142 lines
3.8 KiB
NASM
142 lines
3.8 KiB
NASM
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; Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
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;
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; Copyright 2008 Brian Gladman
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;
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; This file is part of the MPIR Library.
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;
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; The MPIR Library is free software; you can redistribute it and/or
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; modify it under the terms of the GNU Lesser General Public License as
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; published by the Free Software Foundation; either version 2.1 of the
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; License, or (at your option) any later version.
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;
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; The MPIR Library is distributed in the hope that it will be useful,
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; but WITHOUT ANY WARRANTY; without even the implied warranty of
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; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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; Lesser General Public License for more details.
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;
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; You should have received a copy of the GNU Lesser General Public
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; License along with the MPIR Library; see the file COPYING.LIB. If
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; not, write to the Free Software Foundation, Inc., 51 Franklin Street,
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; Fifth Floor, Boston, MA 02110-1301, USA.
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;
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; since the inverse takes a while to setup,plain division is used for small
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; Multiplying works out faster for size>=3 when the divisor is odd or size>=4
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; when the divisor is even.
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;
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; void mpn_divexact_1(mp_ptr, mp_ptr, mp_size_t, mp_limb_t)
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; rdi rsi rdx rcx
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; rcx rdx r8d r9
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%include "yasm_mac.inc"
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%define reg_save_list rsi, rdi
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BITS 64
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extern __gmp_modlimb_invert_table
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LEAF_PROC mpn_divexact_1
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movsxd r8, r8d
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mov r10, rdx
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mov rax, r9
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and rax, byte 1
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add rax, r8
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cmp rax, byte 4
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jae .2
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xor rdx,rdx
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.1:
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mov rax, [r10+r8*8-8]
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div r9
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mov [rcx+r8*8-8], rax
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sub r8, 1
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jnz .1
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ret ; avoid single byte return
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.2:
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FRAME_PROC ?mpn_divexact, 0, reg_save_list
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mov rsi, rdx ; src pointer
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mov rdi, rcx ; dst pointer
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bsf rcx, r9 ; remove powers of two
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shr r9, cl
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mov rax, r9
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shr rax, 1
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and rax, 127
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lea rdx, [rel __gmp_modlimb_invert_table]
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movzx rax, byte [rdx+rax]
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; If f(x) = 0, then x[n+1] = x[n] - f(x) / f'(x) is Newton's iteration for a
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; root. With f(x) = 1/x - v we obtain x[n + 1] = 2 * x[n] - v * x[n] * x[n]
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; as an iteration for x = 1 / v. This provides quadratic convergence so
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; that the number of bits of precision doubles on each iteration. The
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; iteration starts with 8-bit precision.
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lea edx, [rax+rax]
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imul eax, eax
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imul eax, r9d
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sub edx, eax ; inv -> rdx (16-bit approx)
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lea eax, [rdx+rdx]
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imul edx, edx
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imul edx, r9d
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sub eax, edx ; inv -> rdx (32-bit approx)
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lea rdx, [rax+rax]
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imul rax, rax
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imul rax, r9
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sub rdx, rax ; inv -> rdx (64-bit approx)
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lea rsi, [rsi+r8*8]
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lea rdi, [rdi+r8*8]
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neg r8
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mov r10, rdx ; inverse multiplier -> r10
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xor r11, r11
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mov rax, [rsi+r8*8]
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or rcx, rcx
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mov rdx, [rsi+r8*8+8]
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jz .4 ; if divisor is odd
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shrd rax, rdx, cl
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add r8, 1
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jmp .6
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xalign 16
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.3:
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mul r9 ; divisor is odd
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mov rax, [rsi+r8*8]
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sub rdx, r11
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sub rax, rdx
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sbb r11, r11
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.4:
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imul rax, r10
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mov [rdi+r8*8], rax
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add r8, 1
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jnz .3
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jmp .7
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xalign 16
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.5:
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mul r9 ; divisor is even
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sub rdx, r11
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mov rax, [rsi+r8*8-8]
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mov r11, [rsi+r8*8]
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shrd rax, r11, cl
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sub rax, rdx
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sbb r11, r11
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.6:
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imul rax, r10
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mov [rdi+r8*8-8],rax
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add r8, 1
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jnz .5
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mul r9
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mov rax, [rsi-8]
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sub rdx, r11
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shr rax, cl
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sub rax, rdx
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imul rax, r10
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mov [rdi-8], rax
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.7:
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END_PROC reg_save_list
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end
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