--- /dev/null
+/* mpfr_mul -- multiply two floating-point numbers
+
+Copyright 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 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. */
+
+#define MPFR_NEED_LONGLONG_H
+#include "mpfr-impl.h"
+
+
+/********* BEGINNING CHECK *************/
+
+/* Check if we have to check the result of mpfr_mul.
+ TODO: Find a better (and faster?) check than using old implementation */
+#ifdef WANT_ASSERT
+# if WANT_ASSERT >= 3
+
+int mpfr_mul2 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode);
+static int
+mpfr_mul3 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
+{
+ /* Old implementation */
+ int sign_product, cc, inexact;
+ mp_exp_t ax;
+ mp_limb_t *tmp;
+ mp_limb_t b1;
+ mp_prec_t bq, cq;
+ mp_size_t bn, cn, tn, k;
+ MPFR_TMP_DECL(marker);
+
+ /* deal with special cases */
+ if (MPFR_ARE_SINGULAR(b,c))
+ {
+ if (MPFR_IS_NAN(b) || MPFR_IS_NAN(c))
+ {
+ MPFR_SET_NAN(a);
+ MPFR_RET_NAN;
+ }
+ sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
+ if (MPFR_IS_INF(b))
+ {
+ if (MPFR_IS_INF(c) || MPFR_NOTZERO(c))
+ {
+ MPFR_SET_SIGN(a,sign_product);
+ MPFR_SET_INF(a);
+ MPFR_RET(0); /* exact */
+ }
+ else
+ {
+ MPFR_SET_NAN(a);
+ MPFR_RET_NAN;
+ }
+ }
+ else if (MPFR_IS_INF(c))
+ {
+ if (MPFR_NOTZERO(b))
+ {
+ MPFR_SET_SIGN(a, sign_product);
+ MPFR_SET_INF(a);
+ MPFR_RET(0); /* exact */
+ }
+ else
+ {
+ MPFR_SET_NAN(a);
+ MPFR_RET_NAN;
+ }
+ }
+ else
+ {
+ MPFR_ASSERTD(MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
+ MPFR_SET_SIGN(a, sign_product);
+ MPFR_SET_ZERO(a);
+ MPFR_RET(0); /* 0 * 0 is exact */
+ }
+ }
+ MPFR_CLEAR_FLAGS(a);
+ sign_product = MPFR_MULT_SIGN( MPFR_SIGN(b) , MPFR_SIGN(c) );
+
+ ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
+
+ bq = MPFR_PREC(b);
+ cq = MPFR_PREC(c);
+
+ MPFR_ASSERTD(bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
+
+ bn = (bq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of b */
+ cn = (cq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of c */
+ k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
+ tn = (bq + cq + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
+ /* <= k, thus no int overflow */
+ MPFR_ASSERTD(tn <= k);
+
+ /* Check for no size_t overflow*/
+ MPFR_ASSERTD((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
+ MPFR_TMP_MARK(marker);
+ tmp = (mp_limb_t *) MPFR_TMP_ALLOC((size_t) k * BYTES_PER_MP_LIMB);
+
+ /* multiplies two mantissa in temporary allocated space */
+ b1 = (MPFR_LIKELY(bn >= cn)) ?
