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|
// file kernel/n/alpha/mmod.S: operations on residues modulo BASE^n + 1
/*-----------------------------------------------------------------------+
| Copyright 2005-2006, Michel Quercia (michel.quercia@prepas.org) |
| |
| This file is part of Numerix. Numerix is free software; you can |
| redistribute it and/or modify it under the terms of the GNU Lesser |
| General Public License as published by the Free Software Foundation; |
| either version 2.1 of the License, or (at your option) any later |
| version. |
| |
| The Numerix Library is distributed in the hope that it will be |
| useful, but WITHOUT ANY WARRANTY; without even the implied warranty |
| of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| Lesser General Public License for more details. |
| |
| You should have received a copy of the GNU Lesser General Public |
| License along with the GNU MP Library; see the file COPYING. If not, |
| write to the Free Software Foundation, Inc., 59 Temple Place - |
| Suite 330, Boston, MA 02111-1307, USA. |
+-----------------------------------------------------------------------+
| |
| Arithmtique modulo BASE^n + 1 |
| |
+-----------------------------------------------------------------------*/
# +---------------------------------------------------------+
# | Rduction modulo BASE^p + 1 et BASE^(2p) - BASE^p + 1 |
# +---------------------------------------------------------+
# entre :
# r16 = naturel longueur 3p
# r17 = naturel de longueur 3p+1
# r18 = p
# r26 = adresse de retour
#
# contraintes :
# p > 0
#
# sortie :
# r17[0..2p-1] <- (r16) mod BASE^(2p) - BASE^p + 1
# r17[2p..3p] <- (r16) mod BASE^p + 1
#if defined(assembly_sn_mmul) || defined(assembly_sn_msqr)
#define L(x) .Lsn_mred_##x
.align 5
.globl sn_mred
.ent sn_mred
sn_mred:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
L(nogp):
s8addq $18, $16, $19 # r19 <- &a1
s8addq $18, $19, $20 # r20 <- &a2
s8addq $18, $17, $21 # r21 <- &b1
s8addq $18, $21, $22 # r22 <- &b2
bis $31, $31, $0 # r0 <- 0 (retenue de a0-a2)
bis $31, $31, $1 # r1 <- 0 (retenue de a1+a2)
bis $31, $31, $2 # r2 <- 0 (retenue de a0-a1+a2)
bis $18, $18, $8 # r8 <- p
# b0 <- a0 - a2, b1 <- a1 + a2, b2 <- a0 - a1 + a2
.align 5
1:
ldq $3, 0($16) # r3 <- a0[i]
ldq $4, 0($19) # r4 <- a1[i]
ldq $5, 0($20) # r5 <- a2[i]
addq $5, $0, $6 # r6 <- a2[i] + ret0
cmpult $6, $5, $0
subq $3, $6, $6 # r6 <- a0[i] - a2[i] - ret0
stq $6, 0($17) # sauve b0[i]
cmpult $3, $6, $6
addq $6, $0, $0 # r0 <- retenue
addq $4, $1, $6 # r6 <- a1[i] + ret1
cmpult $6, $4, $1
addq $5, $6, $6 # r6 <- a1[i] + a2[i] + ret1
stq $6, 0($21) # sauve b1[i]
cmpult $6, $5, $6
addq $6, $1, $1 # r1 <- retenue
addq $3, $2, $6 # r6 <- a0[i] + ret2
sra $2, 1, $2
cmpult $6, $3, $3
addq $3, $2, $2
subq $6, $4, $4 # r4 <- a0[i] - a1[i] + ret2
cmpult $6, $4, $6
subq $2, $6, $2
addq $4, $5, $6 # r6 <- a0[i] - a1[i] + a2[i] + ret2
stq $6, 0($22) # sauve b2[i]
cmpult $6, $4, $6
addq $6, $2, $2 # r2 <- retenue
lda $8, -1($8) # avance les pointeurs
lda $16, 8($16)
lda $17, 8($17)
lda $19, 8($19)
lda $20, 8($20)
