--- /dev/null
+/* mpfr_sub1 -- internal function to perform a "real" subtraction
+
+Copyright 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. */
+
+#include "mpfr-impl.h"
+
+/* compute sign(b) * (|b| - |c|), with |b| > |c|, diff_exp = EXP(b) - EXP(c)
+ Returns 0 iff result is exact,
+ a negative value when the result is less than the exact value,
+ a positive value otherwise.
+*/
+
+int
+mpfr_sub1 (mpfr_ptr a, mpfr_srcptr b, mpfr_srcptr c, mp_rnd_t rnd_mode)
+{
+ int sign;
+ mp_exp_unsigned_t diff_exp;
+ mp_prec_t cancel, cancel1;
+ mp_size_t cancel2, an, bn, cn, cn0;
+ mp_limb_t *ap, *bp, *cp;
+ mp_limb_t carry, bb, cc, borrow = 0;
+ int inexact, shift_b, shift_c, is_exact = 1, down = 0, add_exp = 0;
+ int sh, k;
+ MPFR_TMP_DECL(marker);
+
+ MPFR_TMP_MARK(marker);
+ ap = MPFR_MANT(a);
+ an = MPFR_LIMB_SIZE(a);
+
+ sign = mpfr_cmp2 (b, c, &cancel);
+ if (MPFR_UNLIKELY(sign == 0))
+ {
+ if (rnd_mode == GMP_RNDD)
+ MPFR_SET_NEG (a);
+ else
+ MPFR_SET_POS (a);
+ MPFR_SET_ZERO (a);
+ MPFR_RET (0);
+ }
+
+ /*
+ * If subtraction: sign(a) = sign * sign(b)
+ * If addition: sign(a) = sign of the larger argument in absolute value.
+ *
+ * Both cases can be simplidied in:
+ * if (sign>0)
+ * if addition: sign(a) = sign * sign(b) = sign(b)
+ * if subtraction, b is greater, so sign(a) = sign(b)
+ * else
+ * if subtraction, sign(a) = - sign(b)
+ * if addition, sign(a) = sign(c) (since c is greater)
+ * But if it is an addition, sign(b) and sign(c) are opposed!
+ * So sign(a) = - sign(b)
+ */
+
+ if (sign < 0) /* swap b and c so that |b| > |c| */
+ {
+ mpfr_srcptr t;
+ MPFR_SET_OPPOSITE_SIGN (a,b);
+ t = b; b = c; c = t;
+ }
+ else
+ MPFR_SET_SAME_SIGN (a,b);
+
+ /* Check if c is too small.
+ A more precise test is to replace 2 by
+ (rnd == GMP_RNDN) + mpfr_power2_raw (b)
+ but it is more expensive and not very useful */
+ if (MPFR_UNLIKELY (MPFR_GET_EXP (c) <= MPFR_GET_EXP (b)
+ - (mp_exp_t) MAX (MPFR_PREC (a), MPFR_PREC (b)) - 2))
+ {
+ /* Remember, we can't have an exact result! */
+ /* A.AAAAAAAAAAAAAAAAA
+ = B.BBBBBBBBBBBBBBB
+ - C.CCCCCCCCCCCCC */
+ /* A = S*ABS(B) +/- ulp(a) */
+ MPFR_SET_EXP (a, MPFR_GET_EXP (b));
+ MPFR_RNDRAW_EVEN (inexact, a, MPFR_MANT (b), MPFR_PREC (b),
+ rnd_mode, MPFR_SIGN (a),
+ if (MPFR_UNLIKELY ( ++MPFR_EXP (a) > __gmpfr_emax))
+ inexact = mpfr_overflow (a, rnd_mode, MPFR_SIGN (a)));
+ /* inexact = mpfr_set4 (a, b, rnd_mode, MPFR_SIGN (a)); */
+ if (inexact == 0)
+ {
+ /* a = b (Exact)
+ But we know it isn't (Since we have to remove `c')
+ So if we round to Zero, we have to remove one ulp.
