# Alpha ev6 mpn_addmul_1 -- Multiply a limb vector with a limb and add # the result to a second limb vector. # # Copyright (C) 2000 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 2.1 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; see the file COPYING.LIB. If not, write to # the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, # MA 02111-1307, USA. # INPUT PARAMETERS # res_ptr $16 # s1_ptr $17 # size $18 # s2_limb $19 # # This code runs at 42 cycles/limb on EV4, 18 cycles/limb on EV5, and # exactly 3.625 cycles/limb on EV6... # # This code was written in close cooperation with ev6 pipeline expert # Steve Root (root@toober.hlo.dec.com). Any errors are tege's fault, though. # # Register usages for unrolled loop: # 0-3 mul's # 4-7 acc's # 8-15 mul results # 20,21 carry's # 22,23 save for stores # # Sustains 8 mul-adds in 29 cycles in the unrolled inner loop. # # The stores can issue a cycle late so we have paired no-op's to 'catch' # them, so that further disturbance to the schedule is damped. # # We couldn't pair the loads, because the entangled schedule of the # carry's has to happen on one side {0} of the machine. Note, the total # use of U0, and the total use of L0 (after attending to the stores). # which is part of the reason why.... # # This is a great schedule for the d_cache, a poor schedule for the # b_cache. The lockup on U0 means that any stall can't be recovered # from. Consider a ldq in L1. say that load gets stalled because it # collides with a fill from the b_Cache. On the next cycle, this load # gets priority. If first looks at L0, and goes there. The instruction # we intended for L0 gets to look at L1, which is NOT where we want # it. It either stalls 1, because it can't go in L0, or goes there, and # causes a further instruction to stall. # # So for b_cache, we're likely going to want to put one or more cycles # back into the code! And, of course, put in prefetches. For the # accumulator, lds, intent to modify. For the multiplier, you might # want ldq, evict next, if you're not wanting to use it again soon. Use # 256 ahead of present pointer value. At a place where we have an mt # followed by a bookkeeping, put the bookkeeping in upper, and the # prefetch into lower. # # Note, the usage of physical registers per cycle is smoothed off, as # much as possible. # # Note, the ldq's and stq's are at the end of the quadpacks. note, we'd # like not to have a ldq or stq to preceded a conditional branch in a # quadpack. The conditional branch moves the retire pointer one cycle # later. # # Optimization notes: # Callee-saves regs: $9 $10 $11 $12 $13 $14 $15 $26 ?$27? # Reserved regs: $29 $30 $31 # Free caller-saves regs in unrolled code: $24 $25 $28 # We should swap some of the callee-saves regs for some of the free # caller-saves regs, saving some overhead cycles. # Most importantly, we should write fast code for the 0-7 case. # The code we use there are for the 21164, and runs at 7 cycles/limb # on the 21264. Should not be hard, if we write specialized code for # 1-7 limbs (the one for 0 limbs should be straightforward). We then just # need a jump table indexed by the low 3 bits of the count argument. .set noreorder .set noat .text .globl __mpn_addmul_1 .ent __mpn_addmul_1 __mpn_addmul_1: .frame $30,0,$26,0 .prologue 0 cmpult $18, 8, $1 beq $1, $Large ldq $2, 0($17) # $2 = s1_limb addq $17, 8, $17 # s1_ptr++ subq $18, 1, $18 # size-- mulq $2, $19, $3 # $3 = prod_low ldq $5, 0($16) # $5 = *res_ptr umulh $2, $19, $0 # $0 = prod_high beq $18, $Lend0b # jump if size was == 1 ldq $2, 0($17) # $2 = s1_limb addq $17, 8, $17 # s1_ptr++ subq $18, 1, $18 # size-- addq $5, $3, $3 cmpult $3, $5, $4 stq $3, 0($16) addq $16, 8, $16 # res_ptr++ beq $18, $Lend0a # jump if size was == 2 .align 3 $Loop0: mulq $2, $19, $3 # $3 = prod_low ldq $5, 0($16) # $5 = *res_ptr addq $4, $0, $0 # cy_limb = cy_limb + 'cy' subq $18, 1, $18 # size-- umulh $2, $19, $4 # $4 = cy_limb ldq $2, 0($17) # $2 = s1_limb addq $17, 8, $17 # s1_ptr++ addq $3, $0, $3 # $3 = cy_limb + prod_low cmpult $3, $0, $0 # $0 = carry from (cy_limb + prod_low) addq $5, $3, $3 cmpult $3, $5, $5 stq $3, 0($16) addq $16, 8, $16 # res_ptr++ addq $5, $0, $0 # combine carries bne $18, $Loop0 $Lend0a: mulq $2, $19, $3 # $3 = prod_low ldq $5, 0($16) # $5 = *res_ptr addq $4, $0, $0 # cy_limb = cy_limb + 'cy' umulh $2, $19, $4 # $4 = cy_limb addq $3, $0, $3 # $3 = cy_limb + prod_low cmpult $3, $0, $0 # $0 = carry from (cy_limb + prod_low) addq $5, $3, $3 cmpult $3, $5, $5 stq $3, 0($16) addq $5, $0, $0 # combine carries addq $4, $0, $0 # cy_limb = prod_high + cy ret $31, ($26), 1 $Lend0b: addq $5, $3, $3 cmpult $3, $5, $5 stq $3, 0($16) addq $0, $5, $0 ret $31, ($26), 1 $Large: lda $30, -240($30) stq $9, 8($30) stq $10, 16($30) stq $11, 24($30) stq $12, 32($30) stq $13, 40($30) stq $14, 48($30) stq $15, 56($30) and $18, 7, $20 # count for the first loop, 0-7 srl $18, 3, $18 # count for unrolled loop bis $31, $31, $0 beq $20, $Lunroll ldq $2, 0($17) # $2 = s1_limb addq $17, 8, $17 # s1_ptr++ subq $20, 1, $20 # size-- mulq $2, $19, $3 # $3 = prod_low ldq $5, 0($16) # $5 = *res_ptr umulh $2, $19, $0 # $0 = prod_high beq $20, $Lend1b # jump if size was == 1 ldq $2, 0($17) # $2 = s1_limb addq $17, 8, $17 # s1_ptr++ subq $20, 1, $20 # size-- addq $5, $3, $3 cmpult $3, $5, $4 stq $3, 0($16) addq $16, 8, $16 # res_ptr++ beq $20, $Lend1a # jump if size was == 2 .align 3 $Loop1: mulq $2, $19, $3 # $3 = prod_low ldq $5, 0($16) # $5 = *res_ptr addq $4, $0, $0 # cy_limb = cy_limb + 'cy' subq $20, 1, $20 # size-- umulh $2, $19, $4 # $4 = cy_limb ldq $2, 0($17) # $2 = s1_limb addq $17, 8, $17 # s1_ptr++ addq $3, $0, $3 # $3 = cy_limb + prod_low cmpult $3, $0, $0 # $0 = carry from (cy_limb + prod_low) addq $5, $3, $3 cmpult $3, $5, $5 stq $3, 0($16) addq $16, 8, $16 # res_ptr++ addq $5, $0, $0 # combine carries bne $20, $Loop1 $Lend1a: mulq $2, $19, $3 # $3 = prod_low ldq $5, 0($16) # $5 = *res_ptr addq $4, $0, $0 # cy_limb = cy_limb + 'cy' umulh $2, $19, $4 # $4 = cy_limb addq $3, $0, $3 # $3 = cy_limb + prod_low cmpult $3, $0, $0 # $0 = carry from (cy_limb + prod_low) addq $5, $3, $3 cmpult $3, $5, $5 stq $3, 0($16) addq $16, 8, $16 # res_ptr++ addq $5, $0, $0 # combine carries addq $4, $0, $0 # cy_limb = prod_high + cy br $31, $Lunroll $Lend1b: addq $5, $3, $3 cmpult $3, $5, $5 stq $3, 0($16) addq $16, 8, $16 # res_ptr++ addq $0, $5, $0 $Lunroll: lda $17, -16($17) # L1 bookkeeping lda $16, -16($16) # L1 bookkeeping bis $0, $31, $12 # ____ UNROLLED LOOP SOFTWARE PIPELINE STARTUP ____ ldq $2, 16($17) # L1 ldq $3, 