mirror of
https://github.com/ioacademy-jikim/debugging
synced 2025-06-09 17:06:24 +00:00
321 lines
11 KiB
C
321 lines
11 KiB
C
|
|
/*---------------------------------------------------------------*/
|
|
/*--- begin host_generic_maddf.c ---*/
|
|
/*---------------------------------------------------------------*/
|
|
|
|
/*
|
|
Compute x * y + z as ternary operation.
|
|
Copyright (C) 2010-2015 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 --*/
|
|
/*---------------------------------------------------------------*/
|