# Self numbers\Phix

My humiliatingly bad prior attempts at this task:

Translation of Go.
Replacing the problematic sv[a+b+... line with a bit of dirty inline assembly improved performance by 90%

(Of course you lose bounds checking, type checking, negative subscripts, fraction handling, and all that jazz.)

We use a string of Y/N for the sieve to force one byte per element ('\0' and 1 would be equally valid).

if machine_bits()=32 then crash("requires 64 bit") end if

function sieve()

string sv = repeat('N',2*1e9+9*9+1) -- (1.86GB)

integer n = 0

for a=0 to 1 do

for b=0 to 9 do

for c=0 to 9 do

for d=0 to 9 do

for e=0 to 9 do

for f=0 to 9 do

for g=0 to 9 do

for h=0 to 9 do

for i=0 to 9 do

for j=0 to 9 do

-- n += 1

-- sv[a+b+c+d+e+f+g+h+i+j+n] = 'Y'

#ilASM{

[32] -- (allows clean compilation on 32 bit, before crash as above)

[64]

mov rax,[a]

mov r12,[b]

mov r13,[c]

mov r14,[d]

mov r15,[e]

add r12,r13

add r14,r15

add rax,r12

mov rdi,[sv]

add rax,r14

mov r12,[f]

mov r13,[g]

mov r14,[h]

mov r15,[i]

add r12,r13

shl rdi,2

mov rcx,[n]

mov r13,[j]

add r14,r15

add rax,r12

add rax,r14

add r13,rcx

add rax,r13

add rcx,1

mov byte[rdi+rax],'Y'

mov [n],rcx }

end for

end for

end for

end for

end for

end for

end for

end for

printf(1,"%d,%d\r",{a,b}) -- (show progress)

end for

end for

return sv

end function

atom t0 = time()

string sv = sieve()

printf(1,"sieve build took %s\n",{elapsed(time()-t0)})

integer count = 0

printf(1,"The first 50 self numbers are:\n")

for i=1 to length(sv) do

if sv[i]='N' then

count += 1

if count <= 50 then

printf(1,"%3d ",i-1)

if remainder(count,10)=0 then

printf(1,"\n")

end if

end if

if count == 1e8 then

printf(1,"\nThe %,dth self number is %,d (%s)\n",

{count,i-1,elapsed(time()-t0)})

exit

end if

end if

end for

- Output:

sieve build took 6.6s The first 50 self numbers are: 1 3 5 7 9 20 31 42 53 64 75 86 97 108 110 121 132 143 154 165 176 187 198 209 211 222 233 244 255 266 277 288 299 310 312 323 334 345 356 367 378 389 400 411 413 424 435 446 457 468 The 100,000,000th self number is 1,022,727,208 (11.0s)

### generator dictionary[edit]

While this is dog-slow (see shocking estimate below), it is interesting to note that even by the time it generates the
10,000,000th number, it is only having to juggle a mere 27 generators.
Just a shame that we had to push over 10,000,000 generators onto that stack, and tried to push quite a few more.
Memory use is pretty low, around ~4MB.

[unlike the above, this is perfectly happy on both 32 and 64 bit]

Long story short: this works much the same as a prime sieve, in which you only need to eliminate multiples
of previous primes. Here, you only need to eliminate digital additions of previous safe numbers.
Only after writing this did I understand how to write a sliding sieve, which it turns out is a much better idea (see below).
Still, this is pretty interesting and quite neat.

integer gd = new_dict(), gdhead = 2, n = 0

function ng(integer n)

integer r = n

while r do

n += remainder(r,10)

r = floor(r/10)

end while

return n

end function

function self(integer /*i*/)

-- note: assumes sequentially invoked (arg i unused)

n += 1

while n=gdhead do

gdhead = pop_dict(gd)[1]

setd(ng(gdhead),0,gd)

n += (n!=gdhead)

end while

setd(ng(n),0,gd)

return n

end function

atom t0 = time()

printf(1,"The first 50 self numbers are:\n")

pp(apply(tagset(50),self),{pp_IntFmt,"%3d",pp_IntCh,false})

constant limit = 10000000

integer chk = 100

printf(1,"\n i n size time\n")

for i=51 to limit do

n = self(i)

if i=chk then

printf(1,"%,11d %,11d %6d %s\n",{i,n,dict_size(gd),elapsed(time()-t0)})

chk *= 10

end if

end for

printf(1,"\nEstimated time for %,d :%s\n",{1e8,elapsed((time()-t0)*1e8/limit)})

- Output:

The first 50 self numbers are: { 1, 3, 5, 7, 9, 20, 31, 42, 53, 64, 75, 86, 97,108,110,121,132,143, 154,165,176,187,198,209,211,222,233,244,255,266,277,288,299,310,312,323, 334,345,356,367,378,389,400,411,413,424,435,446,457,468} i n size time 100 973 18 0.1s 1,000 10,188 13 0.2s 10,000 102,225 10 1.0s 100,000 1,022,675 20 9.3s 1,000,000 10,227,221 17 1 minute and 37s 10,000,000 102,272,662 27 16 minutes and 40s Estimated time for 100,000,000 :2 hours, 46 minutes and 37s

For the record, I would not be at all surprised should a translation of this beat 20 minutes (for 1e8)

### sliding sieve[edit]

Mid-speed, perhaps helped by a slightly smarter way of calculating/updating the digit sums

Similar to some other entries, we (only) need a sieve of 9*9, +1 here as I test an entry after the slide.

--sequence sieve = repeat(0,82), -- (~25% slower)

sequence sieve = repeat(0,8192),

digits = repeat(0,10)

integer offset = 0,

digit_sum = 0,

n = 0

procedure next_self()

while true do

n += 1

for i=length(digits) to 1 by -1 do

integer d = digits[i]

if d!=9 then

digits[i] = d+1

digit_sum += 1

exit

end if

digits[i] = 0

digit_sum -= 9

end for

integer k = n+digit_sum-offset

if k>length(sieve) then

integer j = 1

for i=n-offset to length(sieve) do

sieve[j] = sieve[i]

j += 1

end for

sieve[j..$] = 0

offset = n-1

k = digit_sum+1

end if

sieve[k] = 1

if sieve[n-offset]=0 then exit end if

end while

-- (result in n)

end procedure

constant limit = 100000000

atom t0 = time()

printf(1,"The first 50 self numbers are:\n")

integer chk = 100

for i=1 to limit do

next_self()

if i<=50 then

printf(1," %3d%s",{n,iff(mod(i,25)=0?"\n":"")})

elsif i=chk then

if chk=100 then

printf(1,"\n i n time\n")

end if

printf(1,"%,12d %,13d %s\n",{i,n,elapsed(time()-t0)})

chk *= 10

end if

end for

printf(1,"\nEstimated time for %,d :%s\n",{1e9,elapsed((time()-t0)*1e9/limit)})

- Output:

The first 50 self numbers are: 1 3 5 7 9 20 31 42 53 64 75 86 97 108 110 121 132 143 154 165 176 187 198 209 211 222 233 244 255 266 277 288 299 310 312 323 334 345 356 367 378 389 400 411 413 424 435 446 457 468 i n time 100 973 0.1s 1,000 10,188 0.1s 10,000 102,225 0.1s 100,000 1,022,675 0.1s 1,000,000 10,227,221 0.5s 10,000,000 102,272,662 4.5s 100,000,000 1,022,727,208 44.5s Estimated time for 1,000,000,000 :7 minutes and 25s