X-Git-Url: https://oss.titaniummirror.com/gitweb?a=blobdiff_plain;f=mpfr%2Fsub1.c;fp=mpfr%2Fsub1.c;h=68b5e014a74cce40bab52e90a3ac69e6c6ed5026;hb=6fed43773c9b0ce596dca5686f37ac3fc0fa11c0;hp=0000000000000000000000000000000000000000;hpb=27b11d56b743098deb193d510b337ba22dc52e5c;p=msp430-gcc.git diff --git a/mpfr/sub1.c b/mpfr/sub1.c new file mode 100644 index 00000000..68b5e014 --- /dev/null +++ b/mpfr/sub1.c @@ -0,0 +1,538 @@ +/* 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)); +}