639 lines
12 KiB
NASM
639 lines
12 KiB
NASM
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dnl AMD K8 mpn_sqr_basecase -- square an mpn number.
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dnl This file is just an adaptation of similar file in the k7 directory.
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dnl Adapted by P. Gaudry in April 2005.
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dnl Here is the copyright of the original k7 version:
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dnl Copyright 1999, 2000, 2001, 2002 Free Software Foundation, Inc.
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dnl
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dnl This file is part of the GNU MP Library.
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dnl
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dnl The GNU MP Library is free software; you can rrdistribute it and/or
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dnl modify it under the terms of the GNU Lesser General Public License as
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dnl published by the Free Software Foundation; either version 2.1 of the
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dnl License, or (at your option) any later version.
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dnl
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dnl The GNU MP Library is distributed in the hope that it will be useful,
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dnl but WITHOUT ANY WARRANTY; without even the implied warranty of
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dnl MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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dnl Lesser General Public License for more details.
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dnl
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dnl You should have received a copy of the GNU Lesser General Public
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dnl License along with the GNU MP Library; see the file COPYING.LIB. If
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dnl not, write to the Free Software Foundation, Inc., 59 Temple Place -
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dnl Suite 330, Boston, MA 02111-1307, USA.
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include(`../config.m4')
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deflit(SQR_KARATSUBA_THRESHOLD_MAX, 34)
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ifdef(`SQR_KARATSUBA_THRESHOLD_OVERRIDE',
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`define(`SQR_KARATSUBA_THRESHOLD',SQR_KARATSUBA_THRESHOLD_OVERRIDE)')
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m4_config_gmp_mparam(`SQR_KARATSUBA_THRESHOLD')
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C deflit(UNROLL_COUNT, eval(SQR_KARATSUBA_THRESHOLD-3))
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deflit(UNROLL_COUNT, 31)
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C void mpn_sqr_basecase (mp_ptr dst, mp_srcptr src, mp_size_t size);
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C
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C With a SQR_KARATSUBA_THRESHOLD around 50 this code is about 1500 bytes,
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C which is quite a bit, but is considered good value since squares big
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C enough to use most of the code will be spending quite a few cycles in it.
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define(param_dst, %rdi)
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define(param_src, %rsi)
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define(param_size, %rdx)
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define(PARAM_DST, %r8)
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define(PARAM_SRC, %r9)
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define(PARAM_SIZE, %r10)
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TEXT
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ALIGN(32)
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PROLOGUE(mpn_sqr_basecase)
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movq param_size, %rcx
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movq param_src, %rax
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cmpq $2, %rcx
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movq param_dst, %rdx
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je L(two_limbs)
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ja L(three_or_more)
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C------------------------------------------------------------------------------
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C one limb only
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C rax src
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C rcx size
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C rdx dst
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C
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C rsi src
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C rdi dst
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movq (%rsi), %rax
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mulq %rax
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movq %rdx, 8(%rdi)
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movq %rax, (%rdi)
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ret
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C------------------------------------------------------------------------------
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C
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C Using the read/modify/write "add"s seems to be faster than saving and
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C restoring registers. Perhaps the loads for the first set hide under the
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C mul latency and the second gets store to load forwarding.
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ALIGN(16)
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L(two_limbs):
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C rax
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C rbx
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C rcx
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C rdx
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C rsi src
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C rdi dst
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C
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C r8 s0
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C r9 s1
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movq (%rsi), %r8
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movq 8(%rsi), %r9
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movq %r8, %rax
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mulq %rax C src[0]^2
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movq %rax, (%rdi) C dst[0]
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movq %r9, %rax
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movq %rdx, 8(%rdi) C dst[1]
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mulq %rax C src[1]^2
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movq %rax, 16(%rdi) C dst[2]
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movq %r8, %rax
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movq %rdx, 24(%rdi) C dst[3]
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mulq %r9 C src[0]*src[1]
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addq %rax, 8(%rdi)
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adcq %rdx, 16(%rdi)
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adcq $0, 24(%rdi)
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ASSERT(nc)
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addq %rax, 8(%rdi)
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adcq %rdx, 16(%rdi)
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adcq $0, 24(%rdi)
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ASSERT(nc)
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ret
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C------------------------------------------------------------------------------
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defframe(SAVE_RBX, -8)
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defframe(SAVE_RBP, -16)
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deflit(STACK_SPACE, 16)
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L(three_or_more):
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subq $STACK_SPACE, %rsp
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cmpq $4, %rcx
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jae L(four_or_more)
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deflit(`FRAME',STACK_SPACE)
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C------------------------------------------------------------------------------
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C Three limbs
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C
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C Writing out the loads and stores separately at the end of this code comes
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C out about 10 cycles faster than using adcls to memory.
