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|
dnl SPARC v9 64-bit mpn_mul_1 -- Multiply a limb vector with a limb and store
dnl the result in a second limb vector.
dnl Copyright 1998, 2000-2003 Free Software Foundation, Inc.
dnl This file is part of the GNU MP Library.
dnl
dnl The GNU MP Library is free software; you can redistribute it and/or modify
dnl it under the terms of either:
dnl
dnl * the GNU Lesser General Public License as published by the Free
dnl Software Foundation; either version 3 of the License, or (at your
dnl option) any later version.
dnl
dnl or
dnl
dnl * the GNU General Public License as published by the Free Software
dnl Foundation; either version 2 of the License, or (at your option) any
dnl later version.
dnl
dnl or both in parallel, as here.
dnl
dnl The GNU MP Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
dnl for more details.
dnl
dnl You should have received copies of the GNU General Public License and the
dnl GNU Lesser General Public License along with the GNU MP Library. If not,
dnl see https://www.gnu.org/licenses/.
include(`../config.m4')
C cycles/limb
C UltraSPARC 1&2: 14
C UltraSPARC 3: 18.5
C Algorithm: We use eight floating-point multiplies per limb product, with the
C invariant v operand split into four 16-bit pieces, and the s1 operand split
C into 32-bit pieces. We sum pairs of 48-bit partial products using
C floating-point add, then convert the four 49-bit product-sums and transfer
C them to the integer unit.
C Possible optimizations:
C 1. Align the stack area where we transfer the four 49-bit product-sums
C to a 32-byte boundary. That would minimize the cache collision.
C (UltraSPARC-1/2 use a direct-mapped cache.) (Perhaps even better would
C be to align the area to map to the area immediately before s1?)
C 2. Sum the 4 49-bit quantities using 32-bit operations, as in the
C develop mpn_addmul_2. This would save many integer instructions.
C 3. Unrolling. Questionable if it is worth the code expansion, given that
C it could only save 1 cycle/limb.
C 4. Specialize for particular v values. If its upper 32 bits are zero, we
C could save many operations, in the FPU (fmuld), but more so in the IEU
C since we'll be summing 48-bit quantities, which might be simpler.
C 5. Ideally, we should schedule the f2/f3 and f4/f5 RAW further apart, and
C the i00,i16,i32,i48 RAW less apart. The latter apart-scheduling should
C not be greater than needed for L2 cache latency, and also not so great
C that i16 needs to be copied.
C 6. Avoid performing mem+fa+fm in the same cycle, at least not when we want
C to get high IEU bandwidth. (12 of the 14 cycles will be free for 2 IEU
C ops.)
C Instruction classification (as per UltraSPARC-1/2 functional units):
C 8 FM
C 10 FA
C 11 MEM
C 9 ISHIFT + 10? IADDLOG
C 1 BRANCH
C 49 insns totally (plus three mov insns that should be optimized out)
C The loop executes 53 instructions in 14 cycles on UltraSPARC-1/2, i.e we
C sustain 3.79 instructions/cycle.
C INPUT PARAMETERS
C rp i0
C up i1
C n i2
C v i3
ASM_START()
REGISTER(%g2,#scratch)
REGISTER(%g3,#scratch)
define(`p00', `%f8') define(`p16',`%f10') define(`p32',`%f12') define(`p48',`%f14')
define(`r32',`%f16') define(`r48',`%f18') define(`r64',`%f20') define(`r80',`%f22')
define(`v00',`%f24') define(`v16',`%f26') define(`v32',`%f28') define(`v48',`%f30')
define(`u00',`%f32') define(`u32', `%f34')
define(`a00',`%f36') define(`a16',`%f38') define(`a32',`%f40') define(`a48',`%f42')
define(`cy',`%g1')
define(`rlimb',`%g3')
define(`i00',`%l0') define(`i16',`%l1') define(`i32',`%l2') define(`i48',`%l3')
define(`xffffffff',`%l7')
define(`xffff',`%o0')
PROLOGUE(mpn_mul_1)
C Initialization. (1) Split v operand into four 16-bit chunks and store them
C as IEEE double in fp registers. (2) Clear upper 32 bits of fp register pairs
C f2 and f4. (3) Store masks in registers aliased to `xffff' and `xffffffff'.
