/*---------------------------------------------------------------*/
/*--- begin host_generic_maddf.c ---*/
/*---------------------------------------------------------------*/
/*
Compute x * y + z as ternary operation.
Copyright (C) 2010-2017 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Jakub Jelinek <jakub@redhat.com>, 2010.
The GNU C 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 C 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 C Library; if not, see
<http://www.gnu.org/licenses/>.
*/
/* Generic helper functions for doing FMA, i.e. compute x * y + z
as ternary operation.
These are purely back-end entities and cannot be seen/referenced
from IR. */
#include "libvex_basictypes.h"
#include "host_generic_maddf.h"
#include "main_util.h"
/* This implementation relies on Double being more than twice as
precise as Float and uses rounding to odd in order to avoid problems
with double rounding.
See a paper by Boldo and Melquiond:
http://www.lri.fr/~melquion/doc/08-tc.pdf */
#define FORCE_EVAL(X) __asm __volatile__ ("" : : "m" (X))
#if defined(__x86_64__) && defined(__SSE2_MATH__)
# define ENV_TYPE unsigned int
/* Save current rounding mode into ENV, hold exceptions, set rounding
mode to rounding toward zero. */
# define ROUNDTOZERO(env) \
do { \
unsigned int mxcsr; \
__asm __volatile__ ("stmxcsr %0" : "=m" (mxcsr)); \
(env) = mxcsr; \
mxcsr = (mxcsr | 0x7f80) & ~0x3f; \
__asm __volatile__ ("ldmxcsr %0" : : "m" (mxcsr));\
} while (0)
/* Restore exceptions from ENV, return if inexact exception has been raised
since ROUNDTOZERO. */
# define RESET_TESTINEXACT(env) \
({ \
unsigned int mxcsr, ret; \
__asm __volatile__ ("stmxcsr %0" : "=m" (mxcsr)); \
ret = (mxcsr >> 5) & 1; \
mxcsr = (mxcsr & 0x3d) | (env); \
__asm __volatile__ ("ldmxcsr %0" : : "m" (mxcsr));\
ret; \
})
/* Return if inexact exception has been raised since ROUNDTOZERO. */
# define TESTINEXACT() \
({ \
unsigned int mxcsr; \
__asm __volatile__ ("stmxcsr %0" : "=m" (mxcsr)); \
(mxcsr >> 5) & 1; \
})
#endif
#define DBL_MANT_DIG 53
#define IEEE754_DOUBLE_BIAS 0x3ff
union vg_ieee754_double {
Double d;
/* This is the IEEE 754 double-precision format. */
struct {
#ifdef VKI_BIG_ENDIAN
unsigned int negative:1;
unsigned int exponent:11;
unsigned int mantissa0:20;
unsigned int mantissa1:32;
#else
unsigned int mantissa1:32;
unsigned int mantissa0:20;
unsigned int exponent:11;
unsigned int negative:1;
#endif
} ieee;
};
void VEX_REGPARM(3)
h_generic_calc_MAddF32 ( /*OUT*/Float* res,
Float* argX, Float* argY, Float* argZ )
{
#ifndef ENV_TYPE
/* Lame fallback implementation. */
*res = *argX * *argY + *argZ;
#else
ENV_TYPE env;
/* Multiplication is always exact. */
Double temp = (Double) *argX * (Double) *argY;
union vg_ieee754_double u;
ROUNDTOZERO (env);
/* Perform addition with round to odd. */
u.d = temp + (Double) *argZ;
/* Ensure the addition is not scheduled after fetestexcept call. */
FORCE_EVAL (u.d);
/* Reset rounding mode and test for inexact simultaneously. */
int j = RESET_TESTINEXACT (env);
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
u.ieee.mantissa1 |= j;
/* And finally truncation with round to nearest. */
*res = (Float) u.d;
#endif
}
void VEX_REGPARM(3)
h_generic_calc_MAddF64 ( /*OUT*/Double* res,
Double* argX, Double* argY, Double* argZ )
{
#ifndef ENV_TYPE
/* Lame fallback implementation. */
*res = *argX * *argY + *argZ;
#else
Double x = *argX, y = *argY, z = *argZ;
union vg_ieee754_double u, v, w;
int adjust = 0;
u.d = x;
v.d = y;
w.d = z;
if (UNLIKELY (u.ieee.exponent + v.ieee.exponent
>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG)
|| UNLIKELY (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
|| UNLIKELY (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
|| UNLIKELY (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG)
|| UNLIKELY (u.ieee.exponent + v.ieee.exponent
<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG)) {
/* If z is Inf, but x and y are finite, the result should be
z rather than NaN. */
if (w.ieee.exponent == 0x7ff
&& u.ieee.exponent != 0x7ff
&& v.ieee.exponent != 0x7ff) {
*res = (z + x) + y;
return;
}
/* If x or y or z is Inf/NaN, or if fma will certainly overflow,
or if x * y is less than half of DBL_DENORM_MIN,
compute as x * y + z. */
if (u.ieee.exponent == 0x7ff
|| v.ieee.exponent == 0x7ff
|| w.ieee.exponent == 0x7ff
|| u.ieee.exponent + v.ieee.exponent > 0x7ff + IEEE754_DOUBLE_BIAS
|| u.ieee.exponent + v.ieee.exponent
< IEEE754_DOUBLE_BIAS - DBL_MANT_DIG - 2) {
*res = x * y + z;
return;
}
if (u.ieee.exponent + v.ieee.exponent
>= 0x7ff + IEEE754_DOUBLE_BIAS - DBL_MANT_DIG) {
/* Compute 1p-53 times smaller result and multiply
at the end. */
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent -= DBL_MANT_DIG;
else
v.ieee.exponent -= DBL_MANT_DIG;
/* If x + y exponent is very large and z exponent is very small,
it doesn't matter if we don't adjust it. */
if (w.ieee.exponent > DBL_MANT_DIG)
w.ieee.exponent -= DBL_MANT_DIG;
adjust = 1;
} else if (w.ieee.exponent >= 0x7ff - DBL_MANT_DIG) {
/* Similarly.