lda $21, 8($21)
lda $22, 8($22)
bne $8, 1b
# propage la retenue sortant de b0
beq $0, 2f
bis $18, $18, $8 # r8 <- p
1:
ldq $3, 0($17)
cmpult $3, 1, $0
subq $3, 1, $3
stq $3, 0($17)
beq $0, 2f
lda $8, -1($8)
lda $17, 8($17)
bne $8, 1b # si la retenue traverse b1 alors
br $31, 5f # a1+a2 = BASE^p et il n y a plus rien faire
# recycle la retenue sortant de b1
# si elle vaut 1, il faut ajouter BASE^p - 1 et comme
# b1 <= BASE^p - 2, il ne peut pas y avoir de nouvelle retenue
.align 5
2:
beq $1, 5f
sll $18, 3, $8 # r8 <- 8p
subq $21, $8, $19 # r19 <- &b1
subq $19, $8, $16 # r16 <- &b0
3:
ldq $3, 0($16)
cmpult $3, 1, $0
subq $3, 1, $3
stq $3, 0($16)
beq $0, 4f
lda $8, -8($8)
lda $16, 8($16)
bne $8, 3b
br $31, 5f
.align 5
4:
ldq $3, 0($19)
addq $3, 1, $3
stq $3, 0($19)
lda $19, 8($19)
beq $3, 4b
# recycle la retenue sortant de b2
.align 5
5:
bge $2, 7f
bis $31, $31, $2
6:
ldq $3, 0($21)
addq $3, 1, $3
stq $3, 0($21)
bne $3, 7f
lda $18, -1($18)
lda $21, 8($21)
bne $18, 6b
addq $2, 1, $2
7:
stq $2, 0($22)
# termin
ret $31, ($26),1
.end sn_mred
#undef L
#endif /* defined(assembly_sn_mmul) || defined(assembly_sn_msqr) */
# +-----------------------------------
# | Multiplication modulo BASE^n + 1 |
# +------------------------------------+
# void xn(mmul)(chiffre *a, chiffre *b, long n)
#
# entre :
# a = naturel de longueur n+1
# b = naturel de longueur n+1 non confondu avec a
#
# contrainte : n > 0
#
# sortie :
# a <- (a*b) mod (BASE^n + 1) avec 0 <= a[n] <= 1
# b <- b mod (BASE^n + 1)
#ifdef assembly_sn_mmul
#define L(x) .Lsn_mmul_##x
.align 5
#ifdef debug_mmul
.globl sn_mmul_buggy
.ent sn_mmul_buggy
sn_mmul_buggy:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
#else
.globl sn_mmul
.ent sn_mmul
sn_mmul:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
L(nogp):
#endif
#define _a_ $16
#define _b_ $17
#define _n_ $18
# normalise a
s8addq _n_, _a_, $20
ldq $0, 0($20)
bis _a_, _a_, $20
bis _n_, _n_, $2
bsr $27, sn_decloop
bis _a_, _a_, $20
bis _n_, _n_, $2
bsr $27, sn_incloop
s8addq _n_, _a_, $20
stq $0, 0($20)
bis $0, $0, $3
# normalise b
s8addq _n_, _b_, $20
ldq $0, 0($20)
bis _b_, _b_, $20
bis _n_, _n_, $2
bsr $27, sn_decloop
bis _b_, _b_, $20
bis _n_, _n_, $2
bsr $27, sn_incloop
s8addq _n_, _b_, $20
stq $0, 0($20)
# cas o l un des oprandes vaut BASE^n -> res = oppos(l autre)
bis $0, $3, $0
beq $0, L(norm)
cmoveq $3, _a_, _b_ # b <- nombre opposer
bis $31, $31, $2 # r2 <- 0 (retenue)
.align 5
L(neg):
lda _n_, -1(_n_)
ldq $1, 0(_b_)
addq $2, $1, $1
cmpult $1, $2, $2
subq $0, $1, $1
stq $1, 0(_a_)
cmpult $0, $1, $1
addq $2, $1, $2
bis $31, $31, $0
lda _a_, 8(_a_)
lda _b_, 8(_b_)
bne _n_, L(neg)
addq $31, 1, $1
subq $1, $2, $1
stq $1, 0(_a_)
ret $31, ($26),1
# oprandes normaliss, non gaux BASE^n
# si n est petit ou non divisible par 3, multiplication ordinaire
# puis rduction :
# a*b = x + y*BASE^n + z*BASE^(2n) = x - y + z mod (BASE^n + 1)
.align 5
L(norm):
cmpule _n_, mmul_lim, $0
bne $0, L(simple)
lda $0, 0x5555($31)
sll $0, 16, $1
or $1, $0, $0
sll $0, 32, $1
or $1, $0, $0 # r0 <- (BASE-1)/3
umulh $0, _n_, $0
addq $0, 1, $0 # r0 <- ceil(n/3) = p
addq $0, _n_, $1 # r1 <- n+p, nul mod 4 ssi n = 3p
and $1, 3, $1
beq $1, L(decomp)
L(simple):
s4addq _n_, 8, $0 # rserve 2n+4 chiffres dans la pile
sll $0, 2, $0
subq $30, $0, $30
stq _a_, 0($30) # sauve a,n et l adresse de retour
stq _n_, 8($30)
stq $26, 16($30)
lda $20, 24($30) # r20 <- adresse tampon
bis _n_, _n_, $19 # r19 <- n
bis _b_, _b_, $18 # r18 <- &b
bis $19, $19, $17 # r17 <- n
bsr $26, .Lsn_toommul_nogp # c <- a*b
# point de chute pour msqr
L(simple_aux):
ldq $20, 0($30) # r20 <- a
ldq $17, 8($30) # r17 <- n
bis $17, $17, $19 # r19 <- n
lda $16, 24($30) # r16 <- &c
s8addq $17, $16, $18 # r18 <- &c[n]
bsr $26, .Lsn_sub_nogp # a <- c0 - c1
ldq $26, 16($30) # rcupre l adresse de retour
ldq $20, 0($30) # r20 <- &a
ldq $2, 8($30) # r2 <- n
lda $30, 8($18) # nettoie la pile
s8addq $2, $20, $16 # r16 <- &a[n]
bsr $27, sn_incloop # rinjecte la retenue
stq $0, 0($16)
ret $31, ($26),1
#undef _a_
#undef _b_
#undef _n_
# si n est divisible par 3, on dcompose en une multiplication
# modulo BASE^p + 1 et une modulo BASE^(2p) - BASE^p + 1
.align 5
L(decomp):
#define _a_ 0($30)
#define _b_ 8($30)
#define _c_ 32($30)
#define _p_ 16($30)
#define _ra_ 24($30)
# rserve 6p+4 chiffres dans la pile
sll $0, 1, $1
s4addq $0, $1, $1
s8addq $1, 32, $1
subq $30, $1, $30
stq $16, _a_
stq $17, _b_
stq $0, _p_
stq $26, _ra_
# dcompose a et b modulo BASE^(2p) - BASE^p + 1 et BASE^p + 1
bis $16, $16, $17 # r17 <- &a
bis $0, $0, $18 # r18 <- p
bsr $26, .Lsn_mred_nogp # dcompose a sur place
ldq $16, _b_
lda $17, _c_
ldq $18, _p_
bsr $26, .Lsn_mred_nogp # dcompose b dans c[0..3p]
# a[2p..3p] <- (a*b) mod BASE^p + 1
ldq $16, _a_
lda $17, _c_
ldq $18, _p_
sll $18, 1, $0
s8addq $0, $16, $16 # r16 <- &a[2p]
s8addq $0, $17, $17 # r17 <- &c[2p]
bsr $26, .Lsn_mmul_nogp
# c[2p..6p-1] <- (a*b) mod (BASE^(2p) - BASE^p + 1), non rduit
ldq $16, _a_
lda $18, _c_
ldq $17, _p_
sll $17, 1, $17 # r17 <- 2p
bis $17, $17, $19 # r19 <- 2p
s8addq $17, $18, $20 # r20 <- &c[2p]
bsr $26, .Lsn_toommul_nogp
# point de chute pour msqr
L(decomp_aux):
# a[0..2p-1] <- (a*b) mod (BASE^(2p) - BASE^p + 1)
# a[2p..3p] <- a[0..2p-1] - (a*b) mod (BASE^p + 1)
ldq $23, _p_
ldq $16, _a_ # r16 <- &a0
lda $19, _c_ # r19 <- &c2
s8addq $23, $19, $19
s8addq $23, $19, $19
s8addq $23, $16, $17 # r17 <- &a1
s8addq $23, $17, $18 # r18 <- &a2
s8addq $23, $19, $20 # r20 <- &c3
s8addq $23, $20, $21 # r21 <- &c4
s8addq $23, $21, $22 # r22 <- &c5
bis $31, $31, $0 # r0 <- 0 (retenue(c2-c4-c5))
bis $31, $31, $1 # r1 <- 0 (retenue(c3+c4))
bis $31, $31, $2 # r2 <- 0 (retenue(a0-a1-a2))
bis $2, $2, $24 # r24 <- a2[p] (a2 mod (BASE-1))
bis $23, $23, $8 # r8 <- p (compteur)
.align 5
1:
ldq $3, 0($19) # r3 <- c2[i]
ldq $4, 0($20) # r4 <- c3[i]
ldq $5, 0($21) # r5 <- c4[i]
ldq $6, 0($22) # r6 <- c5[i]
addq $5, $6, $6 # r6 <- c4[i] + c5[i]
cmpult $6, $5, $7
addq $0, $6, $6 # r6 <- c4[i] + c5[i] + ret0
cmpult $6, $0, $0
addq $7, $0, $0
cmpult $3, $6, $7
subq $3, $6, $3 # r3 <- c2[i] - c4[i] - c5[i] - ret0
addq $7, $0, $0 # r0 <- retenue
stq $3, 0($16) # sauve a0[i]
addq $4, $5, $4 # r4 <- c3[i] + c4[i]
