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-rw-r--r--mpfr/src/gmp_op.c489
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diff --git a/mpfr/src/gmp_op.c b/mpfr/src/gmp_op.c
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+/* Implementations of operations between mpfr and mpz/mpq data
+
+Copyright 2001, 2003-2016 Free Software Foundation, Inc.
+Contributed by the AriC and Caramba projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 3 of the License, or (at your
+option) any later version.
+
+The GNU MPFR Library 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 Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
+http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
+51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+/* Init and set a mpfr_t with enough precision to store a mpz.
+ This function should be called in the extended exponent range. */
+static void
+init_set_z (mpfr_ptr t, mpz_srcptr z)
+{
+ mpfr_prec_t p;
+ int i;
+
+ if (mpz_size (z) <= 1)
+ p = GMP_NUMB_BITS;
+ else
+ MPFR_MPZ_SIZEINBASE2 (p, z);
+ mpfr_init2 (t, p);
+ i = mpfr_set_z (t, z, MPFR_RNDN);
+ /* Possible assertion failure in case of overflow. Such cases,
+ which imply that z is huge (if the function is called in
+ the extended exponent range), are currently not supported,
+ just like precisions around MPFR_PREC_MAX. */
+ MPFR_ASSERTN (i == 0); (void) i; /* use i to avoid a warning */
+}
+
+/* Init, set a mpfr_t with enough precision to store a mpz_t without round,
+ call the function, and clear the allocated mpfr_t */
+static int
+foo (mpfr_ptr x, mpfr_srcptr y, mpz_srcptr z, mpfr_rnd_t r,
+ int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t))
+{
+ mpfr_t t;
+ int i;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ MPFR_SAVE_EXPO_MARK (expo);
+ init_set_z (t, z); /* There should be no exceptions. */
+ i = (*f) (x, y, t, r);
+ MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
+ mpfr_clear (t);
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (x, i, r);
+}
+
+static int
+foo2 (mpfr_ptr x, mpz_srcptr y, mpfr_srcptr z, mpfr_rnd_t r,
+ int (*f)(mpfr_ptr, mpfr_srcptr, mpfr_srcptr, mpfr_rnd_t))
+{
+ mpfr_t t;
+ int i;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ MPFR_SAVE_EXPO_MARK (expo);
+ init_set_z (t, y); /* There should be no exceptions. */
+ i = (*f) (x, t, z, r);
+ MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
+ mpfr_clear (t);
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (x, i, r);
+}
+
+int
+mpfr_mul_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
+{
+ return foo (y, x, z, r, mpfr_mul);
+}
+
+int
+mpfr_div_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
+{
+ return foo (y, x, z, r, mpfr_div);
+}
+
+int
+mpfr_add_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
+{
+ /* Mpz 0 is unsigned */
+ if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
+ return mpfr_set (y, x, r);
+ else
+ return foo (y, x, z, r, mpfr_add);
+}
+
+int
+mpfr_sub_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mpfr_rnd_t r)
+{
+ /* Mpz 0 is unsigned */
+ if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
+ return mpfr_set (y, x, r);
+ else
+ return foo (y, x, z, r, mpfr_sub);
+}
+
+int
+mpfr_z_sub (mpfr_ptr y, mpz_srcptr x, mpfr_srcptr z, mpfr_rnd_t r)
+{
+ /* Mpz 0 is unsigned */
+ if (MPFR_UNLIKELY (mpz_sgn (x) == 0))
+ return mpfr_neg (y, z, r);
+ else
+ return foo2 (y, x, z, r, mpfr_sub);
+}
+
+int
+mpfr_cmp_z (mpfr_srcptr x, mpz_srcptr z)
+{
+ mpfr_t t;
+ int res;
+ mpfr_prec_t p;
+ unsigned int flags;
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ return mpfr_cmp_si (x, mpz_sgn (z));
+
+ if (mpz_size (z) <= 1)
+ p = GMP_NUMB_BITS;
+ else
+ MPFR_MPZ_SIZEINBASE2 (p, z);
+ mpfr_init2 (t, p);
+ flags = __gmpfr_flags;
+ if (mpfr_set_z (t, z, MPFR_RNDN))
+ {
+ /* overflow (t is an infinity) or underflow */
+ mpfr_div_2ui (t, t, 2, MPFR_RNDZ); /* if underflow, set t to zero */
+ __gmpfr_flags = flags; /* restore the flags */
+ /* The real value of t (= z), which falls outside the exponent range,
+ has been replaced by an equivalent value for the comparison: zero
+ or an infinity. */
+ }
+ res = mpfr_cmp (x, t);
+ mpfr_clear (t);
+ return res;
+}
+
+/* Compute y = RND(x*n/d), where n and d are mpz integers.
