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git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@29042 a95241bf-73f2-0310-859d-f6bbb57e9c96
257 lines
8.2 KiB
C
257 lines
8.2 KiB
C
/* mpfr_pow_z -- power function x^z with z a MPZ
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Copyright 2005, 2006, 2007 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the MPFR Library.
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The MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the MPFR Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#define MPFR_NEED_LONGLONG_H
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#include "mpfr-impl.h"
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static int
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mpfr_pow_pos_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mp_rnd_t rnd)
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{
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mpfr_t res;
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mp_prec_t prec, err;
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int inexact;
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mp_rnd_t rnd1;
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mpz_t absz;
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mp_size_t size_z;
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MPFR_ZIV_DECL (loop);
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MPFR_ASSERTD (mpz_sgn (z) != 0);
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if (MPFR_UNLIKELY (mpz_cmpabs_ui (z, 1) == 0))
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return mpfr_set (y, x, rnd);
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rnd1 = MPFR_IS_POS (x) ? GMP_RNDU : GMP_RNDD; /* away */
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absz[0] = z[0];
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SIZ (absz) = ABS(SIZ(absz)); /* Hack to get abs(z) */
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MPFR_MPZ_SIZEINBASE2 (size_z, z);
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prec = MPFR_PREC (y) + 3 + size_z + MPFR_INT_CEIL_LOG2 (MPFR_PREC (y));
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mpfr_init2 (res, prec);
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MPFR_ZIV_INIT (loop, prec);
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for (;;)
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{
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mp_size_t i = size_z;
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/* now 2^(i-1) <= z < 2^i */
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/* see pow_ui.c for the error analusis, which is identical */
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MPFR_ASSERTD (prec > (mpfr_prec_t) i);
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err = prec - 1 - (mpfr_prec_t) i;
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MPFR_ASSERTD (i >= 2);
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mpfr_clear_overflow ();
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mpfr_clear_underflow ();
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/* First step: compute square from y */
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inexact = mpfr_mul (res, x, x, GMP_RNDU);
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if (mpz_tstbit (absz, i-2))
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inexact |= mpfr_mul (res, res, x, rnd1);
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for (i -= 3; i >= 0 && !mpfr_underflow_p() && !mpfr_overflow_p (); i--)
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{
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inexact |= mpfr_mul (res, res, res, GMP_RNDU);
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if (mpz_tstbit (absz, i))
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inexact |= mpfr_mul (res, res, x, rnd1);
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}
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/* printf ("pow_z ");
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mpfr_dump_mant (MPFR_MANT (res), prec, MPFR_PREC (x), err); */
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if (MPFR_LIKELY (inexact == 0
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|| mpfr_overflow_p () || mpfr_underflow_p ()
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|| MPFR_CAN_ROUND (res, err, MPFR_PREC (y), rnd)))
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break;
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/* Actualisation of the precision */
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MPFR_ZIV_NEXT (loop, prec);
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mpfr_set_prec (res, prec);
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}
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MPFR_ZIV_FREE (loop);
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inexact = mpfr_set (y, res, rnd);
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mpfr_clear (res);
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/* Check Overflow */
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if (MPFR_UNLIKELY (mpfr_overflow_p ()))
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return mpfr_overflow (y, rnd,
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mpz_odd_p (absz) ? MPFR_SIGN (x) : MPFR_SIGN_POS);
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/* Check Underflow */
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else if (MPFR_UNLIKELY (mpfr_underflow_p ()))
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{
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if (rnd == GMP_RNDN)
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rnd = GMP_RNDZ;
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return mpfr_underflow (y, rnd,
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mpz_odd_p (absz) ? MPFR_SIGN (x) : MPFR_SIGN_POS);
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}
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return inexact;
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}
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/* The computation of y=pow(x,z) is done by
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* y=pow_ui(x,z) if z>0
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* else
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* y=1/pow_ui(x,z) if z<0
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*/
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int
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mpfr_pow_z (mpfr_ptr y, mpfr_srcptr x, mpz_srcptr z, mp_rnd_t rnd)
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{
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int inexact;
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mpz_t tmp;
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MPFR_SAVE_EXPO_DECL (expo);
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if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x)))
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{
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if (MPFR_IS_NAN (x))
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{
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MPFR_SET_NAN (y);
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MPFR_RET_NAN;
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}
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else if (mpz_sgn (z) == 0) /* y^0 = 1 for any y except NAN */
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return mpfr_set_ui (y, 1, rnd);
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else if (MPFR_IS_INF (x))
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{
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/* Inf^n = Inf, (-Inf)^n = Inf for n even, -Inf for n odd */
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/* Inf ^(-n) = 0, sign = + if x>0 or z even */
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if (mpz_sgn (z) > 0)
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MPFR_SET_INF (y);
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else
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MPFR_SET_ZERO (y);
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if (MPFR_UNLIKELY (MPFR_IS_NEG (x) && mpz_odd_p (z)))
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MPFR_SET_NEG (y);
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else
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MPFR_SET_POS (y);
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MPFR_RET (0);
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}