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C rax src
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C rcx size
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C rdx dst
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movq %rbx, SAVE_RBX
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movq %rax, %rbx C src
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movq (%rax), %rax
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movq %rdx, %rcx C dst
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mulq %rax C src[0] ^ 2
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movq %rax, (%rcx)
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movq 8(%rbx), %rax
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movq %rdx, 8(%rcx)
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mulq %rax C src[1] ^ 2
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movq %rax, 16(%rcx)
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movq 16(%rbx), %rax
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movq %rdx, 24(%rcx)
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mulq %rax C src[2] ^ 2
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movq %rax, 32(%rcx)
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movq (%rbx), %rax
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movq %rdx, 40(%rcx)
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mulq 8(%rbx) C src[0] * src[1]
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movq %rax, %rsi
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movq (%rbx), %rax
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movq %rdx, %rdi
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mulq 16(%rbx) C src[0] * src[2]
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addq %rax, %rdi
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movq %rbp, SAVE_RBP
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movq $0, %rbp
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movq 8(%rbx), %rax
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adcq %rdx, %rbp
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mulq 16(%rbx) C src[1] * src[2]
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xorq %rbx, %rbx
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addq %rax, %rbp
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adcq $0, %rdx
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C rax
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C rbx zero, will be dst[5]
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C rcx dst
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C rdx dst[4]
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C rsi dst[1]
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C rdi dst[2]
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C rbp dst[3]
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adcq $0, %rdx
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addq %rsi, %rsi
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adcq %rdi, %rdi
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movq 8(%rcx), %rax
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adcq %rbp, %rbp
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adcq %rdx, %rdx
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adcq $0, %rbx
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addq %rax, %rsi
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movq 16(%rcx), %rax
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adcq %rax, %rdi
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movq 24(%rcx), %rax
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movq %rsi, 8(%rcx)
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adcq %rax, %rbp
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movq 32(%rcx), %rax
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movq %rdi, 16(%rcx)
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adcq %rax, %rdx
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movq 40(%rcx), %rax
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movq %rbp, 24(%rcx)
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adcq %rbx, %rax
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ASSERT(nc)
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movq SAVE_RBX, %rbx
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movq SAVE_RBP, %rbp
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movq %rdx, 32(%rcx)
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movq %rax, 40(%rcx)
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addq $FRAME, %rsp
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ret
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C------------------------------------------------------------------------------
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L(four_or_more):
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C First multiply src[0]*src[1..size-1] and store at dst[1..size].
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C Further products are added in rather than stored.
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C rax src
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C rbx
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C rcx size
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C rdx dst
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C rsi
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C rdi
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C rbp
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defframe(`VAR_COUNTER',-24)
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defframe(`VAR_JMP', -32)
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deflit(EXTRA_STACK_SPACE, 16)
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movq param_dst, PARAM_DST
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movq param_src, PARAM_SRC
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movq %rcx, PARAM_SIZE
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movq %rbx, SAVE_RBX
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leaq (%rdx,%rcx,8), %rdi C &dst[size]
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movq %rbp, SAVE_RBP
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leaq (%rax,%rcx,8), %rsi C &src[size]
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movq (%rax), %rbp C multiplier
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movq $0, %rbx
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decq %rcx
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negq %rcx
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subq $EXTRA_STACK_SPACE, %rsp
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deflit(`FRAME', STACK_SPACE+EXTRA_STACK_SPACE)
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L(mul_1):
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C rax scratch
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C rbx carry
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C rcx counter
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C rdx scratch
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C rsi &src[size]
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C rdi &dst[size]
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C rbp multiplier
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movq (%rsi,%rcx,8), %rax
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mulq %rbp
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addq %rbx, %rax
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movq %rax, (%rdi,%rcx,8)
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movq $0, %rbx
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adcq %rdx, %rbx
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incq %rcx
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jnz L(mul_1)
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C Add products src[n]*src[n+1..size-1] at dst[2*n-1...], for each n=1..size-2.
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C
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C The last two products, which are the bottom right corner of the product
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C triangle, are left to the end. These are src[size-3]*src[size-2,size-1]
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C and src[size-2]*src[size-1]. If size is 4 then it's only these corner
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C cases that need to be done.