If z exponent is very large and x and y exponents are
very small, it doesn't matter if we don't adjust it. */
if (u.ieee.exponent > v.ieee.exponent) {
if (u.ieee.exponent > DBL_MANT_DIG)
u.ieee.exponent -= DBL_MANT_DIG;
} else if (v.ieee.exponent > DBL_MANT_DIG)
v.ieee.exponent -= DBL_MANT_DIG;
w.ieee.exponent -= DBL_MANT_DIG;
adjust = 1;
} else if (u.ieee.exponent >= 0x7ff - DBL_MANT_DIG) {
u.ieee.exponent -= DBL_MANT_DIG;
if (v.ieee.exponent)
v.ieee.exponent += DBL_MANT_DIG;
else
v.d *= 0x1p53;
} else if (v.ieee.exponent >= 0x7ff - DBL_MANT_DIG) {
v.ieee.exponent -= DBL_MANT_DIG;
if (u.ieee.exponent)
u.ieee.exponent += DBL_MANT_DIG;
else
u.d *= 0x1p53;
} else /* if (u.ieee.exponent + v.ieee.exponent
<= IEEE754_DOUBLE_BIAS + DBL_MANT_DIG) */ {
if (u.ieee.exponent > v.ieee.exponent)
u.ieee.exponent += 2 * DBL_MANT_DIG;
else
v.ieee.exponent += 2 * DBL_MANT_DIG;
if (w.ieee.exponent <= 4 * DBL_MANT_DIG + 4) {
if (w.ieee.exponent)
w.ieee.exponent += 2 * DBL_MANT_DIG;
else
w.d *= 0x1p106;
adjust = -1;
}
/* Otherwise x * y should just affect inexact
and nothing else. */
}
x = u.d;
y = v.d;
z = w.d;
}
/* Multiplication m1 + m2 = x * y using Dekker's algorithm. */
# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1)
Double x1 = x * C;
Double y1 = y * C;
Double m1 = x * y;
x1 = (x - x1) + x1;
y1 = (y - y1) + y1;
Double x2 = x - x1;
Double y2 = y - y1;
Double m2 = (((x1 * y1 - m1) + x1 * y2) + x2 * y1) + x2 * y2;
# undef C
/* Addition a1 + a2 = z + m1 using Knuth's algorithm. */
Double a1 = z + m1;
Double t1 = a1 - z;
Double t2 = a1 - t1;
t1 = m1 - t1;
t2 = z - t2;
Double a2 = t1 + t2;
ENV_TYPE env;
ROUNDTOZERO (env);
/* Perform m2 + a2 addition with round to odd. */
u.d = a2 + m2;
if (UNLIKELY (adjust < 0)) {
if ((u.ieee.mantissa1 & 1) == 0)
u.ieee.mantissa1 |= TESTINEXACT ();
v.d = a1 + u.d;
/* Ensure the addition is not scheduled after fetestexcept call. */
FORCE_EVAL (v.d);
}
/* Reset rounding mode and test for inexact simultaneously. */
int j = RESET_TESTINEXACT (env) != 0;
if (LIKELY (adjust == 0)) {
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
u.ieee.mantissa1 |= j;
/* Result is a1 + u.d. */
*res = a1 + u.d;
} else if (LIKELY (adjust > 0)) {
if ((u.ieee.mantissa1 & 1) == 0 && u.ieee.exponent != 0x7ff)
u.ieee.mantissa1 |= j;
/* Result is a1 + u.d, scaled up. */
*res = (a1 + u.d) * 0x1p53;
} else {
/* If a1 + u.d is exact, the only rounding happens during
scaling down. */
if (j == 0) {
*res = v.d * 0x1p-106;
return;
}
/* If result rounded to zero is not subnormal, no double
rounding will occur. */
if (v.ieee.exponent > 106) {
*res = (a1 + u.d) * 0x1p-106;
return;
}
/* If v.d * 0x1p-106 with round to zero is a subnormal above
or equal to DBL_MIN / 2, then v.d * 0x1p-106 shifts mantissa
down just by 1 bit, which means v.ieee.mantissa1 |= j would
change the round bit, not sticky or guard bit.
v.d * 0x1p-106 never normalizes by shifting up,
so round bit plus sticky bit should be already enough
for proper rounding. */
if (v.ieee.exponent == 106) {
/* v.ieee.mantissa1 & 2 is LSB bit of the result before rounding,
v.ieee.mantissa1 & 1 is the round bit and j is our sticky
bit. In round-to-nearest 001 rounds down like 00,
011 rounds up, even though 01 rounds down (thus we need
to adjust), 101 rounds down like 10 and 111 rounds up
like 11. */
if ((v.ieee.mantissa1 & 3) == 1) {
v.d *= 0x1p-106;
if (v.ieee.negative)
*res = v.d - 0x1p-1074;
else
*res = v.d + 0x1p-1074;
} else
*res = v.d * 0x1p-106;
return;
}
v.ieee.mantissa1 |= j;
*res = v.d * 0x1p-106;
return;
}
#endif
}
/*---------------------------------------------------------------*/
/*--- end host_generic_maddf.c --*/
/*---------------------------------------------------------------*/