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Add fma() and fmaf(), which implement a fused multiply-add operation.

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This commit is contained in:
David Schultz 2005-01-22 09:53:18 +00:00
parent c81d2c74ac
commit d5580d091a
8 changed files with 412 additions and 3 deletions
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10
lib/msun/Makefile
View File

@ -41,6 +41,7 @@
# default standard
#
# XXX MD crud should be in separate makefiles
.if ${MACHINE_ARCH} == "alpha"
ARCH_SRCS = s_copysign.S s_copysignf.S
# XXX Comment from NetBSD/Alpha:
@ -50,6 +51,8 @@ ARCH_SRCS = s_copysign.S s_copysignf.S
#CFLAGS += -mtrap-precision=i -mfp-trap-mode=su
.elif ${MACHINE_ARCH} == "amd64"
ARCH_SRCS = e_sqrt.S s_lrint.S s_llrint.S
.elif ${MACHINE_ARCH} == "ia64"
ARCH_SRCS = s_fma.S s_fmaf.S
.elif ${MACHINE_ARCH} == "i386"
ARCH_SUBDIR= i387
ARCH_SRCS = e_acos.S e_asin.S e_atan2.S e_exp.S e_fmod.S e_log.S e_log10.S \
@ -88,7 +91,8 @@ COMMON_SRCS= b_exp.c b_log.c b_tgamma.c \
s_ceil.c s_ceilf.c s_ceill.c \
s_copysign.c s_copysignf.c s_cos.c s_cosf.c s_erf.c s_erff.c \
s_expm1.c s_expm1f.c s_fabsf.c s_fdim.c s_finite.c s_finitef.c \
s_floor.c s_floorf.c s_floorl.c s_fmax.c s_fmaxf.c s_fmaxl.c s_fmin.c \
s_floor.c s_floorf.c s_floorl.c s_fma.c s_fmaf.c \
s_fmax.c s_fmaxf.c s_fmaxl.c s_fmin.c \
s_fminf.c s_fminl.c s_frexp.c s_frexpf.c s_ilogb.c s_ilogbf.c \
s_ilogbl.c s_isfinite.c s_isnan.c s_isnormal.c s_ldexpf.c \
s_lib_version.c s_llrint.c s_llrintf.c s_llround.c s_llroundf.c \
@ -137,7 +141,8 @@ INCS= fenv.h math.h
MAN= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \
cimag.3 cos.3 cosh.3 erf.3 exp.3 fabs.3 fdim.3 feclearexcept.3 \
fegetenv.3 fegetround.3 fenv.3 floor.3 fmax.3 fmod.3 hypot.3 ieee.3 \
fegetenv.3 fegetround.3 fenv.3 floor.3 \
fma.3 fmax.3 fmod.3 hypot.3 ieee.3 \
ieee_test.3 j0.3 lgamma.3 lrint.3 lround.3 math.3 rint.3 round.3 \
signbit.3 sin.3 sinh.3 sqrt.3 tan.3 tanh.3 trunc.3
@ -167,6 +172,7 @@ MLINKS+=fegetenv.3 feholdexcept.3 fegetenv.3 fesetenv.3 \
fegetenv.3 feupdateenv.3
MLINKS+=fegetround.3 fesetround.3
MLINKS+=floor.3 floorf.3 floor.3 floorl.3
MLINKS+=fma.3 fmaf.3
MLINKS+=fmax.3 fmaxf.3 fmax.3 fmaxl.3 \
fmax.3 fmin.3 fmax.3 fminf.3 fmax.3 fminl.3
MLINKS+=fmod.3 fmodf.3

34
lib/msun/ia64/s_fma.S Normal file
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@ -0,0 +1,34 @@
/*-
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <machine/asm.h>
__FBSDID("$FreeBSD$")
ENTRY(fma, 3)
{
fma.d f8 = f8, f9, f10
br.ret.sptk b0
}

34
lib/msun/ia64/s_fmaf.S Normal file
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@ -0,0 +1,34 @@
/*-
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <machine/asm.h>
__FBSDID("$FreeBSD$")
ENTRY(fmaf, 3)
{
fma.s f8 = f8, f9, f10
br.ret.sptk b0
}

