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Diffstat (limited to 'src/fms.c')
| -rw-r--r-- | src/fms.c | 304 |
1 files changed, 304 insertions, 0 deletions
diff --git a/src/fms.c b/src/fms.c new file mode 100644 index 0000000..2c0fd53 --- /dev/null +++ b/src/fms.c @@ -0,0 +1,304 @@ +/* mpfr_fms -- Floating multiply-subtract + +Copyright 2001, 2002, 2004, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013 Free Software Foundation, Inc. +Contributed by the AriC and Caramel 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 3 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.LESSER. If not, see +http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., +51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ + +#include "mpfr-impl.h" + +/* The fused-multiply-subtract (fms) of x, y and z is defined by: + fms(x,y,z)= x*y - z + Note: this is neither in IEEE754R, nor in LIA-2, but both the + PowerPC and the Itanium define fms as x*y - z. +*/ + +int +mpfr_fms (mpfr_ptr s, mpfr_srcptr x, mpfr_srcptr y, mpfr_srcptr z, + mpfr_rnd_t rnd_mode) +{ + int inexact; + mpfr_t u; + MPFR_SAVE_EXPO_DECL (expo); + MPFR_GROUP_DECL(group); + + MPFR_LOG_FUNC + (("x[%Pu]=%.*Rg y[%Pu]=%.*Rg z[%Pu]=%.*Rg rnd=%d", + mpfr_get_prec (x), mpfr_log_prec, x, + mpfr_get_prec (y), mpfr_log_prec, y, + mpfr_get_prec (z), mpfr_log_prec, z, rnd_mode), + ("s[%Pu]=%.*Rg inexact=%d", + mpfr_get_prec (s), mpfr_log_prec, s, inexact)); + + /* particular cases */ + if (MPFR_UNLIKELY( MPFR_IS_SINGULAR(x) || + MPFR_IS_SINGULAR(y) || + MPFR_IS_SINGULAR(z) )) + { + if (MPFR_IS_NAN(x) || MPFR_IS_NAN(y) || MPFR_IS_NAN(z)) + { + MPFR_SET_NAN(s); + MPFR_RET_NAN; + } + /* now neither x, y or z is NaN */ + else if (MPFR_IS_INF(x) || MPFR_IS_INF(y)) + { + /* cases Inf*0-z, 0*Inf-z, Inf-Inf */ + if ((MPFR_IS_ZERO(y)) || + (MPFR_IS_ZERO(x)) || + (MPFR_IS_INF(z) && + ((MPFR_MULT_SIGN(MPFR_SIGN(x), MPFR_SIGN(y))) == MPFR_SIGN(z)))) + { + MPFR_SET_NAN(s); + MPFR_RET_NAN; + } + else if (MPFR_IS_INF(z)) /* case Inf-Inf already checked above */ + { + MPFR_SET_INF(s); + MPFR_SET_OPPOSITE_SIGN(s, z); + MPFR_RET(0); + } + else /* z is finite */ + { + MPFR_SET_INF(s); + MPFR_SET_SIGN(s, MPFR_MULT_SIGN(MPFR_SIGN(x) , MPFR_SIGN(y))); + MPFR_RET(0); + } + } + /* now x and y are finite */ + else if (MPFR_IS_INF(z)) + { + MPFR_SET_INF(s); + MPFR_SET_OPPOSITE_SIGN(s, z); + MPFR_RET(0); + } + else if (MPFR_IS_ZERO(x) || MPFR_IS_ZERO(y)) + { + if (MPFR_IS_ZERO(z)) + { + int sign_p; + sign_p = MPFR_MULT_SIGN( MPFR_SIGN(x) , MPFR_SIGN(y) ); + MPFR_SET_SIGN(s,(rnd_mode != MPFR_RNDD ? + ((MPFR_IS_NEG_SIGN(sign_p) && MPFR_IS_POS(z)) + ? -1 : 1) : + ((MPFR_IS_POS_SIGN(sign_p) && MPFR_IS_NEG(z)) + ? 