src/gmp-6.1.0/mpn/cray/README

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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
rounding operand sizes up to the next power of 2.)