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INTEL PENTIUM P5 MPN SUBROUTINES This directory contains mpn functions optimized for Intel Pentium (P5,P54) processors. The mmx subdirectory has additional code for Pentium with MMX (P55). STATUS cycles/limb mpn_add_n/sub_n 2.375 mpn_mul_1 12.0 mpn_add/submul_1 14.0 mpn_mul_basecase 14.2 cycles/crossproduct (approx) mpn_sqr_basecase 8 cycles/crossproduct (approx) or 15.5 cycles/triangleproduct (approx) mpn_l/rshift 5.375 normal (6.0 on P54) 1.875 special shift by 1 bit mpn_divrem_1 44.0 mpn_mod_1 28.0 mpn_divexact_by3 15.0 mpn_copyi/copyd 1.0 Pentium MMX gets the following improvements mpn_l/rshift 1.75 mpn_mul_1 12.0 normal, 7.0 for 16-bit multiplier mpn_add_n and mpn_sub_n run at asymptotically 2 cycles/limb. Due to loop overhead and other delays (cache refill?), they run at or near 2.5 cycles/limb. mpn_mul_1, mpn_addmul_1, mpn_submul_1 all run 1 cycle faster than they should. Intel documentation says a mul instruction is 10 cycles, but it measures 9 and the routines using it run as 9. P55 MMX AND X87 The cost of switching between MMX and x87 floating point on P55 is about 100 cycles (fld1/por/emms for instance). In order to avoid that the two aren't mixed and currently that means using MMX and not x87. MMX offers a big speedup for lshift and rshift, and a nice speedup for 16-bit multipliers in mpn_mul_1. If fast code using x87 is found then perhaps the preference for MMX will be reversed. P54 SHLDL mpn_lshift and mpn_rshift run at about 6 cycles/limb on P5 and P54, but the documentation indicates that they should take only 43/8 = 5.375 cycles/limb, or 5 cycles/limb asymptotically. The P55 runs them at the expected speed. It seems that on P54 a shldl or shrdl allows pairing in one following cycle, but not two. For example, back to back repetitions of the following shldl( %cl, %eax, %ebx) xorl %edx, %edx xorl %esi, %esi run at 5 cycles, as expected, but repetitions of the following run at 7 cycles, whereas 6 would be expected (and is achieved on P55), shldl( %cl, %eax, %ebx) xorl %edx, %edx xorl %esi, %esi xorl %edi, %edi xorl %ebp, %ebp Three xorls run at 7 cycles too, so it doesn't seem to be just that pairing inhibited is only in the second following cycle (or something like that). Avoiding this problem would bring P54 shifts down from 6.0 c/l to 5.5 with a pattern of shift, 2 loads, shift, 2 stores, shift, etc. A start has been made on something like that, but it's not yet complete. OTHER NOTES Prefetching Destinations Pentium doesn't allocate cache lines on writes, unlike most other modern processors. Since the functions in the mpn class do array writes, we have to handle allocating the destination cache lines by reading a word from it in the loops, to achieve the best performance. Prefetching Sources Prefetching of sources is pointless since there's no out-of-order loads. Any load instruction blocks until the line is brought to L1, so it may as well be the load that wants the data which blocks. Data Cache Bank Clashes Pairing of memory operations requires that the two issued operations refer to different cache banks (ie. different addresses modulo 32 bytes). The simplest way to ensure this is to read/write two words from the same object. If we make operations on different objects, they might or might not be to the same cache bank. PIC %eip Fetching A simple call $+5 and popl can be used to get %eip, there's no need to balance calls and returns since P5 doesn't have any return stack branch prediction. Float Multiplies fmul is pairable and can be issued every 2 cycles (with a 4 cycle latency for data ready to use). This is a lot better than integer mull or imull at 9 cycles non-pairing. Unfortunately the advantage is quickly eaten away by needing to throw data through memory back to the integer registers to adjust for fild and fist being signed, and to do things like propagating carry bits. REFERENCES "Intel Architecture Optimization Manual", 1997, order number 242816. This is mostly about P5, the parts about P6 aren't relevant. Available on-line: http://download.intel.com/design/PentiumII/manuals/242816.htm ---------------- Local variables: mode: text fill-column: 76 End: