else fmpz_set(res, a);
return;
} else
{
if (fmpz_is_one(b))
{
fmpz_set_ui(res, 0L);
return;
}
temp = (fmpz_t) flint_stack_alloc(sizea - sizeb + 1);
temp2 = (fmpz_t) flint_stack_alloc(sizeb + 2);
mpn_tdiv_qr(temp, temp2+1, 0, a+1, sizea, b+1, sizeb);
temp2[0] = sizeb;
NORM(temp2);
if (a0 < 0L)
{
unsigned long i = 0;
for (; i < sizeb; i++)
{
if (temp2[i+1]) break;
}
if (i < sizeb)
{
fmpz_sub(temp2, b, temp2);
}
fmpz_set(res, temp2);
} else fmpz_set(res, temp2);
flint_stack_release();
flint_stack_release();
}
}
/*
If b divides a then return 1 and the quotient, else return 0
*/
int fmpz_divides(fmpz_t q, const fmpz_t a, const fmpz_t b)
{
long a0 = a[0];
long b0 = b[0];
unsigned long sizea = FLINT_ABS(a0);
unsigned long sizeb = FLINT_ABS(b0);
mp_limb_t mslimb;
fmpz_t temp;
if (sizeb == 0)
{
printf("Error: division by zero!\n");
abort();
} else if (sizea == 0)
{
q[0] = 0;
return 1;
} else if (sizea < sizeb)
{
return 0;
} else if (sizea == sizeb)
{
int cmp = fmpz_cmpabs(a, b);
if (cmp < 0) return 0;
if (cmp == 0)
{
if ((long) (a0 ^ b0) < 0L) q[0] = -1L;
else q[0] = 1L;
q[1] = 1;
return 1;
}
}
if (fmpz_is_one(b))
{
fmpz_set(q, a);
return 1;
}
if (fmpz_is_m1(b))
{
fmpz_neg(q, a);
return 1;
}
temp = (fmpz_t) flint_stack_alloc(sizeb + 2);
mpn_tdiv_qr(q+1, temp+1, 0, a+1, sizea, b+1, sizeb);
temp[0] = sizeb;
NORM(temp);
if (temp[0] != 0)
{
flint_stack_release();
return 0;
}
q[0] = sizea - sizeb + 1;
NORM(q);
if ((long) (a0 ^ b0) < 0L) q[0] = -q[0];
flint_stack_release();
return 1;
}
void fmpz_tdiv_ui(fmpz_t output, const fmpz_t input, const unsigned long x)
{
output[0] = input[0];
unsigned long size = FLINT_ABS(input[0]);
mpn_divmod_1(output+1, input+1, size, x);
NORM(output);
}
/*
Returns input % x. Output will be reduced mod x.
*/
unsigned long fmpz_mod_ui(const fmpz_t input, const unsigned long x)
{
unsigned long size = FLINT_ABS(input[0]);
unsigned long mod;
mod = mpn_mod_1(input+1, size, x);
if (!mod) return mod;
else if ((long) input[0] < 0L)
{
return x - mod;
} else return mod;
}
// truncated multiplication for fmpz
void fmpz_mul_trunc(fmpz_t res, fmpz_t a, fmpz_t b, unsigned long trunc)
{
unsigned long sizea = FLINT_MIN(fmpz_size(a), trunc);
unsigned long sizeb = FLINT_MIN(fmpz_size(b), trunc);
while ((!a[sizea]) && (sizea)) sizea--;
while ((!b[sizeb]) && (sizeb)) sizeb--;
if ((sizea == 0) || (sizeb == 0)) {
res[0] = 0;
return;
}
if (trunc >= sizea + sizeb) {
mp_limb_t mslimb;
if (sizea >= sizeb) mslimb = F_mpn_mul(res+1, a+1, sizea, b+1, sizeb);
else mslimb = F_mpn_mul(res+1, b+1, sizeb, a+1, sizea);
res[0] = sizea + sizeb - (mslimb == 0);
} else {
mp_limb_t mslimb;
fmpz_t temp = flint_stack_alloc(sizea + sizeb + 1);
if (sizea >= sizeb) mslimb = F_mpn_mul_trunc(temp+1, a+1, sizea, b+1, sizeb, trunc);
else mslimb = F_mpn_mul_trunc(temp+1, b+1, sizeb, a+1, sizea, trunc);
temp[0] = trunc;
if (UNLIKELY(!mslimb))
__fmpz_normalise(temp); // normalise if most significant limb == 0
fmpz_set(res, temp);
