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dnl Itanium-2 mpn_gcd_1 -- mpn by 1 gcd.
dnl Copyright 2002, 2003, 2004, 2005 Free Software Foundation, Inc.
dnl This file is part of the GNU MP Library.
dnl The GNU MP 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
dnl by the Free Software Foundation; either version 2.1 of the License, or (at
dnl your option) any later version.
dnl The GNU MP 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 You should have received a copy of the GNU Lesser General Public License
dnl along with the GNU MP Library; see the file COPYING.LIB. If not, write
dnl to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
dnl Boston, MA 02110-1301, USA.
include(`../config.m4')
C cycles/bitpair (1x1 gcd)
C itanium2: 6.3
C itanium: 14 (approx)
C mpn_gcd_1 (mp_srcptr xp, mp_size_t xsize, mp_limb_t y);
C
C The entry sequence is designed to expect xsize>1 and hence a modexact
C call. This ought to be more common than a 1x1 operation. Our critical
C path is thus stripping factors of 2 from y, calling modexact, then
C stripping factors of 2 from the x remainder returned.
C
C The common factors of 2 between x and y must be determined using the
C original x, not the remainder from the modexact. This is done with
C x_orig which is xp[0]. There's plenty of time to do this while the rest
C of the modexact etc is happening.
C
C It's possible xp[0] is zero. In this case the trailing zeros calculation
C popc((x-1)&~x) gives 63, and that's clearly no less than what y will
C have, making min(x_twos,y_twos) == y_twos.
C
C The main loop consists of transforming x,y to abs(x-y),min(x,y), and then
C stripping factors of 2 from abs(x-y). Those factors of two are
C determined from just y-x, without the abs(), since there's the same
C number of trailing zeros on n or -n in twos complement. That makes the
C dependent chain
C
C cycles
C 1 sub x-y and x-y-1
C 3 andcm (x-y-1)&~(x-y)
C 2 popcnt trailing zeros
C 3 shr.u strip abs(x-y)
C ---
C 9
C
C The selection of x-y versus y-x for abs(x-y), and the selection of the
C minimum of x and y, is done in parallel with the above.
C
C The algorithm takes about 0.68 iterations per bit (two N bit operands) on
C average, hence the final 6.3 cycles/bitpair.
C
C The loop is not as fast as one might hope, since there's extra latency
C from andcm going across to the `multimedia' popcnt, and vice versa from
C multimedia shr.u back to the integer sub.
C
C The loop branch is .sptk.clr since we usually expect a good number of
C iterations, and the iterations are data dependent so it's unlikely past
C results will predict anything much about the future.
C
C Not done:
C
C An alternate algorithm which didn't strip all twos, but instead applied
C tbit and predicated extr on x, and then y, was attempted. The loop was 6
C cycles, but the algorithm is an average 1.25 iterations per bitpair for a
C total 7.25 c/bp, which is slower than the current approach.
C
C Alternatives:
C
C Perhaps we could do something tricky by extracting a few high bits and a
C few low bits from the operands, and looking up a table which would give a
C set of predicates to control some shifts or subtracts or whatever. That
C could knock off multiple bits per iteration.
C
C The right shifts are a bit of a bottleneck (shr at 2 or 3 cycles, or extr
C only going down I0), perhaps it'd be possible to shift left instead,
C using add. That would mean keeping track of the lowest not-yet-zeroed
C bit, using some sort of mask.
C
C Itanium-1:
C
C This code is not designed for itanium-1 and in fact doesn't run well on
C that chip. The loop seems to be about 21 cycles, probably because we end
C up with a 10 cycle replay for not forcibly scheduling the shr.u latency.
C Lack of branch hints might introduce a couple of bubbles too.
C
ASM_START()
.explicit C What does this mean?
