1Copyright 2000, 2001, 2002 Free Software Foundation, Inc. 2 3This file is part of the GNU MP Library. 4 5The GNU MP Library is free software; you can redistribute it and/or modify 6it under the terms of the GNU Lesser General Public License as published by 7the Free Software Foundation; either version 3 of the License, or (at your 8option) any later version. 9 10The GNU MP Library is distributed in the hope that it will be useful, but 11WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 12or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public 13License for more details. 14 15You should have received a copy of the GNU Lesser General Public License 16along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. 17 18 19 20 21 22 23The code in this directory works for Cray vector systems such as C90, 24J90, T90 (both the CFP variant and the IEEE variant) and SV1. (For 25the T3E and T3D systems, see the `alpha' subdirectory at the same 26level as the directory containing this file.) 27 28The cfp subdirectory is for systems utilizing the traditional Cray 29floating-point format, and the ieee subdirectory is for the newer 30systems that use the IEEE floating-point format. 31 32There are several issues that reduces speed on Cray systems. For 33systems with cfp floating point, the main obstacle is the forming of 34128-bit products. For IEEE systems, adding, and in particular 35computing carry is the main issue. There are no vectorizing 36unsigned-less-than instructions, and the sequence that implement that 37operation is very long. 38 39Shifting is the only operation that is simple to make fast. All Cray 40systems have a bitblt instructions (Vi Vj,Vj<Ak and Vi Vj,Vj>Ak) that 41should be really useful. 42 43For best speed for cfp systems, we need a mul_basecase, since that 44reduces the need for carry propagation to a minimum. Depending on the 45size (vn) of the smaller of the two operands (V), we should split U and V 46in different chunk sizes: 47 48U split in 2 32-bit parts 49V split according to the table: 50parts 4 5 6 7 8 51bits/part 16 13 11 10 8 52max allowed vn 1 8 32 64 256 53number of multiplies 8 10 12 14 16 54peak cycles/limb 4 5 6 7 8 55 56U split in 3 22-bit parts 57V split according to the table: 58parts 3 4 5 59bits/part 22 16 13 60max allowed vn 16 1024 8192 61number of multiplies 9 12 15 62peak cycles/limb 4.5 6 7.5 63 64U split in 4 16-bit parts 65V split according to the table: 66parts 4 67bits/part 16 68max allowed vn 65536 69number of multiplies 16 70peak cycles/limb 8 71 72(A T90 CPU can accumulate two products per cycle.) 73 74IDEA: 75* Rewrite mpn_add_n: 76 short cy[n + 1]; 77 #pragma _CRI ivdep 78 for (i = 0; i < n; i++) 79 { s = up[i] + vp[i]; 80 rp[i] = s; 81 cy[i + 1] = s < up[i]; } 82 more_carries = 0; 83 #pragma _CRI ivdep 84 for (i = 1; i < n; i++) 85 { s = rp[i] + cy[i]; 86 rp[i] = s; 87 more_carries += s < cy[i]; } 88 cys = 0; 89 if (more_carries) 90 { 91 cys = rp[1] < cy[1]; 92 for (i = 2; i < n; i++) 93 { rp[i] += cys; 94 cys = rp[i] < cys; } 95 } 96 return cys + cy[n]; 97 98* Write mpn_add3_n for adding three operands. First add operands 1 99 and 2, and generate cy[]. Then add operand 3 to the partial result, 100 and accumulate carry into cy[]. Finally propagate carry just like 101 in the new mpn_add_n. 102 103IDEA: 104 105Store fewer bits, perhaps 62, per limb. That brings mpn_add_n time 106down to 2.5 cycles/limb and mpn_addmul_1 times to 4 cycles/limb. By 107storing even fewer bits per limb, perhaps 56, it would be possible to 108write a mul_mul_basecase that would run at effectively 1 cycle/limb. 109(Use VM here to better handle the romb-shaped multiply area, perhaps 110rouding operand sizes up to the next power of 2.) 111