here is the first stab at mul_basecase. It's basically just an inlined version
of
mpn_zero(xp,xn);
rp[xn]=mpn_addmul(rp,xp,xn,yp[0]);
rp++;yp++yn--;
while(yn>=1)
{rp[xn]=mpn_addmul(rp,xp,xn,yp[0]);
rp++;yp++,yn--;}
for the timings in the result file attatched , I skipped the mpn_zero, so when
i put the proper mpn_mul_1 bit in , these are the timing we should get.
As the unrolled loop is 4-way , there's a bit of duplication which can be
absorbed into a few macros.
The straight substitution of the above c-algorithm is not going to get any
faster. We could though trim a few cycles of the small sizes , and perhaps do
the 1-4 limbs cases separatly
Possibly a mpn_addmul_2 may help , and perhaps....
--~--~---------~--~----~------------~-------~--~----~
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-~----------~----~----~----~------~----~------~--~---
# rdi rsi rdx rcx
r8
#mul_basecase( rp=rdi up=rsi un vp=r13
vn=r8 )
.global jay
jay:
cmp $1,%rdx
jne skip
mov (%rsi),%rax
mulq (%rcx)
mov %rax,(%rdi)
mov %rdx,8(%rdi)
ret
skip:
push %rbx
push %r12
push %r13
push %r14
push %r15
mov %rdx,%r14
mov %rdx,%r15
sub $5,%r14
and $3,%r15
neg %r14
lea -40(%rdi,%rdx,8),%rdi
lea -40(%rsi,%rdx,8),%rsi
mov %rcx,%r13
mov (%r13),%rcx
mov %r14,%rbx
# mpn_zero(rdi,un)
call theaddmul
lea 8(%rdi),%rdi
lea 8(%r13),%r13
dec %r8
jz next4
cmp $0,%r15
jne case1
# r15 is 0 , so bx would be 1 , so left is 2
loop1:
mov (%r13),%rcx
mov %r14,%rbx
#call theaddmul2
mov (%rsi,%rbx,8),%rax
mul %rcx
mov %rax,%r9
mov %rdx,%r10
mov 8(%rsi,%rbx,8),%rax
cmp $0,%rbx
jge next22
.align 16
loop22:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add $4,%rbx
mov 8(%rsi,%rbx,8),%rax
jnc loop22
next22:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
add %r12,24(%rdi,%rbx,8)
adc $0,%r9
mov %r9,32(%rdi,%rbx,8)
lea 8(%rdi),%rdi
lea 8(%r13),%r13
dec %r8
jnz loop1
next4:
pop %r15
pop %r14
pop %r13
pop %r12
pop %rbx
ret
case1:
cmp $1,%r15
jne case2
# r15 is 1 , so bx would be 0 , so left is 3
loop2:
mov (%r13),%rcx
mov %r14,%rbx
#call theaddmul3
mov (%rsi,%rbx,8),%rax
mul %rcx
mov %rax,%r9
mov %rdx,%r10
mov 8(%rsi,%rbx,8),%rax
cmp $0,%rbx
jge next33
.align 16
loop33:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add $4,%rbx
mov 8(%rsi,%rbx,8),%rax
jnc loop33
next33:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add %r9,32(%rdi,%rbx,8)
adc $0,%r10
mov %r10,40(%rdi,%rbx,8)
lea 8(%rdi),%rdi
lea 8(%r13),%r13
dec %r8
jnz loop2
pop %r15
pop %r14
pop %r13
pop %r12
pop %rbx
ret
case2:
cmp $2,%r15
jne case3
# r15 is 2 , so bx would be 3 , so left is 0
loop3:
mov (%r13),%rcx
mov %r14,%rbx
#call theaddmul0
mov (%rsi,%rbx,8),%rax
mul %rcx
mov %rax,%r9
mov %rdx,%r10
mov 8(%rsi,%rbx,8),%rax
cmp $0,%rbx
jge next00
.align 16
loop00:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add $4,%rbx
mov 8(%rsi,%rbx,8),%rax
jnc loop00
next00:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