1 : -1))); + MPFR_SET_ZERO(s); + MPFR_RET(0); + } + else + return mpfr_neg (s, z, rnd_mode); + } + else /* necessarily z is zero here */ + { + MPFR_ASSERTD(MPFR_IS_ZERO(z)); + return mpfr_mul (s, x, y, rnd_mode); + } + } + + /* If we take prec(u) >= prec(x) + prec(y), the product u <- x*y + is exact, except in case of overflow or underflow. */ + MPFR_SAVE_EXPO_MARK (expo); + MPFR_GROUP_INIT_1 (group, MPFR_PREC(x) + MPFR_PREC(y), u); + + if (MPFR_UNLIKELY (mpfr_mul (u, x, y, MPFR_RNDN))) + { + /* overflow or underflow - this case is regarded as rare, thus + does not need to be very efficient (even if some tests below + could have been done earlier). + It is an overflow iff u is an infinity (since MPFR_RNDN was used). + Alternatively, we could test the overflow flag, but in this case, + mpfr_clear_flags would have been necessary. */ + if (MPFR_IS_INF (u)) /* overflow */ + { + /* Let's eliminate the obvious case where x*y and z have the + same sign. No possible cancellation -> real overflow. + Also, we know that |z| < 2^emax. If E(x) + E(y) >= emax+3, + then |x*y| >= 2^(emax+1), and |x*y - z| >= 2^emax. This case + is also an overflow. */ + if (MPFR_SIGN (u) != MPFR_SIGN (z) || + MPFR_GET_EXP (x) + MPFR_GET_EXP (y) >= __gmpfr_emax + 3) + { + MPFR_GROUP_CLEAR (group); + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_overflow (s, rnd_mode, - MPFR_SIGN (z)); + } + + /* E(x) + E(y) <= emax+2, therefore |x*y| < 2^(emax+2), and + (x/4)*y does not overflow (let's recall that the result + is exact with an unbounded exponent range). It does not + underflow either, because x*y overflows and the exponent + range is large enough. */ + inexact = mpfr_div_2ui (u, x, 2, MPFR_RNDN); + MPFR_ASSERTN (inexact == 0); + inexact = mpfr_mul (u, u, y, MPFR_RNDN); + MPFR_ASSERTN (inexact == 0); + + /* Now, we need to subtract z/4... But it may underflow! */ + { + mpfr_t zo4; + mpfr_srcptr zz; + MPFR_BLOCK_DECL (flags); + + if (MPFR_GET_EXP (u) > MPFR_GET_EXP (z) && + MPFR_GET_EXP (u) - MPFR_GET_EXP (z) > MPFR_PREC (u)) + { + /* |z| < ulp(u)/2, therefore one can use z instead of z/4. */ + zz = z; + } + else + { + mpfr_init2 (zo4, MPFR_PREC (z)); + if (mpfr_div_2ui (zo4, z, 2, MPFR_RNDZ)) + { + /* The division by 4 underflowed! */ + MPFR_ASSERTN (0); /* TODO... */ + } + zz = zo4; + } + + /* Let's recall that u = x*y/4 and zz = z/4 (or z if the + following subtraction would give the same result). */ + MPFR_BLOCK (flags, inexact = mpfr_sub (s, u, zz, rnd_mode)); + /* u and zz have the same sign, so that an overflow + is not possible. But an underflow is theoretically + possible! */ + if (MPFR_UNDERFLOW (flags)) + { + MPFR_ASSERTN (zz != z); + MPFR_ASSERTN (0); /* TODO... */ + mpfr_clears (zo4, u, (mpfr_ptr) 0); + } + else + { + int inex2; + + if (zz != z) + mpfr_clear (zo4); + MPFR_GROUP_CLEAR (group); + MPFR_ASSERTN (! MPFR_OVERFLOW (flags)); + inex2 = mpfr_mul_2ui (s, s, 2, rnd_mode); + if (inex2) /* overflow */ + { + inexact = inex2; + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); + } + goto