+ mpn_mul (tmp, MPFR_MANT(b), bn, MPFR_MANT(c), cn)
+ : mpn_mul (tmp, MPFR_MANT(c), cn, MPFR_MANT(b), bn);
+
+ /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
+ with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
+ b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */
+
+ /* if the mantissas of b and c are uniformly distributed in ]1/2, 1],
+ then their product is in ]1/4, 1/2] with probability 2*ln(2)-1 ~ 0.386
+ and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
+ tmp += k - tn;
+ if (MPFR_UNLIKELY(b1 == 0))
+ mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
+ cc = mpfr_round_raw (MPFR_MANT (a), tmp, bq + cq,
+ MPFR_IS_NEG_SIGN(sign_product),
+ MPFR_PREC (a), rnd_mode, &inexact);
+
+ /* cc = 1 ==> result is a power of two */
+ if (MPFR_UNLIKELY(cc))
+ MPFR_MANT(a)[MPFR_LIMB_SIZE(a)-1] = MPFR_LIMB_HIGHBIT;
+
+ MPFR_TMP_FREE(marker);
+
+ {
+ mp_exp_t ax2 = ax + (mp_exp_t) (b1 - 1 + cc);
+ if (MPFR_UNLIKELY( ax2 > __gmpfr_emax))
+ return mpfr_overflow (a, rnd_mode, sign_product);
+ if (MPFR_UNLIKELY( ax2 < __gmpfr_emin))
+ {
+ /* In the rounding to the nearest mode, if the exponent of the exact
+ result (i.e. before rounding, i.e. without taking cc into account)
+ is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
+ both arguments are powers of 2), then round to zero. */
+ if (rnd_mode == GMP_RNDN &&
+ (ax + (mp_exp_t) b1 < __gmpfr_emin ||
+ (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
+ rnd_mode = GMP_RNDZ;
+ return mpfr_underflow (a, rnd_mode, sign_product);
+ }
+ MPFR_SET_EXP (a, ax2);
+ MPFR_SET_SIGN(a, sign_product);
+ }
+ MPFR_RET (inexact);
+}
+
+int
+mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
+{
+ mpfr_t ta, tb, tc;
+ int inexact1, inexact2;
+
+ mpfr_init2 (ta, MPFR_PREC (a));
+ mpfr_init2 (tb, MPFR_PREC (b));
+ mpfr_init2 (tc, MPFR_PREC (c));
+ MPFR_ASSERTN (mpfr_set (tb, b, GMP_RNDN) == 0);
+ MPFR_ASSERTN (mpfr_set (tc, c, GMP_RNDN) == 0);
+
+ inexact2 = mpfr_mul3 (ta, tb, tc, rnd_mode);
+ inexact1 = mpfr_mul2 (a, b, c, rnd_mode);
+ if (mpfr_cmp (ta, a) || inexact1*inexact2 < 0
+ || (inexact1*inexact2 == 0 && (inexact1|inexact2) != 0))
+ {
