Calculate day number from an unix-timestamp in a math way?

Question

How can i calculate day number from a unix-timestamp, in a mathematical way and without using any functions and in simple math formula.

1313905026 --> 8 (Today 08/21

Answer 1

A unix timestamp doesn't include leap seconds, so we don't have to worry about that. Here is a branch-less¹, loop-less algorithm for getting the y/m/d fields from a unix timestamp:

#include 

int
main()
{
    int s = 1313905026;
    int z = s / 86400 + 719468;
    int era = (z >= 0 ? z : z - 146096) / 146097;
    unsigned doe = static_cast(z - era * 146097);
    unsigned yoe = (doe - doe/1460 + doe/36524 - doe/146096) / 365;
    int y = static_cast(yoe) + era * 400;
    unsigned doy = doe - (365*yoe + yoe/4 - yoe/100);
    unsigned mp = (5*doy + 2)/153;
    unsigned d = doy - (153*mp+2)/5 + 1;
    unsigned m = mp + (mp < 10 ? 3 : -9);
    y += (m <= 2);
    std::cout << m << '/' << d << '/' << y << '\n'; // 8/21/2011
}

This outputs:

8/21/2011

As you're not interested in y and m (only in d), you can eliminate the last couple of lines from the above computation.

This algorithm is described in excruciating detail here. The link includes a complete derivation, and unit tests spanning millions of years (which is overkill).

---

¹ Branch-less: What looks like small branches in the algorithm above are optimized away by clang at -O3 on macOS:

__Z14get_day_numberi:                   ## @_Z14get_day_numberi
    .cfi_startproc
## BB#0:
    pushq   %rbp
Ltmp0:
    .cfi_def_cfa_offset 16
Ltmp1:
    .cfi_offset %rbp, -16
    movq    %rsp, %rbp
Ltmp2:
    .cfi_def_cfa_register %rbp
    movslq  %edi, %rax
    imulq   $-1037155065, %rax, %rcx ## imm = 0xFFFFFFFFC22E4507
    shrq    $32, %rcx
    addl    %ecx, %eax
    movl    %eax, %ecx
    shrl    $31, %ecx
    sarl    $16, %eax
    leal    (%rax,%rcx), %edx
    leal    719468(%rax,%rcx), %esi
    testl   %esi, %esi
    leal    573372(%rax,%rcx), %eax
    cmovnsl %esi, %eax
    cltq
    imulq   $963315389, %rax, %rcx  ## imm = 0x396B06BD
    movq    %rcx, %rsi
    shrq    $63, %rsi
    shrq    $32, %rcx
    sarl    $15, %ecx
    addl    %esi, %ecx
    imull   $146097, %ecx, %ecx     ## imm = 0x23AB1
    movl    %eax, %esi
    subl    %ecx, %esi
    subl    %eax, %esi
    leal    719468(%rsi,%rdx), %eax
    movl    %eax, %ecx
    shrl    $2, %ecx
    imulq   $1506180313, %rcx, %rdx ## imm = 0x59C67CD9
    shrq    $39, %rdx
    movl    %eax, %esi
    subl    %edx, %esi
    imulq   $963321983, %rcx, %rcx  ## imm = 0x396B207F
    shrq    $43, %rcx
    addl    %esi, %ecx
    movl    %eax, %edx
    shrl    $4, %edx
    imulq   $7525953, %rdx, %rdx    ## imm = 0x72D641
    shrq    $36, %rdx
    subl    %edx, %ecx
    imulq   $1729753953, %rcx, %rsi ## imm = 0x6719F361
    shrq    $32, %rsi
    movl    %ecx, %r8d
    subl    %ecx, %eax
    movl    %ecx, %edi
    movl    $3855821599, %edx       ## imm = 0xE5D32B1F
    imulq   %rcx, %rdx
    subl    %esi, %ecx
    shrl    %ecx
    addl    %esi, %ecx
    shrl    $8, %ecx
    imull   $365, %ecx, %ecx        ## imm = 0x16D
    subl    %ecx, %r8d
    shrl    $2, %edi
    imulq   $1506180313, %rdi, %rcx ## imm = 0x59C67CD9
    shrq    $39, %rcx
    shrq    $47, %rdx
    addl    %r8d, %eax
    subl    %ecx, %eax
    leal    (%rax,%rdx), %ecx
    leal    2(%rcx,%rcx,4), %esi
    movl    $3593175255, %edi       ## imm = 0xD62B80D7
    imulq   %rsi, %rdi
    shrq    $39, %rdi
    imull   $153, %edi, %edi
    subl    %edi, %esi
    leal    4(%rcx,%rcx,4), %ecx
    subl    %esi, %ecx
    movl    $3435973837, %esi       ## imm = 0xCCCCCCCD
    imulq   %rcx, %rsi
    shrq    $34, %rsi
    leal    1(%rax,%rdx), %eax
    subl    %esi, %eax
    popq    %rbp
    retq
    .cfi_endproc