void __fmpz_multi_CRT_sign(fmpz_t output, fmpz_t input, fmpz_comb_t comb)
{
unsigned long n = comb->n;
if (n == 0L)
{
if (input[0] == 0L)
{
fmpz_set_ui(output, 0L);
return;
}
unsigned long p = comb->primes[0];
if ((p - input[1]) < input[1]) fmpz_set_si(output, (long) (input[1] - p));
else fmpz_set_ui(output, input[1]);
return;
}
fmpz_t temp = fmpz_init(fmpz_size(comb->comb[n-1][0]) + 1);
fmpz_sub(temp, input, comb->comb[comb->n - 1][0]);
if (fmpz_cmpabs(temp, input) <= 0L) fmpz_set(output, temp);
else fmpz_set(output, input);
fmpz_clear(temp);
return;
}
void _fmpz_mod_poly_evaluate_fmpz(fmpz_t res, const fmpz *poly, slong len,
const fmpz_t a, const fmpz_t p)
{
if (len == 0)
{
fmpz_zero(res);
}
else if (len == 1 || fmpz_is_zero(a))
{
fmpz_set(res, poly);
}
else
{
slong i = len - 1;
fmpz_t t;
fmpz_init(t);
fmpz_set(res, poly + i);
for (i = len - 2; i >= 0; i--)
{
fmpz_mul(t, res, a);
fmpz_mod(t, t, p);
fmpz_add(res, poly + i, t);
}
fmpz_clear(t);
if (fmpz_cmpabs(res, p) >= 0)
fmpz_sub(res, res, p);
}
}
void fmpz_multi_mod_ui(unsigned long * out, fmpz_t in, fmpz_comb_t comb, fmpz_t ** temp)
{
ulong i, j, k;
ulong n = comb->n;
long log_comb;
ulong size;
mp_limb_t * ptr;
ulong num;
unsigned long num_primes = comb->num_primes;
if (num_primes == 1) // we are reducing modulo a single prime which is assumed to be big enough
{
if ((long)in[0] > 0L) out[0] = in[1];
else if ((long)in[0] < 0L) out[0] = comb->primes[0] - in[1];
else out[0] = 0L;
return;
}
log_comb = n - 1;
// find level in comb with entries bigger than the input integer
log_comb = 0;
if ((long) in[0] < 0L)
while ((fmpz_bits(in) >= fmpz_bits(comb->comb[log_comb][0]) - 1) && (log_comb < comb->n - 1)) log_comb++;
else
while (fmpz_cmpabs(in, comb->comb[log_comb][0]) >= 0) log_comb++;
num = (1L<<(n - log_comb - 1));
// set each entry of this level of temp to the input integer
for (i = 0; i < num; i++)
{
fmpz_set(temp[log_comb][i], in);
}
log_comb--;
num *= 2;
// fill in other entries of temp by taking entries of temp at higher level mod pairs from comb
while (log_comb > FLINT_LOG_MULTI_MOD_CUTOFF) // keep going until we reach the basecase
{
for (i = 0, j = 0; i < num; i += 2, j++)
{
fmpz_mod(temp[log_comb][i], temp[log_comb + 1][j], comb->comb[log_comb][i]);
fmpz_mod(temp[log_comb][i+1], temp[log_comb + 1][j], comb->comb[log_comb][i+1]);
}
num *= 2;
log_comb--;
}
// do basecase
num /= 2;
log_comb++;
ulong stride = (1L << (log_comb + 1));
for (i = 0, j = 0; j < num_primes; i++, j += stride)
{
fmpz_multi_mod_ui_basecase(out + j, temp[log_comb][i], comb->primes + j, FLINT_MIN(stride, num_primes - j));
}
}
void
elem_add(elem_ptr res, elem_srcptr op1, elem_srcptr op2, const ring_t ring)
{
switch (ring->type)
{
case TYPE_FMPZ:
fmpz_add(res, op1, op2);
break;
case TYPE_LIMB:
*((mp_ptr) res) = *((mp_srcptr) op1) + *((mp_srcptr) op2);
break;
case TYPE_POLY:
elem_poly_add(res, op1, op2, ring);
break;
case TYPE_MOD:
{
switch (RING_PARENT(ring)->type)
{
case TYPE_LIMB:
*((mp_ptr) res) = n_addmod(*((mp_srcptr) op1), *((mp_srcptr) op2), ring->nmod.n);
break;
case TYPE_FMPZ:
fmpz_add(res, op1, op2);
if (fmpz_cmpabs(res, RING_MODULUS(ring)) >= 0)
fmpz_sub(res, res, RING_MODULUS(ring));
break;
default:
NOT_IMPLEMENTED("add (mod)", ring);
}
}
break;
case TYPE_FRAC:
elem_frac_add(res, op1, op2, ring);
break;
case TYPE_COMPLEX:
elem_add(REALPART(res, ring), REALPART(op1, ring), REALPART(op2, ring), ring->parent);
elem_add(IMAGPART(res, ring), IMAGPART(op1, ring), IMAGPART(op2, ring), ring->parent);
break;
default:
NOT_IMPLEMENTED("add", ring);
}
}
void test1(mp_limb_t log2,const fmpz_t b,const fmpz_t z)
{
if( (fmpz_cmp_ui(z,0)<=0) || (log2==0) )
return;