save %sp, -256, %sp
mov -1, %g4
srlx %g4, 48, xffff C store mask in register `xffff'
and %i3, xffff, %g2
stx %g2, [%sp+2223+0]
srlx %i3, 16, %g3
and %g3, xffff, %g3
stx %g3, [%sp+2223+8]
srlx %i3, 32, %g2
and %g2, xffff, %g2
stx %g2, [%sp+2223+16]
srlx %i3, 48, %g3
stx %g3, [%sp+2223+24]
srlx %g4, 32, xffffffff C store mask in register `xffffffff'
sllx %i2, 3, %i2
mov 0, cy C clear cy
add %i0, %i2, %i0
add %i1, %i2, %i1
neg %i2
add %i1, 4, %i5
add %i0, -32, %i4
add %i0, -16, %i0
ldd [%sp+2223+0], v00
ldd [%sp+2223+8], v16
ldd [%sp+2223+16], v32
ldd [%sp+2223+24], v48
ld [%sp+2223+0],%f2 C zero f2
ld [%sp+2223+0],%f4 C zero f4
ld [%i5+%i2], %f3 C read low 32 bits of up[i]
ld [%i1+%i2], %f5 C read high 32 bits of up[i]
fxtod v00, v00
fxtod v16, v16
fxtod v32, v32
fxtod v48, v48
C Start real work. (We sneakingly read f3 and f5 above...)
C The software pipeline is very deep, requiring 4 feed-in stages.
fxtod %f2, u00
fxtod %f4, u32
fmuld u00, v00, a00
fmuld u00, v16, a16
fmuld u00, v32, p32
fmuld u32, v00, r32
fmuld u00, v48, p48
addcc %i2, 8, %i2
bnz,pt %xcc, .L_two_or_more
fmuld u32, v16, r48
.L_one:
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
fdtox a00, a00
faddd p48, r48, a48
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
fdtox a32, a32
fdtox a48, a48
std a00, [%sp+2223+0]
std a16, [%sp+2223+8]
std a32, [%sp+2223+16]
std a48, [%sp+2223+24]
add %i2, 8, %i2
fdtox r64, a00
fdtox r80, a16
ldx [%sp+2223+0], i00
ldx [%sp+2223+8], i16
ldx [%sp+2223+16], i32
ldx [%sp+2223+24], i48
std a00, [%sp+2223+0]
std a16, [%sp+2223+8]
add %i2, 8, %i2
mov i00, %g5 C i00+ now in g5
ldx [%sp+2223+0], i00
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
sllx i48, 32, %l6 C (i48 << 32)
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
add %l6, %o2, %o2 C mi64- in %o2
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
add cy, %g5, %o4 C x = prev(i00) + cy
b .L_out_1
add %i2, 8, %i2
.L_two_or_more:
ld [%i5+%i2], %f3 C read low 32 bits of up[i]
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
ld [%i1+%i2], %f5 C read high 32 bits of up[i]
fdtox a00, a00
faddd p48, r48, a48
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
fdtox a32, a32
fxtod %f2, u00
fxtod %f4, u32
fdtox a48, a48
std a00, [%sp+2223+0]
fmuld u00, v00, p00
std a16, [%sp+2223+8]
fmuld u00, v16, p16
std a32, [%sp+2223+16]
fmuld u00, v32, p32
std a48, [%sp+2223+24]
faddd p00, r64, a00
fmuld u32, v00, r32
faddd p16, r80, a16
fmuld u00, v48, p48
addcc %i2, 8, %i2
bnz,pt %xcc, .L_three_or_more
fmuld u32, v16, r48
.L_two:
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
fdtox a00, a00
faddd p48, r48, a48
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
ldx [%sp+2223+0], i00
fdtox a32, a32
ldx [%sp+2223+8], i16
ldx [%sp+2223+16], i32
ldx [%sp+2223+24], i48
fdtox a48, a48
std a00, [%sp+2223+0]
std a16, [%sp+2223+8]
std a32, [%sp+2223+16]
std a48, [%sp+2223+24]
add %i2, 8, %i2
fdtox r64, a00
mov i00, %g5 C i00+ now in g5
fdtox r80, a16
ldx [%sp+2223+0], i00
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
ldx [%sp+2223+16], i32
sllx i48, 32, %l6 C (i48 << 32)
ldx [%sp+2223+24], i48
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
add %l6, %o2, %o2 C mi64- in %o2
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
add cy, %g5, %o4 C x = prev(i00) + cy
b .L_out_2
add %i2, 8, %i2
.L_three_or_more:
ld [%i5+%i2], %f3 C read low 32 bits of up[i]
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
ld [%i1+%i2], %f5 C read high 32 bits of up[i]
fdtox a00, a00
faddd p48, r48, a48
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
ldx [%sp+2223+0], i00
fdtox a32, a32
ldx [%sp+2223+8], i16
fxtod %f2, u00
ldx [%sp+2223+16], i32
fxtod %f4, u32
ldx [%sp+2223+24], i48
fdtox a48, a48
std a00, [%sp+2223+0]
fmuld u00, v00, p00
std a16, [%sp+2223+8]
fmuld u00, v16, p16
std a32, [%sp+2223+16]
fmuld u00, v32, p32
std a48, [%sp+2223+24]
faddd p00, r64, a00
fmuld u32, v00, r32
faddd p16, r80, a16
fmuld u00, v48, p48
addcc %i2, 8, %i2
bnz,pt %xcc, .L_four_or_more
fmuld u32, v16, r48
.L_three:
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
fdtox a00, a00
faddd p48, r48, a48
mov i00, %g5 C i00+ now in g5
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
ldx [%sp+2223+0], i00
fdtox a32, a32
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
ldx [%sp+2223+16], i32
sllx i48, 32, %l6 C (i48 << 32)
ldx [%sp+2223+24], i48
fdtox a48, a48
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
std a32, [%sp+2223+16]
add %l6, %o2, %o2 C mi64- in %o2
std a48, [%sp+2223+24]
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
add cy, %g5, %o4 C x = prev(i00) + cy
b .L_out_3
add %i2, 8, %i2
.L_four_or_more:
ld [%i5+%i2], %f3 C read low 32 bits of up[i]
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
ld [%i1+%i2], %f5 C read high 32 bits of up[i]
fdtox a00, a00
faddd p48, r48, a48
mov i00, %g5 C i00+ now in g5
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
ldx [%sp+2223+0], i00
fdtox a32, a32
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
fxtod %f2, u00
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
ldx [%sp+2223+16], i32
fxtod %f4, u32
sllx i48, 32, %l6 C (i48 << 32)
ldx [%sp+2223+24], i48
fdtox a48, a48
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
fmuld u00, v00, p00
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
fmuld u00, v16, p16
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
std a32, [%sp+2223+16]
fmuld u00, v32, p32
add %l6, %o2, %o2 C mi64- in %o2
std a48, [%sp+2223+24]
faddd p00, r64, a00
fmuld u32, v00, r32
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
faddd p16, r80, a16
fmuld u00, v48, p48
add cy, %g5, %o4 C x = prev(i00) + cy
addcc %i2, 8, %i2
bnz,pt %xcc, .Loop
fmuld u32, v16, r48
.L_four:
b,a .L_out_4
C BEGIN MAIN LOOP
.align 16
.Loop:
C 00
srlx %o4, 16, %o5 C (x >> 16)
ld [%i5+%i2], %f3 C read low 32 bits of up[i]
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
C 01
add %o5, %o2, %o2 C mi64 in %o2 2nd ASSIGNMENT
and %o4, xffff, %o5 C (x & 0xffff)
ld [%i1+%i2], %f5 C read high 32 bits of up[i]
fdtox a00, a00
C 02
faddd p48, r48, a48
C 03
srlx %o2, 48, %o7 C (mi64 >> 48)
mov i00, %g5 C i00+ now in g5
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
C 04
sllx %o2, 16, %i3 C (mi64 << 16)
add %o7, %o1, cy C new cy
ldx [%sp+2223+0], i00
fdtox a32, a32
C 05
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
fxtod %f2, u00
C 06
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
ldx [%sp+2223+16], i32
fxtod %f4, u32
C 07
sllx i48, 32, %l6 C (i48 << 32)
or %i3, %o5, %o5
ldx [%sp+2223+24], i48
fdtox a48, a48
C 08
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
fmuld u00, v00, p00
C 09
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