+ Otherwise the result is correctly rounded. */
+ if (MPFR_IS_LIKE_RNDZ (rnd_mode, MPFR_IS_NEG (a)))
+ {
+ mpfr_nexttozero (a);
+ MPFR_RET (- MPFR_INT_SIGN (a));
+ }
+ MPFR_RET (MPFR_INT_SIGN (a));
+ }
+ else
+ {
+ /* A.AAAAAAAAAAAAAA
+ = B.BBBBBBBBBBBBBBB
+ - C.CCCCCCCCCCCCC */
+ /* It isn't exact so Prec(b) > Prec(a) and the last
+ Prec(b)-Prec(a) bits of `b' are not zeros.
+ Which means that removing c from b can't generate a carry
+ execpt in case of even rounding.
+ In all other case the result and the inexact flag should be
+ correct (We can't have an exact result).
+ In case of EVEN rounding:
+ 1.BBBBBBBBBBBBBx10
+ - 1.CCCCCCCCCCCC
+ = 1.BBBBBBBBBBBBBx01 Rounded to Prec(b)
+ = 1.BBBBBBBBBBBBBx Nearest / Rounded to Prec(a)
+ Set gives:
+ 1.BBBBBBBBBBBBB0 if inexact == EVEN_INEX (x == 0)
+ 1.BBBBBBBBBBBBB1+1 if inexact == -EVEN_INEX (x == 1)
+ which means we get a wrong rounded result if x==1,
+ i.e. inexact= MPFR_EVEN_INEX */
+ if (MPFR_UNLIKELY (inexact == MPFR_EVEN_INEX*MPFR_INT_SIGN (a)))
+ {
+ mpfr_nexttozero (a);
+ inexact = -MPFR_INT_SIGN (a);
+ }
+ MPFR_RET (inexact);
+ }
+ }
+
+ diff_exp = (mp_exp_unsigned_t) MPFR_GET_EXP (b) - MPFR_GET_EXP (c);
+
+ /* reserve a space to store b aligned with the result, i.e. shifted by
+ (-cancel) % BITS_PER_MP_LIMB to the right */
+ bn = MPFR_LIMB_SIZE (b);
+ MPFR_UNSIGNED_MINUS_MODULO (shift_b, cancel);
+ cancel1 = (cancel + shift_b) / BITS_PER_MP_LIMB;
+
+ /* the high cancel1 limbs from b should not be taken into account */
+ if (MPFR_UNLIKELY (shift_b == 0))
+ {
+ bp = MPFR_MANT(b); /* no need of an extra space */
+ /* Ensure ap != bp */
+ if (MPFR_UNLIKELY (ap == bp))
+ {
+ bp = (mp_ptr) MPFR_TMP_ALLOC(bn * BYTES_PER_MP_LIMB);
+ MPN_COPY (bp, ap, bn);
+ }
+ }
+ else
+ {
+ bp = (mp_ptr) MPFR_TMP_ALLOC ((bn + 1) * BYTES_PER_MP_LIMB);
+ bp[0] = mpn_rshift (bp + 1, MPFR_MANT(b), bn++, shift_b);
+ }
+
+ /* reserve a space to store c aligned with the result, i.e. shifted by
+ (diff_exp-cancel) % BITS_PER_MP_LIMB to the right */
+ cn = MPFR_LIMB_SIZE(c);
+ if ((UINT_MAX % BITS_PER_MP_LIMB) == (BITS_PER_MP_LIMB-1)
+ && ((-(unsigned) 1)%BITS_PER_MP_LIMB > 0))
+ shift_c = (diff_exp - cancel) % BITS_PER_MP_LIMB;
+ else
+ {
+ shift_c = diff_exp - (cancel % BITS_PER_MP_LIMB);
+ shift_c = (shift_c + BITS_PER_MP_LIMB) % BITS_PER_MP_LIMB;
+ }
+ MPFR_ASSERTD( shift_c >= 0 && shift_c < BITS_PER_MP_LIMB);
+
+ if (MPFR_UNLIKELY(shift_c == 0))
+ {
+ cp = MPFR_MANT(c);
+ /* Ensure ap != cp */
+ if (ap == cp)
+ {
+ cp = (mp_ptr) MPFR_TMP_ALLOC (cn * BYTES_PER_MP_LIMB);
+ MPN_COPY(cp, ap, cn);
+ }
+ }
+ else
+ {
+ cp = (mp_ptr) MPFR_TMP_ALLOC ((cn + 1) * BYTES_PER_MP_LIMB);
+ cp[0] = mpn_rshift (cp + 1, MPFR_MANT(c), cn++, shift_c);
