113 lines
3.7 KiB
Plaintext
113 lines
3.7 KiB
Plaintext
Copyright 2000, 2001, 2002 Free Software Foundation, Inc.
|
|
|
|
This file is part of the GNU MP Library.
|
|
|
|
The GNU MP 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 MP 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 MP Library; see the file COPYING.LIB. If not, write to
|
|
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
|
|
02110-1301, USA.
|
|
|
|
|
|
|
|
|
|
|
|
|
|
The code in this directory works for Cray vector systems such as C90,
|
|
J90, T90 (both the CFP variant and the IEEE variant) and SV1. (For
|
|
the T3E and T3D systems, see the `alpha' subdirectory at the same
|
|
level as the directory containing this file.)
|
|
|
|
The cfp subdirectory is for systems utilizing the traditional Cray
|
|
floating-point format, and the ieee subdirectory is for the newer
|
|
systems that use the IEEE floating-point format.
|
|
|
|
There are several issues that reduces speed on Cray systems. For
|
|
systems with cfp floating point, the main obstacle is the forming of
|
|
128-bit products. For IEEE systems, adding, and in particular
|
|
computing carry is the main issue. There are no vectorizing
|
|
unsigned-less-than instructions, and the sequence that implement that
|
|
opetration is very long.
|
|
|
|
Shifting is the only operation that is simple to make fast. All Cray
|
|
systems have a bitblt instructions (Vi Vj,Vj<Ak and Vi Vj,Vj>Ak) that
|
|
should be really useful.
|
|
|
|
For best speed for cfp systems, we need a mul_basecase, since that
|
|
reduces the need for carry propagation to a minimum. Depending on the
|
|
size (vn) of the smaller of the two operands (V), we should split U and V
|
|
in different chunk sizes:
|
|
|
|
U split in 2 32-bit parts
|
|
V split according to the table:
|
|
parts 4 5 6 7 8
|
|
bits/part 16 13 11 10 8
|
|
max allowed vn 1 8 32 64 256
|
|
number of multiplies 8 10 12 14 16
|
|
peak cycles/limb 4 5 6 7 8
|
|
|
|
U split in 3 22-bit parts
|
|
V split according to the table:
|
|
parts 3 4 5
|
|
bits/part 22 16 13
|
|
max allowed vn 16 1024 8192
|
|
number of multiplies 9 12 15
|
|
peak cycles/limb 4.5 6 7.5
|
|
|
|
U split in 4 16-bit parts
|
|
V split according to the table:
|
|
parts 4
|
|
bits/part 16
|
|
max allowed vn 65536
|
|
number of multiplies 16
|
|
peak cycles/limb 8
|
|
|
|
(A T90 CPU can accumulate two products per cycle.)
|
|
|
|
IDEA:
|
|
* Rewrite mpn_add_n:
|
|
short cy[n + 1];
|
|
#pragma _CRI ivdep
|
|
for (i = 0; i < n; i++)
|
|
{ s = up[i] + vp[i];
|
|
rp[i] = s;
|
|
cy[i + 1] = s < up[i]; }
|
|
more_carries = 0;
|
|
#pragma _CRI ivdep
|
|
for (i = 1; i < n; i++)
|
|
{ s = rp[i] + cy[i];
|
|
rp[i] = s;
|
|
more_carries += s < cy[i]; }
|
|
cys = 0;
|
|
if (more_carries)
|
|
{
|
|
cys = rp[1] < cy[1];
|
|
for (i = 2; i < n; i++)
|
|
{ rp[i] += cys;
|
|
cys = rp[i] < cys; }
|
|
}
|
|
return cys + cy[n];
|
|
|
|
* Write mpn_add3_n for adding three operands. First add operands 1
|
|
and 2, and generate cy[]. Then add operand 3 to the partial result,
|
|
and accumulate carry into cy[]. Finally propagate carry just like
|
|
in the new mpn_add_n.
|
|
|
|
IDEA:
|
|
|
|
Store fewer bits, perhaps 62, per limb. That brings mpn_add_n time
|
|
down to 2.5 cycles/limb and mpn_addmul_1 times to 4 cycles/limb. By
|
|
storing even fewer bits per limb, perhaps 56, it would be possible to
|
|
write a mul_mul_basecase that would run at effectively 1 cycle/limb.
|
|
(Use VM here to better handle the romb-shaped multiply area, perhaps
|
|
rouding operand sizes up to the next power of 2.)
|