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|
dnl Alpha ev6 mpn_mul_1 -- Multiply a limb vector with a limb and store the
dnl result in a second limb vector.
dnl Copyright 2000, 2001, 2005 Free Software Foundation, Inc.
dnl This file is part of the GNU MP Library.
dnl
dnl The GNU MP Library is free software; you can redistribute it and/or modify
dnl it under the terms of either:
dnl
dnl * the GNU Lesser General Public License as published by the Free
dnl Software Foundation; either version 3 of the License, or (at your
dnl option) any later version.
dnl
dnl or
dnl
dnl * the GNU General Public License as published by the Free Software
dnl Foundation; either version 2 of the License, or (at your option) any
dnl later version.
dnl
dnl or both in parallel, as here.
dnl
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 General Public License
dnl for more details.
dnl
dnl You should have received copies of the GNU General Public License and the
dnl GNU Lesser General Public License along with the GNU MP Library. If not,
dnl see https://www.gnu.org/licenses/.
include(`../config.m4')
C INPUT PARAMETERS
C res_ptr r16
C s1_ptr r17
C size r18
C s2_limb r19
C This code runs at 2.25 cycles/limb on EV6.
C This code was written in close cooperation with ev6 pipeline expert
C Steve Root. Any errors are tege's fault, though.
C Code structure:
C code for n < 8
C code for n > 8 code for (n mod 8)
C code for (n div 8) feed-in code
C 8-way unrolled loop
C wind-down code
C Some notes about unrolled loop:
C
C r1-r8 multiplies and workup
C r21-r28 multiplies and workup
C r9-r12 loads
C r0 -1
C r20,r29,r13-r15 scramble
C
C We're doing 7 of the 8 carry propagations with a br fixup code and 1 with a
C put-the-carry-into-hi. The idea is that these branches are very rarely
C taken, and since a non-taken branch consumes no resources, that is better
C than an addq.
C
C Software pipeline: a load in cycle #09, feeds a mul in cycle #16, feeds an
C add NEXT cycle #09 which feeds a store in NEXT cycle #02
C The code could use some further work:
C 1. Speed up really small multiplies. The default alpha/mul_1.asm code is
C faster than this for size < 3.
C 2. Improve feed-in code, perhaps with the equivalent of switch(n%8) unless
C that is too costly.
C 3. Consider using 4-way unrolling, even if that runs slower.
C 4. Reduce register usage. In particular, try to avoid using r29.
ASM_START()
PROLOGUE(mpn_mul_1)
cmpult r18, 8, r1
beq r1, $Large
$Lsmall:
ldq r2,0(r17) C r2 = s1_limb
lda r18,-1(r18) C size--
mulq r2,r19,r3 C r3 = prod_low
bic r31,r31,r4 C clear cy_limb
umulh r2,r19,r0 C r0 = prod_high
beq r18,$Le1a C jump if size was == 1
ldq r2,8(r17) C r2 = s1_limb
lda r18,-1(r18) C size--