+ }
+
+#ifdef DEBUG
+ printf ("shift_b=%d shift_c=%d diffexp=%lu\n", shift_b, shift_c,
+ (unsigned long) diff_exp);
+#endif
+
+ MPFR_ASSERTD (ap != cp);
+ MPFR_ASSERTD (bp != cp);
+
+ /* here we have shift_c = (diff_exp - cancel) % BITS_PER_MP_LIMB,
+ 0 <= shift_c < BITS_PER_MP_LIMB
+ thus we want cancel2 = ceil((cancel - diff_exp) / BITS_PER_MP_LIMB) */
+
+ cancel2 = (long int) (cancel - (diff_exp - shift_c)) / BITS_PER_MP_LIMB;
+ /* the high cancel2 limbs from b should not be taken into account */
+#ifdef DEBUG
+ printf ("cancel=%lu cancel1=%lu cancel2=%ld\n",
+ (unsigned long) cancel, (unsigned long) cancel1, (long) cancel2);
+#endif
+
+ /* ap[an-1] ap[0]
+ <----------------+-----------|---->
+ <----------PREC(a)----------><-sh->
+ cancel1
+ limbs bp[bn-cancel1-1]
+ <--...-----><----------------+-----------+----------->
+ cancel2
+ limbs cp[cn-cancel2-1] cancel2 >= 0
+ <--...--><----------------+----------------+---------------->
+ (-cancel2) cancel2 < 0
+ limbs <----------------+---------------->
+ */
+
+ /* first part: put in ap[0..an-1] the value of high(b) - high(c),
+ where high(b) consists of the high an+cancel1 limbs of b,
+ and high(c) consists of the high an+cancel2 limbs of c.
+ */
+
+ /* copy high(b) into a */
+ if (MPFR_LIKELY(an + (mp_size_t) cancel1 <= bn))
+ /* a: <----------------+-----------|---->
+ b: <-----------------------------------------> */
+ MPN_COPY (ap, bp + bn - (an + cancel1), an);
+ else
+ /* a: <----------------+-----------|---->
+ b: <-------------------------> */
+ if ((mp_size_t) cancel1 < bn) /* otherwise b does not overlap with a */
+ {
+ MPN_ZERO (ap, an + cancel1 - bn);
+ MPN_COPY (ap + an + cancel1 - bn, bp, bn - cancel1);
+ }
+ else
+ MPN_ZERO (ap, an);
+
+#ifdef DEBUG
+ printf("after copying high(b), a="); mpfr_print_binary(a); putchar('\n');
+#endif
+
+ /* subtract high(c) */
+ if (MPFR_LIKELY(an + cancel2 > 0)) /* otherwise c does not overlap with a */
+ {
+ mp_limb_t *ap2;
+
+ if (cancel2 >= 0)
+ {
+ if (an + cancel2 <= cn)
+ /* a: <----------------------------->
+ c: <-----------------------------------------> */
+ mpn_sub_n (ap, ap, cp + cn - (an + cancel2), an);
+ else
+ /* a: <---------------------------->
+ c: <-------------------------> */
+ {
+ ap2 = ap + an + cancel2 - cn;
+ if (cn > cancel2)
+ mpn_sub_n (ap2, ap2, cp, cn - cancel2);
+ }
+ }
+ else /* cancel2 < 0 */
+ {
+ if (an + cancel2 <= cn)
+ /* a: <----------------------------->
+ c: <-----------------------------> */
+ borrow = mpn_sub_n (ap, ap, cp + cn - (an + cancel2),
+ an + cancel2);
+ else
+ /* a: <---------------------------->
+ c: <----------------> */
+ {
+ ap2 = ap + an + cancel2 - cn;
+ borrow = mpn_sub_n (ap2, ap2, cp, cn);
+ }