+ fprintf (stderr, "mpfr_mul return different values for %s\n"
+ "Prec_a = %lu, Prec_b = %lu, Prec_c = %lu\nB = ",
+ mpfr_print_rnd_mode (rnd_mode),
+ MPFR_PREC (a), MPFR_PREC (b), MPFR_PREC (c));
+ mpfr_out_str (stderr, 16, 0, tb, GMP_RNDN);
+ fprintf (stderr, "\nC = ");
+ mpfr_out_str (stderr, 16, 0, tc, GMP_RNDN);
+ fprintf (stderr, "\nOldMul: ");
+ mpfr_out_str (stderr, 16, 0, ta, GMP_RNDN);
+ fprintf (stderr, "\nNewMul: ");
+ mpfr_out_str (stderr, 16, 0, a, GMP_RNDN);
+ fprintf (stderr, "\nNewInexact = %d | OldInexact = %d\n",
+ inexact1, inexact2);
+ MPFR_ASSERTN(0);
+ }
+
+ mpfr_clears (ta, tb, tc, (mpfr_ptr) 0);
+ return inexact1;
+}
+
+# define mpfr_mul mpfr_mul2
+# endif
+#endif
+
+/****** END OF CHECK *******/
+
+/* Multiply 2 mpfr_t */
+
+int
+mpfr_mul (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
+{
+ int sign, inexact;
+ mp_exp_t ax, ax2;
+ mp_limb_t *tmp;
+ mp_limb_t b1;
+ mp_prec_t bq, cq;
+ mp_size_t bn, cn, tn, k;
+ MPFR_TMP_DECL (marker);
+
+ MPFR_LOG_FUNC (("b[%#R]=%R c[%#R]=%R rnd=%d", b, b, c, c, rnd_mode),
+ ("a[%#R]=%R inexact=%d", a, a, inexact));
+
+ /* deal with special cases */
+ if (MPFR_ARE_SINGULAR (b, c))
+ {
+ if (MPFR_IS_NAN (b) || MPFR_IS_NAN (c))
+ {
+ MPFR_SET_NAN (a);
+ MPFR_RET_NAN;
+ }
+ sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
+ if (MPFR_IS_INF (b))
+ {
+ if (!MPFR_IS_ZERO (c))
+ {
+ MPFR_SET_SIGN (a, sign);
+ MPFR_SET_INF (a);
+ MPFR_RET (0);
+ }
+ else
+ {
+ MPFR_SET_NAN (a);
+ MPFR_RET_NAN;
+ }
+ }
+ else if (MPFR_IS_INF (c))
+ {
+ if (!MPFR_IS_ZERO (b))
+ {
+ MPFR_SET_SIGN (a, sign);
+ MPFR_SET_INF (a);
+ MPFR_RET(0);
+ }
+ else
+ {
+ MPFR_SET_NAN (a);
+ MPFR_RET_NAN;
+ }
+ }
+ else
+ {
+ MPFR_ASSERTD (MPFR_IS_ZERO(b) || MPFR_IS_ZERO(c));
+ MPFR_SET_SIGN (a, sign);
+ MPFR_SET_ZERO (a);
+ MPFR_RET (0);
+ }
+ }
+ MPFR_CLEAR_FLAGS (a);
+ sign = MPFR_MULT_SIGN (MPFR_SIGN (b), MPFR_SIGN (c));
+
+ ax = MPFR_GET_EXP (b) + MPFR_GET_EXP (c);
+ /* Note: the exponent of the exact result will be e = bx + cx + ec with
+ ec in {-1,0,1} and the following assumes that e is representable. */
+
+ /* FIXME: Useful since we do an exponent check after ?