stq r3,0(r16)
beq r18,$Le2a C jump if size was == 2
ALIGN(8)
$Lopa: mulq r2,r19,r3 C r3 = prod_low
addq r4,r0,r0 C cy_limb = cy_limb + 'cy'
lda r18,-1(r18) C size--
umulh r2,r19,r4 C r4 = cy_limb
ldq r2,16(r17) C r2 = s1_limb
lda r17,8(r17) C s1_ptr++
addq r3,r0,r3 C r3 = cy_limb + prod_low
stq r3,8(r16)
cmpult r3,r0,r0 C r0 = carry from (cy_limb + prod_low)
lda r16,8(r16) C res_ptr++
bne r18,$Lopa
$Le2a: mulq r2,r19,r3 C r3 = prod_low
addq r4,r0,r0 C cy_limb = cy_limb + 'cy'
umulh r2,r19,r4 C r4 = cy_limb
addq r3,r0,r3 C r3 = cy_limb + prod_low
cmpult r3,r0,r0 C r0 = carry from (cy_limb + prod_low)
stq r3,8(r16)
addq r4,r0,r0 C cy_limb = prod_high + cy
ret r31,(r26),1
$Le1a: stq r3,0(r16)
ret r31,(r26),1
$Large:
lda r30, -224(r30)
stq r26, 0(r30)
stq r9, 8(r30)
stq r10, 16(r30)
stq r11, 24(r30)
stq r12, 32(r30)
stq r13, 40(r30)
stq r14, 48(r30)
stq r15, 56(r30)
stq r29, 64(r30)
and r18, 7, r20 C count for the first loop, 0-7
srl r18, 3, r18 C count for unrolled loop
bis r31, r31, r21
beq r20, $L_8_or_more C skip first loop
$L_9_or_more:
ldq r2,0(r17) C r2 = s1_limb
lda r17,8(r17) C s1_ptr++
lda r20,-1(r20) C size--
mulq r2,r19,r3 C r3 = prod_low
umulh r2,r19,r21 C r21 = prod_high
beq r20,$Le1b C jump if size was == 1
bis r31, r31, r0 C FIXME: shouldn't need this
ldq r2,0(r17) C r2 = s1_limb
lda r17,8(r17) C s1_ptr++
lda r20,-1(r20) C size--
stq r3,0(r16)
lda r16,8(r16) C res_ptr++
beq r20,$Le2b C jump if size was == 2
ALIGN(8)
$Lopb: mulq r2,r19,r3 C r3 = prod_low
addq r21,r0,r0 C cy_limb = cy_limb + 'cy'
lda r20,-1(r20) C size--
umulh r2,r19,r21 C r21 = prod_high
ldq r2,0(r17) C r2 = s1_limb
lda r17,8(r17) C s1_ptr++
addq r3,r0,r3 C r3 = cy_limb + prod_low
stq r3,0(r16)
cmpult r3,r0,r0 C r0 = carry from (cy_limb + prod_low)
lda r16,8(r16) C res_ptr++
bne r20,$Lopb
$Le2b: mulq r2,r19,r3 C r3 = prod_low
addq r21,r0,r0 C cy_limb = cy_limb + 'cy'
umulh r2,r19,r21 C r21 = prod_high
addq r3,r0,r3 C r3 = cy_limb + prod_low
cmpult r3,r0,r0 C r0 = carry from (cy_limb + prod_low)
stq r3,0(r16)
lda r16,8(r16) C res_ptr++
addq r21,r0,r21 C cy_limb = prod_high + cy
br r31, $L_8_or_more
$Le1b: stq r3,0(r16)
lda r16,8(r16) C res_ptr++
$L_8_or_more:
lda r0, -1(r31) C put -1 in r0, for tricky loop control
lda r17, -32(r17) C L1 bookkeeping
lda r18, -1(r18) C decrement count
ldq r9, 32(r17) C L1
ldq r10, 40(r17) C L1
mulq r9, r19, r22 C U1 #07
ldq r11, 48(r17) C L1
umulh r9, r19, r23 C U1 #08
ldq r12, 56(r17) C L1
mulq r10, r19, r24 C U1 #09
ldq r9, 64(r17) C L1
lda r17, 64(r17) C L1 bookkeeping
umulh r10, r19, r25 C U1 #11
mulq r11, r19, r26 C U1 #12
umulh r11, r19, r27 C U1 #13
mulq r12, r19, r28 C U1 #14
ldq r10, 8(r17) C L1
umulh r12, r19, r1 C U1 #15
ldq r11, 16(r17) C L1
