--- /dev/null
+/* mpfr_mpn_exp -- auxiliary function for mpfr_get_str and mpfr_set_str
+
+Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+Contributed by Alain Delplanque and Paul Zimmermann.
+
+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 2.1 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.LIB. If not, 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"
+
+/* this function computes an approximation of b^e in {a, n}, with exponent
+ stored in exp_r. The computed value is rounded towards zero (truncated).
+ It returns an integer f such that the final error is bounded by 2^f ulps,
+ that is:
+ a*2^exp_r <= b^e <= 2^exp_r (a + 2^f),
+ where a represents {a, n}, i.e. the integer
+ a[0] + a[1]*B + ... + a[n-1]*B^(n-1) where B=2^BITS_PER_MP_LIMB
+
+ Return -1 is the result is exact.
+ Return -2 if an overflow occurred in the computation of exp_r.
+*/
+
+long
+mpfr_mpn_exp (mp_limb_t *a, mp_exp_t *exp_r, int b, mp_exp_t e, size_t n)
+{
+ mp_limb_t *c, B;
+ mp_exp_t f, h;
+ int i;
+ unsigned long t; /* number of bits in e */
+ unsigned long bits;
+ size_t n1;
+ unsigned int error; /* (number - 1) of loop a^2b inexact */
+ /* error == t means no error */
+ int err_s_a2 = 0;
+ int err_s_ab = 0; /* number of error when shift A^2, AB */
+ MPFR_TMP_DECL(marker);
+
+ MPFR_ASSERTN(e > 0);
+ MPFR_ASSERTN((2 <= b) && (b <= 36));
+
+ MPFR_TMP_MARK(marker);
+
+ /* initialization of a, b, f, h */
+
+ /* normalize the base */
+ B = (mp_limb_t) b;
+ count_leading_zeros (h, B);
+
+ bits = BITS_PER_MP_LIMB - h;
+
+ B = B << h;
+ h = - h;
+
+ /* allocate space for A and set it to B */
+ c = (mp_limb_t*) MPFR_TMP_ALLOC(2 * n * BYTES_PER_MP_LIMB);
+ a [n - 1] = B;
+ MPN_ZERO (a, n - 1);
+ /* initial exponent for A: invariant is A = {a, n} * 2^f */
+ f = h - (n - 1) * BITS_PER_MP_LIMB;
+
+ /* determine number of bits in e */
+ count_leading_zeros (t, (mp_limb_t) e);
+
+ t = BITS_PER_MP_LIMB - t; /* number of bits of exponent e */
+
+ error = t; /* error <= BITS_PER_MP_LIMB */
+
+ MPN_ZERO (c, 2 * n);
+
+ for (i = t - 2; i >= 0; i--)
+ {
+
+ /* determine precision needed */
+ bits = n * BITS_PER_MP_LIMB - mpn_scan1 (a, 0);
+ n1 = (n * BITS_PER_MP_LIMB - bits) / BITS_PER_MP_LIMB;
+
+ /* square of A : {c+2n1, 2(n-n1)} = {a+n1, n-n1}^2 */
+ mpn_sqr_n (c + 2 * n1, a + n1, n - n1);
+
+ /* set {c+n, 2n1-n} to 0 : {c, n} = {a, n}^2*K^n */
+
+ /* check overflow on f */
+ if (MPFR_UNLIKELY(f < MPFR_EXP_MIN/2 || f > MPFR_EXP_MAX/2))
+ {
+ overflow:
+ MPFR_TMP_FREE(marker);
+ return -2;
+ }
+ /* FIXME: Could f = 2*f + n * BITS_PER_MP_LIMB be used? */
+ f = 2*f;
+ MPFR_SADD_OVERFLOW (f, f, n * BITS_PER_MP_LIMB,
+ mp_exp_t, mp_exp_unsigned_t,
+ MPFR_EXP_MIN, MPFR_EXP_MAX,
+ goto overflow, goto overflow);
+ if ((c[2*n - 1] & MPFR_LIMB_HIGHBIT) == 0)
+ {
+ /* shift A by one bit to the left */
+ mpn_lshift (a, c + n, n, 1);
+ a[0] |= mpn_lshift (c + n - 1, c + n - 1, 1, 1);
+ f --;
+ if (error != t)
+ err_s_a2 ++;
+ }
+ else
+ MPN_COPY (a, c + n, n);
+
+ if ((error == t) && (2 * n1 <= n) &&
+ (mpn_scan1 (c + 2 * n1, 0) < (n - 2 * n1) * BITS_PER_MP_LIMB))
+ error = i;
+
+ if (e & ((mp_exp_t) 1 << i))
+ {
+ /* multiply A by B */
+ c[2 * n - 1] = mpn_mul_1 (c + n - 1, a, n, B);
+ f += h + BITS_PER_MP_LIMB;
+ if ((c[2 * n - 1] & MPFR_LIMB_HIGHBIT) == 0)
+ { /* shift A by one bit to the left */
+ mpn_lshift (a, c + n, n, 1);
+ a[0] |= mpn_lshift (c + n - 1, c + n - 1, 1, 1);
+ f --;
+ }
+ else
+ {
+ MPN_COPY (a, c + n, n);
+ if (error != t)
+ err_s_ab ++;
+ }
+ if ((error == t) && (c[n - 1] != 0))
+ error = i;
+ }
+ }
+
+ MPFR_TMP_FREE(marker);
+
+ *exp_r = f;
+
+ if (error == t)
+ return -1; /* result is exact */
+ else /* error <= t-2 <= BITS_PER_MP_LIMB-2
+ err_s_ab, err_s_a2 <= t-1 */
+ {
+ /* if there are p loops after the first inexact result, with
+ j shifts in a^2 and l shifts in a*b, then the final error is
+ at most 2^(p+ceil((j+1)/2)+l+1)*ulp(res).
+ This is bounded by 2^(5/2*t-1/2) where t is the number of bits of e.
+ */
+ error = error + err_s_ab + err_s_a2 / 2 + 3; /* <= 5t/2-1/2 */
+#if 0
+ if ((error - 1) >= ((n * BITS_PER_MP_LIMB - 1) / 2))
+ error = n * BITS_PER_MP_LIMB; /* result is completely wrong:
+ this is very unlikely since error is
+ at most 5/2*log_2(e), and
+ n * BITS_PER_MP_LIMB is at least
+ 3*log_2(e) */
+#endif
+ return error;
+ }
+}
projects / msp430-gcc.git / blobdiff