+ ap2 = ap + an + cancel2;
+ mpn_sub_1 (ap2, ap2, -cancel2, borrow);
+ }
+ }
+
+#ifdef DEBUG
+ printf("after subtracting high(c), a=");
+ mpfr_print_binary(a);
+ putchar('\n');
+#endif
+
+ /* now perform rounding */
+ sh = (mp_prec_t) an * BITS_PER_MP_LIMB - MPFR_PREC(a);
+ /* last unused bits from a */
+ carry = ap[0] & MPFR_LIMB_MASK (sh);
+ ap[0] -= carry;
+
+ if (MPFR_LIKELY(rnd_mode == GMP_RNDN))
+ {
+ if (MPFR_LIKELY(sh))
+ {
+ is_exact = (carry == 0);
+ /* can decide except when carry = 2^(sh-1) [middle]
+ or carry = 0 [truncate, but cannot decide inexact flag] */
+ down = (carry < (MPFR_LIMB_ONE << (sh - 1)));
+ if (carry > (MPFR_LIMB_ONE << (sh - 1)))
+ goto add_one_ulp;
+ else if ((0 < carry) && down)
+ {
+ inexact = -1; /* result if smaller than exact value */
+ goto truncate;
+ }
+ }
+ }
+ else /* directed rounding: set rnd_mode to RNDZ iff towards zero */
+ {
+ if (MPFR_IS_RNDUTEST_OR_RNDDNOTTEST(rnd_mode, MPFR_IS_NEG(a)))
+ rnd_mode = GMP_RNDZ;
+
+ if (carry)
+ {
+ if (rnd_mode == GMP_RNDZ)
+ {
+ inexact = -1;
+ goto truncate;
+ }
+ else /* round away */
+ goto add_one_ulp;
+ }
+ }
+
+ /* we have to consider the low (bn - (an+cancel1)) limbs from b,
+ and the (cn - (an+cancel2)) limbs from c. */
+ bn -= an + cancel1;
+ cn0 = cn;
+ cn -= (long int) an + cancel2;
+
+#ifdef DEBUG
+ printf ("last %d bits from a are %lu, bn=%ld, cn=%ld\n",
+ sh, (unsigned long) carry, (long) bn, (long) cn);
+#endif
+
+ for (k = 0; (bn > 0) || (cn > 0); k = 1)
+ {
+ /* get next limbs */
+ bb = (bn > 0) ? bp[--bn] : 0;
+ if ((cn > 0) && (cn-- <= cn0))
+ cc = cp[cn];
+ else
+ cc = 0;
+
+ /* down is set when low(b) < low(c) */
+ if (down == 0)
+ down = (bb < cc);
+
+ /* the case rounding to nearest with sh=0 is special since one couldn't
+ subtract above 1/2 ulp in the trailing limb of the result */
+ if ((rnd_mode == GMP_RNDN) && sh == 0 && k == 0)
+ {
+ mp_limb_t half = MPFR_LIMB_HIGHBIT;
+
+ is_exact = (bb == cc);
+
+ /* add one ulp if bb > cc + half
+ truncate if cc - half < bb < cc + half
+ sub one ulp if bb < cc - half
+ */
+
+ if (down)
+ {
+ if (cc >= half)
+ cc -= half;
+ else
+ bb += half;
+ }
+ else /* bb >= cc */
+ {
+ if (cc < half)
+ cc += half;
+ else
+ bb -= half;
+ }
+ }
+
+#ifdef DEBUG
+ printf (" bb=%lu cc=%lu down=%d is_exact=%d\n",
+ (unsigned long) bb, (unsigned long) cc, down, is_exact);
+#endif
+ if (bb < cc)
+ {
+ if (rnd_mode == GMP_RNDZ)
+ goto sub_one_ulp;
+ else if (rnd_mode != GMP_RNDN) /* round away */
+ {
+ inexact = 1;
+ goto truncate;
+ }
+ else /* round to nearest: special case here since for sh=k=0
+ bb = bb0 - MPFR_LIMB_HIGHBIT */
+ {
+ if (is_exact && sh == 0)
+ {
+ /* For k=0 we can't decide exactness since it may depend
+ from low order bits.