mulq r9, r19, r2 C U1 #16
ldq r12, 24(r17) C L1
umulh r9, r19, r3 C U1 #17
addq r21, r22, r13 C L1 mov
mulq r10, r19, r4 C U1 #18
addq r23, r24, r22 C L0 sum 2 mul's
cmpult r13, r21, r14 C L1 carry from sum
bgt r18, $L_16_or_more
cmpult r22, r24, r24 C U0 carry from sum
umulh r10, r19, r5 C U1 #02
addq r25, r26, r23 C U0 sum 2 mul's
mulq r11, r19, r6 C U1 #03
cmpult r23, r26, r25 C U0 carry from sum
umulh r11, r19, r7 C U1 #04
addq r27, r28, r28 C U0 sum 2 mul's
mulq r12, r19, r8 C U1 #05
cmpult r28, r27, r15 C L0 carry from sum
lda r16, 32(r16) C L1 bookkeeping
addq r13, r31, r13 C U0 start carry cascade
umulh r12, r19, r21 C U1 #06
br r31, $ret0c
$L_16_or_more:
C ---------------------------------------------------------------
subq r18,1,r18
cmpult r22, r24, r24 C U0 carry from sum
ldq r9, 32(r17) C L1
umulh r10, r19, r5 C U1 #02
addq r25, r26, r23 C U0 sum 2 mul's
mulq r11, r19, r6 C U1 #03
cmpult r23, r26, r25 C U0 carry from sum
umulh r11, r19, r7 C U1 #04
addq r27, r28, r28 C U0 sum 2 mul's
mulq r12, r19, r8 C U1 #05
cmpult r28, r27, r15 C L0 carry from sum
lda r16, 32(r16) C L1 bookkeeping
addq r13, r31, r13 C U0 start carry cascade
umulh r12, r19, r21 C U1 #06
C beq r13, $fix0w C U0
$ret0w: addq r22, r14, r26 C L0
ldq r10, 40(r17) C L1
mulq r9, r19, r22 C U1 #07
beq r26, $fix1w C U0
$ret1w: addq r23, r24, r27 C L0
ldq r11, 48(r17) C L1
umulh r9, r19, r23 C U1 #08
beq r27, $fix2w C U0
$ret2w: addq r28, r25, r28 C L0
ldq r12, 56(r17) C L1
mulq r10, r19, r24 C U1 #09
beq r28, $fix3w C U0
$ret3w: addq r1, r2, r20 C L0 sum 2 mul's
ldq r9, 64(r17) C L1
addq r3, r4, r2 C L0 #10 2 mul's
lda r17, 64(r17) C L1 bookkeeping
cmpult r20, r1, r29 C U0 carry from sum
umulh r10, r19, r25 C U1 #11
cmpult r2, r4, r4 C U0 carry from sum
stq r13, -32(r16) C L0
stq r26, -24(r16) C L1
mulq r11, r19, r26 C U1 #12
addq r5, r6, r14 C U0 sum 2 mul's
stq r27, -16(r16) C L0
stq r28, -8(r16) C L1
umulh r11, r19, r27 C U1 #13
cmpult r14, r6, r3 C U0 carry from sum
C could do cross-jumping here:
C bra $L_middle_of_unrolled_loop
mulq r12, r19, r28 C U1 #14
addq r7, r3, r5 C L0 eat carry
addq r20, r15, r20 C U0 carry cascade
ldq r10, 8(r17) C L1
umulh r12, r19, r1 C U1 #15
beq r20, $fix4 C U0
$ret4w: addq r2, r29, r6 C L0
ldq r11, 16(r17) C L1
mulq r9, r19, r2 C U1 #16
beq r6, $fix5 C U0
$ret5w: addq r14, r4, r7 C L0
ldq r12, 24(r17) C L1
umulh r9, r19, r3 C U1 #17
beq r7, $fix6 C U0
$ret6w: addq r5, r8, r8 C L0 sum 2
addq r21, r22, r13 C L1 sum 2 mul's
mulq r10, r19, r4 C U1 #18
addq r23, r24, r22 C L0 sum 2 mul's
cmpult r13, r21, r14 C L1 carry from sum
ble r18, $Lend C U0
C ---------------------------------------------------------------
ALIGN(16)
$Loop:
umulh r0, r18, r18 C U1 #01 decrement r18!