add %r10,8(%rdi,%rbx,8)
adc $0,%r11
mov %r11,16(%rdi,%rbx,8)
lea 8(%rdi),%rdi
lea 8(%r13),%r13
dec %r8
jnz loop3
pop %r15
pop %r14
pop %r13
pop %r12
pop %rbx
ret
case3:
# r15 is 3 , so bx would be 2 , so left is 1
loop4:
mov (%r13),%rcx
mov %r14,%rbx
#call theaddmul1
mov (%rsi,%rbx,8),%rax
mul %rcx
mov %rax,%r9
mov %rdx,%r10
mov 8(%rsi,%rbx,8),%rax
cmp $0,%rbx
jge next11
.align 16
loop11:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add $4,%rbx
mov 8(%rsi,%rbx,8),%rax
jnc loop11
next11:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
add %r11,16(%rdi,%rbx,8)
adc $0,%r12
mov %r12,24(%rdi,%rbx,8)
lea 8(%rdi),%rdi
lea 8(%r13),%r13
dec %r8
jnz loop4
pop %r15
pop %r14
pop %r13
pop %r12
pop %rbx
ret
// addmul_1 which stores top limb rather than return
// uses bx,r12 but doesn't pop/push it
// n>=2
theaddmul:
mov (%rsi,%rbx,8),%rax
mul %rcx
mov %rax,%r9
mov %rdx,%r10
mov 8(%rsi,%rbx,8),%rax
cmp $0,%rbx
jge next
.align 16
loop:
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add $4,%rbx
mov 8(%rsi,%rbx,8),%rax
jnc loop
next:
cmp $0,%rbx
jne next1
#if we could do another 4 loads we would loop it
#here is 3 loads ie if bx=0
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mov $0,%r10d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
mov 32(%rsi,%rbx,8),%rax
mul %rcx
add %r12,24(%rdi,%rbx,8)
adc %rax,%r9
adc %rdx,%r10
add %r9,32(%rdi,%rbx,8)
adc $0,%r10
mov %r10,40(%rdi,%rbx,8)
ret
next1:
cmp $1,%rbx
jne next2
#here is 2 loads ie if bx=1
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
mov 24(%rsi,%rbx,8),%rax
mov $0,%r9d
mul %rcx
add %r11,16(%rdi,%rbx,8)
adc %rax,%r12
adc %rdx,%r9
add %r12,24(%rdi,%rbx,8)
adc $0,%r9
mov %r9,32(%rdi,%rbx,8)
ret
next2:
cmp $2,%rbx
jne next3
#here is 1 load ie if bx=2
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
mov 16(%rsi,%rbx,8),%rax
mul %rcx
add %r10,8(%rdi,%rbx,8)
adc %rax,%r11
mov $0,%r12d
adc %rdx,%r12
add %r11,16(%rdi,%rbx,8)
adc $0,%r12
mov %r12,24(%rdi,%rbx,8)
ret
next3:
#here is 0 loads ie if bx=3
mov $0,%r11d
mul %rcx
add %r9,(%rdi,%rbx,8)
adc %rax,%r10
adc %rdx,%r11
add %r10,8(%rdi,%rbx,8)
adc $0,%r11
mov %r11,16(%rdi,%rbx,8)
ret
#include <stdio.h>
#include <stdlib.h>
#include "gmpextra.h"
#include "gmpextra-1.0.1/gmp-impl.h"
#include "rdtsc.h"
void jay(mp_ptr rp,mp_srcptr xp,mp_size_t xn,mp_srcptr yp,mp_size_t yn);
#define DISP(xp,xn) do{int __t;printf("%s=",#xp);for(__t=(xn)-1;__t>=0;__t--)printf("%lX ",(xp)[__t]);printf("\n");}while(0)
int main(void)
{mp_limb_t xp[2048],yp[2048],rp[2048],zp[2048];mp_size_t xn,yn,zn;unsigned long t1,t2;double f,o,n;
for(xn=1;xn<30;xn++)
{for(yn=1;yn<=xn;yn++)
{mpn_random(xp,xn);mpn_random(yp,yn);zn=xn*yn;
mpn_mul_basecase(zp,xp,xn,yp,yn);
MPN_ZERO(rp,xn);jay(rp,xp,xn,yp,yn);
if(mpn_cmp(zp,rp,xn+yn)!=0){printf("error %d %d\n",xn,yn);abort();}
mpn_mul_basecase(zp,xp,xn,yp,yn);t1=rdtsc();mpn_mul_basecase(zp,xp,xn,yp,yn);t1=rdtsc()-t1;
MPN_ZERO(rp,xn);jay(rp,xp,xn,yp,yn);t2=rdtsc();//MPN_ZERO(rp,xn);
jay(rp,xp,xn,yp,yn);t2=rdtsc()-t2;
o=t1;o=o/zn;
n=t2;n=n/zn;
f=t1;f=f/t2;
printf("xn=%d\tyn=%d\told===%d\told=%f\tnew===%d\tnew=%f\tratio=%f\n",xn,yn,t1,o,t2,n,f);
}
}
return 0;}
xn=1 yn=1 old===27 old=27.000000 new===28 new=28.000000
ratio=0.964286
xn=2 yn=1 old===35 old=17.500000 new===37 new=18.500000
ratio=0.945946
xn=2 yn=2 old===24 old=6.000000 new===45 new=11.250000
ratio=0.533333
xn=3 yn=1 old===55 old=18.333333 new===62 new=20.666667
ratio=0.887097
xn=3 yn=2 old===77 old=12.833333 new===87 new=14.500000
ratio=0.885057
xn=3 yn=3 old===120 old=13.333333 new===89 new=9.888889
ratio=1.348315
xn=4 yn=1 old===44 old=11.000000 new===39 new=9.750000
ratio=1.128205
xn=4 yn=2 old===95 old=11.875000 new===61 new=7.625000
ratio=1.557377
xn=4 yn=3 old===120 old=10.000000 new===105 new=8.750000
ratio=1.142857
xn=4 yn=4 old===117 old=7.312500 new===102 new=6.375000
ratio=1.147059
xn=5 yn=1 old===75 old=15.000000 new===62 new=12.400000
ratio=1.209677
xn=5 yn=2 old===123 old=12.300000 new===74 new=7.400000
ratio=1.662162
xn=5 yn=3 old===123 old=8.200000 new===100 new=6.666667
ratio=1.230000
xn=5 yn=4 old===156 old=7.800000 new===144 new=7.200000
ratio=1.083333
xn=5 yn=5 old===187 old=7.480000 new===143 new=5.720000
ratio=1.307692
xn=6 yn=1 old===67 old=11.166667 new===59 new=9.833333
ratio=1.135593
xn=6 yn=2 old===114 old=9.500000 new===142 new=11.833333
ratio=0.802817
xn=6 yn=3 old===131 old=7.277778 new===138 new=7.666667
ratio=0.949275
xn=6 yn=4 old===161 old=6.708333 new===157 new=6.541667
ratio=1.025478
xn=6 yn=5 old===180 old=6.000000 new===181 new=6.033333
ratio=0.994475
xn=6 yn=6 old===203 old=5.638889 new===196 new=5.444444
ratio=1.035714
xn=7 yn=1 old===68 old=9.714286 new===87 new=12.428571
ratio=0.781609
xn=7 yn=2 old===93 old=6.642857 new===122 new=8.714286
ratio=0.762295
xn=7 yn=3 old===129 old=6.142857 new===167 new=7.952381
ratio=0.772455
xn=7 yn=4 old===148 old=5.285714 new===172 new=6.142857
ratio=0.860465
xn=7 yn=5 old===181 old=5.171429 new===174 new=4.971429
ratio=1.040230
xn=7 yn=6 old===230 old=5.476190 new===212 new=5.047619
ratio=1.084906
xn=7 yn=7 old===242 old=4.938776 new===237 new=4.836735
ratio=1.021097
xn=8 yn=1 old===59 old=7.375000 new===91 new=11.375000
ratio=0.648352
xn=8 yn=2 old===86 old=5.375000 new===110 new=6.875000
ratio=0.781818
xn=8 yn=3 old===122 old=5.083333 new===129 new=5.375000
ratio=0.945736
xn=8 yn=4 old===160 old=5.000000 new===165 new=5.156250
ratio=0.969697
xn=8 yn=5 old===197 old=4.925000 new===194 new=4.850000
ratio=1.015464
xn=8 yn=6 old===233 old=4.854167 new===210 new=4.375000
ratio=1.109524
xn=8 yn=7 old===266 old=4.750000 new===250 new=4.464286
ratio=1.064000
xn=8 yn=8 old===299 old=4.671875 new===281 new=4.390625
ratio=1.064057
xn=9 yn=1 old===62 old=6.888889 new===70 new=7.777778
