| /* Implementations of operations between mpfr and mpz/mpq data |
| |
| Copyright 2001, 2003-2017 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 "third_party/mpfr/v3_1_6/src/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; |
| } |