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C
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C The unrolled code is the same as in mpn_addmul_1, see that routine for
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C some comments.
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C
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C VAR_COUNTER is the outer loop, running from -size+4 to -1, inclusive.
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C
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C VAR_JMP is the computed jump into the unrolled code, stepped by one code
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C chunk each outer loop.
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C
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C K7 does branch prrdiction on indirect jumps, which is bad since it's a
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C different target each time. There seems no way to avoid this.
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dnl This value also hard coded in some shifts and adds
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deflit(CODE_BYTES_PER_LIMB, 25)
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dnl With the unmodified &src[size] and &dst[size] pointers, the
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dnl displacements in the unrolled code fit in a byte for UNROLL_COUNT
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dnl values up to 31, but above that an offset must be added to them.
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deflit(OFFSET,
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ifelse(eval(UNROLL_COUNT>15),1,
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eval((UNROLL_COUNT-15)*8),
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0))
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dnl Because the last chunk of code is generated differently, a label placed
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dnl at the end doesn't work. Instead calculate the implied end using the
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dnl start and how many chunks of code there are.
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deflit(UNROLL_INNER_END,
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`L(unroll_inner_start)+eval(UNROLL_COUNT*CODE_BYTES_PER_LIMB)')
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C rax
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C rbx carry
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C rcx
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C rdx
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C rsi &src[size]
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C rdi &dst[size]
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C rbp
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movq PARAM_SIZE, %rcx
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movq %rbx, (%rdi)
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subq $4, %rcx
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jz L(corner)
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negq %rcx
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ifelse(OFFSET,0,,`subq $OFFSET, %rdi')
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ifelse(OFFSET,0,,`subq $OFFSET, %rsi')
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movq %rcx, %rdx
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shlq $4, %rcx
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movq %rdx, %r11
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shlq $3, %r11
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addq %rdx, %r11
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C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC Change here!!!!
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ifdef(`PIC',`
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call L(pic_calc)
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L(here):
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',`
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leaq UNROLL_INNER_END-eval(2*CODE_BYTES_PER_LIMB)(%rcx,%r11), %rcx
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')
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C The calculated jump mustn't come out to before the start of the
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C code available. This is the limit UNROLL_COUNT puts on the src
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C operand size, but checked here directly using the jump address.
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ASSERT(ae,
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`movq_text_address(L(unroll_inner_start), %rax)
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cmpq %rax, %rcx')
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C------------------------------------------------------------------------------
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ALIGN(16)
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L(unroll_outer_top):
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C rax
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C rbx high limb to store
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C rcx VAR_JMP
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C rdx VAR_COUNTER, limbs, negative
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C rsi &src[size], constant
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C rdi dst ptr, high of last addmul
|
||
|
|
C rbp
|
||
|
|
|
||
|
|
movq -24+OFFSET(%rsi,%rdx,8), %rbp C next multiplier
|
||
|
|
movq -16+OFFSET(%rsi,%rdx,8), %rax C first of multiplicand
|
||
|
|
|
||
|
|
movq %rdx, VAR_COUNTER
|
||
|
|
|
||
|
|
mulq %rbp
|
||
|
|
|
||
|
|
define(cmovX,`ifelse(eval(UNROLL_COUNT%2),0,`cmovz $@',`cmovnz $@')')
|
||
|
|
|
||
|
|
testb $1, %cl
|
||
|
|
C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCcccc
|
||
|
|
movq %rdx, %rbx C high carry
|
||
|
|
movq %rcx, %rdx C jump
|
||
|
|
|
||
|
|
movq %rax, %rcx C low carry
|
||
|
|
cmovX( %rbx, %rcx) C high carry reverse
|
||
|
|
cmovX( %rax, %rbx) C low carry reverse
|
||
|
|
|
||
|
|
leaq CODE_BYTES_PER_LIMB(%rdx), %rax
|
||
|
|
xorq %rdx, %rdx
|
||
|
|
leaq 8(%rdi), %rdi
|
||
|
|
|
||
|
|
movq %rax, VAR_JMP
|
||
|
|
|
||
|
|
jmp *%rax
|
||
|
|
|
||
|
|
|
||
|
|
ifdef(`PIC',`
|
||
|
|
L(pic_calc):
|
||
|
|
addq (%rsp), %rcx
|
||
|
|
addq $UNROLL_INNER_END-eval(2*CODE_BYTES_PER_LIMB)-L(here), %rcx
|
||
|
|
addq %r11, %rcx
|
||
|
|
ret
|
||
|
|
')
|
||
|
|
|
||
|
|
|
||
|
|
C Must be an even address to preserve the significance of the low
|
||
|
|
C bit of the jump address indicating which way around rcx/rbx should
|
||
|
|
C start.