+ An integer 0 is assumed to have a positive sign.
+ This function is used by mpfr_mul_q and mpfr_div_q.
+ Note: the status of the rational 0/(-1) is not clear (if there is
+ a signed infinity, there should be a signed zero). But infinities
+ are not currently supported/documented in GMP, and if the rational
+ is canonicalized as it should be, the case 0/(-1) cannot occur. */
+static int
+mpfr_muldiv_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr n, mpz_srcptr d,
+ mpfr_rnd_t rnd_mode)
+{
+ if (MPFR_UNLIKELY (mpz_sgn (n) == 0))
+ {
+ if (MPFR_UNLIKELY (mpz_sgn (d) == 0))
+ MPFR_SET_NAN (y);
+ else
+ {
+ mpfr_mul_ui (y, x, 0, MPFR_RNDN); /* exact: +0, -0 or NaN */
+ if (MPFR_UNLIKELY (mpz_sgn (d) < 0))
+ MPFR_CHANGE_SIGN (y);
+ }
+ return 0;
+ }
+ else if (MPFR_UNLIKELY (mpz_sgn (d) == 0))
+ {
+ mpfr_div_ui (y, x, 0, MPFR_RNDN); /* exact: +Inf, -Inf or NaN */
+ if (MPFR_UNLIKELY (mpz_sgn (n) < 0))
+ MPFR_CHANGE_SIGN (y);
+ return 0;
+ }
+ else
+ {
+ mpfr_prec_t p;
+ mpfr_t tmp;
+ int inexact;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ /* With the current MPFR code, using mpfr_mul_z and mpfr_div_z
+ for the general case should be faster than doing everything
+ in mpn, mpz and/or mpq. MPFR_SAVE_EXPO_MARK could be avoided
+ here, but it would be more difficult to handle corner cases. */
+ MPFR_MPZ_SIZEINBASE2 (p, n);
+ mpfr_init2 (tmp, MPFR_PREC (x) + p);
+ inexact = mpfr_mul_z (tmp, x, n, MPFR_RNDN);
+ /* Since |n| >= 1, an underflow is not possible. And the precision of
+ tmp has been chosen so that inexact != 0 iff there's an overflow. */
+ if (MPFR_UNLIKELY (inexact != 0))
+ {
+ mpfr_t x0;
+ mpfr_exp_t ex;
+ MPFR_BLOCK_DECL (flags);
+
+ /* intermediate overflow case */
+ MPFR_ASSERTD (mpfr_inf_p (tmp));
+ ex = MPFR_GET_EXP (x); /* x is a pure FP number */
+ MPFR_ALIAS (x0, x, MPFR_SIGN(x), 0); /* x0 = x / 2^ex */
+ MPFR_BLOCK (flags,
+ inexact = mpfr_mul_z (tmp, x0, n, MPFR_RNDN);
+ MPFR_ASSERTD (inexact == 0);
+ inexact = mpfr_div_z (y, tmp, d, rnd_mode);
+ /* Just in case the division underflows
+ (highly unlikely, not supported)... */
+ MPFR_ASSERTN (!MPFR_BLOCK_EXCEP));
+ MPFR_EXP (y) += ex;
+ /* Detect highly unlikely, not supported corner cases... */
+ MPFR_ASSERTN (MPFR_EXP (y) >= __gmpfr_emin && MPFR_IS_PURE_FP (y));
+ /* The potential overflow will be detected by mpfr_check_range. */
+ }
+ else
+ inexact = mpfr_div_z (y, tmp, d, rnd_mode);
+
+ mpfr_clear (tmp);
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, inexact, rnd_mode);
+ }
+}
+
+int
+mpfr_mul_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
+{
+ return mpfr_muldiv_z (y, x, mpq_numref (z), mpq_denref (z), rnd_mode);
+}
+
+int
+mpfr_div_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
+{
+ return mpfr_muldiv_z (y, x, mpq_denref (z), mpq_numref (z), rnd_mode);
+}
+
+int
+mpfr_add_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z, mpfr_rnd_t rnd_mode)
+{
+ mpfr_t t,q;
+ mpfr_prec_t p;
