README
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- 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 3 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. If not, see http://www.gnu.org/licenses/.
- 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
- operation 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.)