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glibc/sysdeps/alpha/alphaev6/addmul_1.S

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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) 2000-2024 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. If not, see <https://www.gnu.org/licenses/>.
# 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
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