105
lib/msun/man/fma.3 Normal file
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@ -0,0 +1,105 @@
.\" Copyright (c) 2005 David Schultz <das@FreeBSD.org>
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" $FreeBSD$
.\"
.Dd January 22, 2005
.Dt FMA 3
.Os
.Sh NAME
.Nm fma ,
.Nm fmaf
.Nd fused multiply-add
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Ft double
.Fn fma "double x" "double y" "double z"
.Ft float
.Fn fmaf "float x" "float y" "float z"
.Sh DESCRIPTION
The
.Fn fma
and
.Fn fmaf
functions return
.No "(x * y) + z" ,
computed with only one rounding error.
Using the ordinary multiplication and addition operators, by contrast,
results in two roundings: one for the intermediate product and one for
the final result.
.Pp
For instance, the expression
.No "1.2e100 * 2.0e208 - 1.4e308"
produces \*(If due to overflow in the intermediate product, whereas
.No "fma(1.2e100, 2.0e208, -1.4e308)"
returns approximately 1.0e308.
.Pp
The fused multiply-add operation is often used to improve the
accuracy of calculations such as dot products.
It may also be used to improve performance on machines that implement
it natively.
The macros
.Dv FP_FAST_FMA
and
.Dv FP_FAST_FMAF
may be defined in
.In math.h
to indicate that
.Fn fma
and
.Fn fmaf
(respectively) have comparable or faster speed than a multiply
operation followed by an add operation.
.Sh IMPLEMENTATION NOTES
In general,
.Fn fma
and
.Fn fmaf
will behave as one would expect if
.No "x * y + z"
were computed with unbounded precision and range,
then rounded to the precision of the return type.
However, on some platforms, if
.Fa z
is \*(Na, these functions may not raise an exception even
when the computation of
.No "x * y"
would have otherwise generated an invalid exception.
.Sh SEE ALSO
.Xr fenv 3 ,
.Xr math 3
.Sh STANDARDS
The
.Fn fma
and
.Fn fmaf
functions conform to
.St -isoC-99 .
A fused multiply-add operation with virtually identical
characteristics appears in IEEE draft standard 754R.
.Sh HISTORY
These routines first appeared in
.Fx 5.4 .

2
lib/msun/man/math.3
View File

@ -107,7 +107,7 @@ expm1 exp(x)\-1 1
fabs absolute value 0
fdim positive difference 1
floor integer no greater than 0
.\" fma multiply-add ???
fma multiply-add 1
fmax maximum function 0
fmin minimum function 0
fmod remainder function ???

5
lib/msun/src/math.h
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@ -68,6 +68,11 @@ extern const union __nan_un {
#define MATH_ERREXCEPT 2
#define math_errhandling MATH_ERREXCEPT
#ifdef __ia64__
#define FP_FAST_FMA
#endif
#define FP_FAST_FMAF
/* Symbolic constants to classify floating point numbers. */
#define FP_INFINITE 0x01
#define FP_NAN 0x02