cmpult $4, $5, $5
addq $4, $1, $4 # r4 <- c3[i] + c4[i] + ret1
cmpult $4, $1, $1
addq $5, $1, $1 # r1 <- retenue
stq $4, 0($17) # sauve a1[i]
ldq $7, 0($18) # r7 <- a2[i]
addq $4, $2, $4 # r4 <- a1[i] + ret2
cmpult $4, $2, $2
addq $7, $4, $4 # r4 <- a1[i] + a2[i] + ret2
cmpult $4, $7, $5
addq $5, $2, $2
subq $3, $4, $4 # r4 <- a0[i] - a1[i] - a2[i] - ret2
cmpult $3, $4, $5
addq $2, $5, $2 # r2 <- retenue
stq $4, 0($18) # sauve a2[i]
addq $4, $24, $24 # mise jour de a2 mod (BASE-1)
cmpult $24, $4, $4
addq $4, $24, $24
lda $8, -1($8) # avance les pointeurs
lda $16, 8($16)
lda $17, 8($17)
lda $18, 8($18)
lda $19, 8($19)
lda $20, 8($20)
lda $21, 8($21)
lda $22, 8($22)
bne $8, 1b
addq $0, $2, $2 # r2 <- retenue finale sortant de a2
addq $1, $2, $2
ldq $3, 0($18)
addq $2, $3, $2
# propage la retenue sur a1 (0,-1,-2)
beq $0, 2f
bis $23, $23, $8
1:
ldq $3, 0($16)
subq $3, $0, $0
stq $0, 0($16)
cmpult $3, $0, $0
beq $0, 2f
lda $8, -1($8)
lda $16, 8($16)
bne $8, 1b
subq $1, $0, $1
2:
# recycle la retenue sur a2 (-1,0,1)
beq $1, 3f
bis $23, $23, $8 # r8 <- p
sll $23, 3, $0
subq $17, $0, $19 # r19 <- &a1
subq $19, $0, $16 # r16 <- &a0
subq $31, $1, $0 # r0 <- -r1
subq $2, $1, $2 # ret(a2) -= 3*r1
subq $2, $1, $2
subq $2, $1, $2
1:
ldq $3, 0($16) # a0 -= r1
addq $3, $0, $3
stq $3, 0($16)
cmpult $3, $0, $3
sra $0, 1, $0
addq $3, $0, $0
beq $0, 2f
lda $8, -1($8)
lda $16, 8($16)
bne $8, 1b
br $31, 3f
2:
ldq $3, 0($19) # a1 += r1
addq $3, $1, $3
stq $3, 0($19)
cmpult $3, $1, $3
sra $1, 1, $1
addq $3, $1, $1
lda $19, 8($19)
bne $1, 2b
3:
# Ici -r2 contient la retenue sortant de a2 (entre -3 et 8) et
# r24 contient le rsidu de a2 modulo BASE-1.
# On doit recycler la retenue sortante et faire en sorte que le
# nombre final soit non nul, divisible par 3
# -> ajouter (x-r2)*BASE^p + x
# avec 2x + r24 - r2 = 0 mod 3 et 0 < x-r2 <= BASE-2
subq $24, $2, $0 # r0 <- x = r24 - r2 mod (BASE-1)
cmpult $24, $0, $24
sra $2, 63, $3
addq $24, $3, $24
subq $0, $24, $0
subq $0, $2, $1 # r1:(-r2) <- x-r2 mod BASE^2
cmpult $0, $1, $2
addq $2, $3, $2
addq $31, 9, $3 # r3 <- 9 (correctif si x - r2 < BASE/2)
subq $31, 9, $4 # r4 <- -9 (correctif si x - r2 >= BASE/2)
cmovgt $2, $3, $4 # x - r2 < 0 => 9 9
cmovlt $2, $4, $3 # x - r2 >= BASE => -9 -9
cmovlt $1, $4, $3 # x - r2 >= BASE/2 => -9 -9
addq $3, $0, $0 # corrige x et x-r2
addq $3, $1, $1
bis $23, $23, $8 # ajoute x
1:
ldq $3, 0($17)
addq $3, $0, $3
cmpult $3, $0, $0
stq $3, 0($17)
beq $0, 2f
lda $8, -1($8)
lda $17, 8($17)
bne $8, 1b
2:
addq $0, $1, $1 # a2[p] <- x-r2 + ret
stq $1, 0($18)
# a2 <- a2/(-3), a0 <- a0 + a2/(-3), a1 <- a1 - a2/(-3)
ldq $16, _a_ # r16 <- &a0
s8addq $23, $16, $17 # r17 <- &a1
s8addq $23, $17, $18 # r18 <- &a2
lda $0, 0x5555($31)
sll $0, 16, $1
or $1, $0, $0
sll $0, 32, $1
or $1, $0, $0 # r0 <- (BASE-1)/3
bis $31, $31, $1 # r1 <- 0 (retenue(a2*(BASE-1)/3))
bis $31, $31, $2 # r2:r3 <- 0 (retenue(a2/(-3)))
bis $31, $31, $3
bis $31, $31, $4 # r4 <- 0 (retenue(a0+a2))
bis $31, $31, $5 # r5 <- 0 (retenue(a1-a2))
addq $23, 1, $8 # r8 <- p+1
.align 5
1:
ldq $6, 0($18) # r6 <- a2[i]