fmuld u00, v16, p16
C 10
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
std a32, [%sp+2223+16]
fmuld u00, v32, p32
C 11
add %l6, %o2, %o2 C mi64- in %o2
std a48, [%sp+2223+24]
faddd p00, r64, a00
fmuld u32, v00, r32
C 12
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
stx %o5, [%i4+%i2]
faddd p16, r80, a16
fmuld u00, v48, p48
C 13
add cy, %g5, %o4 C x = prev(i00) + cy
addcc %i2, 8, %i2
bnz,pt %xcc, .Loop
fmuld u32, v16, r48
C END MAIN LOOP
.L_out_4:
srlx %o4, 16, %o5 C (x >> 16)
fmuld u32, v32, r64 C FIXME not urgent
faddd p32, r32, a32
add %o5, %o2, %o2 C mi64 in %o2 2nd ASSIGNMENT
and %o4, xffff, %o5 C (x & 0xffff)
fdtox a00, a00
faddd p48, r48, a48
srlx %o2, 48, %o7 C (mi64 >> 48)
mov i00, %g5 C i00+ now in g5
fmuld u32, v48, r80 C FIXME not urgent
fdtox a16, a16
sllx %o2, 16, %i3 C (mi64 << 16)
add %o7, %o1, cy C new cy
ldx [%sp+2223+0], i00
fdtox a32, a32
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
ldx [%sp+2223+16], i32
sllx i48, 32, %l6 C (i48 << 32)
or %i3, %o5, %o5
ldx [%sp+2223+24], i48
fdtox a48, a48
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
std a32, [%sp+2223+16]
add %l6, %o2, %o2 C mi64- in %o2
std a48, [%sp+2223+24]
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
stx %o5, [%i4+%i2]
add cy, %g5, %o4 C x = prev(i00) + cy
add %i2, 8, %i2
.L_out_3:
srlx %o4, 16, %o5 C (x >> 16)
add %o5, %o2, %o2 C mi64 in %o2 2nd ASSIGNMENT
and %o4, xffff, %o5 C (x & 0xffff)
fdtox r64, a00
srlx %o2, 48, %o7 C (mi64 >> 48)
mov i00, %g5 C i00+ now in g5
fdtox r80, a16
sllx %o2, 16, %i3 C (mi64 << 16)
add %o7, %o1, cy C new cy
ldx [%sp+2223+0], i00
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
ldx [%sp+2223+16], i32
sllx i48, 32, %l6 C (i48 << 32)
or %i3, %o5, %o5
ldx [%sp+2223+24], i48
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
std a00, [%sp+2223+0]
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
std a16, [%sp+2223+8]
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
add %l6, %o2, %o2 C mi64- in %o2
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
stx %o5, [%i4+%i2]
add cy, %g5, %o4 C x = prev(i00) + cy
add %i2, 8, %i2
.L_out_2:
srlx %o4, 16, %o5 C (x >> 16)
add %o5, %o2, %o2 C mi64 in %o2 2nd ASSIGNMENT
and %o4, xffff, %o5 C (x & 0xffff)
srlx %o2, 48, %o7 C (mi64 >> 48)
mov i00, %g5 C i00+ now in g5
sllx %o2, 16, %i3 C (mi64 << 16)
add %o7, %o1, cy C new cy
ldx [%sp+2223+0], i00
srlx i16, 48, %l4 C (i16 >> 48)
mov i16, %g2
ldx [%sp+2223+8], i16
srlx i48, 16, %l5 C (i48 >> 16)
mov i32, %g4 C i32+ now in g4
sllx i48, 32, %l6 C (i48 << 32)
or %i3, %o5, %o5
srlx %g4, 32, %o3 C (i32 >> 32)
add %l5, %l4, %o1 C hi64- in %o1
sllx %g4, 16, %o2 C (i32 << 16)
add %o3, %o1, %o1 C hi64 in %o1 1st ASSIGNMENT
sllx %o1, 48, %o3 C (hi64 << 48)
add %g2, %o2, %o2 C mi64- in %o2
add %l6, %o2, %o2 C mi64- in %o2
sub %o2, %o3, %o2 C mi64 in %o2 1st ASSIGNMENT
stx %o5, [%i4+%i2]
add cy, %g5, %o4 C x = prev(i00) + cy
add %i2, 8, %i2
.L_out_1:
srlx %o4, 16, %o5 C (x >> 16)
add %o5, %o2, %o2 C mi64 in %o2 2nd ASSIGNMENT
and %o4, xffff, %o5 C (x & 0xffff)
srlx %o2, 48, %o7 C (mi64 >> 48)
sllx %o2, 16, %i3 C (mi64 << 16)
add %o7, %o1, cy C new cy
or %i3, %o5, %o5
stx %o5, [%i4+%i2]
sllx i00, 0, %g2
add %g2, cy, cy
sllx i16, 16, %g3
add %g3, cy, cy
return %i7+8
mov cy, %o0
EPILOGUE(mpn_mul_1)
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