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- # 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