cmpult r8, r5, r29 C L0 carry from last bunch
cmpult r22, r24, r24 C U0 carry from sum
ldq r9, 32(r17) C L1
umulh r10, r19, r5 C U1 #02
addq r25, r26, r23 C U0 sum 2 mul's
stq r20, 0(r16) C L0
stq r6, 8(r16) C L1
mulq r11, r19, r6 C U1 #03
cmpult r23, r26, r25 C U0 carry from sum
stq r7, 16(r16) C L0
stq r8, 24(r16) C L1
umulh r11, r19, r7 C U1 #04
bis r31, r31, r31 C L0 st slosh
bis r31, r31, r31 C L1 st slosh
addq r27, r28, r28 C U0 sum 2 mul's
mulq r12, r19, r8 C U1 #05
cmpult r28, r27, r15 C L0 carry from sum
lda r16, 64(r16) C L1 bookkeeping
addq r13, r29, r13 C U0 start carry cascade
umulh r12, r19, r21 C U1 #06
beq r13, $fix0 C U0
$ret0: addq r22, r14, r26 C L0
ldq r10, 40(r17) C L1
mulq r9, r19, r22 C U1 #07
beq r26, $fix1 C U0
$ret1: addq r23, r24, r27 C L0
ldq r11, 48(r17) C L1
umulh r9, r19, r23 C U1 #08
beq r27, $fix2 C U0
$ret2: addq r28, r25, r28 C L0
ldq r12, 56(r17) C L1
mulq r10, r19, r24 C U1 #09
beq r28, $fix3 C U0
$ret3: addq r1, r2, r20 C L0 sum 2 mul's
ldq r9, 64(r17) C L1
addq r3, r4, r2 C L0 #10 2 mul's
bis r31, r31, r31 C U1 mul hole
lda r17, 64(r17) C L1 bookkeeping
cmpult r20, r1, r29 C U0 carry from sum
umulh r10, r19, r25 C U1 #11
cmpult r2, r4, r4 C U0 carry from sum
stq r13, -32(r16) C L0
stq r26, -24(r16) C L1
mulq r11, r19, r26 C U1 #12
addq r5, r6, r14 C U0 sum 2 mul's
stq r27, -16(r16) C L0
stq r28, -8(r16) C L1
umulh r11, r19, r27 C U1 #13
bis r31, r31, r31 C L0 st slosh
bis r31, r31, r31 C L1 st slosh
cmpult r14, r6, r3 C U0 carry from sum
$L_middle_of_unrolled_loop:
mulq r12, r19, r28 C U1 #14
addq r7, r3, r5 C L0 eat carry
addq r20, r15, r20 C U0 carry cascade
ldq r10, 8(r17) C L1
umulh r12, r19, r1 C U1 #15
beq r20, $fix4 C U0
$ret4: addq r2, r29, r6 C L0
ldq r11, 16(r17) C L1
mulq r9, r19, r2 C U1 #16
beq r6, $fix5 C U0
$ret5: addq r14, r4, r7 C L0
ldq r12, 24(r17) C L1
umulh r9, r19, r3 C U1 #17
beq r7, $fix6 C U0
$ret6: addq r5, r8, r8 C L0 sum 2
addq r21, r22, r13 C L1 sum 2 mul's
mulq r10, r19, r4 C U1 #18
addq r23, r24, r22 C L0 sum 2 mul's
cmpult r13, r21, r14 C L1 carry from sum
bgt r18, $Loop C U0
C ---------------------------------------------------------------
$Lend:
cmpult r8, r5, r29 C L0 carry from last bunch
cmpult r22, r24, r24 C U0 carry from sum
umulh r10, r19, r5 C U1 #02
addq r25, r26, r23 C U0 sum 2 mul's
stq r20, 0(r16) C L0
stq r6, 8(r16) C L1
mulq r11, r19, r6 C U1 #03
cmpult r23, r26, r25 C U0 carry from sum
stq r7, 16(r16) C L0