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else /* x is zero */
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{
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MPFR_ASSERTD (MPFR_IS_ZERO(x));
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if (mpz_sgn (z) > 0)
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/* 0^n = +/-0 for any n */
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MPFR_SET_ZERO (y);
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else
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/* 0^(-n) if +/- INF */
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MPFR_SET_INF (y);
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if (MPFR_LIKELY (MPFR_IS_POS (x) || mpz_even_p (z)))
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MPFR_SET_POS (y);
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else
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MPFR_SET_NEG (y);
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MPFR_RET(0);
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}
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}
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if (MPFR_UNLIKELY (mpz_sgn (z) == 0))
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/* y^0 = 1 for any y except NAN */
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return mpfr_set_ui (y, 1, rnd);
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/* detect exact powers: x^-n is exact iff x is a power of 2
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Do it if n > 0 too (faster). */
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if (MPFR_UNLIKELY (mpfr_cmp_si_2exp (x, MPFR_SIGN (x),
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MPFR_EXP (x) - 1) == 0))
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{
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mp_exp_t expx = MPFR_EXP (x); /* warning: x and y may be the same
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variable */
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mpfr_set_si (y, mpz_odd_p (z) ? MPFR_INT_SIGN(x) : 1, rnd);
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MPFR_ASSERTD (MPFR_IS_FP (y));
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mpz_init (tmp);
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mpz_mul_si (tmp, z, expx-1);
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MPFR_ASSERTD (MPFR_GET_EXP (y) == 1);
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mpz_add_ui (tmp, tmp, 1);
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inexact = 0;
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if (MPFR_UNLIKELY (mpz_cmp_si (tmp, __gmpfr_emin) < 0))
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{
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/* The following test is necessary because in the rounding to the
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* nearest mode, mpfr_underflow always rounds away from 0. In
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* this rounding mode, we need to round to 0 if:
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* _ |y| < 2^(emin-2), or
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* _ |y| = 2^(emin-2) and the absolute value of the exact
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* result is <= 2^(emin-2).
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* NOTE: y is a power of 2 and inexact = 0!
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*/
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if (rnd == GMP_RNDN && mpz_cmp_si (tmp, __gmpfr_emin-1) < 0)
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rnd = GMP_RNDZ;
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inexact = mpfr_underflow (y, rnd, MPFR_SIGN (y));
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}
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else if (MPFR_UNLIKELY (mpz_cmp_si (tmp, __gmpfr_emax) > 0))
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inexact = mpfr_overflow (y, rnd, MPFR_SIGN(x));
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else
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MPFR_SET_EXP (y, mpz_get_si (tmp));
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mpz_clear (tmp);
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MPFR_RET (inexact);
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}
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MPFR_SAVE_EXPO_MARK (expo);
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__gmpfr_emin -= 3; /* So that we can check for underflow properly */
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if (mpz_sgn (z) > 0)
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inexact = mpfr_pow_pos_z (y, x, z, rnd);
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else
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{
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/* Declaration of the intermediary variable */
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mpfr_t t;
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mp_prec_t Nt; /* Precision of the intermediary variable */
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MPFR_ZIV_DECL (loop);
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/* compute the precision of intermediary variable */
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Nt = MAX (MPFR_PREC (x), MPFR_PREC (y));
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/* the optimal number of bits : see algorithms.ps */
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Nt = Nt + 3 + MPFR_INT_CEIL_LOG2 (Nt);
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/* initialise of intermediary variable */
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mpfr_init2 (t, Nt);
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MPFR_ZIV_INIT (loop, Nt);
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for (;;)
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{
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/* compute 1/(x^n) n>0 */
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mpfr_pow_pos_z (t, x, z, GMP_RNDN);
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mpfr_ui_div (t, 1, t, GMP_RNDN);
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/* FIXME: old code improved, but I think this is still incorrect. */
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if (MPFR_UNLIKELY (MPFR_IS_ZERO (t)))
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{
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MPFR_ZIV_FREE (loop);
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mpfr_clear (t);
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_underflow (y, rnd == GMP_RNDN ? GMP_RNDZ : rnd,
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mpz_odd_p (z) ? MPFR_SIGN (x) :
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MPFR_SIGN_POS);
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}
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if (MPFR_UNLIKELY (MPFR_IS_INF (t)))
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{
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MPFR_ZIV_FREE (loop);
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mpfr_clear (t);
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_overflow (y, rnd,
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mpz_odd_p (z) ? MPFR_SIGN (x) :
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MPFR_SIGN_POS);
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}
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if (MPFR_LIKELY (MPFR_CAN_ROUND (t, Nt-3, MPFR_PREC (y), rnd)))
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break;
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/* actualisation of the precision */
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MPFR_ZIV_NEXT (loop, Nt);
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mpfr_set_prec (t, Nt);
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}
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MPFR_ZIV_FREE (loop);
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inexact = mpfr_set (y, t, rnd);
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mpfr_clear (t);
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}
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MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags);
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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_check_range (y, inexact, rnd);
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}
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