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add mag_div_lower, mag_inv, mag_inv_lower

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This commit is contained in:
Fredrik Johansson 2018-01-01 02:25:17 +01:00
parent c78bf6734a
commit 948cd473e2
5 changed files with 166 additions and 1 deletions
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12
doc/source/mag.rst
View file

@ -242,6 +242,18 @@ Arithmetic
Sets *z* to an upper bound for `x / y`.
.. function:: void mag_div_lower(mag_t z, const mag_t x, const mag_t y)
Sets *z* to a lower bound for `x / y`.
.. function:: void mag_inv(mag_t z, const mag_t x)
Sets *z* to an upper bound for `1 / x`.
.. function:: void mag_inv_lower(mag_t z, const mag_t x)
Sets *z* to a lower bound for `1 / x`.
.. function:: void mag_mul_lower(mag_t z, const mag_t x, const mag_t y)
.. function:: void mag_mul_ui_lower(mag_t z, const mag_t x, ulong y)

19
mag.h
View file

@ -298,6 +298,25 @@ void mag_add_ui(mag_t z, const mag_t x, ulong y);
void mag_add_ui_2exp_si(mag_t z, const mag_t x, ulong y, slong e);
void mag_div(mag_t z, const mag_t x, const mag_t y);
void mag_div_lower(mag_t z, const mag_t x, const mag_t y);
MAG_INLINE void
mag_inv(mag_t res, const mag_t x)
{
mag_t t;
mag_init(t); /* no need to free */
mag_one(t);
mag_div(res, t, x);
}
MAG_INLINE void
mag_inv_lower(mag_t res, const mag_t x)
{
mag_t t;
mag_init(t); /* no need to free */
mag_one(t);
mag_div_lower(res, t, x);
}
MAG_INLINE void
mag_mul_2exp_si(mag_t z, const mag_t x, slong y)

51
mag/div_lower.c Normal file
View file

@ -0,0 +1,51 @@
/*
Copyright (C) 2017 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "mag.h"
void
mag_div_lower(mag_t z, const mag_t x, const mag_t y)
{
if (mag_is_special(x) || mag_is_special(y))
{
if (mag_is_inf(x) && !mag_is_inf(y))
mag_inf(z);
else
mag_zero(z);
}
else
{
mp_limb_t q;
slong fix;
#if FLINT_BITS == 64
q = (MAG_MAN(x) << MAG_BITS) / MAG_MAN(y);
#else
mp_limb_t hi, lo, r;
lo = MAG_MAN(x) << MAG_BITS;
hi = MAG_MAN(x) >> (FLINT_BITS - MAG_BITS);
udiv_qrnnd(q, r, hi, lo, MAG_MAN(y));
#endif
fix = q >> MAG_BITS;
q = q >> fix;
/* could overflow to next power of two */
if (q >> MAG_BITS)
{
q >>= 1;
fix += 1;
}
MAG_MAN(z) = q;
_fmpz_sub2_fast(MAG_EXPREF(z), MAG_EXPREF(x), MAG_EXPREF(y), fix);
}
}

2
mag/test/t-div.c
View file

@ -42,7 +42,7 @@ int main()
mag_get_fmpr(x, xb);
mag_get_fmpr(y, yb);
fmpr_div(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN);
fmpr_div(z, x, y, MAG_BITS + 10, FMPR_RND_UP);
fmpr_mul_ui(z2, z, 1025, MAG_BITS, FMPR_RND_UP);
fmpr_mul_2exp_si(z2, z2, -10);

83
mag/test/t-div_lower.c Normal file
View file

@ -0,0 +1,83 @@
/*
Copyright (C) 2014 Fredrik Johansson
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "mag.h"
int main()
{
slong iter;
flint_rand_t state;
flint_printf("div_lower....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
fmpr_t x, y, z, z2, w;
mag_t xb, yb, zb;
fmpr_init(x);
fmpr_init(y);
fmpr_init(z);
fmpr_init(z2);
fmpr_init(w);
mag_init(xb);
mag_init(yb);
mag_init(zb);
mag_randtest_special(xb, state, 10);
mag_randtest_special(yb, state, 10);
mag_get_fmpr(x, xb);
mag_get_fmpr(y, yb);
fmpr_div(z, x, y, MAG_BITS + 10, FMPR_RND_DOWN);
fmpr_mul_ui(z2, z, 1023, MAG_BITS, FMPR_RND_DOWN);
fmpr_mul_2exp_si(z2, z2, -10);
mag_div_lower(zb, xb, yb);
mag_get_fmpr(w, zb);
MAG_CHECK_BITS(xb)
MAG_CHECK_BITS(yb)
MAG_CHECK_BITS(zb)
if (!(fmpr_cmpabs(z2, w) <= 0 && fmpr_cmpabs(w, z) <= 0))
{
flint_printf("FAIL\n\n");
flint_printf("x = "); fmpr_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpr_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpr_print(z); flint_printf("\n\n");
flint_printf("w = "); fmpr_print(w); flint_printf("\n\n");
flint_abort();
}
fmpr_clear(x);
fmpr_clear(y);
fmpr_clear(z);
fmpr_clear(z2);
fmpr_clear(w);
mag_clear(xb);
mag_clear(yb);
mag_clear(zb);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}