|
||
|
|
ALIGN(2)
|
||
|
|
|
||
|
|
L(unroll_inner_start):
|
||
|
|
C rax next limb
|
||
|
|
C rbx carry high
|
||
|
|
C rcx carry low
|
||
|
|
C rdx scratch
|
||
|
|
C rsi src
|
||
|
|
C rdi dst
|
||
|
|
C rbp multiplier
|
||
|
|
|
||
|
|
forloop(`i', UNROLL_COUNT, 1, `
|
||
|
|
deflit(`disp_src', eval(-i*8 + OFFSET))
|
||
|
|
deflit(`disp_dst', eval(disp_src - 8))
|
||
|
|
|
||
|
|
m4_assert(`disp_src>=-128 && disp_src<128')
|
||
|
|
m4_assert(`disp_dst>=-128 && disp_dst<128')
|
||
|
|
|
||
|
|
ifelse(eval(i%2),0,`
|
||
|
|
.byte 0x90
|
||
|
|
adcq %rdx, %rbx
|
||
|
|
Zdisp( movq, disp_src,(%rsi), %rax)
|
||
|
|
|
||
|
|
mulq %rbp
|
||
|
|
|
||
|
|
Zdisp( addq, %rcx, disp_dst,(%rdi))
|
||
|
|
movq $0, %rcx
|
||
|
|
|
||
|
|
adcq %rax, %rbx
|
||
|
|
|
||
|
|
',`
|
||
|
|
dnl this bit comes out last
|
||
|
|
.byte 0x90
|
||
|
|
adcq %rdx, %rcx
|
||
|
|
Zdisp( movq, disp_src,(%rsi), %rax)
|
||
|
|
|
||
|
|
mulq %rbp
|
||
|
|
|
||
|
|
Zdisp( addq, %rbx, disp_dst,(%rdi))
|
||
|
|
|
||
|
|
ifelse(forloop_last,0,
|
||
|
|
` movq $0, %rbx')
|
||
|
|
|
||
|
|
adcq %rax, %rcx
|
||
|
|
')
|
||
|
|
')
|
||
|
|
|
||
|
|
C rax next limb
|
||
|
|
C rbx carry high
|
||
|
|
C rcx carry low
|
||
|
|
C rdx scratch
|
||
|
|
C rsi src
|
||
|
|
C rdi dst
|
||
|
|
C rbp multiplier
|
||
|
|
|
||
|
|
adcq $0, %rdx
|
||
|
|
addq %rcx, -8+OFFSET(%rdi)
|
||
|
|
movq VAR_JMP, %rcx
|
||
|
|
|
||
|
|
adcq $0, %rdx
|
||
|
|
|
||
|
|
movq %rdx, m4_empty_if_zero(OFFSET) (%rdi)
|
||
|
|
movq VAR_COUNTER, %rdx
|
||
|
|
|
||
|
|
incq %rdx
|
||
|
|
jnz L(unroll_outer_top)
|
||
|
|
|
||
|
|
|
||
|
|
ifelse(OFFSET,0,,`
|
||
|
|
addq $OFFSET, %rsi
|
||
|
|
addq $OFFSET, %rdi
|
||
|
|
')
|
||
|
|
|
||
|
|
|
||
|
|
C------------------------------------------------------------------------------
|
||
|
|
L(corner):
|
||
|
|
C rsi &src[size]
|
||
|
|
C rdi &dst[2*size-5]
|
||
|
|
|
||
|
|
movq -24(%rsi), %rbp
|
||
|
|
movq -16(%rsi), %rax
|
||
|
|
movq %rax, %rcx
|
||
|
|
|
||
|
|
mulq %rbp
|
||
|
|
|
||
|
|
addq %rax, -8(%rdi)
|
||
|
|
movq -8(%rsi), %rax
|
||
|
|
|
||
|
|
adcq $0, %rdx
|
||
|
|
movq %rdx, %rbx
|
||
|
|
movq %rax, %rsi
|
||
|
|
|
||
|
|
mulq %rbp
|
||
|
|
|
||
|
|
addq %rbx, %rax
|
||
|
|
|
||
|
|
adcq $0, %rdx
|
||
|
|
addq %rax, (%rdi)
|
||
|
|
movq %rsi, %rax
|
||
|
|
|
||
|
|
adcq $0, %rdx
|
||
|
|
movq %rdx, %rbx
|
||
|
|
|
||
|
|
mulq %rcx
|
||
|
|
|
||
|
|
addq %rbx, %rax
|
||
|
|
movq %rax, 8(%rdi)
|
||
|
|
|
||
|
|
adcq $0, %rdx
|
||
|
|
movq %rdx, 16(%rdi)
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
C Left shift of dst[1..2*size-2], high bit shifted out becomes dst[2*size-1].
