mpir/mpn/x86_64w/dive_1.asm

;  Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
;
;  Copyright 2008 Brian Gladman
;
;  This file is part of the MPIR Library.
;
;  The MPIR 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 MPIR 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 MPIR Library; see the file COPYING.LIB.  If
;  not, write to the Free Software Foundation, Inc., 51 Franklin Street,
;  Fifth Floor, Boston, MA 02110-1301, USA.

; AMD64 mpn_divexact_1 -- mpn by limb exact division
;
;  Calling interface:
;
; void mpn_divexact_1(
;     mp_ptr dst,           rcx
;       mp_srcptr src,      rdx
;       mp_size_t size,      r8
;       mp_limb_t divisor    r9
; )
;
; since the inverse takes a while to setup,plain division is used for small
; Multiplying works out faster for size>=3 when the divisor is odd or size>=4
; when the divisor is even.
;
; This is an SEH Frame Function with a leaf prologue

%include "x86_64_asm.inc"

%define reg_save_list       rsi, rdi

    bits    64
    section .text

    extern  __gmp_modlimb_invert_table
    global  __gmpn_divexact_1

%ifdef DLL
    export  __gmpn_divexact_1
%endif

__gmpn_divexact_1:
    movsxd  r8,r8d
    mov     r10,rdx
    mov     rax,r9
    and     rax,byte 1
    add     rax,r8
    cmp     rax,byte 4
    jae     L_mul_by_inverse
    xor     rdx,rdx
L_div_top:
    mov     rax,[r10+r8*8-8]
    div     r9
    mov     [rcx+r8*8-8],rax
    dec     r8
    jnz     L_div_top
    rep     ret         ; avoid single byte return

prologue    L_mul_by_inverse, 0, reg_save_list
    mov     rsi,rdx     ; src pointer
    mov     rdi,rcx     ; dst pointer
    mov     rax,r9
    stc
    sbb     rcx,rcx     ; -1 -> rcx, r11
    mov     r11,rcx
L_strip_twos:
    shr     rax,1
    inc     rcx
    jnc     L_strip_twos
    lea     r9,[rax+rax+1]
    and     rax,byte 127
    lea     rdx,[rel __gmp_modlimb_invert_table]
    movzx   rax,byte [rdx+rax]

; If f(x) = 0, then x[n+1] = x[n] - f(x) / f'(x) is Newton's iteration for a
; root. With f(x) = 1/x - v we obtain x[n + 1] = 2 * x[n] - v * x[n] * x[n]
; as an iteration for x = 1 / v.  This provides quadratic convergence so
; that the number of bits of precision doubles on each iteration.  The
; iteration starts with 8-bit precision.

    lea     edx, [rax+rax]
    imul    eax, eax
    imul    eax, r9d
    sub     edx, eax           ; inv -> rdx (16-bit approx)

    lea     eax, [rdx+rdx]
    imul    edx, edx
    imul    edx, r9d
    sub     eax, edx           ; inv -> rcx (32-bit approx)

    lea     rdx, [rax+rax]
    imul    rax, rax
    imul    rax, r9
    sub     rdx, rax           ; inv -> rcx (64-bit approx)

    mov     r8,r8
    lea     rsi,[rsi+r8*8]
    lea     rdi,[rdi+r8*8]
    neg     r8

    mov     r10,rdx
    xor     r11,r11
    mov     rax,[rsi+r8*8]
    or      rcx,rcx
    mov     rdx,[rsi+r8*8+8]
    jz      L_odd_entry
    shrd    rax, rdx, cl
    inc     r8
    jmp     L_even_entry

L_odd_top:
    mul     r9
    mov     rax,[rsi+r8*8]
    sub     rdx,r11
    sub     rax,rdx
    sbb     r11,r11
L_odd_entry:
    imul    rax,r10
    mov     [rdi+r8*8],rax
    inc     r8
    jnz     L_odd_top
    jmp     L_exit

L_even_top:
    mul     r9
    sub     rdx,r11
    mov     rax,[rsi+r8*8-8]
    mov     r11,[rsi+r8*8]
    shrd    rax,r11,cl
    sub     rax,rdx
    sbb     r11,r11

L_even_entry:
    imul    rax,r10
    mov     [rdi+r8*8-8],rax
    inc     r8
    jnz     L_even_top
    mul     r9
    mov     rax,[rsi-8]
    sub     rdx,r11
    shr     rax,cl
    sub     rax,rdx
    imul    rax,r10
    mov     [rdi-8],rax
L_exit:
    epilogue reg_save_list

    end