--- /dev/null
+/* mpfr_rem1 -- internal function
+ mpfr_fmod -- compute the floating-point remainder of x/y
+ mpfr_remquo and mpfr_remainder -- argument reduction functions
+
+Copyright 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao 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 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. */
+
+# include "mpfr-impl.h"
+
+/* we return as many bits as we can, keeping just one bit for the sign */
+# define WANTED_BITS (sizeof(long) * CHAR_BIT - 1)
+
+/*
+ rem1 works as follows:
+ The first rounding mode rnd_q indicate if we are actually computing
+ a fmod (GMP_RNDZ) or a remainder/remquo (GMP_RNDN).
+
+ Let q = x/y rounded to an integer in the direction rnd_q.
+ Put x - q*y in rem, rounded according to rnd.
+ If quo is not null, the value stored in *quo has the sign of q,
+ and agrees with q with the 2^n low order bits.
+ In other words, *quo = q (mod 2^n) and *quo q >= 0.
+ If rem is zero, then it has the sign of x.
+ The returned 'int' is the inexact flag giving the place of rem wrt x - q*y.
+
+ If x or y is NaN: *quo is undefined, rem is NaN.
+ If x is Inf, whatever y: *quo is undefined, rem is NaN.
+ If y is Inf, x not NaN nor Inf: *quo is 0, rem is x.
+ If y is 0, whatever x: *quo is undefined, rem is NaN.
+ If x is 0, whatever y (not NaN nor 0): *quo is 0, rem is x.
+
+ Otherwise if x and y are neither NaN, Inf nor 0, q is always defined,
+ thus *quo is.
+ Since |x - q*y| <= y/2, no overflow is possible.
+ Only an underflow is possible when y is very small.
+ */
+
+static int
+mpfr_rem1 (mpfr_ptr rem, long *quo, mp_rnd_t rnd_q,
+ mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+ mp_exp_t ex, ey;
+ int compare, inex, q_is_odd, sign, signx = MPFR_SIGN (x);
+ mpz_t mx, my, r;
+
+ MPFR_ASSERTD (rnd_q == GMP_RNDN || rnd_q == GMP_RNDZ);
+
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (x) || MPFR_IS_SINGULAR (y)))
+ {
+ if (MPFR_IS_NAN (x) || MPFR_IS_NAN (y) || MPFR_IS_INF (x)
+ || MPFR_IS_ZERO (y))
+ {
+ /* for remquo, quo is undefined */
+ MPFR_SET_NAN (rem);
+ MPFR_RET_NAN;
+ }
+ else /* either y is Inf and x is 0 or non-special,
+ or x is 0 and y is non-special,
+ in both cases the quotient is zero. */
+ {
+ if (quo)
+ *quo = 0;
+ return mpfr_set (rem, x, rnd);
+ }
+ }
+
+ /* now neither x nor y is NaN, Inf or zero */
+
+ mpz_init (mx);
+ mpz_init (my);
+ mpz_init (r);
+
+ ex = mpfr_get_z_exp (mx, x); /* x = mx*2^ex */
+ ey = mpfr_get_z_exp (my, y); /* y = my*2^ey */
+
+ /* to get rid of sign problems, we compute it separately:
+ quo(-x,-y) = quo(x,y), rem(-x,-y) = -rem(x,y)
+ quo(-x,y) = -quo(x,y), rem(-x,y) = -rem(x,y)
+ thus quo = sign(x/y)*quo(|x|,|y|), rem = sign(x)*rem(|x|,|y|) */
+ sign = (signx == MPFR_SIGN (y)) ? 1 : -1;
+ mpz_abs (mx, mx);
+ mpz_abs (my, my);
+ q_is_odd = 0;
+
+ /* divide my by 2^k if possible to make operations mod my easier */
+ {
+ unsigned long k = mpz_scan1 (my, 0);
+ ey += k;
+ mpz_div_2exp (my, my, k);
+ }
+
+ if (ex <= ey)
+ {
+ /* q = x/y = mx/(my*2^(ey-ex)) */
+ mpz_mul_2exp (my, my, ey - ex); /* divide mx by my*2^(ey-ex) */
+ if (rnd_q == GMP_RNDZ)
+ /* 0 <= |r| <= |my|, r has the same sign as mx */
+ mpz_tdiv_qr (mx, r, mx, my);
+ else
+ /* 0 <= |r| <= |my|, r has the same sign as my */
+ mpz_fdiv_qr (mx, r, mx, my);
+
+ if (rnd_q == GMP_RNDN)
+ q_is_odd = mpz_tstbit (mx, 0);
+ if (quo) /* mx is the quotient */
+ {
+ mpz_tdiv_r_2exp (mx, mx, WANTED_BITS);
+ *quo = mpz_get_si (mx);
+ }
+ }
+ else /* ex > ey */
+ {
+ if (quo)
+ /* for remquo, to get the low WANTED_BITS more bits of the quotient,
+ we first compute R = X mod Y*2^WANTED_BITS, where X and Y are
+ defined below. Then the low WANTED_BITS of the quotient are
+ floor(R/Y). */
+ mpz_mul_2exp (my, my, WANTED_BITS); /* 2^WANTED_BITS*Y */
+ else
+ /* Let X = mx*2^(ex-ey) and Y = my. Then both X and Y are integers.