flint_stack_release();
}
if ((long) (a[0] ^ b[0]) < 0L) res[0] = -res[0];
}
// Compute a*b mod m
void fmpz_mulmod(fmpz_t res, fmpz_t a, fmpz_t b, fmpz_t m)
{
fmpz_t ab = fmpz_init(fmpz_size(a) + fmpz_size(b));
fmpz_mul(ab, a, b);
fmpz_mod(res, ab, m);
fmpz_clear(ab);
}
// Compute a/b mod m
void fmpz_divmod(fmpz_t res, fmpz_t a, fmpz_t b, fmpz_t m)
{
fmpz_t b_inv = fmpz_init(fmpz_size(m));
fmpz_invert(b_inv, b, m);
fmpz_t ab = fmpz_init(fmpz_size(a) + fmpz_size(b_inv));
fmpz_mul(ab, a, b_inv);
fmpz_mod(res, ab, m);
fmpz_clear(ab);
fmpz_clear(b_inv);
}
/*
Raise input to the power exp
Very simplistic at this point. It just converts to an mpz_t and uses
GMP's mpz_pow_ui function
*/
void fmpz_pow_ui(fmpz_t output, const fmpz_t input, const unsigned long exp)
{
mpz_t power;
mpz_init(power);
fmpz_to_mpz(power, input);
mpz_pow_ui(power, power, exp);
mpz_to_fmpz(output, power);
mpz_clear(power);
}
unsigned long __fmpz_power_of_two(const fmpz_t x)
{
if (x[0] == 0) return -1L;
return mpn_scan1(x + 1, 0);
}
void fmpz_mul_2exp(fmpz_t output, fmpz_t x, unsigned long exp)
{
unsigned long limbs = (exp >> FLINT_LG_BITS_PER_LIMB);
unsigned long bits = (exp & (FLINT_BITS - 1));
mp_limb_t msl = 0L;
if (x[0] == 0)
{
output[0] = 0L;
return;
}
if (bits)
{
msl = mpn_lshift(output + limbs + 1, x + 1, FLINT_ABS(x[0]), bits);
if (msl) output[limbs + FLINT_ABS(x[0]) + 1] = msl;
} else F_mpn_copy(output + limbs + 1, x + 1, FLINT_ABS(x[0]));
if (limbs) F_mpn_clear(output + 1, limbs);
if ((long) x[0] >= 0L) output[0] = x[0] + limbs + (msl != 0L);
else output[0] = x[0] - limbs - (msl != 0L);
}
void fmpz_div_2exp(fmpz_t output, fmpz_t x, unsigned long exp)
{
unsigned long limbs = (exp >> FLINT_LG_BITS_PER_LIMB);
unsigned long bits = (exp & (FLINT_BITS - 1));
if ((x[0] == 0) || (limbs >= FLINT_ABS(x[0])))
{
output[0] = 0L;
return;
}
if (bits)
{
fmpz_t temp = fmpz_init(FLINT_ABS(x[0]) - limbs);
mpn_rshift(temp + 1, x + limbs + 1, FLINT_ABS(x[0]) - limbs, bits);
if ((long) x[0] >= 0L) temp[0] = x[0] - limbs;
else temp[0] = limbs + x[0];
NORM(temp);
fmpz_set(output, temp);
fmpz_clear(temp);
} else
{
F_mpn_copy(output + 1, x + limbs + 1, FLINT_ABS(x[0]) - limbs);
if ((long) x[0] >= 0L) output[0] = x[0] - limbs;
else output[0] = limbs + x[0];
}
}
/*void fmpz_gcd(fmpz_t output, fmpz_t x1, fmpz_t x2)
{
if (x1[0] == 0)
{
fmpz_set(output, x2);
if ((long) output[0] < 0L) output[0] = -output[0];
return;
}
if (x2[0] == 0)
{
fmpz_set(output, x1);
if ((long) output[0] < 0L) output[0] = -output[0];
return;
}
unsigned long twos1 = __fmpz_power_of_two(x1);
unsigned long twos2 = __fmpz_power_of_two(x2);
unsigned long n1, n2;
fmpz_t a1 = fmpz_stack_init(FLINT_ABS(x1[0]) - (twos1 >> FLINT_LG_BITS_PER_LIMB));
fmpz_t a2 = fmpz_stack_init(FLINT_ABS(x2[0]) - (twos2 >> FLINT_LG_BITS_PER_LIMB));
fmpz_div_2exp(a1, x1, twos1);
if ((long) a1[0] < 0L) a1[0] = -a1[0];
fmpz_div_2exp(a2, x2, twos2);
if ((long) a2[0] < 0L) a2[0] = -a2[0];