175 lines
5.0 KiB
ActionScript
175 lines
5.0 KiB
ActionScript
; Copyright 2000, 2001, 2002, 2003, 2004, 2005, 2006 Free Software
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; Foundation, Inc.
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;
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; Copyright 2008 William Hart
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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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; cycles/limb
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; Hammer: 10
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; Prescott/Nocona: 33
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; mp_limb_t mpn_modexact_1_odd (mp_srcptr src, mp_size_t size,
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; mp_limb_t divisor);
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; mp_limb_t mpn_modexact_1c_odd (mp_srcptr src, mp_size_t size,
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; mp_limb_t divisor, mp_limb_t carry);
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;
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; The dependent chain in the main loop is
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;
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; cycles
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; sub rax, r8 1
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; imul rax, r9 4
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; mul rsi 5
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; ----
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; total 10
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;
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; The movq load from src seems to need to be scheduled back before the jz to
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; achieve this speed, out-of-order execution apparently can't completely
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; hide the latency otherwise.
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;
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; The l=src[i]-cbit step is rotated back too, since that allows us to avoid
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; it for the first iteration (where there's no cbit).
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;
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; The code alignment used (32-byte) for the loop also seems necessary.
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; Without that the non-PIC case has adcq crossing the 0x60 offset,
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; apparently making it run at 11 cycles instead of 10.
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;
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; Not done:
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;
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; divq for size==1 was measured at about 79 cycles, compared to the inverse
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; at about 25 cycles (both including function call overheads), so that's not
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; used.
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;
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; Enhancements:
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;
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; For PIC, we shouldn't really need the GOT fetch for modlimb_invert_table,
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; it'll be in rodata or text in libgmp.so and can be accessed directly %rip
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; relative. This would be for small model only (something we don't
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; presently detect, but which is all that gcc 3.3.3 supports), since 8-byte
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; PC-relative relocations are apparently not available. Some rough
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; experiments with binutils 2.13 looked worrylingly like it might come out
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; with an unwanted text segment relocation though, even with ".protected".
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; AMD64 mpn_modexact_1_odd -- exact division style remainder.
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;
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; mp_limb_t mpn_modexact_1_odd (
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; mp_srcptr src, rdi
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; mp_size_t size, rsi
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; mp_limb_t divisor rdx
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; );
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; mp_limb_t mpn_modexact_1c_odd (
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; mp_srcptr src, rdi
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; mp_size_t size, rsi
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; mp_limb_t divisor, rdx
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; mp_limb_t carry rcx
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; );
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;
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%include '../yasm_mac.inc'
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BITS 64
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align 32
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G_EXTERN __gmp_modlimb_invert_table
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GLOBAL_FUNC mpn_modexact_1_odd
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mov ecx, 0 ; carry
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GLOBAL_FUNC mpn_modexact_1c_odd
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mov r8, rdx
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shr edx, 1
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%ifdef GSYM_PREFIX
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%define mod_table ___gmp_modlimb_invert_table
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%else
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%define mod_table __gmp_modlimb_invert_table
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%endif
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; first use Newton's iteration to invert the divisor limb (d) using
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; f(x) = 1/x - d and x[i+1] = x[i] - f(x[i]) / f'(x[i]) to give
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; the iteration formula: x[i+1] = x[i] * (2 - d * x[i])
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%ifdef PIC
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mov r9, [mod_table wrt rip wrt ..gotpcrel]
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%else
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lea r9, [mod_table wrt rip]
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%endif
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and edx, 127
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mov r10, rcx
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movzx edx, byte [rdx+r9] ; inv -> rdx (8-bit approx)
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mov rax, [rdi] ; first limb of numerator
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lea r11, [rdi+rsi*8] ; pointer to top of src
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mov rdi, r8 ; save divisor
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lea ecx, [rdx+rdx]
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imul rdx, rdx
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neg rsi ; limb offset from top of src
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imul edx, edi
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sub ecx, edx ; inv -> rcx (16-bit approx)
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lea edx, [rcx+rcx]
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imul ecx, ecx
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imul ecx, edi
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sub edx, ecx ; inv -> rdx (32-bit approx)
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xor ecx, ecx
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lea r9, [rdx+rdx]
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imul rdx, rdx
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imul rdx, r8
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sub r9, rdx ; inv -> r10 (64-bit approx)
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mov rdx, r10 ; intial carry -> rdx
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inc rsi ; adjust limb offset
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jz label1
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align 16
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label0: ; now multiply through by inverse in loop
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sub rax, rdx
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adc rcx, 0
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imul rax, r9
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mul r8
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mov rax, [r11+rsi*8]
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sub rax, rcx
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setc cl
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inc rsi
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jnz label0
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label1: ; do final multiply
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sub rax, rdx
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adc rcx, 0
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imul rax, r9
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mul r8
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lea rax, [rcx+rdx] ; return remainder
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ret
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