4b6574a6f6
include/math.h has a mechanism to redirect internal calls to various libm functions, that can often be inlined by the compiler, to call non-exported __* names for those functions in the case when the calls aren't inlined, with the redirection being disabled when NO_MATH_REDIRECT. Add fma to the functions to which this mechanism is applied. At present, libm-internal fma calls (generally to __builtin_fma* functions) are only done when it's known the call will be inlined, with alternative code not relying on an fma operation being used in the caller otherwise. This patch is in preparation for adding the TS 18661 / C2X narrowing fma functions to glibc; it will be natural for the narrowing function implementations to call the underlying fma functions unconditionally, with this either being inlined or resulting in an __fma* call. (Using two levels of round-to-odd computation like that, in the case where there isn't an fma hardware instruction, isn't optimal but is certainly a lot simpler for the initial implementation than writing different narrowing fma implementations for all the various pairs of formats.) Tested with build-many-glibcs.py that installed stripped shared libraries are unchanged by the patch (using <https://sourceware.org/pipermail/libc-alpha/2021-September/130991.html> to fix installed library stripping in build-many-glibcs.py). Also tested for x86_64.
298 lines
9.6 KiB
C
298 lines
9.6 KiB
C
/* Compute x * y + z as ternary operation.
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Copyright (C) 2010-2021 Free Software Foundation, Inc.
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This file is part of the GNU C Library.
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The GNU C Library is free software; you can redistribute it and/or
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modify it under the terms of the GNU Lesser General Public
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License as published by the Free Software Foundation; either
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version 2.1 of the License, or (at your option) any later version.
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The GNU C Library is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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Lesser General Public License for more details.
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You should have received a copy of the GNU Lesser General Public
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License along with the GNU C Library; if not, see
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<https://www.gnu.org/licenses/>. */
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#define NO_MATH_REDIRECT
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#include <float.h>
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#include <math.h>
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#include <fenv.h>
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#include <ieee754.h>
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#include <math-barriers.h>
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#include <libm-alias-ldouble.h>
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#include <tininess.h>
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/* This implementation uses rounding to odd to avoid problems with
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double rounding. See a paper by Boldo and Melquiond:
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http://www.lri.fr/~melquion/doc/08-tc.pdf */
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long double
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__fmal (long double x, long double y, long double z)
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{
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union ieee854_long_double u, v, w;
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int adjust = 0;
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u.d = x;
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v.d = y;
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w.d = z;
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if (__builtin_expect (u.ieee.exponent + v.ieee.exponent
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>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS
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- LDBL_MANT_DIG, 0)
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|| __builtin_expect (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
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|| __builtin_expect (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
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|| __builtin_expect (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG, 0)
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|| __builtin_expect (u.ieee.exponent + v.ieee.exponent
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<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG, 0))
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{
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/* If z is Inf, but x and y are finite, the result should be
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z rather than NaN. */
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if (w.ieee.exponent == 0x7fff
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&& u.ieee.exponent != 0x7fff
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&& v.ieee.exponent != 0x7fff)
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return (z + x) + y;
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/* If z is zero and x are y are nonzero, compute the result
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as x * y to avoid the wrong sign of a zero result if x * y
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underflows to 0. */
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if (z == 0 && x != 0 && y != 0)
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return x * y;
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/* If x or y or z is Inf/NaN, or if x * y is zero, compute as
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x * y + z. */
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if (u.ieee.exponent == 0x7fff
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|| v.ieee.exponent == 0x7fff
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|| w.ieee.exponent == 0x7fff
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|| x == 0
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|| y == 0)
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return x * y + z;
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/* If fma will certainly overflow, compute as x * y. */
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if (u.ieee.exponent + v.ieee.exponent
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> 0x7fff + IEEE854_LONG_DOUBLE_BIAS)
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return x * y;
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/* If x * y is less than 1/4 of LDBL_TRUE_MIN, neither the
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result nor whether there is underflow depends on its exact
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value, only on its sign. */
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if (u.ieee.exponent + v.ieee.exponent
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< IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG - 2)
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{
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int neg = u.ieee.negative ^ v.ieee.negative;
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long double tiny = neg ? -0x1p-16445L : 0x1p-16445L;
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if (w.ieee.exponent >= 3)
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return tiny + z;
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/* Scaling up, adding TINY and scaling down produces the
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correct result, because in round-to-nearest mode adding
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TINY has no effect and in other modes double rounding is