+ Assume X = R mod Y, then x = X*2^ey = R*2^ey mod (Y*2^ey=y).
+ To be able to perform the rounding, we need the least significant
+ bit of the quotient, i.e., one more bit in the remainder,
+ which is obtained by dividing by 2Y. */
+ mpz_mul_2exp (my, my, 1); /* 2Y */
+
+ mpz_set_ui (r, 2);
+ mpz_powm_ui (r, r, ex - ey, my); /* 2^(ex-ey) mod my */
+ mpz_mul (r, r, mx);
+ mpz_mod (r, r, my);
+
+ if (quo) /* now 0 <= r < 2^WANTED_BITS*Y */
+ {
+ mpz_div_2exp (my, my, WANTED_BITS); /* back to Y */
+ mpz_tdiv_qr (mx, r, r, my);
+ /* oldr = mx*my + newr */
+ *quo = mpz_get_si (mx);
+ q_is_odd = *quo & 1;
+ }
+ else /* now 0 <= r < 2Y */
+ {
+ mpz_div_2exp (my, my, 1); /* back to Y */
+ if (rnd_q == GMP_RNDN)
+ {
+ /* least significant bit of q */
+ q_is_odd = mpz_cmpabs (r, my) >= 0;
+ if (q_is_odd)
+ mpz_sub (r, r, my);
+ }
+ }
+ /* now 0 <= |r| < |my|, and if needed,
+ q_is_odd is the least significant bit of q */
+ }
+
+ if (mpz_cmp_ui (r, 0) == 0)
+ inex = mpfr_set_ui (rem, 0, GMP_RNDN);
+ else
+ {
+ if (rnd_q == GMP_RNDN)
+ {
+ /* FIXME: the comparison 2*r < my could be done more efficiently
+ at the mpn level */
+ mpz_mul_2exp (r, r, 1);
+ compare = mpz_cmpabs (r, my);
+ mpz_div_2exp (r, r, 1);
+ compare = ((compare > 0) ||
+ ((rnd_q == GMP_RNDN) && (compare == 0) && q_is_odd));
+ /* if compare != 0, we need to subtract my to r, and add 1 to quo */
+ if (compare)
+ {
+ mpz_sub (r, r, my);
+ if (quo && (rnd_q == GMP_RNDN))
+ *quo += 1;
+ }
+ }
+ inex = mpfr_set_z (rem, r, rnd);
+ /* if ex > ey, rem should be multiplied by 2^ey, else by 2^ex */
+ MPFR_EXP (rem) += (ex > ey) ? ey : ex;
+ }
+
+ if (quo)
+ *quo *= sign;
+
+ /* take into account sign of x */
+ if (signx < 0)
+ {
+ mpfr_neg (rem, rem, GMP_RNDN);
+ inex = -inex;
+ }
+
+ mpz_clear (mx);
+ mpz_clear (my);
+ mpz_clear (r);
+
+ return inex;
+}
+
+int
+mpfr_remainder (mpfr_ptr rem, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+ return mpfr_rem1 (rem, (long *) 0, GMP_RNDN, x, y, rnd);
+}
+
+int
+mpfr_remquo (mpfr_ptr rem, long *quo,
+ mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+ return mpfr_rem1 (rem, quo, GMP_RNDN, x, y, rnd);
+}
+
+int
+mpfr_fmod (mpfr_ptr rem, mpfr_srcptr x, mpfr_srcptr y, mp_rnd_t rnd)
+{
+ return mpfr_rem1 (rem, (long *) 0, GMP_RNDZ, x, y, rnd);
+}
projects / msp430-gcc.git / blobdiff