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Diffstat (limited to 'mpfr/src/gmp_op.c')
-rw-r--r-- | mpfr/src/gmp_op.c | 489 |
1 files changed, 489 insertions, 0 deletions
diff --git a/mpfr/src/gmp_op.c b/mpfr/src/gmp_op.c new file mode 100644 index 0000000000..9418fa0984 --- /dev/null +++ b/mpfr/src/gmp_op.c @@ -0,0 +1,489 @@ +/* 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; +} |