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harmless. But it may not produce required underflow
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exceptions. */
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v.d = z * 0x1p65L + tiny;
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if (TININESS_AFTER_ROUNDING
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? v.ieee.exponent < 66
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: (w.ieee.exponent == 0
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|| (w.ieee.exponent == 1
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&& w.ieee.negative != neg
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&& w.ieee.mantissa1 == 0
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&& w.ieee.mantissa0 == 0x80000000)))
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{
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long double force_underflow = x * y;
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math_force_eval (force_underflow);
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}
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return v.d * 0x1p-65L;
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}
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if (u.ieee.exponent + v.ieee.exponent
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>= 0x7fff + IEEE854_LONG_DOUBLE_BIAS - LDBL_MANT_DIG)
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{
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/* Compute 1p-64 times smaller result and multiply
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at the end. */
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if (u.ieee.exponent > v.ieee.exponent)
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u.ieee.exponent -= LDBL_MANT_DIG;
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else
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v.ieee.exponent -= LDBL_MANT_DIG;
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/* If x + y exponent is very large and z exponent is very small,
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it doesn't matter if we don't adjust it. */
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if (w.ieee.exponent > LDBL_MANT_DIG)
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w.ieee.exponent -= LDBL_MANT_DIG;
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adjust = 1;
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}
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else if (w.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
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{
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/* Similarly.
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If z exponent is very large and x and y exponents are
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very small, adjust them up to avoid spurious underflows,
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rather than down. */
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if (u.ieee.exponent + v.ieee.exponent
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<= IEEE854_LONG_DOUBLE_BIAS + 2 * LDBL_MANT_DIG)
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{
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if (u.ieee.exponent > v.ieee.exponent)
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u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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else
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v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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}
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else if (u.ieee.exponent > v.ieee.exponent)
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{
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if (u.ieee.exponent > LDBL_MANT_DIG)
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u.ieee.exponent -= LDBL_MANT_DIG;
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}
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else if (v.ieee.exponent > LDBL_MANT_DIG)
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v.ieee.exponent -= LDBL_MANT_DIG;
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w.ieee.exponent -= LDBL_MANT_DIG;
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adjust = 1;
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}
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else if (u.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
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{
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u.ieee.exponent -= LDBL_MANT_DIG;
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if (v.ieee.exponent)
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v.ieee.exponent += LDBL_MANT_DIG;
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else
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v.d *= 0x1p64L;
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}
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else if (v.ieee.exponent >= 0x7fff - LDBL_MANT_DIG)
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{
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v.ieee.exponent -= LDBL_MANT_DIG;
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if (u.ieee.exponent)
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u.ieee.exponent += LDBL_MANT_DIG;
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else
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u.d *= 0x1p64L;
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}
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else /* if (u.ieee.exponent + v.ieee.exponent
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<= IEEE854_LONG_DOUBLE_BIAS + LDBL_MANT_DIG) */
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{
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if (u.ieee.exponent > v.ieee.exponent)
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u.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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else
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v.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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if (w.ieee.exponent <= 4 * LDBL_MANT_DIG + 6)
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{
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if (w.ieee.exponent)
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w.ieee.exponent += 2 * LDBL_MANT_DIG + 2;
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else
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w.d *= 0x1p130L;
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adjust = -1;
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}
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/* Otherwise x * y should just affect inexact
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and nothing else. */
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}
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x = u.d;
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y = v.d;
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z = w.d;
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}
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/* Ensure correct sign of exact 0 + 0. */
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if (__glibc_unlikely ((x == 0 || y == 0) && z == 0))
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{
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x = math_opt_barrier (x);
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return x * y + z;
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}
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fenv_t env;
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feholdexcept (&env);
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fesetround (FE_TONEAREST);
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/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
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#define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1)
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long double x1 = x * C;