mulq $6, $0, $7 # r7:r6 <- a2[i]*(BASE-1)/3
umulh $6, $0, $6
addq $1, $7, $7 # r7:r1 <- a2[i]*(BASE-1)/3 + ret
cmpult $7, $1, $1
addq $6, $1, $1
addq $7, $2, $2 # r2:r3 <- a2/(-3)[i] + ret
cmpult $2, $7, $7
addq $3, $2, $2
cmpult $2, $3, $3
addq $7, $3, $3
stq $2, 0($18) # sauve a2/(-3)[i]
ldq $6, 0($16) # r6 <- a0[i]
addq $2, $6, $6 # r6:r4 <- a0[i] + a2/(-3)[i] + ret
cmpult $6, $2, $7
addq $4, $6, $6
cmpult $6, $4, $4
addq $7, $4, $4
stq $6, 0($16) # sauve a0[i]
ldq $6, 0($17) # r6 <- a1[i]
addq $2, $5, $5 # r6:r5 <- a1[i] - a2/(-3)[i] + ret
cmpult $5, $2, $7
subq $6, $5, $5
cmpult $6, $5, $6
stq $5, 0($17) # sauve a1[i]
addq $6, $7, $5
lda $8, -1($8) # avance les pointeurs
lda $16, 8($16)
lda $17, 8($17)
lda $18, 8($18)
bne $8, 1b
subq $4, 1, $4
subq $5, 1, $5
bis $23, $23, $7 # r7 <- p
addq $23, $23, $8 # r8 <- 2p
# propage la retenue sortant de a0 (-1,0,1)
1:
ldq $0, 0($16)
addq $0, $4, $0
stq $0, 0($16)
cmpult $0, $4, $0
sra $4, 1, $4
addq $0, $4, $4
beq $4, 2f
lda $8, -1($8)
lda $16, 8($16)
bne $8, 1b
# propage la retenue sortant de a1 (-1,0,1)
2:
ldq $0, 0($17)
subq $0, $5, $1
stq $1, 0($17)
cmpult $0, $1, $0
sra $5, 1, $5
addq $0, $5, $5
beq $5, 3f
lda $7, -1($7)
lda $17, 8($17)
bne $7, 2b
# recycle la retenue sortant de a2 (r4 - r5 + BASE)
# on incorpore le chiffre a2[p]-1 et on laisse 1 dans a2[p] pour
# absorber une retenue ventuelle
3:
addq $31, 1, $1
addq $31, 1, $2
ldq $0, -8($18)
stq $2, -8($18)
cmpult $0, 1, $2
subq $0, 1, $0
subq $1, $2, $1
addq $4, $0, $0
cmpult $0, $0, $2
addq $2, $1, $1
cmpult $0, $5, $2
subq $0, $5, $0
subq $2, $1, $1
ldq $18, _a_
ldq $2, 0($18)
subq $2, $0, $3
stq $3, 0($18)
cmpult $2, $3, $0
addq $0, $1, $0
beq $0, 5f
4:
lda $18, 8($18)
ldq $2, 0($18)
subq $2, $0, $3
stq $3, 0($18)
cmpult $2, $3, $1
sra $0, 1, $0
addq $0, $1, $0
bne $0, 4b
5:
# termin
L(done):
ldq $26, _ra_
bis $22, $22, $30 # nettoie la pile
ret $31, ($26),1
#undef _a_
#undef _b_
#undef _c_
#undef _p_
#undef _ra_
#undef L
#ifdef debug_mmul
.end sn_mmul_buggy
#else
.end sn_mmul
#endif
#undef L
#endif /* assembly_sn_mmul */
#if !defined(assembly_sn_mmul) || defined(debug_mmul)
REPLACE(sn_mmul)
#endif
# +---------------------------+
# | Carr modulo BASE^n + 1 |
# +---------------------------+
# void xn(msqr)(chiffre *a, long n)
#
# entre :
# a = naturel de longueur n+1
#
# contrainte : n > 0
#
# sortie :
# a <- a^2 mod (BASE^n + 1), le chiffre de poids fort vaut 0 ou 1
#ifdef assembly_sn_msqr
#define L(x) .Lsn_msqr_##x
.align 5
#ifdef debug_mmul
.globl sn_msqr_buggy
.ent sn_msqr_buggy
sn_msqr_buggy:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
#else
.globl sn_msqr
.ent sn_msqr
sn_msqr:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
L(nogp):
#endif
#define _a_ $16
#define _n_ $17
# normalise a
s8addq _n_, _a_, $20
ldq $0, 0($20)
bis _a_, _a_, $20
bis _n_, _n_, $2
bsr $27, sn_decloop
bis _a_, _a_, $20
bis _n_, _n_, $2
bsr $27, sn_incloop
s8addq _n_, _a_, $20
# cas o a = BASE^n -> res = 1
beq $0, L(norm)
stq $0, 0(_a_)
stq $31, 0($20)
ret $31, ($26),1
# oprande normalis, non gal BASE^n
# si n est petit ou non divisible par 3, carrz ordinaire puis rduction
.align 5
