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99d8158635
git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@29042 a95241bf-73f2-0310-859d-f6bbb57e9c96
196 lines
7.5 KiB
C
196 lines
7.5 KiB
C
/* mpfr_pow_si -- power function x^y with y a signed int
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Copyright 2001, 2002, 2003, 2004, 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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/* 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_si (mpfr_ptr y, mpfr_srcptr x, long int n, mp_rnd_t rnd)
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{
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if (n >= 0)
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return mpfr_pow_ui (y, x, n, rnd);
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else
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{
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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 (MPFR_IS_INF (x))
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{
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MPFR_SET_ZERO (y);
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if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0)
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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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else /* x is zero */
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{
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MPFR_ASSERTD (MPFR_IS_ZERO (x));
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MPFR_SET_INF(y);
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if (MPFR_IS_POS (x) || ((unsigned) n & 1) == 0)
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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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MPFR_CLEAR_FLAGS (y);
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/* detect exact powers: x^(-n) is exact iff x is a power of 2 */
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if (mpfr_cmp_si_2exp (x, MPFR_SIGN(x), MPFR_EXP(x) - 1) == 0)
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{
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mp_exp_t expx = MPFR_EXP (x) - 1, expy;
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MPFR_ASSERTD (n < 0);
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/* Warning: n * expx may overflow!
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* Some systems (apparently alpha-freebsd) abort with
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* LONG_MIN / 1, and LONG_MIN / -1 is undefined.
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* Proof of the overflow checking. The expressions below are
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* assumed to be on the rational numbers, but the word "overflow"
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* still has its own meaning in the C context. / still denotes
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* the integer (truncated) division, and // denotes the exact
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* division.
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* - First, (__gmpfr_emin - 1) / n and (__gmpfr_emax - 1) / n
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* cannot overflow due to the constraints on the exponents of
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* MPFR numbers.
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* - If n = -1, then n * expx = - expx, which is representable
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* because of the constraints on the exponents of MPFR numbers.
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* - If expx = 0, then n * expx = 0, which is representable.
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* - If n < -1 and expx > 0:
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* + If expx > (__gmpfr_emin - 1) / n, then
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* expx >= (__gmpfr_emin - 1) / n + 1
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* > (__gmpfr_emin - 1) // n,
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* and
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* n * expx < __gmpfr_emin - 1,
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* i.e.
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* n * expx <= __gmpfr_emin - 2.
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* This corresponds to an underflow, with a null result in
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* the rounding-to-nearest mode.
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* + If expx <= (__gmpfr_emin - 1) / n, then n * expx cannot
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* overflow since 0 < expx <= (__gmpfr_emin - 1) / n and
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* 0 > n * expx >= n * ((__gmpfr_emin - 1) / n)
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* >= __gmpfr_emin - 1.
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* - If n < -1 and expx < 0:
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* + If expx < (__gmpfr_emax - 1) / n, then
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* expx <= (__gmpfr_emax - 1) / n - 1
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* < (__gmpfr_emax - 1) // n,
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* and
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* n * expx > __gmpfr_emax - 1,
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* i.e.
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* n * expx >= __gmpfr_emax.
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* This corresponds to an overflow (2^(n * expx) has an
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* exponent > __gmpfr_emax).
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* + If expx >= (__gmpfr_emax - 1) / n, then n * expx cannot
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* overflow since 0 > expx >= (__gmpfr_emax - 1) / n and
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* 0 < n * expx <= n * ((__gmpfr_emax - 1) / n)
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* <= __gmpfr_emax - 1.
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* Note: one could use expx bounds based on MPFR_EXP_MIN and
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* MPFR_EXP_MAX instead of __gmpfr_emin and __gmpfr_emax. The
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* current bounds do not lead to noticeably slower code and
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* allow us to avoid a bug in Sun's compiler for Solaris/x86
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* (when optimizations are enabled).
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*/
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expy =
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n != -1 && expx > 0 && expx > (__gmpfr_emin - 1) / n ?
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MPFR_EMIN_MIN - 2 /* Underflow */ :
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n != -1 && expx < 0 && expx < (__gmpfr_emax - 1) / n ?
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MPFR_EMAX_MAX /* Overflow */ : n * expx;
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return mpfr_set_si_2exp (y, n % 2 ? MPFR_INT_SIGN (x) : 1,
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expy, rnd);
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}
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/* General case */
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{
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/* Declaration of the intermediary variable */
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mpfr_t t;
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/* Declaration of the size variable */
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mp_prec_t Ny = MPFR_PREC (y); /* target precision */
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mp_prec_t Nt; /* working precision */
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mp_exp_t err; /* error */
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int inexact;
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unsigned long abs_n;
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MPFR_SAVE_EXPO_DECL (expo);
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MPFR_ZIV_DECL (loop);
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abs_n = - (unsigned long) n;
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/* compute the precision of intermediary variable */
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/* the optimal number of bits : see algorithms.tex */
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Nt = Ny + 3 + MPFR_INT_CEIL_LOG2 (Ny);
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MPFR_SAVE_EXPO_MARK (expo);
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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), with n > 0 */
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mpfr_pow_ui (t, x, abs_n, 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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abs_n & 1 ? 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, abs_n & 1 ? MPFR_SIGN (x) :
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MPFR_SIGN_POS);
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}
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/* error estimate -- see pow function in algorithms.ps */
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err = Nt - 3;
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if (MPFR_LIKELY (MPFR_CAN_ROUND (t, err, Ny, rnd)))
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break;
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/* actualisation of the precision */
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Nt += BITS_PER_MP_LIMB;
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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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MPFR_SAVE_EXPO_FREE (expo);
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return mpfr_check_range (y, inexact, rnd);
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}
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}
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}
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