+ mpfr_exp_t err;
+ int res;
+ MPFR_SAVE_EXPO_DECL (expo);
+ MPFR_ZIV_DECL (loop);
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ {
+ if (MPFR_IS_NAN (x))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ else if (MPFR_IS_INF (x))
+ {
+ if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 &&
+ MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)),
+ MPFR_SIGN (x)) <= 0))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ MPFR_SET_INF (y);
+ MPFR_SET_SAME_SIGN (y, x);
+ MPFR_RET (0);
+ }
+ else
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO (x));
+ if (MPFR_UNLIKELY (mpq_sgn (z) == 0))
+ return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */
+ else
+ return mpfr_set_q (y, z, rnd_mode);
+ }
+ }
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ p = MPFR_PREC (y) + 10;
+ mpfr_init2 (t, p);
+ mpfr_init2 (q, p);
+
+ MPFR_ZIV_INIT (loop, p);
+ for (;;)
+ {
+ MPFR_BLOCK_DECL (flags);
+
+ res = mpfr_set_q (q, z, MPFR_RNDN); /* Error <= 1/2 ulp(q) */
+ /* If z if @INF@ (1/0), res = 0, so it quits immediately */
+ if (MPFR_UNLIKELY (res == 0))
+ /* Result is exact so we can add it directly! */
+ {
+ res = mpfr_add (y, x, q, rnd_mode);
+ break;
+ }
+ MPFR_BLOCK (flags, mpfr_add (t, x, q, MPFR_RNDN));
+ /* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow,
+ but such an exception is very unlikely as it would be possible
+ only if q has a huge numerator or denominator. Not supported! */
+ MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)));
+ /* Error / ulp(t) <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t))
+ If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t)))
+ <= 2^(EXP(q)-EXP(t))
+ If EXP(q)-EXP(t)<0, <= 2^0 */
+ /* We can get 0, but we can't round since q is inexact */
+ if (MPFR_LIKELY (!MPFR_IS_ZERO (t)))
+ {
+ err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0);
+ if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode)))
+ {
+ res = mpfr_set (y, t, rnd_mode);
+ break;
+ }
+ }
+ MPFR_ZIV_NEXT (loop, p);
+ mpfr_set_prec (t, p);
+ mpfr_set_prec (q, p);
+ }
+ MPFR_ZIV_FREE (loop);
+ mpfr_clear (t);
+ mpfr_clear (q);
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, res, rnd_mode);
+}
+
+int
+mpfr_sub_q (mpfr_ptr y, mpfr_srcptr x, mpq_srcptr z,mpfr_rnd_t rnd_mode)
+{
+ mpfr_t t,q;
+ mpfr_prec_t p;
+ int res;
+ mpfr_exp_t err;
+ MPFR_SAVE_EXPO_DECL (expo);
+ MPFR_ZIV_DECL (loop);
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ {
+ if (MPFR_IS_NAN (x))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ else if (MPFR_IS_INF (x))
+ {
+ if (MPFR_UNLIKELY (mpz_sgn (mpq_denref (z)) == 0 &&
+ MPFR_MULT_SIGN (mpz_sgn (mpq_numref (z)),
+ MPFR_SIGN (x)) >= 0))
+ {
+ MPFR_SET_NAN (y);
+ MPFR_RET_NAN;
+ }
+ MPFR_SET_INF (y);
+ MPFR_SET_SAME_SIGN (y, x);
+ MPFR_RET (0);
+ }
+ else
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO (x));
+
+ if (MPFR_UNLIKELY (mpq_sgn (z) == 0))