L(norm):
stq $0, 0($20)
cmpule _n_, msqr_lim, $0
bne $0, L(simple)
lda $0, 0x5555($31)
sll $0, 16, $1
or $1, $0, $0
sll $0, 32, $1
or $1, $0, $0 # r0 <- (BASE-1)/3
umulh $0, _n_, $0
addq $0, 1, $0 # r0 <- ceil(n/3) = p
addq $0, _n_, $1 # r1 <- n+p, nul mod 4 ssi n = 3p
and $1, 3, $1
beq $1, L(decomp)
L(simple):
s4addq _n_, 8, $0 # rserve 2n+4 chiffres dans la pile
sll $0, 2, $0
subq $30, $0, $30
stq _a_, 0($30) # sauve a,n et l adresse de retour
stq _n_, 8($30)
stq $26, 16($30)
lda $18, 24($30) # r18 <- adresse tampon
bsr $26, .Lsn_toomsqr_nogp # c <- a^2
br $31, .Lsn_mmul_simple_aux # continue avec mmul
#undef _a_
#undef _n_
# si n est divisible par 3, on dcompose en un carr
# modulo BASE^p + 1 et un modulo BASE^(2p) - BASE^p + 1
.align 5
L(decomp):
#define _a_ 0($30)
#define _b_ 8($30)
#define _c_ 32($30)
#define _p_ 16($30)
#define _ra_ 24($30)
# rserve 6p+4 chiffres dans la pile
sll $0, 1, $1
s4addq $0, $1, $1
s8addq $1, 32, $1
subq $30, $1, $30
stq $16, _a_
stq $16, _b_
stq $0, _p_
stq $26, _ra_
# dcompose a modulo BASE^(2p) - BASE^p + 1 et BASE^p + 1
bis $16, $16, $17 # r17 <- &a
bis $0, $0, $18 # r18 <- p
bsr $26, .Lsn_mred_nogp # dcompose a sur place
# a[2p..3p] <- a^2 mod BASE^p + 1
ldq $16, _a_
ldq $17, _p_
sll $17, 1, $0
s8addq $0, $16, $16 # r16 <- &a[2p]
bsr $26, .Lsn_msqr_nogp
# c[2p..6p-1] <- a^2 mod (BASE^(2p) - BASE^p + 1), non rduit
ldq $16, _a_
lda $18, _c_
ldq $17, _p_
sll $17, 1, $17 # r17 <- 2p
s8addq $17, $18, $18 # r18 <- &c[2p]
bsr $26, .Lsn_toomsqr_nogp
br $31, .Lsn_mmul_decomp_aux # continue avec mmul
#undef _a_
#undef _b_
#undef _c_
#undef _p_
#undef _ra_
#undef L
#ifdef debug_mmul
.end sn_msqr_buggy
#else
.end sn_msqr
#endif
#undef L
#endif /* assembly_sn_msqr */
#if !defined(assembly_sn_msqr) || defined(debug_mmul)
REPLACE(sn_msqr)
#endif
# +------------------------------+
# | Papillon modulo BASE^n + 1 |
# +------------------------------+
# void xn(butterfly1)(chiffre *a, chiffre *b, long n, long q, int s)
#
# entre :
# a = naturel de longueur n+1
# b = naturel de longueur n+1 non confondu avec a
# q = entier positif ou nul
# s = 0 ou 1
#
# contraintes : n >= 3 et si q est impair, n doir tre pair
#
# sortie :
# a <- a + (-1)^s * b * 2^(q/2) mod (BASE^n + 1)
# b <- a - (-1)^s * b * 2^(q/2) mod (BASE^n + 1)
#
# remarque : 2^(1/2) = BASE^(3n/4)*(BASE^(n/2) + 1) mod (BASE^n + 1)
#ifdef assembly_sn_butterfly
#define L(x) .Lsn_butterfly_##x
.align 5
#ifdef debug_butterfly
.globl sn_butterfly_buggy
.ent sn_butterfly_buggy
sn_butterfly_buggy:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
#else
.globl sn_butterfly
.ent sn_butterfly
sn_butterfly:
.frame $30,0,$26,0
.prologue 1
ldgp $gp, 0($27)
#endif
# sauvegarde les paramtres
#define _a_ $22
#define _b_ $23
#define _n_ $24
#define _q_ $19
#define _s_ $28
bis $16, $16, _a_
bis $17, $17, _b_
bis $18, $18, _n_
bis $20, $20, _s_
# force 2 <= a[n] <= BASE-3 pour absorber les retenues
s8addq _n_, _a_, $0 # r0 <- &a[n]
ldq $1, 0($0) # r1 <- a[n]
cmpult $1, 2, $2 # r2 <- a[n] < 2 ?
addq $1, 2, $3 # r3 <- a[n] >= BASE-2 ?