end; + } + } + } + else /* underflow: one has |xy| < 2^(emin-1). */ + { + unsigned long scale = 0; + mpfr_t scaled_z; + mpfr_srcptr new_z; + mpfr_exp_t diffexp; + mpfr_prec_t pzs; + int xy_underflows; + + /* Let's scale z so that ulp(z) > 2^emin and ulp(s) > 2^emin + (the + 1 on MPFR_PREC (s) is necessary because the exponent + of the result can be EXP(z) - 1). */ + diffexp = MPFR_GET_EXP (z) - __gmpfr_emin; + pzs = MAX (MPFR_PREC (z), MPFR_PREC (s) + 1); + if (diffexp <= pzs) + { + mpfr_uexp_t uscale; + mpfr_t scaled_v; + MPFR_BLOCK_DECL (flags); + + uscale = (mpfr_uexp_t) pzs - diffexp + 1; + MPFR_ASSERTN (uscale > 0); + MPFR_ASSERTN (uscale <= ULONG_MAX); + scale = uscale; + mpfr_init2 (scaled_z, MPFR_PREC (z)); + inexact = mpfr_mul_2ui (scaled_z, z, scale, MPFR_RNDN); + MPFR_ASSERTN (inexact == 0); /* TODO: overflow case */ + new_z = scaled_z; + /* Now we need to recompute u = xy * 2^scale. */ + MPFR_BLOCK (flags, + if (MPFR_GET_EXP (x) < MPFR_GET_EXP (y)) + { + mpfr_init2 (scaled_v, MPFR_PREC (x)); + mpfr_mul_2ui (scaled_v, x, scale, MPFR_RNDN); + mpfr_mul (u, scaled_v, y, MPFR_RNDN); + } + else + { + mpfr_init2 (scaled_v, MPFR_PREC (y)); + mpfr_mul_2ui (scaled_v, y, scale, MPFR_RNDN); + mpfr_mul (u, x, scaled_v, MPFR_RNDN); + }); + mpfr_clear (scaled_v); + MPFR_ASSERTN (! MPFR_OVERFLOW (flags)); + xy_underflows = MPFR_UNDERFLOW (flags); + } + else + { + new_z = z; + xy_underflows = 1; + } + + if (xy_underflows) + { + /* Let's replace xy by sign(xy) * 2^(emin-1). */ + MPFR_PREC (u) = MPFR_PREC_MIN; + mpfr_setmin (u, __gmpfr_emin); + MPFR_SET_SIGN (u, MPFR_MULT_SIGN (MPFR_SIGN (x), + MPFR_SIGN (y))); + } + + { + MPFR_BLOCK_DECL (flags); + + MPFR_BLOCK (flags, inexact = mpfr_sub (s, u, new_z, rnd_mode)); + MPFR_GROUP_CLEAR (group); + if (scale != 0) + { + int inex2; + + mpfr_clear (scaled_z); + /* Here an overflow is theoretically possible, in which case + the result may be wrong, hence the assert. An underflow + is not possible, but let's check that anyway. */ + MPFR_ASSERTN (! MPFR_OVERFLOW (flags)); /* TODO... */ + MPFR_ASSERTN (! MPFR_UNDERFLOW (flags)); /* not possible */ + inex2 = mpfr_div_2ui (s, s, scale, MPFR_RNDN); + /* FIXME: this seems incorrect. MPFR_RNDN -> rnd_mode? + Also, handle the double rounding case: + s / 2^scale = 2^(emin - 2) in MPFR_RNDN. */ + if (inex2) /* underflow */ + inexact = inex2; + } + } + + /* FIXME/TODO: I'm not sure that the following is correct. + Check for possible spurious exceptions due to intermediate + computations. */ + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); + goto end; + } + } + + inexact = mpfr_sub (s, u, z, rnd_mode); + MPFR_GROUP_CLEAR (group); + MPFR_SAVE_EXPO_UPDATE_FLAGS (expo, __gmpfr_flags); + end: + MPFR_SAVE_EXPO_FREE (expo); + return mpfr_check_range (s, inexact, rnd_mode); +} |