int r0=fmpz_cmpabs(z,b);
int r1=cmp_positive_log2(z,log2);
#if LOUD
fmpz_hex_print("2**y=",b,0);
fmpz_hex_print(" z=",z,0);
flint_printf(" r0/1: %d/%d\n",r0,r1);
#endif
if( r0>0 )
assert( r1>0 );
if( r0<0 )
assert( r1<0 );
if( r0==0 )
assert( 0 == r1 );
}
int
fmpr_cmpabs(const fmpr_t x, const fmpr_t y)
{
int res, xsign, ysign;
fmpr_t t;
if (fmpr_equal(x, y))
return 0;
if (fmpr_is_special(x) || fmpr_is_special(y))
{
if (fmpr_is_nan(x) || fmpr_is_nan(y))
return 0;
if (fmpr_is_zero(x)) return -1;
if (fmpr_is_zero(y)) return 1;
if (fmpr_is_inf(x)) return fmpr_is_inf(y) ? 0 : 1;
if (fmpr_is_inf(y)) return -1;
return -1;
}
/* Reduces to integer comparison if bottom exponents are the same */
if (fmpz_equal(fmpr_expref(x), fmpr_expref(y)))
{
res = fmpz_cmpabs(fmpr_manref(x), fmpr_manref(y));
if (res != 0)
res = (res < 0) ? -1 : 1;
}
else
{
/* TODO: compare position of top exponents to avoid subtraction */
xsign = fmpr_sgn(x);
ysign = fmpr_sgn(y);
fmpr_init(t);
if (xsign == ysign)
fmpr_sub(t, x, y, 2, FMPR_RND_DOWN);
else
fmpr_add(t, x, y, 2, FMPR_RND_DOWN);
res = fmpr_sgn(t) * xsign;
fmpr_clear(t);
}
return res;
}
void _fmpz_mod_poly_compose_horner(fmpz *res, const fmpz *poly1, long len1,
const fmpz *poly2, long len2,
const fmpz_t p)
{
if (len1 == 1 || len2 == 0)
{
fmpz_set(res, poly1);
}
else
{
const long alloc = (len1 - 1) * (len2 - 1) + 1;
long i = len1 - 1, lenr = len2;
fmpz * t = _fmpz_vec_init(alloc);
/*
Perform the first two steps as one,
"res = a(m) * poly2 + a(m-1)".
*/
{
_fmpz_mod_poly_scalar_mul_fmpz(res, poly2, len2, poly1 + i, p);
i--;
fmpz_add(res, res, poly1 + i);
if (fmpz_cmpabs(res, p) >= 0)
fmpz_sub(res, res, p);
}
while (i > 0)
{
i--;
_fmpz_mod_poly_mul(t, res, lenr, poly2, len2, p);
lenr += len2 - 1;
_fmpz_mod_poly_add(res, t, lenr, poly1 + i, 1, p);
}
_fmpz_vec_clear(t, alloc);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("cmpabs....");
fflush(stdout);
flint_randinit(state);
/* compare with fmpz */
{
arf_t x, y;
fmpz_t X, Y;
arf_init(x);
arf_init(y);
fmpz_init(X);
fmpz_init(Y);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
int cmp1, cmp2;
fmpz_randtest(X, state, 1 + n_randint(state, 1000));
switch (n_randint(state, 8))
{
case 0:
fmpz_neg(Y, X);
break;
case 1:
fmpz_set(Y, X);
break;
default:
fmpz_randtest(Y, state, 1 + n_randint(state, 1000));
}
arf_set_fmpz(x, X);
arf_set_fmpz(y, Y);
cmp1 = arf_cmpabs(x, y);
cmp2 = fmpz_cmpabs(X, Y);
cmp2 = (cmp2 > 0) - (cmp2 < 0);
if (cmp1 != cmp2)
{
flint_printf("FAIL\n\n");
flint_printf("x = "); arf_debug(x); flint_printf("\n\n");
flint_printf("y = "); arf_debug(y); flint_printf("\n\n");
flint_printf("X = "); fmpz_print(X); flint_printf("\n\n");
flint_printf("Y = "); fmpz_print(Y); flint_printf("\n\n");
flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2);
abort();
}
}
arf_clear(x);
arf_clear(y);
fmpz_clear(X);
fmpz_clear(Y);
}
/* compare with mpfr */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
slong bits;
arf_t x, y;
mpfr_t X, Y;
int cmp1, cmp2;
bits = 2 + n_randint(state, 200);
arf_init(x);
arf_init(y);
mpfr_init2(X, bits);
mpfr_init2(Y, bits);
arf_randtest_special(x, state, bits, 10);
arf_randtest_special(y, state, bits, 10);
arf_get_mpfr(X, x, MPFR_RNDN);
arf_get_mpfr(Y, y, MPFR_RNDN);
mpfr_abs(X, X, MPFR_RNDN);
mpfr_abs(Y, Y, MPFR_RNDN);
cmp1 = arf_cmpabs(x, y);
cmp2 = mpfr_cmp(X, Y);
if (cmp1 != cmp2)
{
flint_printf("FAIL\n\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2);
abort();
}
arf_clear(x);
arf_clear(y);
mpfr_clear(X);
mpfr_clear(Y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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_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();
}
}