cmpult $3, $1, $3
subq $2, $3, $2 # r2 <- 1 si a[n] < 2, -1 si a[n] >= BASE-2, 0 sinon
beq $2, 2f # pas besoin de correction
sll $2, 1, $2 # r2 <- 2 ou -2
addq $2, $1, $1 # a <- a + r2*(BASE^n + 1)
stq $1, 0($0)
bis _a_, _a_, $0
1:
ldq $1, 0($0)
addq $1, $2, $1
stq $1, 0($0)
cmpult $1, $2, $1
sra $2, 2, $2
addq $1, $2, $2
lda $0, 8($0)
bne $2, 1b
2:
# si q est impair, multiplie b par BASE^(n/2) + 1
blbc _q_, L(q_even)
s4subq _n_, _n_, $0 # q <- q + 3*n*HW/2
sll $0, 5, $0
addq _q_, $0, _q_
s8addq _n_, _b_, $7 # r7 <- b[n]
ldq $7, 0($7)
srl _n_, 1, $2 # r2 <- -n/2
subq $31, $2, $2
and $2, 31, $3 # r3 <- (-n/2) mod 32
bic $2, 31, $2 # r2 <- -32*ceil(n/64)
sll $3, 3, $4
subq _b_, $4, $16 # r16 <- &a0[-(-n/2) mod 32]
s4addq _n_, $16, $18 # r18 <- &a1[-(-n/2) mod 32]
s4addq _n_, $16, $20 # r20 <- &a1[-(-n/2) mod 32]
bis $16, $16, $21 # r21 <- &a0[-(-n/2) mod 32]
subq $4, $3, $4 # r27 <- adresse de saut dans addsubloop
lda $27, sn_addsubloop
s8addq $4, $27, $27
bis $31, $31, $0 # r0 <- 0 (retenue(b0+b1)
srl $7, 1, $1 # r1 <- floor(b[n]/2) (retenue(b0-b1)
subq $7, $1, $8 # r8 <- ceil(b[n]/2)
jsr $27, ($27) # b0 <- b0-b1-b[n]/2, b1 <- b1+b0
addq $0, $8, $8 # b[n] <- retenue sortant du haut
stq $8, 0($20)
addq $7, $1, $1 # r1:r0 <- retenue sortant du bas
cmpult $1, $7, $0
ldq $2, 0($21) # cumule b1[0]
subq $2, $1, $1
stq $1, 0($21)
cmpult $2, $1, $1
addq $1, $0, $0 # r0 <- nouvelle retenue
lda $20, 8($21)
subq $31, 1, $2
bsr $27, sn_decloop # la propage sur b1 (pas de dbordement)
.align 5
L(q_even):
# dcompose le dcalage en nombre et fraction de chiffre
srl _q_, 1, $8 # r8 <- (q/2) mod HW = k
and $8, 63, $8
srl _q_, 7, _q_ # q <- (q/2)/HW
1:
cmpult _q_, _n_, $1
subq _q_, _n_, _q_ # rduit q modulo n
xor _s_, 1, _s_
beq $1, 1b
addq _q_, _n_, _q_
# b <- b*2^k mod (BASE^n + 1), normalis
beq $8, 1f
addq $31, 64, $7 # r7 <- 64-k
subq $7, $8, $7
subq $31, _n_, $2 # r2 <- -n
and $2, 31, $3 # r3 <- (-n) mod 32
bic $2, 31, $2 # r2 <- -32*ceil(n/32)
sll $3, 3, $4
subq _b_, $4, $16 # r16 <- &b[-(-n) mod 32]
subq _b_, $4, $20 # r20 <- &b[-(-n) mod 32]
s4addq $3, $3, $3
lda $27, sn_shuploop # r27 <- adresse de saut dans shuploop
s4addq $3, $27, $27
bis $31, $31, $0 # r0 <- 0 (retenue)
jsr $27, ($27) # b[0..n-1] <<= k
ldq $1, 0($16) # dcale le dernier chiffre dans r0:r1
sll $1, $8, $3
bis $0, $3, $0
srl $1, $7, $1
br $31, 2f
.align 5
1:
s8addq _n_, _b_, $20 # cas k=0: normalise b
ldq $0, 0($20) # r0:r1 <- b[n]
bis $31, $31, $1
2:
ldq $2, 0(_b_) # traite le premier chiffre part
subq $2, $0, $0
stq $0, 0(_b_)
cmpult $2, $0, $0
addq $1, $0, $0 # r0 <- retenue sur b[1]
lda $20, 8(_b_) # r20 <- &b[1]
subq _n_, 1, $2 # r2 <- n-1
bsr $27, sn_decloop # b[1..n-1] -= ret
bis _b_, _b_, $20 # recycle la retenue sortante
bis _n_, _n_, $2
bsr $27, sn_incloop
bis $0, $0, $7 # r7 <- retenue
# x <- b*BASE^q mod (BASE^n + 1)
bne _q_, 1f # si q = 0, n effectue pas la copie
bis $31, $31, $8 # r8 <- 0 (nb chiffres empils)
bis _b_, _b_, $18 # r18 <- b = x