|
||
|
|
|
||
|
|
L(lshift_start):
|
||
|
|
movq PARAM_SIZE, %rax
|
||
|
|
movq PARAM_DST, %rdi
|
||
|
|
|
||
|
|
movq %rax, %r11
|
||
|
|
shlq $1, %r11
|
||
|
|
leaq (%rdi,%r11,8), %rdi
|
||
|
|
notq %rax C -size-1, preserve carry
|
||
|
|
|
||
|
|
leaq 2(%rax), %rax C -(size-1)
|
||
|
|
movq %rax, %r11
|
||
|
|
shlq $1, %r11
|
||
|
|
|
||
|
|
xorq %rcx, %rcx C clear carry
|
||
|
|
|
||
|
|
L(lshift):
|
||
|
|
C rax counter, negative
|
||
|
|
C rbx
|
||
|
|
C rcx
|
||
|
|
C rdx
|
||
|
|
C rsi
|
||
|
|
C rdi dst, pointing just after last limb
|
||
|
|
C rbp
|
||
|
|
|
||
|
|
rclq -8(%rdi,%r11,8)
|
||
|
|
rclq (%rdi,%r11,8)
|
||
|
|
incq %r11
|
||
|
|
incq %r11
|
||
|
|
incq %rax
|
||
|
|
jnz L(lshift)
|
||
|
|
|
||
|
|
setc %al
|
||
|
|
|
||
|
|
movq PARAM_SRC, %rsi
|
||
|
|
movq %rax, -8(%rdi) C dst most significant limb
|
||
|
|
|
||
|
|
movq PARAM_SIZE, %rcx
|
||
|
|
|
||
|
|
|
||
|
|
C Now add in the squares on the diagonal, src[0]^2, src[1]^2, ...,
|
||
|
|
C src[size-1]^2. dst[0] hasn't yet been set at all yet, and just gets the
|
||
|
|
C low limb of src[0]^2.
|
||
|
|
|
||
|
|
movq (%rsi), %rax C src[0]
|
||
|
|
|
||
|
|
mulq %rax
|
||
|
|
|
||
|
|
leaq (%rsi,%rcx,8), %rsi C src point just after last limb
|
||
|
|
negq %rcx
|
||
|
|
|
||
|
|
movq %rcx, %r11
|
||
|
|
shlq $1, %r11
|
||
|
|
|
||
|
|
movq %rax, (%rdi,%r11,8) C dst[0]
|
||
|
|
incq %rcx
|
||
|
|
incq %r11
|
||
|
|
incq %r11
|
||
|
|
|
||
|
|
L(diag):
|
||
|
|
C rax scratch
|
||
|
|
C rbx scratch
|
||
|
|
C rcx counter, negative
|
||
|
|
C rdx carry
|
||
|
|
C rsi src just after last limb
|
||
|
|
C rdi dst just after last limb
|
||
|
|
C rbp
|
||
|
|
|
||
|
|
movq %rdx, %rbx
|
||
|
|
movq (%rsi,%rcx,8), %rax
|
||
|
|
|
||
|
|
mulq %rax
|
||
|
|
|
||
|
|
addq %rbx, -8(%rdi,%r11,8)
|
||
|
|
adcq %rax, (%rdi,%r11,8)
|
||
|
|
adcq $0, %rdx
|
||
|
|
|
||
|
|
incq %rcx
|
||
|
|
incq %r11
|
||
|
|
incq %r11
|
||
|
|
|
||
|
|
jnz L(diag)
|
||
|
|
|
||
|
|
movq SAVE_RBX, %rbx
|
||
|
|
|
||
|
|
addq %rdx, -8(%rdi) C dst most significant limb
|
||
|
|
|
||
|
|
movq SAVE_RBP, %rbp
|
||
|
|
addq $FRAME, %rsp
|
||
|
|
|
||
|
|
ret
|
||
|
|
|
||
|
|
EPILOGUE()
|