mpn/x86_64/divrem_1.asm

dnl  x86-64 mpn_divrem_1 -- mpn by limb division.

dnl  Copyright 2004, 2005, 2007, 2008, 2009 Free Software Foundation, Inc.

dnl  This file is part of the GNU MP Library.

dnl  The GNU MP Library is free software; you can redistribute it and/or modify
dnl  it under the terms of the GNU Lesser General Public License as published
dnl  by the Free Software Foundation; either version 3 of the License, or (at
dnl  your option) any later version.

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 Lesser General Public
dnl  License for more details.

dnl  You should have received a copy of the GNU Lesser General Public License
dnl  along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.

include(`../config.m4')


C		norm	unorm	frac
C K8		13	13	12
C P4		44.2	44.2	42.3
C P6 core2	25	24.5	19.3
C P6 corei7	21.5	20.7	18
C P6 atom	42	52	37

C TODO
C  * Compute the inverse without relying on the div instruction.
C    Newton's method and mulq, or perhaps the faster fdiv.
C  * Tune prologue.
C  * Optimize for Core 2.

C The code for unnormalized divisors works also for normalized divisors, but
C for some reason it runs really slowly (on K8) for that case.  Use special
C code until we can address this.  The Intel Atom is also affected, but
C understandably (shld slowness).
define(`SPECIAL_CODE_FOR_NORMALIZED_DIVISOR',1)

C mp_limb_t
C mpn_divrem_1 (mp_ptr qp, mp_size_t fn,
C               mp_srcptr np, mp_size_t nn, mp_limb_t d)

C mp_limb_t
C mpn_preinv_divrem_1 (mp_ptr qp, mp_size_t fn,
C                      mp_srcptr np, mp_size_t nn, mp_limb_t d,
C                      mp_limb_t dinv, int cnt)

C INPUT PARAMETERS
define(`qp',		`%rdi')
define(`fn_param',	`%rsi')
define(`up_param',	`%rdx')
define(`un_param',	`%rcx')
define(`d',		`%r8')
define(`dinv',		`%r9')		C only for mpn_preinv_divrem_1
C       shift passed on stack		C only for mpn_preinv_divrem_1

define(`cnt',		`%rcx')
define(`up',		`%rsi')
define(`fn',		`%r12')
define(`un',		`%rbx')


C rax rbx rcx rdx rsi rdi rbp r8  r9  r10 r11 r12 r13 r14 r15
C         cnt         qp      d  dinv

ASM_START()
	TEXT
	ALIGN(16)
PROLOGUE(mpn_preinv_divrem_1)
	xor	%eax, %eax
	push	%r13
	push	%r12
	push	%rbp
	push	%rbx

	mov	fn_param, fn
	mov	un_param, un
	add	fn_param, un_param
	mov	up_param, up

	lea	-8(qp,un_param,8), qp

	test	d, d
	js	L(nent)
	mov	40(%rsp), R8(cnt)
	shl	R8(cnt), d
	jmp	L(uent)
EPILOGUE()

	ALIGN(16)
PROLOGUE(mpn_divrem_1)
	xor	%eax, %eax
	push	%r13
	push	%r12
	push	%rbp
	push	%rbx

	mov	fn_param, fn
	mov	un_param, un
	add	fn_param, un_param
	mov	up_param, up
	je	L(ret)

	lea	-8(qp,un_param,8), qp
	xor	R32(%rbp), R32(%rbp)


ifdef(`SPECIAL_CODE_FOR_NORMALIZED_DIVISOR',`
	test	d, d
	jns	L(unnormalized)

L(normalized):
	test	un, un
	je	L(8)			C un == 0
	mov	-8(up,un,8), %rbp
	dec	un
	mov	%rbp, %rax
	sub	d, %rbp
	cmovb	%rax, %rbp
	sbb	%eax, %eax
	inc	%eax
	mov	%rax, (qp)
	lea	-8(qp), qp
L(8):
	mov	d, %rdx
	mov	$-1, %rax
	not	%rdx
	div	d			C FREE rax rdx rcx r9 r10 r11
	mov	%rax, dinv
	mov	%rbp, %rax
	jmp	L(nent)

