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dnl ******************************************************************************
dnl Copyright 2009 Paul Zimmermann and Alexander Kruppa.
dnl
dnl This file is part of the ECM Library.
dnl
dnl The ECM Library is free software; you can redistribute it and/or modify
dnl it under the terms of the GNU Lesser General Public License as published by
dnl the Free Software Foundation; either version 3 of the License, or (at your
dnl option) any later version.
dnl
dnl The ECM Library is distributed in the hope that it will be useful, but
dnl WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
dnl or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
dnl License for more details.
dnl
dnl You should have received a copy of the GNU Lesser General Public License
dnl along with the ECM Library; see the file COPYING.LIB. If not, write to
dnl the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
dnl MA 02110-1301, USA.
dnl ******************************************************************************
dnl
dnl void ecm_redc3(mp_limb_t * c, const mp_limb_t * m, size_t n, mp_limb_t m_inv)
dnl
dnl input arguments:
dnl
dnl r3: ptr to c[0], the least significant word of the number to be reduced
dnl c[0 ... 2*n-1] is of length 2*n words
dnl r4: ptr to m[0], the least significant word of the modulus m of length n
dnl r5: the length n
dnl r6: m_inv = -1/m mod 2^64
dnl
dnl the residue (before adding the word carries) will be in c[n ... 2*n-1].
dnl c[0 ... n-1] will contain the high word carries from each inner loop pass.
dnl These carry words are added by the calling routine to obtain the final
dnl residue.
dnl Use `C' to remove comments in .asm -> .s conversion.
dnl Copied from GMP 4.2.
define(C, `
dnl')
include(`config.m4')
GLOBL GSYM_PREFIX`'ecm_redc3
GLOBL .GSYM_PREFIX`'ecm_redc3
.section ".opd", "aw"
.align 3
GSYM_PREFIX`'ecm_redc3:
.quad .GSYM_PREFIX`'ecm_redc3, .TOC.@tocbase, 0
.size GSYM_PREFIX`'ecm_redc3, 24
TEXT
.align 5 C 32 byte alignment
.GSYM_PREFIX`'ecm_redc3:
cmpdi r5, 1 C length = 1?
bne 1f
ld r12, 0(r3) C c[0]
ld r0, 0(r4) C m[0]
mulld r7, r6, r12 C u = c[0] * m_inv mod 2^64
mulld r11, r0, r7 C m[0]*u low
mulhdu r10, r0, r7 C m[0]*u high
addc r11, r11, r12 C c[0] + m[0]*u low = 0
addze r10, r10 C carry to high half
std r10, 0(r3) C store the "carry" word
blr
nop
nop
nop
nop
nop
1:
mflr r0 C save return addr
stdu r0, -8(r1) C on the stack
stdu r13, -8(r1) C save r13
dnl
dnl get inner loop count and jump offset
dnl
subi r7, r5, 2 C r7 = n - 2
andi. r8, r7, 15 C r8 = (n - 2) mod 16
sldi r8, r8, 5 C r8 * 32 = byte offset
srdi r7, r7, 4 C int((n - 2)/16)
dnl
dnl compute the address of inner loop end and subtract the offset
dnl
bl nxt C put the address of the next instruction
C into the link register
nxt: C
mflr r9 C r9 = address of this instruction
addi r9, r9, 640 C add offset to v_1 from nxt
C WARNING: any changes to the code between
C the labels "nxt" and "v_1" may require
C recomputation of the offset above.
sub r9, r9, r8 C offset back to desired starting point
mtlr r9 C and now we can branch directly to our target
mtctr r5 C outer loop count n
addi r13, r7, 1 C inner loop counter
nop
nop
OuterLoop: C execute n times
dnl compute u, set addr's
ld r12, 0(r3) C c[0]
mr r8, r4 C r8 = working copy of m address
ld r0, 0(r8) C m[0]
mulld r7, r6, r12 C u = c[0] * m_inv mod 2^64
mfctr r5 C save current outer loop count
dnl start inner
mulld r11, r0, r7 C m[0]*u low
mtctr r13 C inner loop count
mulhdu r10, r0, r7 C m[0]*u high
ldu r0, 8(r8) C m[1]
addc r11, r11, r12 C m[0]*u low + c[0] (don't bother storing zero)
mulld r11, r0, r7 C m[1]*u low
ldu r12, 8(r3) C c[1], update c address
mr r9, r3 C r9 = working copy of c addr
mulhdu r0, r0, r7 C m[1]*u high
adde r11, r10, r11 C m[1]*u low + m[0]*u high + cy
addze r10, r0 C m[1]*u high + cy
blr C jump to start of the (n-2) mod 16 section
C (or to v_1, if (n-2) mod 16 = 0)
nop
nop
nop
nop
nop
nop
nop
ILoop:
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 15
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 14
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 13
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 12
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 11
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 10
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 9
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 8
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 7
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 6
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 5
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 4
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 3
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 2
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
dnl
dnl start (n-2) mod 16 = 1
dnl
ldu r0, 8(r8) C m[i]
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
mulld r11, r0, r7 C m[i]*u low
ldu r12, 8(r9) C c[i]
mulhdu r0, r0, r7 C m[i]*u high
adde r11, r10, r11 C m[i]*u low + m[i-1]*u high + cy
addze r10, r0 C r10 = m[i]*u + cy
v_1:
bdnz ILoop C blr above jumps directly to this bdnz instruction
C when (n-2) mod 16 = 0
dnl finish inner
addc r11, r11, r12 C m[i-1]*u low + m[i-2]*u high + c[i-1]
std r11, 0(r9) C store it in c[i-1]
addze r10, r10 C result cy = 0 always
std r10, -8(r3) C store the "carry" word
mtctr r5 C restore outer loop count
bdnz OuterLoop
ld r13, 0(r1) C restore r13
ld r0, 8(r1) C original return address
addi r1, r1, 16 C restore stack ptr
mtlr r0
blr
.size .GSYM_PREFIX`'ecm_redc3, .-.GSYM_PREFIX`'ecm_redc3
|