+ * It is useful iff the precision is big, there is an overflow
+ * and we are doing further mults...*/
+#ifdef HUGE
+ if (MPFR_UNLIKELY (ax > __gmpfr_emax + 1))
+ return mpfr_overflow (a, rnd_mode, sign);
+ if (MPFR_UNLIKELY (ax < __gmpfr_emin - 2))
+ return mpfr_underflow (a, rnd_mode == GMP_RNDN ? GMP_RNDZ : rnd_mode,
+ sign);
+#endif
+
+ bq = MPFR_PREC (b);
+ cq = MPFR_PREC (c);
+
+ MPFR_ASSERTD (bq+cq > bq); /* PREC_MAX is /2 so no integer overflow */
+
+ bn = (bq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of b */
+ cn = (cq+BITS_PER_MP_LIMB-1)/BITS_PER_MP_LIMB; /* number of limbs of c */
+ k = bn + cn; /* effective nb of limbs used by b*c (= tn or tn+1) below */
+ tn = (bq + cq + BITS_PER_MP_LIMB - 1) / BITS_PER_MP_LIMB;
+ MPFR_ASSERTD (tn <= k); /* tn <= k, thus no int overflow */
+
+ /* Check for no size_t overflow*/
+ MPFR_ASSERTD ((size_t) k <= ((size_t) -1) / BYTES_PER_MP_LIMB);
+ MPFR_TMP_MARK (marker);
+ tmp = (mp_limb_t *) MPFR_TMP_ALLOC ((size_t) k * BYTES_PER_MP_LIMB);
+
+ /* multiplies two mantissa in temporary allocated space */
+ if (MPFR_UNLIKELY (bn < cn))
+ {
+ mpfr_srcptr z = b;
+ mp_size_t zn = bn;
+ b = c;
+ bn = cn;
+ c = z;
+ cn = zn;
+ }
+ MPFR_ASSERTD (bn >= cn);
+ if (MPFR_LIKELY (bn <= 2))
+ {
+ if (bn == 1)
+ {
+ /* 1 limb * 1 limb */
+ umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
+ b1 = tmp[1];
+ }
+ else if (MPFR_UNLIKELY (cn == 1))
+ {
+ /* 2 limbs * 1 limb */
+ mp_limb_t t;
+ umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
+ umul_ppmm (tmp[2], t, MPFR_MANT (b)[1], MPFR_MANT (c)[0]);
+ add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t);
+ b1 = tmp[2];
+ }
+ else
+ {
+ /* 2 limbs * 2 limbs */
+ mp_limb_t t1, t2, t3;
+ /* First 2 limbs * 1 limb */
+ umul_ppmm (tmp[1], tmp[0], MPFR_MANT (b)[0], MPFR_MANT (c)[0]);
+ umul_ppmm (tmp[2], t1, MPFR_MANT (b)[1], MPFR_MANT (c)[0]);
+ add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], 0, t1);
+ /* Second, the other 2 limbs * 1 limb product */
+ umul_ppmm (t1, t2, MPFR_MANT (b)[0], MPFR_MANT (c)[1]);
+ umul_ppmm (tmp[3], t3, MPFR_MANT (b)[1], MPFR_MANT (c)[1]);
+ add_ssaaaa (tmp[3], t1, tmp[3], t1, 0, t3);
+ /* Sum those two partial products */
+ add_ssaaaa (tmp[2], tmp[1], tmp[2], tmp[1], t1, t2);
+ tmp[3] += (tmp[2] < t1);
+ b1 = tmp[3];
+ }
+ b1 >>= (BITS_PER_MP_LIMB - 1);
+ tmp += k - tn;
+ if (MPFR_UNLIKELY (b1 == 0))
+ mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
+ }
+ else
+ /* Mulders' mulhigh. Disable if squaring, since it is not tuned for
+ such a case */
+ if (MPFR_UNLIKELY (bn > MPFR_MUL_THRESHOLD && b != c))
+ {
+ mp_limb_t *bp, *cp;
+ mp_size_t n;
+ mp_prec_t p;
+
+ /* Fist check if we can reduce the precision of b or c:
+ exact values are a nightmare for the short product trick */
+ bp = MPFR_MANT (b);
+ cp = MPFR_MANT (c);
+ MPFR_ASSERTN (MPFR_MUL_THRESHOLD >= 1);
+ if (MPFR_UNLIKELY ((bp[0] == 0 && bp[1] == 0) ||
+ (cp[0] == 0 && cp[1] == 0)))
+ {
+ mpfr_t b_tmp, c_tmp;
+
+ MPFR_TMP_FREE (marker);
+ /* Check for b */
+ while (*bp == 0)
+ {
+ bp++;
+ bn--;
+ MPFR_ASSERTD (bn > 0);
+ } /* This must end since the MSL is != 0 */
+
+ /* Check for c too */
+ while (*cp == 0)
+ {
+ cp++;
+ cn--;
+ MPFR_ASSERTD (cn > 0);
+ } /* This must end since the MSL is != 0 */
+
+ /* It is not the faster way, but it is safer */
+ MPFR_SET_SAME_SIGN (b_tmp, b);
+ MPFR_SET_EXP (b_tmp, MPFR_GET_EXP (b));
+ MPFR_PREC (b_tmp) = bn * BITS_PER_MP_LIMB;
+ MPFR_MANT (b_tmp) = bp;
+
+ MPFR_SET_SAME_SIGN (c_tmp, c);
+ MPFR_SET_EXP (c_tmp, MPFR_GET_EXP (c));
+ MPFR_PREC (c_tmp) = cn * BITS_PER_MP_LIMB;
+ MPFR_MANT (c_tmp) = cp;
+
+ /* Call again mpfr_mul with the fixed arguments */
+ return mpfr_mul (a, b_tmp, c_tmp, rnd_mode);
+ }
+
+ /* Compute estimated precision of mulhigh.
+ We could use `+ (n < cn) + (n < bn)' instead of `+ 2',
+ but does it worth it? */
+ n = MPFR_LIMB_SIZE (a) + 1;
+ n = MIN (n, cn);
+ MPFR_ASSERTD (n >= 1 && 2*n <= k && n <= cn && n <= bn);
+ p = n * BITS_PER_MP_LIMB - MPFR_INT_CEIL_LOG2 (n + 2);
+ bp += bn - n;
+ cp += cn - n;
+
+ /* Check if MulHigh can produce a roundable result.
