1Copyright 2000-2002 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 either: 7 8 * the GNU Lesser General Public License as published by the Free 9 Software Foundation; either version 3 of the License, or (at your 10 option) any later version. 11 12or 13 14 * the GNU General Public License as published by the Free Software 15 Foundation; either version 2 of the License, or (at your option) any 16 later version. 17 18or both in parallel, as here. 19 20The GNU MP Library is distributed in the hope that it will be useful, but 21WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY 22or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 23for more details. 24 25You should have received copies of the GNU General Public License and the 26GNU Lesser General Public License along with the GNU MP Library. If not, 27see https://www.gnu.org/licenses/. 28 29 30 31 32 33 34The code in this directory works for Cray vector systems such as C90, 35J90, T90 (both the CFP variant and the IEEE variant) and SV1. (For 36the T3E and T3D systems, see the `alpha' subdirectory at the same 37level as the directory containing this file.) 38 39The cfp subdirectory is for systems utilizing the traditional Cray 40floating-point format, and the ieee subdirectory is for the newer 41systems that use the IEEE floating-point format. 42 43There are several issues that reduces speed on Cray systems. For 44systems with cfp floating point, the main obstacle is the forming of 45128-bit products. For IEEE systems, adding, and in particular 46computing carry is the main issue. There are no vectorizing 47unsigned-less-than instructions, and the sequence that implement that 48operation is very long. 49 50Shifting is the only operation that is simple to make fast. All Cray 51systems have a bitblt instructions (Vi Vj,Vj<Ak and Vi Vj,Vj>Ak) that 52should be really useful. 53 54For best speed for cfp systems, we need a mul_basecase, since that 55reduces the need for carry propagation to a minimum. Depending on the 56size (vn) of the smaller of the two operands (V), we should split U and V 57in different chunk sizes: 58 59U split in 2 32-bit parts 60V split according to the table: 61parts 4 5 6 7 8 62bits/part 16 13 11 10 8 63max allowed vn 1 8 32 64 256 64number of multiplies 8 10 12 14 16 65peak cycles/limb 4 5 6 7 8 66 67U split in 3 22-bit parts 68V split according to the table: 69parts 3 4 5 70bits/part 22 16 13 71max allowed vn 16 1024 8192 72number of multiplies 9 12 15 73peak cycles/limb 4.5 6 7.5 74 75U split in 4 16-bit parts 76V split according to the table: 77parts 4 78bits/part 16 79max allowed vn 65536 80number of multiplies 16 81peak cycles/limb 8 82 83(A T90 CPU can accumulate two products per cycle.) 84 85IDEA: 86* Rewrite mpn_add_n: 87 short cy[n + 1]; 88 #pragma _CRI ivdep 89 for (i = 0; i < n; i++) 90 { s = up[i] + vp[i]; 91 rp[i] = s; 92 cy[i + 1] = s < up[i]; } 93 more_carries = 0; 94 #pragma _CRI ivdep 95 for (i = 1; i < n; i++) 96 { s = rp[i] + cy[i]; 97 rp[i] = s; 98 more_carries += s < cy[i]; } 99 cys = 0; 100 if (more_carries) 101 { 102 cys = rp[1] < cy[1]; 103 for (i = 2; i < n; i++) 104 { rp[i] += cys; 105 cys = rp[i] < cys; } 106 } 107 return cys + cy[n]; 108 109* Write mpn_add3_n for adding three operands. First add operands 1 110 and 2, and generate cy[]. Then add operand 3 to the partial result, 111 and accumulate carry into cy[]. Finally propagate carry just like 112 in the new mpn_add_n. 113 114IDEA: 115 116Store fewer bits, perhaps 62, per limb. That brings mpn_add_n time 117down to 2.5 cycles/limb and mpn_addmul_1 times to 4 cycles/limb. By 118storing even fewer bits per limb, perhaps 56, it would be possible to 119write a mul_mul_basecase that would run at effectively 1 cycle/limb. 120(Use VM here to better handle the romb-shaped multiply area, perhaps 121rounding operand sizes up to the next power of 2.) 122