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long double y1 = y * C;
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long double m1 = x * y;
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x1 = (x - x1) + x1;
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y1 = (y - y1) + y1;
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long double x2 = x - x1;
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long double y2 = y - y1;
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long double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
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/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
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long double a1 = z + m1;
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long double t1 = a1 - z;
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long double t2 = a1 - t1;
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t1 = m1 - t1;
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t2 = z - t2;
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long double a2 = t1 + t2;
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/* Ensure the arithmetic is not scheduled after feclearexcept call. */
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math_force_eval (m2);
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math_force_eval (a2);
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feclearexcept (FE_INEXACT);
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/* If the result is an exact zero, ensure it has the correct sign. */
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if (a1 == 0 && m2 == 0)
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{
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feupdateenv (&env);
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/* Ensure that round-to-nearest value of z + m1 is not reused. */
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z = math_opt_barrier (z);
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return z + m1;
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}
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fesetround (FE_TOWARDZERO);
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/* Perform m2 + a2 addition with round to odd. */
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u.d = a2 + m2;
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if (__glibc_likely (adjust == 0))
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{
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if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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feupdateenv (&env);
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/* Result is a1 + u.d. */
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return a1 + u.d;
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}
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else if (__glibc_likely (adjust > 0))
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{
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if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7fff)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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feupdateenv (&env);
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/* Result is a1 + u.d, scaled up. */
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return (a1 + u.d) * 0x1p64L;
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}
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else
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{
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if ((u.ieee.mantissa1 & 1) == 0)
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u.ieee.mantissa1 |= fetestexcept (FE_INEXACT) != 0;
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v.d = a1 + u.d;
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/* Ensure the addition is not scheduled after fetestexcept call. */
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math_force_eval (v.d);
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int j = fetestexcept (FE_INEXACT) != 0;
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feupdateenv (&env);
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/* Ensure the following computations are performed in default rounding
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mode instead of just reusing the round to zero computation. */
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asm volatile ("" : "=m" (u) : "m" (u));
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/* If a1 + u.d is exact, the only rounding happens during
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scaling down. */
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if (j == 0)
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return v.d * 0x1p-130L;
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/* If result rounded to zero is not subnormal, no double
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rounding will occur. */
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if (v.ieee.exponent > 130)
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return (a1 + u.d) * 0x1p-130L;
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/* If v.d * 0x1p-130L with round to zero is a subnormal above
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or equal to LDBL_MIN / 2, then v.d * 0x1p-130L shifts mantissa
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down just by 1 bit, which means v.ieee.mantissa1 |= j would
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change the round bit, not sticky or guard bit.
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v.d * 0x1p-130L never normalizes by shifting up,
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so round bit plus sticky bit should be already enough
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for proper rounding. */
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if (v.ieee.exponent == 130)
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{
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/* If the exponent would be in the normal range when
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rounding to normal precision with unbounded exponent
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range, the exact result is known and spurious underflows
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must be avoided on systems detecting tininess after
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rounding. */
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if (TININESS_AFTER_ROUNDING)
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{
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w.d = a1 + u.d;
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if (w.ieee.exponent == 131)
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return w.d * 0x1p-130L;
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}
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/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
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v.ieee.mantissa1 & 1 is the round bit and j is our sticky
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bit. */
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w.d = 0.0L;
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w.ieee.mantissa1 = ((v.ieee.mantissa1 & 3) << 1) | j;
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w.ieee.negative = v.ieee.negative;
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v.ieee.mantissa1 &= ~3U;
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v.d *= 0x1p-130L;
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w.d *= 0x1p-2L;
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return v.d + w.d;
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}
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v.ieee.mantissa1 |= j;
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return v.d * 0x1p-130L;
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}
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}
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libm_alias_ldouble (__fma, fma)
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