+ For k=1, the first low limbs matched: low(b)-low(c)<0. */
+ if (k)
+ {
+ inexact = 1;
+ goto truncate;
+ }
+ }
+ else if (down && sh == 0)
+ goto sub_one_ulp;
+ else
+ {
+ inexact = (is_exact) ? 1 : -1;
+ goto truncate;
+ }
+ }
+ }
+ else if (bb > cc)
+ {
+ if (rnd_mode == GMP_RNDZ)
+ {
+ inexact = -1;
+ goto truncate;
+ }
+ else if (rnd_mode != GMP_RNDN) /* round away */
+ goto add_one_ulp;
+ else /* round to nearest */
+ {
+ if (is_exact)
+ {
+ inexact = -1;
+ goto truncate;
+ }
+ else if (down)
+ {
+ inexact = 1;
+ goto truncate;
+ }
+ else
+ goto add_one_ulp;
+ }
+ }
+ }
+
+ if ((rnd_mode == GMP_RNDN) && !is_exact)
+ {
+ /* even rounding rule */
+ if ((ap[0] >> sh) & 1)
+ {
+ if (down)
+ goto sub_one_ulp;
+ else
+ goto add_one_ulp;
+ }
+ else
+ inexact = (down) ? 1 : -1;
+ }
+ else
+ inexact = 0;
+ goto truncate;
+
+ sub_one_ulp: /* sub one unit in last place to a */
+ mpn_sub_1 (ap, ap, an, MPFR_LIMB_ONE << sh);
+ inexact = -1;
+ goto end_of_sub;
+
+ add_one_ulp: /* add one unit in last place to a */
+ if (MPFR_UNLIKELY(mpn_add_1 (ap, ap, an, MPFR_LIMB_ONE << sh)))
+ /* result is a power of 2: 11111111111111 + 1 = 1000000000000000 */
+ {
+ ap[an-1] = MPFR_LIMB_HIGHBIT;
+ add_exp = 1;
+ }
+ inexact = 1; /* result larger than exact value */
+
+ truncate:
+ if (MPFR_UNLIKELY((ap[an-1] >> (BITS_PER_MP_LIMB - 1)) == 0))
+ /* case 1 - epsilon */
+ {
+ ap[an-1] = MPFR_LIMB_HIGHBIT;
+ add_exp = 1;
+ }
+
+ end_of_sub:
+ /* we have to set MPFR_EXP(a) to MPFR_EXP(b) - cancel + add_exp, taking
+ care of underflows/overflows in that computation, and of the allowed
+ exponent range */
+ if (MPFR_LIKELY(cancel))
+ {
+ mp_exp_t exp_a;
+
+ cancel -= add_exp; /* still valid as unsigned long */
+ exp_a = MPFR_GET_EXP (b) - cancel;
+ if (MPFR_UNLIKELY(exp_a < __gmpfr_emin))
+ {
+ MPFR_TMP_FREE(marker);
+ if (rnd_mode == GMP_RNDN &&
+ (exp_a < __gmpfr_emin - 1 ||
+ (inexact >= 0 && mpfr_powerof2_raw (a))))
+ rnd_mode = GMP_RNDZ;
+ return mpfr_underflow (a, rnd_mode, MPFR_SIGN(a));
+ }
+ MPFR_SET_EXP (a, exp_a);
+ }
+ else /* cancel = 0: MPFR_EXP(a) <- MPFR_EXP(b) + add_exp */
+ {
+ /* in case cancel = 0, add_exp can still be 1, in case b is just
+ below a power of two, c is very small, prec(a) < prec(b),
+ and rnd=away or nearest */
+ mp_exp_t exp_b;
+
+ exp_b = MPFR_GET_EXP (b);
+ if (MPFR_UNLIKELY(add_exp && exp_b == __gmpfr_emax))
+ {
+ MPFR_TMP_FREE(marker);
+ return mpfr_overflow (a, rnd_mode, MPFR_SIGN(a));
+ }
+ MPFR_SET_EXP (a, exp_b + add_exp);
+ }
+ MPFR_TMP_FREE(marker);
+#ifdef DEBUG
+ printf ("result is a="); mpfr_print_binary(a); putchar('\n');
+#endif
+ /* check that result is msb-normalized */
+ MPFR_ASSERTD(ap[an-1] > ~ap[an-1]);
+ MPFR_RET (inexact * MPFR_INT_SIGN (a));
+}
projects / msp430-gcc.git / blobdiff