s8addq _n_, _b_, $20
stq $7, 0($20) # sauve b[n]
br $31, L(add_sub)
.align 5
1:
addq _n_, 2, $8 # r8 <- n+1, arrondi au pair suprieur
bic $8, 1, $8
sll $8, 3, $0 # rserve ce nombre de chiffres dans la pile
subq $30, $0, $30
subq _n_, _q_, $6 # si q <= n-q, dcale vers le haut
cmpule _q_, $6, $5 # sinon dcale vers le bas
bne $5, L(shift_up)
# ici q > n-q, multiplie par BASE^(n-q) et inverse le signe
xor _s_, 1, _s_
s8addq $6, _b_, $16 # r16 <- &b[n-q]
subq $31, _q_, $2
and $2, 31, $3 # r3 <- 8*((-q) mod 32)
sll $3, 3, $3
lda $27, sn_cpuploop
subq $16, $3, $16 # cadre les pointeurs
subq $30, $3, $20
addq $27, $3, $27
bic $2, 31, $2 # r2 <- -32*ceil(q mod 32)
jsr $27, ($27) # x[0..q-1] <- b[n-q..n-1]
bis _b_, _b_, $16 # x[q] <- b[n] - b[0]
ldq $1, 0($16)
subq $7, $1, $1
stq $1, 0($20)
cmpult $7, $1, $0
br $31, 2f
.align 5
1:
ldq $1, 0($16) # retranche b[1..q-1]
addq $1, $0, $1
cmpult $1, $0, $0
subq $31, $1, $1
stq $1, 0($20)
cmpult $31, $1, $1
addq $1, $0, $0
2:
lda $6, -1($6)
lda $16, 8($16)
lda $20, 8($20)
bne $6, 1b
stq $31, 0($20) # x[n] <- 0
subq $31, 1, $2
bis $30, $30, $20
bsr $27, sn_incloop # propage la retenue
bis $30, $30, $18 # r18 <- &x
br $31, L(add_sub)
# ici q >= n-q, multiplie par BASE^q
.align 5
L(shift_up):
s8addq _q_, $30, $20 # r20 <- &x[q]
subq _q_, _n_, $2
and $2, 31, $3 # r3 <- 8*((q-n) mod 32)
sll $3, 3, $3
lda $27, sn_cpuploop
subq _b_, $3, $16 # cadre les pointeurs
subq $20, $3, $20
addq $27, $3, $27
bic $2, 31, $2 # r2 <- -32*ceil((n-q) mod 32)
jsr $27, ($27) # x[q..n-1] <- b[0..n-q-1]
addq $31, 1, $0
stq $0, 0($20) # x[n] <- 1
bis $30, $30, $20 # r20 <- &x[0]
beq _q_, 3f
ldq $1, 0($16)
subq $0, $1, $1 # x[0] <- 1 - b[q]
cmpult $0, $1, $0
stq $1, 0($20)
br $31, 2f # retranche b[1..q-1]
.align 5
1:
ldq $1, 0($16)
addq $1, $0, $1
cmpult $1, $0, $0
subq $31, $1, $1
stq $1, 0($20)
cmpult $31, $1, $1
addq $1, $0, $0
2:
lda _q_, -1(_q_)
lda $16, 8($16)
lda $20, 8($20)
bne _q_, 1b
addq $0, $7, $0 # ret += b[n]
subq $31, 1, $2
bsr $27, sn_decloop # propage la retenue
bis $30, $30, $18 # r18 <- &x
# a <- a - (-1)^s*x, b <- a + (-1)^s*x
L(add_sub):
bis _a_, _a_, $16 # r16 <- &a
bis _b_, _b_, $20 # r20 <- &b
addq _n_, 1, $2
subq $31, $2, $2
and $2, 31, $3 # r3 <- (-n-1) mod 32
bic $2, 31, $2 # r2 <- -32*ceil((n+1)/32)
sll $3, 3, $0
subq $16, $0, $16 # cadre les pointeurs
subq $18, $0, $18
subq $20, $0, $20
lda $27, sn_addsubloop
subq $0, $3, $0
s8addq $0, $27, $27 # r27 <- adresse de saut dans addsubloop
cmoveq _s_, $16, $21 # r21 <- &a si s = 0
cmovne _s_, $20, $21 # r21 <- &a si s = 1
cmovne _s_, $16, $20 # r20 <- &b si s = 1
bis $31, $31, $0 # init retenues
bis $31, $31, $1
jsr $27, ($27) # effectue l addition-soustraction
# termin
s8addq $8, $30, $30 # nettoie la pile
ret $31, ($26),1
#undef _a_
#undef _b_
#undef _n_
#undef _q_
#undef _s_
#ifdef debug_butterfly
.end sn_butterfly_buggy
#else
.end sn_butterfly
#endif
#undef L
#endif /* assembly_sn_butterfly */
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