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(6)

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()