+ return mpfr_set (y, x, rnd_mode); /* signed 0 - Unsigned 0 */
+ else
+ {
+ res = mpfr_set_q (y, z, MPFR_INVERT_RND (rnd_mode));
+ MPFR_CHANGE_SIGN (y);
+ return -res;
+ }
+ }
+ }
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ p = MPFR_PREC (y) + 10;
+ mpfr_init2 (t, p);
+ mpfr_init2 (q, p);
+
+ MPFR_ZIV_INIT (loop, p);
+ for(;;)
+ {
+ MPFR_BLOCK_DECL (flags);
+
+ res = mpfr_set_q(q, z, MPFR_RNDN); /* Error <= 1/2 ulp(q) */
+ /* If z if @INF@ (1/0), res = 0, so it quits immediately */
+ if (MPFR_UNLIKELY (res == 0))
+ /* Result is exact so we can add it directly!*/
+ {
+ res = mpfr_sub (y, x, q, rnd_mode);
+ break;
+ }
+ MPFR_BLOCK (flags, mpfr_sub (t, x, q, MPFR_RNDN));
+ /* Error on t is <= 1/2 ulp(t), except in case of overflow/underflow,
+ but such an exception is very unlikely as it would be possible
+ only if q has a huge numerator or denominator. Not supported! */
+ MPFR_ASSERTN (! (MPFR_OVERFLOW (flags) || MPFR_UNDERFLOW (flags)));
+ /* Error / ulp(t) <= 1/2 + 1/2 * 2^(EXP(q)-EXP(t))
+ If EXP(q)-EXP(t)>0, <= 2^(EXP(q)-EXP(t)-1)*(1+2^-(EXP(q)-EXP(t)))
+ <= 2^(EXP(q)-EXP(t))
+ If EXP(q)-EXP(t)<0, <= 2^0 */
+ /* We can get 0, but we can't round since q is inexact */
+ if (MPFR_LIKELY (!MPFR_IS_ZERO (t)))
+ {
+ err = (mpfr_exp_t) p - 1 - MAX (MPFR_GET_EXP(q)-MPFR_GET_EXP(t), 0);
+ res = MPFR_CAN_ROUND (t, err, MPFR_PREC (y), rnd_mode);
+ if (MPFR_LIKELY (res != 0)) /* We can round! */
+ {
+ res = mpfr_set (y, t, rnd_mode);
+ break;
+ }
+ }
+ MPFR_ZIV_NEXT (loop, p);
+ mpfr_set_prec (t, p);
+ mpfr_set_prec (q, p);
+ }
+ MPFR_ZIV_FREE (loop);
+ mpfr_clear (t);
+ mpfr_clear (q);
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return mpfr_check_range (y, res, rnd_mode);
+}
+
+int
+mpfr_cmp_q (mpfr_srcptr x, mpq_srcptr q)
+{
+ mpfr_t t;
+ int res;
+ mpfr_prec_t p;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ if (MPFR_UNLIKELY (mpq_denref (q) == 0))
+ {
+ /* q is an infinity or NaN */
+ mpfr_init2 (t, 2);
+ mpfr_set_q (t, q, MPFR_RNDN);
+ res = mpfr_cmp (x, t);
+ mpfr_clear (t);
+ return res;
+ }
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ return mpfr_cmp_si (x, mpq_sgn (q));
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ /* x < a/b ? <=> x*b < a */
+ MPFR_MPZ_SIZEINBASE2 (p, mpq_denref (q));
+ mpfr_init2 (t, MPFR_PREC(x) + p);
+ res = mpfr_mul_z (t, x, mpq_denref (q), MPFR_RNDN);
+ MPFR_ASSERTD (res == 0);
+ res = mpfr_cmp_z (t, mpq_numref (q));
+ mpfr_clear (t);
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return res;
+}
+
+int
+mpfr_cmp_f (mpfr_srcptr x, mpf_srcptr z)
+{
+ mpfr_t t;
+ int res;
+ MPFR_SAVE_EXPO_DECL (expo);
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
+ return mpfr_cmp_si (x, mpf_sgn (z));
+
+ MPFR_SAVE_EXPO_MARK (expo);
+
+ mpfr_init2 (t, MPFR_PREC_MIN + ABS(SIZ(z)) * GMP_NUMB_BITS );
+ res = mpfr_set_f (t, z, MPFR_RNDN);
+ MPFR_ASSERTD (res == 0);
+ res = mpfr_cmp (x, t);
+ mpfr_clear (t);
+
+ MPFR_SAVE_EXPO_FREE (expo);
+ return res;
+}