+ We may lost 1 bit due to RNDN, 1 due to final shift. */
+ if (MPFR_UNLIKELY (MPFR_PREC (a) > p - 5))
+ {
+ if (MPFR_UNLIKELY (MPFR_PREC (a) > p - 5 + BITS_PER_MP_LIMB
+ || bn <= MPFR_MUL_THRESHOLD+1))
+ {
+ /* MulHigh can't produce a roundable result. */
+ MPFR_LOG_MSG (("mpfr_mulhigh can't be used (%lu VS %lu)\n",
+ MPFR_PREC (a), p));
+ goto full_multiply;
+ }
+ /* Add one extra limb to mantissa of b and c. */
+ if (bn > n)
+ bp --;
+ else
+ {
+ bp = (mp_limb_t*) MPFR_TMP_ALLOC ((n+1) * sizeof (mp_limb_t));
+ bp[0] = 0;
+ MPN_COPY (bp + 1, MPFR_MANT (b) + bn - n, n);
+ }
+ if (cn > n)
+ cp --; /* FIXME: Could this happen? */
+ else
+ {
+ cp = (mp_limb_t*) MPFR_TMP_ALLOC ((n+1) * sizeof (mp_limb_t));
+ cp[0] = 0;
+ MPN_COPY (cp + 1, MPFR_MANT (c) + cn - n, n);
+ }
+ /* We will compute with one extra limb */
+ n++;
+ p = n * BITS_PER_MP_LIMB - MPFR_INT_CEIL_LOG2 (n + 2);
+ /* Due to some nasty reasons we can have only 4 bits */
+ MPFR_ASSERTD (MPFR_PREC (a) <= p - 4);
+
+ if (MPFR_LIKELY (k < 2*n))
+ {
+ tmp = (mp_limb_t*) MPFR_TMP_ALLOC (2 * n * sizeof (mp_limb_t));
+ tmp += 2*n-k; /* `tmp' still points to an area of `k' limbs */
+ }
+ }
+ MPFR_LOG_MSG (("Use mpfr_mulhigh (%lu VS %lu)\n", MPFR_PREC (a), p));
+ /* Compute an approximation of the product of b and c */
+ mpfr_mulhigh_n (tmp + k - 2 * n, bp, cp, n);
+ /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
+ with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
+ b1 = tmp[k-1] >> (BITS_PER_MP_LIMB - 1); /* msb from the product */
+
+ /* If the mantissas of b and c are uniformly distributed in (1/2, 1],
+ then their product is in (1/4, 1/2] with probability 2*ln(2)-1
+ ~ 0.386 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
+ if (MPFR_UNLIKELY (b1 == 0))
+ /* Warning: the mpfr_mulhigh_n call above only surely affects
+ tmp[k-n-1..k-1], thus we shift only those limbs */
+ mpn_lshift (tmp + k - n - 1, tmp + k - n - 1, n + 1, 1);
+ tmp += k - tn;
+ MPFR_ASSERTD (MPFR_LIMB_MSB (tmp[tn-1]) != 0);
+
+ if (MPFR_UNLIKELY (!mpfr_round_p (tmp, tn, p+b1-1, MPFR_PREC(a)
+ + (rnd_mode == GMP_RNDN))))
+ {
+ tmp -= k - tn; /* tmp may have changed, FIX IT!!!!! */
+ goto full_multiply;
+ }
+ }
+ else
+ {
+ full_multiply:
+ MPFR_LOG_MSG (("Use mpn_mul\n", 0));
+ b1 = mpn_mul (tmp, MPFR_MANT (b), bn, MPFR_MANT (c), cn);
+
+ /* now tmp[0]..tmp[k-1] contains the product of both mantissa,
+ with tmp[k-1]>=2^(BITS_PER_MP_LIMB-2) */
+ b1 >>= BITS_PER_MP_LIMB - 1; /* msb from the product */
+
+ /* if the mantissas of b and c are uniformly distributed in (1/2, 1],
+ then their product is in (1/4, 1/2] with probability 2*ln(2)-1
+ ~ 0.386 and in [1/2, 1] with probability 2-2*ln(2) ~ 0.614 */
+ tmp += k - tn;
+ if (MPFR_UNLIKELY (b1 == 0))
+ mpn_lshift (tmp, tmp, tn, 1); /* tn <= k, so no stack corruption */
+ }
+
+ ax2 = ax + (mp_exp_t) (b1 - 1);
+ MPFR_RNDRAW (inexact, a, tmp, bq+cq, rnd_mode, sign, ax2++);
+ MPFR_TMP_FREE (marker);
+ MPFR_EXP (a) = ax2; /* Can't use MPFR_SET_EXP: Expo may be out of range */
+ MPFR_SET_SIGN (a, sign);
+ if (MPFR_UNLIKELY (ax2 > __gmpfr_emax))
+ return mpfr_overflow (a, rnd_mode, sign);
+ if (MPFR_UNLIKELY (ax2 < __gmpfr_emin))
+ {
+ /* In the rounding to the nearest mode, if the exponent of the exact
+ result (i.e. before rounding, i.e. without taking cc into account)
+ is < __gmpfr_emin - 1 or the exact result is a power of 2 (i.e. if
+ both arguments are powers of 2), then round to zero. */
+ if (rnd_mode == GMP_RNDN
+ && (ax + (mp_exp_t) b1 < __gmpfr_emin
+ || (mpfr_powerof2_raw (b) && mpfr_powerof2_raw (c))))
+ rnd_mode = GMP_RNDZ;
+ return mpfr_underflow (a, rnd_mode, sign);
+ }
+ MPFR_RET (inexact);
+}
projects / msp430-gcc.git / blobdiff