Auto merge of rust-lang#130002 - orlp:better-div-floor-ceil, r=thomcc

better implementation of signed div_floor/ceil

Tracking issue for signed `div_floor`/`div_ceil`: rust-lang#88581.

This PR improves the implementation of those two functions by adding a better branchless algorithm. Side-by-side comparison of `i32::div_floor` on x86-64:

```asm
div_floor_new:                               div_floor_old:
        push    rax                                  push    rax
        test    esi, esi                             test    esi, esi
        je      .LBB0_3                              je      .LBB1_6
        mov     eax, esi                             mov     eax, esi
        not     eax                                  not     eax
        lea     ecx, [rdi - 2147483648]              lea     ecx, [rdi - 2147483648]
        or      ecx, eax                             or      ecx, eax
        je      .LBB0_2                              je      .LBB1_7
        mov     eax, edi                             mov     eax, edi
        cdq                                          cdq
        idiv    esi                                  idiv    esi
        xor     esi, edi                             test    edx, edx
        sar     esi, 31                              setg    cl
        test    edx, edx                             test    esi, esi
        cmove   esi, edx                             sets    dil
        add     eax, esi                             test    dil, cl
        pop     rcx                                  jne     .LBB1_4
        ret                                          test    edx, edx
.LBB0_3:                                             setns   cl
        lea     rdi, [rip + .L__unnamed_1]           test    esi, esi
        call    qword ptr [rip + panic...]          setle   dl
.LBB0_2:                                             or      dl, cl
        lea     rdi, [rip + .L__unnamed_1]           jne     .LBB1_5
        call    qword ptr [rip + panic...]   .LBB1_4:
                                                     dec     eax
                                             .LBB1_5:
                                                     pop     rcx
                                                     ret
                                             .LBB1_6:
                                                     lea     rdi, [rip + .L__unnamed_2]
                                                     call    qword ptr [rip + panic...]
                                             .LBB1_7:
                                                     lea     rdi, [rip + .L__unnamed_2]
                                                     call    qword ptr [rip + panic...]
```

And on Aarch64:

```asm
_div_floor_new:                                   _div_floor_old:
        stp     x29, x30, [sp, #-16]!                     stp     x29, x30, [sp, #-16]!
        mov     x29, sp                                   mov     x29, sp
        cbz     w1, LBB0_4                                cbz     w1, LBB1_9
        mov     w8, #-2147483648                          mov     x8, x0
        cmp     w0, w8                                    mov     w9, #-2147483648
        b.ne    LBB0_3                                    cmp     w0, w9
        cmn     w1, #1                                    b.ne    LBB1_3
        b.eq    LBB0_5                                    cmn     w1, #1
LBB0_3:                                                   b.eq    LBB1_10
        sdiv    w8, w0, w1                        LBB1_3:
        msub    w9, w8, w1, w0                            sdiv    w0, w8, w1
        eor     w10, w1, w0                               msub    w8, w0, w1, w8
        asr     w10, w10, rust-lang#31                             tbz     w1, rust-lang#31, LBB1_5
        cmp     w9, #0                                    cmp     w8, #0
        csel    w9, wzr, w10, eq                          b.gt    LBB1_7
        add     w0, w9, w8                        LBB1_5:
        ldp     x29, x30, [sp], rust-lang#16                       cmp     w1, #1
        ret                                               b.lt    LBB1_8
LBB0_4:                                                   tbz     w8, rust-lang#31, LBB1_8
        adrp    x0, l___unnamed_1@PAGE            LBB1_7:
        add     x0, x0, l___unnamed_1@PAGEOFF             sub     w0, w0, #1
        bl      panic...                          LBB1_8:
LBB0_5:                                                   ldp     x29, x30, [sp], rust-lang#16
        adrp    x0, l___unnamed_1@PAGE                    ret
        add     x0, x0, l___unnamed_1@PAGEOFF     LBB1_9:
        bl      panic...                                  adrp    x0, l___unnamed_2@PAGE
                                                          add     x0, x0, l___unnamed_2@PAGEOFF
                                                          bl      panic...
                                                  LBB1_10:
                                                          adrp    x0, l___unnamed_2@PAGE
                                                          add     x0, x0, l___unnamed_2@PAGEOFF
                                                          bl      panic...
```

Author: bors

library/core/src/num/int_macros.rs

@@ -3023,8 +3023,16 @@ macro_rules! int_impl {
         pub const fn div_floor(self, rhs: Self) -> Self {
             let d = self / rhs;
             let r = self % rhs;
-            if (r > 0 && rhs < 0) || (r < 0 && rhs > 0) {
-                d - 1
+
+            // If the remainder is non-zero, we need to subtract one if the
+            // signs of self and rhs differ, as this means we rounded upwards
+            // instead of downwards. We do this branchlessly by creating a mask
+            // which is all-ones iff the signs differ, and 0 otherwise. Then by
+            // adding this mask (which corresponds to the signed value -1), we
+            // get our correction.
+            let correction = (self ^ rhs) >> (Self::BITS - 1);
+            if r != 0 {
+                d + correction
             } else {
                 d
             }
@@ -3059,8 +3067,12 @@ macro_rules! int_impl {
         pub const fn div_ceil(self, rhs: Self) -> Self {
             let d = self / rhs;
             let r = self % rhs;
-            if (r > 0 && rhs > 0) || (r < 0 && rhs < 0) {
-                d + 1
+
+            // When remainder is non-zero we have a.div_ceil(b) == 1 + a.div_floor(b),
+            // so we can re-use the algorithm from div_floor, just adding 1.
+            let correction = 1 + ((self ^ rhs) >> (Self::BITS - 1));
+            if r != 0 {
+                d + correction
             } else {
                 d
             }