ratio=0.885714
xn=9 yn=2 old===93 old=5.166667 new===116 new=6.444444
ratio=0.801724
xn=9 yn=3 old===133 old=4.925926 new===148 new=5.481481
ratio=0.898649
xn=9 yn=4 old===174 old=4.833333 new===212 new=5.888889
ratio=0.820755
xn=9 yn=5 old===215 old=4.777778 new===233 new=5.177778
ratio=0.922747
xn=9 yn=6 old===255 old=4.722222 new===254 new=4.703704
ratio=1.003937
xn=9 yn=7 old===290 old=4.603175 new===289 new=4.587302
ratio=1.003460
xn=9 yn=8 old===325 old=4.513889 new===316 new=4.388889
ratio=1.028481
xn=9 yn=9 old===361 old=4.456790 new===347 new=4.283951
ratio=1.040346
xn=10 yn=1 old===64 old=6.400000 new===96 new=9.600000
ratio=0.666667
xn=10 yn=2 old===113 old=5.650000 new===158 new=7.900000
ratio=0.715190
xn=10 yn=3 old===160 old=5.333333 new===199 new=6.633333
ratio=0.804020
xn=10 yn=4 old===205 old=5.125000 new===205 new=5.125000
ratio=1.000000
xn=10 yn=5 old===250 old=5.000000 new===228 new=4.560000
ratio=1.096491
xn=10 yn=6 old===294 old=4.900000 new===272 new=4.533333
ratio=1.080882
xn=10 yn=7 old===332 old=4.742857 new===311 new=4.442857
ratio=1.067524
xn=10 yn=8 old===371 old=4.637500 new===346 new=4.325000
ratio=1.072254
xn=10 yn=9 old===409 old=4.544444 new===381 new=4.233333
ratio=1.073491
xn=10 yn=10 old===459 old=4.590000 new===416 new=4.160000
ratio=1.103365
xn=11 yn=1 old===67 old=6.090909 new===121 new=11.000000
ratio=0.553719
xn=11 yn=2 old===119 old=5.409091 new===164 new=7.454545
ratio=0.725610
xn=11 yn=3 old===169 old=5.121212 new===159 new=4.818182
ratio=1.062893
xn=11 yn=4 old===234 old=5.318182 new===200 new=4.545455
ratio=1.170000
xn=11 yn=5 old===264 old=4.800000 new===240 new=4.363636
ratio=1.100000
xn=11 yn=6 old===318 old=4.818182 new===285 new=4.318182
ratio=1.115789
xn=11 yn=7 old===369 old=4.792208 new===327 new=4.246753
ratio=1.128440
xn=11 yn=8 old===411 old=4.670455 new===362 new=4.113636
ratio=1.135359
xn=11 yn=9 old===445 old=4.494949 new===399 new=4.030303
ratio=1.115288
xn=11 yn=10 old===498 old=4.527273 new===436 new=3.963636
ratio=1.142202
xn=11 yn=11 old===550 old=4.545455 new===473 new=3.909091
ratio=1.162791
xn=12 yn=1 old===72 old=6.000000 new===76 new=6.333333
ratio=0.947368
xn=12 yn=2 old===127 old=5.291667 new===143 new=5.958333
ratio=0.888112
xn=12 yn=3 old===180 old=5.000000 new===168 new=4.666667
ratio=1.071429
xn=12 yn=4 old===233 old=4.854167 new===191 new=3.979167
ratio=1.219895
xn=12 yn=5 old===285 old=4.750000 new===250 new=4.166667
ratio=1.140000
xn=12 yn=6 old===336 old=4.666667 new===300 new=4.166667
ratio=1.120000
xn=12 yn=7 old===395 old=4.702381 new===344 new=4.095238
ratio=1.148256
xn=12 yn=8 old===440 old=4.583333 new===381 new=3.968750
ratio=1.154856
xn=12 yn=9 old===479 old=4.435185 new===420 new=3.888889
ratio=1.140476
xn=12 yn=10 old===535 old=4.458333 new===459 new=3.825000
ratio=1.165577
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