C HP's assembler requires these declarations for importing mpn_modexact_1c_odd
.global mpn_modexact_1c_odd
.type mpn_modexact_1c_odd,@function
PROLOGUE(mpn_gcd_1)
C r32 xp
C r33 xsize
C r34 y
define(x, r8)
define(xp_orig, r32)
define(xsize, r33)
define(y, r34) define(inputs, 3)
define(save_rp, r35)
define(save_pfs, r36)
define(x_orig, r37)
define(x_orig_one, r38)
define(y_twos, r39) define(locals, 5)
define(out_xp, r40)
define(out_xsize, r41)
define(out_divisor, r42)
define(out_carry, r43) define(outputs, 4)
.prologue
{ .mmi;
ifdef(`HAVE_ABI_32',
` addp4 r9 = 0, xp_orig define(xp,r9)', C M0
` define(xp,xp_orig)')
.save ar.pfs, save_pfs
alloc save_pfs = ar.pfs, inputs, locals, outputs, 0 C M2
.save rp, save_rp
mov save_rp = b0 C I0
}{ .body
add r10 = -1, y C M3 y-1
} ;;
{ .mmi; ld8 x = [xp] C M0 x = xp[0] if no modexact
ld8 x_orig = [xp] C M1 orig x for common twos
cmp.ne p6,p0 = 1, xsize C I0
}{ .mmi; andcm y_twos = r10, y C M2 (y-1)&~y
mov out_xp = xp_orig C M3
mov out_xsize = xsize C I1
} ;;
mov out_carry = 0
C
popcnt y_twos = y_twos C I0 y twos
;;
C
{ .mmi; add x_orig_one = -1, x_orig C M0 orig x-1
shr.u out_divisor = y, y_twos C I0 y without twos
}{ shr.u y = y, y_twos C I1 y without twos
(p6) br.call.sptk.many b0 = mpn_modexact_1c_odd C if xsize>1
} ;;
C modexact can leave x==0
{ .mmi; cmp.eq p6,p0 = 0, x C M0 if {xp,xsize} % y == 0
andcm x_orig = x_orig_one, x_orig C M1 orig (x-1)&~x
add r9 = -1, x C I0 x-1
} ;;
{ .mmi; andcm r9 = r9, x C M0 (x-1)&~x
mov b0 = save_rp C I0
} ;;
C
popcnt x_orig = x_orig C I0 orig x twos
popcnt r9 = r9 C I0 x twos
;;
C
{ cmp.lt p7,p0 = x_orig, y_twos C M0 orig x_twos < y_twos
shr.u x = x, r9 C I0 x odd
} ;;
{ (p7) mov y_twos = x_orig C M0 common twos
add r10 = -1, y C I0 y-1
(p6) br.dpnt.few .Ldone_y C B0 x%y==0 then result y
} ;;
C
C No noticable difference in speed for the loop aligned to
C 32 or just 16.
.Ltop:
C r8 x
C r10 y-1
C r34 y
C r38 common twos, for use at end
{ .mmi; cmp.gtu p8,p9 = x, y C M0 x>y
cmp.ne p10,p0 = x, y C M1 x==y
sub r9 = y, x C I0 d = y - x
}{ .mmi; sub r10 = r10, x C M2 d-1 = y - x - 1
} ;;
{ .mmi; .pred.rel "mutex", p8, p9
(p8) sub x = x, y C M0 x>y use x=x-y, y unchanged
(p9) mov y = x C M1 y>=x use y=x
(p9) mov x = r9 C I0 y>=x use x=y-x
}{ .mmi; andcm r9 = r10, r9 C M2 (d-1)&~d
;;
add r10 = -1, y C M0 new y-1
popcnt r9 = r9 C I0 twos on x-y
} ;;
{ shr.u x = x, r9 C I0 new x without twos
(p10) br.sptk.few.clr .Ltop
} ;;
C result is y
.Ldone_y:
shl r8 = y, y_twos C I common factors of 2
;;
mov ar.pfs = save_pfs C I0
br.ret.sptk.many b0
EPILOGUE()
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