mpir/mpn/x86_64w/modexact_1c_odd.asm

; PROLOGUE(mpn_modexact_1c_odd)

;  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.
;
;  mp_limb_t  mpn_modexact_1_odd(mp_ptr, mp_size_t, mp_limb_t)
;  mp_limb_t mpn_modexact_1c_odd(mp_ptr, mp_size_t, mp_limb_t, mp_limb_t)
;  rax                              rdi        rsi        rdx        rcx
;  rax                              rcx        rdx         r8         r9

%include "yasm_mac.inc"

%define reg_save_list       rsi, rdi

    BITS 64
    
    extern  __gmp_modlimb_invert_table

    LEAF_PROC mpn_modexact_1_odd
    mov     r9, 0               ; carry

    FRAME_PROC mpn_modexact_1c_odd, 0, reg_save_list
    
    ; first use Newton's iteration to invert the divisor limb (d) using 
    ; f(x) = 1/x - d  and x[i+1] = x[i] - f(x[i]) / f'(x[i]) to give
    ; the iteration formula: x[i+1] = x[i] * (2 - d * x[i])
    
    mov     rsi, rdx
    mov     rdx, r8    
    shr     edx, 1              ; div / 2
    lea     r10, [rel __gmp_modlimb_invert_table]
    and     edx, 127
    movzx   edx, byte [rdx+r10] ; inv -> rdx (8-bit approx)

    mov     rax, [rcx]          ; first limb of numerator
    lea     r11, [rcx+rsi*8]    ; pointer to top of src
    mov     rdi, r8             ; save divisor

    lea     ecx, [rdx+rdx]
    imul    edx, edx
    neg     rsi                 ; limb offset from top of src
    imul    edx, edi
    sub     ecx, edx            ; inv -> rcx (16-bit approx)

    lea     edx, [rcx+rcx]
    imul    ecx, ecx
    imul    ecx, edi
    sub     edx, ecx            ; inv -> rdx (32-bit approx)
    xor     ecx, ecx

    lea     r10, [rdx+rdx]
    imul    rdx, rdx
    imul    rdx, r8
    sub     r10, rdx            ; inv -> r10 (64-bit approx)

    mov     rdx, r9             ; intial carry -> rdx
    add     rsi, 1              ; adjust limb offset
    jz      .2

    mov     r9, r11
    lea     rsi,[r11+rsi*8]
    
    xalign    16
.1: sub     rax, rdx
    adc     rcx, 0
    imul    rax, r10
    mul     r8
    lodsq
    sub     rax, rcx
    setc    cl
    cmp     r9, rsi
    jne     .1
.2: sub     rax, rdx
    adc     rcx, 0
    imul    rax, r10
    mul     r8
    lea     rax, [rcx+rdx]
    END_PROC reg_save_list

    end