	ALIGN(16)
L(nloop):				C		    cycK8  cycP6  cycP4
	mov	(up,un,8), %r10		C
	lea	1(%rax), %rbp		C
	mul	dinv			C		     0,13   0,19  0,45
	add	%r10, %rax		C		     4      8     12
	adc	%rbp, %rdx		C		     5      9     13
	mov	%rax, %rbp		C		     5      9     13
	mov	%rdx, %r13		C		     6      11    23
	imul	d, %rdx			C		     6      11    23
	sub	%rdx, %r10		C		     10     16    33
	mov	d, %rax			C
	add	%r10, %rax		C		     11     17    34
	cmp	%rbp, %r10		C		     11     17    34
	cmovb	%r10, %rax		C		     12     18    35
	adc	$-1, %r13		C
	cmp	d, %rax			C
	jae	L(nfx)			C
L(nok):	mov	%r13, (qp)		C
	sub	$8, qp			C
L(nent):dec	un			C
	jns	L(nloop)		C

	xor	%ecx, %ecx
	jmp	L(87)

L(nfx):	sub	d, %rax
	inc	%r13
	jmp	L(nok)
')

L(unnormalized):
	test	un, un
	je	L(44)
	mov	-8(up,un,8), %rax
	cmp	d, %rax
	jae	L(44)
	mov	%rbp, (qp)
	mov	%rax, %rbp
	lea	-8(qp), qp
	je	L(ret)
	dec	un
L(44):
	bsr	d, %rcx
	not	%ecx
	sal	%cl, d
	sal	%cl, %rbp
	mov	d, %rdx
	mov	$-1, %rax
	not	%rdx
	div	d			C FREE rax rdx r9 r10 r11
	test	un, un
	mov	%rax, dinv
	mov	%rbp, %rax
	je	L(87)
L(uent):
	mov	-8(up,un,8), %rbp
	shr	%cl, %rax
	shld	%cl, %rbp, %rax
	sub	$2, un
	js	L(ulast)

	ALIGN(16)
L(uloop):
	nop
	mov	(up,un,8), %r10
	lea	1(%rax), %r11
	shld	%cl, %r10, %rbp
	mul	dinv
	add	%rbp, %rax
	adc	%r11, %rdx
	mov	%rax, %r11
	mov	%rdx, %r13
	imul	d, %rdx
	sub	%rdx, %rbp
	mov	d, %rax
	add	%rbp, %rax
	cmp	%r11, %rbp
	cmovb	%rbp, %rax
	adc	$-1, %r13
	cmp	d, %rax
	jae	L(ufx)
L(uok):	mov	%r13, (qp)
	sub	$8, qp
	dec	un
	mov	%r10, %rbp
	jns	L(uloop)
L(ulast):
	lea	1(%rax), %r11
	sal	%cl, %rbp
	mul	dinv
	add	%rbp, %rax
	adc	%r11, %rdx
	mov	%rax, %r11
	mov	%rdx, %r13
	imul	d, %rdx
	sub	%rdx, %rbp
	mov	d, %rax
	add	%rbp, %rax
	cmp	%r11, %rbp
	cmovb	%rbp, %rax
	adc	$-1, %r13
	cmp	d, %rax
	jae	L(93)
L(69):	mov	%r13, (qp)
	sub	$8, qp
	jmp	L(87)

L(ufx):	sub	d, %rax
	inc	%r13
	jmp	L(uok)

L(93):	sub	d, %rax
	inc	%r13
	jmp	L(69)

L(87):	mov	d, %rbp
	neg	%rbp
	jmp	L(87b)

	ALIGN(16)
L(floop):				C		    cycK8  cycP6  cycP4
	lea	1(%rax), %r11		C
	mul	dinv			C		     0,12
	add	%r11, %rdx		C		     5
	mov	%rax, %r11		C		     4
	mov	%rdx, %r13		C		     6
	imul	%rbp, %rdx		C		     6
	mov	d, %rax			C
	add	%rdx, %rax		C		     10
	cmp	%r11, %rdx		C		     10
	cmovb	%rdx, %rax		C		     11
	adc	$-1, %r13		C
	mov	%r13, (qp)		C
	sub	$8, qp			C
L(87b):	dec	fn			C
	jns	L(floop)		C

	shr	%cl, %rax
L(ret):	pop	%rbx
	pop	%rbp
	pop	%r12
	pop	%r13
	ret
EPILOGUE()