How to get checksums for templates

Question

I have a 64-bit number (but used only 42 least significant bits) and you want to calculate the sum of the bit 4 in the n, n+m, n+m*2and n+m*3(note: anything that can make a sum> 4 is invalid) for some fixed m and each value of n, which puts all bits in a number

as an example, using m=3and considering a 16-bit number

0010 1011 0110 0001

I need to calculate

2, 3, 1, 2, 3, 0, 3

Does anyone have any (cool) ideas on how to do this? I'm fine with a little cool.

---

My current thought is to make bit shifted copies of the input to align the values ​​to be added, and then build a logical tree to make a 4x 1-bit adder.

v1 = In;
v2 = In<<3;
v3 = In<<6;
v4 = In<<9;

a1 = v1 ^ v2;
a2 = v1 & v2;
b1 = v3 ^ v4;
b2 = v3 & v4;
c2 = a1 & b1;
d2 = a2 ^ b2;

o1 = a1 ^ b1;
o2 = c2 ^ d2;
o4 = a2 & b2;

, 3 ints, .

edit: , , - o4, o2&o1, o2 o1 , .

---

-

arr = [0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4];

for(int i = 0; i < N; i++)
{
   out[i] = arr[(In & 0b1001001001) % 30]; 
   In >>= 1;
}

, , 4 16 ( ) 0-15, mod 30. , 3 4 , .

---

p.s.

. . , .

Answer 1

, , : D parallelism SSE - .

unsigned short out[64];
const unsigned long long mask      = 0x0249024902490249ul;
const unsigned long long shiftmask = 0x0001000100010001ul;

unsigned long long t = (unsigned short)(in >> 38) | (unsigned long long)(unsigned short)(in >> 39) > 40) > 41) << 48;
t &= mask;
*((unsigned long long*)(out + 38)) = (t & shiftmask) + (t >> 3 & shiftmask) + (t >> 6 & shiftmask) + (t >> 9 & shiftmask);

[... snipsnap ...]

t = (unsigned short)(in >> 2) | (unsigned long long)(unsigned short)(in >> 3) > 4) > 5) << 48;
t &= mask;
*((unsigned long long*)(out + 2)) = (t & shiftmask) + (t >> 3 & shiftmask) + (t >> 6 & shiftmask) + (t >> 9 & shiftmask);

t = (unsigned short)in | (unsigned long long)(unsigned short)(in >> 1) << 16;
t &= mask;
*((unsigned int*)out) = (unsigned int)((t & shiftmask) + (t >> 3 & shiftmask) + (t >> 6 & shiftmask) + (t >> 9 & shiftmask));

---

, , , - QWORD. , .

unsigned short out[64];
const unsigned long long Xmask = 0x249024902490249ull;
const unsigned long long Ymask = 0x7000700070007u;

unsigned long long x = (in >> 14 & 0xFFFFu) | (in >> 20 & 0xFFFFu) > 26 & 0xFFFFu) > 32) << 48;
unsigned long long y;
y = x & Xmask;
y += y >> 6;
y += y >> 3;
y &= Ymask;
out[32] = (unsigned short)(y >> 48);
out[26] = (unsigned short)(y >> 32);
out[20] = (unsigned short)(y >> 16);
out[14] = (unsigned short)(y      );

x >>= 1;
y = x & Xmask;
y += y >> 6;
y += y >> 3;
y &= Ymask;
out[33] = (unsigned short)(y >> 48);
out[27] = (unsigned short)(y >> 32);
out[21] = (unsigned short)(y >> 16);
out[15] = (unsigned short)(y      );

[snisnap]

x >>= 1;
y = x & Xmask;
y += y >> 6;
y += y >> 3;
y &= Ymask;
out[37] = (unsigned short)(y >> 48);
out[31] = (unsigned short)(y >> 32);
out[25] = (unsigned short)(y >> 16);
out[19] = (unsigned short)(y      );

x >>= 1;
x &= 0xFFFF000000000000ul;
x |= (in & 0xFFFFu) | (in >> 5 & 0xFFFFu) > 10 & 0xFFFFu) << 32;
y = x & Xmask;
y += y >> 6;
y += y >> 3;
y &= Ymask;
out[38] = (unsigned short)(y >> 48);
out[10] = (unsigned short)(y >> 32);
out[ 5] = (unsigned short)(y >> 16);
out[ 0] = (unsigned short)(y      );

[snipsnap]

x >>= 1;
y = x & Xmask;
y += y >> 6;
y += y >> 3;
y &= Ymask;
out[ 9] = (unsigned short)(y >> 16);
out[ 4] = (unsigned short)(y      );

50 native ++ ( ouputs ^^), 64- :
: ~ 5700
: ~ 4200
: ~ 2400
: ~ 1600

Answer 2

, , , , m .

loop 
   s[3*i] += x & (1 << 0);
   s[3*i+1] += x & (1 << 1);
   s[3*i+2] += x & (1 << 2);
   x >> 3;

. , , .

loop 
   s[3*i] += p[3*i]   = x & (1 << 0);
   s[3*i+1] += p[3*i+1] = x & (1 << 1);
   s[3*i+2] += p[3*i+2] = x & (1 << 2);

   s[3*i] -= p[3*i-10];
   s[3*i+1] -= p[3*i-9];
   s[3*i+2] -= p[3*i-8];
   x >> 3;

, .

, .

s[0] = (x & (1<<0)) + (x & (1<<3)) + (x & (1<<6)) + (x & (1<<9));

... ( .)