24($17) # L1 lda $18, -1($18) # L1 bookkeeping ldq $6, 16($16) # L1 ldq $7, 24($16) # L1 ldq $0, 32($17) # L1 mulq $19, $2, $13 # U1 ldq $1, 40($17) # L1 umulh $19, $2, $14 # U1 mulq $19, $3, $15 # U1 lda $17, 64($17) # L1 bookkeeping ldq $4, 32($16) # L1 ldq $5, 40($16) # L1 umulh $19, $3, $8 # U1 ldq $2, -16($17) # L1 mulq $19, $0, $9 # U1 ldq $3, -8($17) # L1 umulh $19, $0, $10 # U1 addq $6, $13, $6 # L0 lo + acc mulq $19, $1, $11 # U1 cmpult $6, $13, $20 # L0 lo add => carry lda $16, 64($16) # L1 bookkeeping addq $6, $12, $22 # U0 hi add => answer cmpult $22, $12, $21 # L0 hi add => carry addq $14, $20, $14 # U0 hi mul + carry ldq $6, -16($16) # L1 addq $7, $15, $23 # L0 lo + acc addq $14, $21, $14 # U0 hi mul + carry ldq $7, -8($16) # L1 umulh $19, $1, $12 # U1 cmpult $23, $15, $20 # L0 lo add => carry addq $23, $14, $23 # U0 hi add => answer ldq $0, 0($17) # L1 mulq $19, $2, $13 # U1 cmpult $23, $14, $21 # L0 hi add => carry addq $8, $20, $8 # U0 hi mul + carry ldq $1, 8($17) # L1 umulh $19, $2, $14 # U1 addq $4, $9, $4 # L0 lo + acc stq $22, -48($16) # L0 stq $23, -40($16) # L1 mulq $19, $3, $15 # U1 addq $8, $21, $8 # U0 hi mul + carry cmpult $4, $9, $20 # L0 lo add => carry addq $4, $8, $22 # U0 hi add => answer ble $18, $Lend # U1 bookkeeping # ____ MAIN UNROLLED LOOP ____ .align 4 $Loop: bis $31, $31, $31 # U1 mt cmpult $22, $8, $21 # L0 hi add => carry addq $10, $20, $10 # U0 hi mul + carry ldq $4, 0($16) # L1 bis $31, $31, $31 # U1 mt addq $5, $11, $23 # L0 lo + acc addq $10, $21, $10 # L0 hi mul + carry ldq $5, 8($16) # L1 umulh $19, $3, $8 # U1 cmpult $23, $11, $20 # L0 lo add => carry addq $23, $10, $23 # U0 hi add => answer ldq $2, 16($17) # L1 mulq $19, $0, $9 # U1 cmpult $23, $10, $21 # L0 hi add => carry addq $12, $20, $12 # U0 hi mul + carry ldq $3, 24($17) # L1 umulh $19, $0, $10 # U1 addq $6, $13, $6 # L0 lo + acc stq $22, -32($16) # L0 stq $23, -24($16) # L1 bis $31, $31, $31 # L0 st slosh mulq $19, $1, $11 # U1 bis $31, $31, $31 # L1 st slosh addq $12, $21, $12 # U0 hi mul + carry cmpult $6, $13, $20 # L0 lo add => carry bis $31, $31, $31 # U1 mt lda $18, -1($18) # L1 bookkeeping addq $6, $12, $22 # U0 hi add => answer bis $31, $31, $31 # U1 mt cmpult $22, $12, $21 # L0 hi add => carry addq $14, $20, $14 # U0 hi mul + carry ldq $6, 16($16) # L1 bis $31, $31, $31 # U1 mt addq $7, $15, $23 # L0 lo + acc addq $14, $21, $14 # U0 hi mul + carry ldq $7, 24($16) # L1 umulh $19, $1, $12 # U1 cmpult $23, $15, $20 # L0 lo add => carry addq $23, $14, $23 # U0 hi add => answer ldq $0, 32($17) # L1 mulq $19, $2, $13 # U1 cmpult $23, $14, $21 # L0 hi add => carry addq $8, $20, $8 # U0 hi mul + carry ldq $1, 40($17) # L1 umulh $19, $2, $14 # U1 addq $4, $9, $4 # U0 lo + acc stq $22, -16($16) # L0 stq $23, -8($16) # L1 bis $31, $31, $31 # L0 st slosh mulq $19, $3, $15 # U1 bis $31, $31, $31 # L1 st slosh addq $8, $21, $8 # L0 hi mul + carry cmpult $4, $9, $20 # L0 lo add => carry bis $31, $31, $31 # U1 mt lda $17, 64($17) # L1 bookkeeping addq $4, $8, $22 # U0 hi add => answer bis $31, $31, $31 # U1 mt cmpult $22, $8, $21 # L0 hi add => carry addq $10, $20, $10 # U0 hi mul + carry ldq $4, 32($16) # L1 bis $31, $31, $31 # U1 mt addq $5, $11, $23 # L0 lo + acc addq $10, $21, $10 # L0 hi mul + carry ldq $5, 40($16) # L1 umulh $19, $3, $8 # U1 cmpult $23, $11, $20 # L0 lo add => carry addq $23, $10, $23 # U0 hi add => answer ldq $2, -16($17) # L1 mulq $19, $0, $9 # U1 cmpult $23, $10, $21 # L0 hi add => carry addq $12, $20, $12 # U0 hi mul + carry ldq $3, -8($17) # L1 umulh $19, $0, $10 # U1 addq $6, $13, $6 # L0 lo + acc stq $22, 0($16) # L0 stq $23, 8($16) # L1 bis $31, $31, $31 # L0 st slosh mulq $19, $1, $11 # U1 bis $31, $31, $31 # L1 st slosh addq $12, $21, $12 # U0 hi mul + carry cmpult $6, $13, $20 # L0 lo add => carry bis $31, $31, $31 # U1 mt lda $16, 64($16) # L1 bookkeeping addq $6, $12, $22 # U0 hi add => answer bis $31, $31, $31 # U1 mt cmpult $22, $12, $21 # L0 hi add => carry addq $14, $20, $14 # U0 hi mul + carry ldq $6, -16($16) # L1 bis $31, $31, $31 # U1 mt addq $7, $15, $23 # L0 lo + acc addq $14, $21, $14 # U0 hi mul + carry ldq $7, -8($16) # L1 umulh $19, $1, $12 # U1 cmpult $23, $15, $20 # L0 lo add => carry addq $23, $14, $23 # U0 hi add => answer ldq $0, 0($17) # L1 mulq $19, $2, $13 # U1 cmpult $23, $14, $21 # L0 hi add => carry addq $8, $20, $8 # U0 hi mul + carry ldq $1, 8($17) # L1 umulh $19, $2, $14 # U1 addq $4, $9, $4 # L0 lo + acc stq $22, -48($16) # L0 stq $23, -40($16) # L1 bis $31, $31, $31 # L0 st slosh mulq $19, $3, $15 # U1 bis $31, $31, $31 # L1 st slosh addq $8, $21, $8 # U0 hi mul + carry cmpult $4, $9, $20 # L0 lo add => carry addq $4, $8, $22 # U0 hi add => answer bis $31, $31, $31 # L1 mt bgt $18, $Loop # U1 bookkeeping # ____ UNROLLED LOOP SOFTWARE PIPELINE FINISH ____ $Lend: cmpult $22, $8, $21 # L0 hi add => carry addq $10, $20, $10 # U0 hi mul + carry ldq $4, 0($16) # L1 addq $5, $11, $23 # L0 lo + acc addq $10, $21, $10 # L0 hi mul + carry ldq $5, 8($16) # L1 umulh $19, $3, $8 # U1 cmpult $23, $11, $20 # L0 lo add => carry addq $23, $10, $23 # U0 hi add => answer mulq $19, $0, $9 # U1 cmpult $23, $10, $21 # L0 hi add => carry addq $12, $20, $12 # U0 hi mul + carry umulh $19, $0, $10 # U1 addq $6, $13, $6 # L0 lo + acc stq $22, -32($16) # L0 stq $23, -24($16) # L1 mulq $19, $1, $11 # U1 addq $12, $21, $12 # U0 hi mul + carry cmpult $6, $13, $20 # L0 lo add => carry addq $6, $12, $22 # U0 hi add => answer cmpult $22, $12, $21 # L0 hi add => carry addq $14, $20, $14 # U0 hi mul + carry addq $7, $15, $23 # L0 lo + acc addq $14, $21, $14 # U0 hi mul + carry umulh $19, $1, $12 # U1 cmpult $23, $15, $20 # L0 lo add => carry addq $23, $14, $23 # U0 hi add => answer cmpult $23, $14, $21 # L0 hi add => carry addq $8, $20, $8 # U0 hi mul + carry addq $4, $9, $4 # U0 lo + acc stq $22, -16($16) # L0 stq $23, -8($16) # L1 bis $31, $31, $31 # L0 st slosh addq $8, $21, $8 # L0 hi mul + carry cmpult $4, $9, $20 # L0 lo add => carry addq $4, $8, $22 # U0 hi add => answer cmpult $22, $8, $21 # L0 hi add => carry addq $10, $20, $10 # U0 hi mul + carry addq $5, $11, $23 # L0 lo + acc addq $10, $21, $10 # L0 hi mul + carry cmpult $23, $11, $20 # L0 lo add => carry addq $23, $10, $23 # U0 hi add => answer cmpult $23, $10, $21 # L0 hi add => carry addq $12, $20, $12 # U0 hi mul + carry stq $22, 0($16) # L0 stq $23, 8($16) # L1 addq $12, $21, $0 # U0 hi mul + carry ldq $9, 8($30) ldq $10, 16($30) ldq $11, 24($30) ldq $12, 32($30) ldq $13, 40($30) ldq $14, 48($30) ldq $15, 56($30) lda $30, 240($30) ret $31, ($26), 1 .end __mpn_addmul_1