stq r8, 24(r16) C L1
umulh r11, r19, r7 C U1 #04
addq r27, r28, r28 C U0 sum 2 mul's
mulq r12, r19, r8 C U1 #05
cmpult r28, r27, r15 C L0 carry from sum
lda r16, 64(r16) C L1 bookkeeping
addq r13, r29, r13 C U0 start carry cascade
umulh r12, r19, r21 C U1 #06
beq r13, $fix0c C U0
$ret0c: addq r22, r14, r26 C L0
beq r26, $fix1c C U0
$ret1c: addq r23, r24, r27 C L0
beq r27, $fix2c C U0
$ret2c: addq r28, r25, r28 C L0
beq r28, $fix3c C U0
$ret3c: addq r1, r2, r20 C L0 sum 2 mul's
addq r3, r4, r2 C L0 #10 2 mul's
lda r17, 64(r17) C L1 bookkeeping
cmpult r20, r1, r29 C U0 carry from sum
cmpult r2, r4, r4 C U0 carry from sum
stq r13, -32(r16) C L0
stq r26, -24(r16) C L1
addq r5, r6, r14 C U0 sum 2 mul's
stq r27, -16(r16) C L0
stq r28, -8(r16) C L1
cmpult r14, r6, r3 C U0 carry from sum
addq r7, r3, r5 C L0 eat carry
addq r20, r15, r20 C U0 carry cascade
beq r20, $fix4c C U0
$ret4c: addq r2, r29, r6 C L0
beq r6, $fix5c C U0
$ret5c: addq r14, r4, r7 C L0
beq r7, $fix6c C U0
$ret6c: addq r5, r8, r8 C L0 sum 2
cmpult r8, r5, r29 C L0 carry from last bunch
stq r20, 0(r16) C L0
stq r6, 8(r16) C L1
stq r7, 16(r16) C L0
stq r8, 24(r16) C L1
addq r29, r21, r0
ldq r26, 0(r30)
ldq r9, 8(r30)
ldq r10, 16(r30)
ldq r11, 24(r30)
ldq r12, 32(r30)
ldq r13, 40(r30)
ldq r14, 48(r30)
ldq r15, 56(r30)
ldq r29, 64(r30)
lda r30, 224(r30)
ret r31, (r26), 1
C $fix0w: bis r14, r29, r14 C join carries
C br r31, $ret0w
$fix1w: bis r24, r14, r24 C join carries
br r31, $ret1w
$fix2w: bis r25, r24, r25 C join carries
br r31, $ret2w
$fix3w: bis r15, r25, r15 C join carries
br r31, $ret3w
$fix0: bis r14, r29, r14 C join carries
br r31, $ret0
$fix1: bis r24, r14, r24 C join carries
br r31, $ret1
$fix2: bis r25, r24, r25 C join carries
br r31, $ret2
$fix3: bis r15, r25, r15 C join carries
br r31, $ret3
$fix4: bis r29, r15, r29 C join carries
br r31, $ret4
$fix5: bis r4, r29, r4 C join carries
br r31, $ret5
$fix6: addq r5, r4, r5 C can't carry twice!
br r31, $ret6
$fix0c: bis r14, r29, r14 C join carries
br r31, $ret0c
$fix1c: bis r24, r14, r24 C join carries
br r31, $ret1c
$fix2c: bis r25, r24, r25 C join carries
br r31, $ret2c
$fix3c: bis r15, r25, r15 C join carries
br r31, $ret3c
$fix4c: bis r29, r15, r29 C join carries
br r31, $ret4c
$fix5c: bis r4, r29, r4 C join carries
br r31, $ret5c
$fix6c: addq r5, r4, r5 C can't carry twice!
br r31, $ret6c
EPILOGUE(mpn_mul_1)
ASM_END()
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