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dnl x86-64 mpn_div_qr_1n_pi1
dnl -- Divide an mpn number by a normalized single-limb number,
dnl using a single-limb inverse.
dnl Contributed to the GNU project by Niels Möller
dnl Copyright 2013 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 c/l
C AMD K8,K9 13
C AMD K10 13
C AMD bull 16.5
C AMD pile 15
C AMD steam ?
C AMD bobcat 16
C AMD jaguar ?
C Intel P4 47 poor
C Intel core 19.25
C Intel NHM 18
C Intel SBR 15 poor
C Intel IBR 13
C Intel HWL 11.7
C Intel BWL ?
C Intel atom 52 very poor
C VIA nano 19
C INPUT Parameters
define(`QP', `%rdi')
define(`UP', `%rsi')
define(`UN_INPUT', `%rdx')
define(`U1', `%rcx') C Also in %rax
define(`D', `%r8')
define(`DINV', `%r9')
C Invariants
define(`B2', `%rbp')
define(`B2md', `%rbx')
C Variables
define(`UN', `%r8') C Overlaps D input
define(`T', `%r10')
define(`U0', `%r11')
define(`U2', `%r12')
define(`Q0', `%r13')
define(`Q1', `%r14')
define(`Q2', `%r15')
ABI_SUPPORT(STD64)
ASM_START()
TEXT
ALIGN(16)
PROLOGUE(mpn_div_qr_1n_pi1)
FUNC_ENTRY(4)
IFDOS(` mov 56(%rsp), %r8 ')
IFDOS(` mov 64(%rsp), %r9 ')
dec UN_INPUT
jnz L(first)
C Just a single 2/1 division.
C T, U0 are allocated in scratch registers
lea 1(U1), T
mov U1, %rax
mul DINV
mov (UP), U0
add U0, %rax
adc T, %rdx
mov %rdx, T
imul D, %rdx
sub %rdx, U0
cmp U0, %rax
lea (U0, D), %rax
cmovnc U0, %rax
sbb $0, T
cmp D, %rax
jc L(single_div_done)
sub D, %rax
add $1, T
L(single_div_done):
mov T, (QP)
FUNC_EXIT()
ret
L(first):
C FIXME: Could delay some of these until we enter the loop.
push %r15
push %r14
push %r13
push %r12
push %rbx
push %rbp
mov D, B2
imul DINV, B2
neg B2
mov B2, B2md
sub D, B2md
C D not needed until final reduction
push D
mov UN_INPUT, UN C Clobbers D
mov DINV, %rax
mul U1
mov %rax, Q0
add U1, %rdx
mov %rdx, T
mov B2, %rax
mul U1
mov -8(UP, UN, 8), U0
mov (UP, UN, 8), U1
mov T, (QP, UN, 8)
add %rax, U0
adc %rdx, U1
sbb U2, U2
dec UN
mov U1, %rax
jz L(final)
ALIGN(16)
C Loop is 28 instructions, 30 decoder slots, should run in 10 cycles.
C At entry, %rax holds an extra copy of U1
L(loop):
C {Q2, Q1, Q0} <-- DINV * U1 + B (Q0 + U2 DINV) + B^2 U2
C Remains to add in B (U1 + c)
mov DINV, Q1
mov U2, Q2
and U2, Q1
neg Q2
mul DINV
add %rdx, Q1
adc $0, Q2
add Q0, Q1
mov %rax, Q0
mov B2, %rax
lea (B2md, U0), T
adc $0, Q2
C {U2, U1, U0} <-- (U0 + U2 B2 -c U) B + U1 B2 + u
mul U1
and B2, U2
add U2, U0
cmovnc U0, T
C {QP+UN, ...} <-- {QP+UN, ...} + {Q2, Q1} + U1 + c
adc U1, Q1
mov -8(UP, UN, 8), U0
adc Q2, 8(QP, UN, 8)
jc L(q_incr)
L(q_incr_done):
add %rax, U0
mov T, %rax
adc %rdx, %rax
mov Q1, (QP, UN, 8)
sbb U2, U2
dec UN
mov %rax, U1
jnz L(loop)
L(final):
pop D
mov U2, Q1
and D, U2
sub U2, %rax
neg Q1
mov %rax, U1
sub D, %rax
cmovc U1, %rax
sbb $-1, Q1
lea 1(%rax), T
mul DINV
add U0, %rax
adc T, %rdx
mov %rdx, T
imul D, %rdx
sub %rdx, U0
cmp U0, %rax
lea (U0, D), %rax
cmovnc U0, %rax
sbb $0, T
cmp D, %rax
jc L(div_done)
sub D, %rax
add $1, T
L(div_done):
add T, Q0
mov Q0, (QP)
adc Q1, 8(QP)
jnc L(done)
L(final_q_incr):
addq $1, 16(QP)
lea 8(QP), QP
jc L(final_q_incr)
L(done):
pop %rbp
pop %rbx
pop %r12
pop %r13
pop %r14
pop %r15
FUNC_EXIT()
ret
L(q_incr):
C U1 is not live, so use it for indexing
lea 16(QP, UN, 8), U1
L(q_incr_loop):
addq $1, (U1)
jnc L(q_incr_done)
lea 8(U1), U1
jmp L(q_incr_loop)
EPILOGUE()
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