178
lib/msun/src/s_fma.c Normal file
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@ -0,0 +1,178 @@
/*-
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
#include <fenv.h>
#include <float.h>
#include <math.h>
/*
* Fused multiply-add: Compute x * y + z with a single rounding error.
*
* We use scaling to avoid overflow/underflow, along with the
* canonical precision-doubling technique adapted from:
*
* Dekker, T. A Floating-Point Technique for Extending the
* Available Precision. Numer. Math. 18, 224-242 (1971).
*
* This algorithm is sensitive to the rounding precision. FPUs such
* as the i387 must be set in double-precision mode if variables are
* to be stored in FP registers in order to avoid incorrect results.
* This is the default on FreeBSD, but not on many other systems.
*
* Tests on an Itanium 2 indicate that the hardware's FMA instruction
* is almost twice as fast as this implementation. The hardware
* instruction should be used on platforms that support it.
*
* XXX May incur an absolute error of 0x1p-1074 for subnormal results
* due to double rounding induced by the final scaling operation.
*
* XXX On machines supporting quad precision, we should use that, but
* see the caveat in s_fmaf.c.
*/
double
fma(double x, double y, double z)
{
static const double split = 0x1p27 + 1.0;
double xs, ys, zs;
double c, cc, hx, hy, p, q, tx, ty;
double r, rr, s;
int oround;
int ex, ey, ez;
int spread;
if (x == 0.0 || y == 0.0)
return (z);
if (z == 0.0)
return (x * y);
/* Results of frexp() are undefined for these cases. */
if (!isfinite(x) || !isfinite(y) || !isfinite(z))
return (x * y + z);
xs = frexp(x, &ex);
ys = frexp(y, &ey);
zs = frexp(z, &ez);
oround = fegetround();
spread = ex + ey - ez;
/*
* If x * y and z are many orders of magnitude apart, the scaling
* will overflow, so we handle these cases specially. Rounding
* modes other than FE_TONEAREST are painful.
*/
if (spread > DBL_MANT_DIG * 2) {
fenv_t env;
feraiseexcept(FE_INEXACT);
switch(oround) {
case FE_TONEAREST:
return (x * y);
case FE_TOWARDZERO:
if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
return (x * y);
feholdexcept(&env);
r = x * y;
if (!fetestexcept(FE_INEXACT))
r = nextafter(r, 0);
feupdateenv(&env);
return (r);
case FE_DOWNWARD:
if (z > 0.0)
return (x * y);
feholdexcept(&env);
r = x * y;
if (!fetestexcept(FE_INEXACT))
r = nextafter(r, -INFINITY);
feupdateenv(&env);
return (r);
default: /* FE_UPWARD */
if (z < 0.0)
return (x * y);
feholdexcept(&env);
r = x * y;
if (!fetestexcept(FE_INEXACT))
r = nextafter(r, INFINITY);
feupdateenv(&env);
return (r);
}
}
if (spread < -DBL_MANT_DIG) {
feraiseexcept(FE_INEXACT);
if (!isnormal(z))
feraiseexcept(FE_UNDERFLOW);
switch (oround) {
case FE_TONEAREST:
return (z);
case FE_TOWARDZERO:
if (x > 0.0 ^ y < 0.0 ^ z < 0.0)
return (z);
else
return (nextafter(z, 0));
case FE_DOWNWARD:
if (x > 0.0 ^ y < 0.0)
return (z);
else
return (nextafter(z, -INFINITY));
default: /* FE_UPWARD */
if (x > 0.0 ^ y < 0.0)
return (nextafter(z, INFINITY));
else
return (z);
}
}
/*
* Use Dekker's algorithm to perform the multiplication and
* subsequent addition in twice the machine precision.
* Arrange so that x * y = c + cc, and x * y + z = r + rr.
*/
fesetround(FE_TONEAREST);
p = xs * split;
hx = xs - p;
hx += p;
tx = xs - hx;
p = ys * split;
hy = ys - p;
hy += p;
ty = ys - hy;
p = hx * hy;
q = hx * ty + tx * hy;
c = p + q;
cc = p - c + q + tx * ty;
zs = ldexp(zs, -spread);
r = c + zs;
s = r - c;
rr = (c - (r - s)) + (zs - s) + cc;
fesetround(oround);
return (ldexp(r + rr, ex + ey));
}

47
lib/msun/src/s_fmaf.c Normal file
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@ -0,0 +1,47 @@
/*-
* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG>
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*/
#include <sys/cdefs.h>
__FBSDID("$FreeBSD$");
/*
* Fused multiply-add: Compute x * y + z with a single rounding error.
*
* A double has more than twice as much precision than a float, so
* direct double-precision arithmetic suffices.
*
* XXX We are relying on the compiler to convert from double to float
* using the current rounding mode and with the appropriate
* side-effects. But on at least one platform (gcc 3.4.2/sparc64),
* this appears to be too much to ask for. The precision
* reduction should be done manually.
*/
float
fmaf(float x, float y, float z)
{
return ((double)x * y + z);
}