commit for once

1 files changed, 81 insertions, 0 deletions

diff --git a/3/10_control_and_data/49_variable_stack.c b/3/10_control_and_data/49_variable_stack.c
new file mode 100644
index 0000000..d72c235
--- /dev/null
+++ b/3/10_control_and_data/49_variable_stack.c
@@ -0,0 +1,81 @@
+// A.
+// vframe:
+//      pushq       %rbp
+//      movq        %rsp, %rbp
+//      subq        $16, %rsp
+//      leaq        22(,%rdi,8), %rax
+//      andq        $-16, %rax
+//
+//
+//      bitlevel representation of -16
+//              1111111111111111111111111111111111111111111111111111111111110000
+//
+//      rax
+//      22 + n*8
+//      n=0     0000000000000000000000000000000000000000000000000000000000010110    22
+//      n=1     0000000000000000000000000000000000000000000000000000000000011110    30
+//      n=2     0000000000000000000000000000000000000000000000000000000000100110    38
+//      n=3     0000000000000000000000000000000000000000000000000000000000101110    46
+//      n=4     0000000000000000000000000000000000000000000000000000000000110110    54
+//      n=5     0000000000000000000000000000000000000000000000000000000000111110    62
+//
+//      (22 + n*8) & -16
+//      n=0     0000000000000000000000000000000000000000000000000000000000010000    16 8n+16
+//      n=1     0000000000000000000000000000000000000000000000000000000000010000    16 8n+8
+//      n=2     0000000000000000000000000000000000000000000000000000000000100000    32 8n+16
+//      n=3     0000000000000000000000000000000000000000000000000000000000100000    32 8n+8
+//      n=4     0000000000000000000000000000000000000000000000000000000000110000    48
+//      n=5     0000000000000000000000000000000000000000000000000000000000110000    48
+//
+// print("{:064b}".format((0*8+22) & -16))
+// print("{:064b}".format((1*8+22) & -16))
+// print("{:064b}".format((2*8+22) & -16))
+// print("{:064b}".format((3*8+22) & -16))
+// print("{:064b}".format((4*8+22) & -16))
+// print("{:064b}".format((5*8+22) & -16))
+//
+// B.
+// vframe:
+//      pushq       %rbp
+//      movq        %rsp, %rbp
+//      subq        $16, %rsp
+//      leaq        22(,%rdi,8), %rax
+//      andq        $-16, %rax
+//
+//      subq        %rax, %rsp
+//
+//      leaq        7(%rsp), %rax           rax <- (rsp+7) = (rsp+(n-1)), n = 8
+//      shrq        $3, %rax                rax <- (floor(rax/8))
+//      leaq        0(,%rax,8), %r8         r8 <- ceil(rsp/8)*8
+//
+// Important We are growing the stack downwards.
+// But the array index grows upwards.
+//
+//  See 2.3.7 for derivation.
+// If x%(1<<k) == 0 then the bias has no effect, rounding down does not happen, there is no fraction.
+// else
+//  Since the operation of adding the bias and then flooring happens,
+//  this results in rounding towards zero, or taking the ceiling.
+//
+// So if rsp was a multiple of 8 then nothing happens.
+// Otherwise the start of the array is set to the first multiple of 8 towards the bottom of the stack (ceil goes towards greater addresses of the bottom).
+//
+// C.
+//
+// s_2 = (- s_1
+//          (+ (if (odd? n) 8 16) (* n 8) )
+//       )
+//
+// p = ceil(s2/8)*8
+// e2 = (- p s2)
+// e1 = (- s2 s1 e2 8n)
+//
+// 2065 - (8+5*8)
+//
+//      n       s_1         s_2         p           e_1         e_2
+//      5       2065        2017        2024        1           7
+//      6       2064        2000        2000        16          0
+//
+// D.
+//      p is 8byte aligned owing to the 8-10 instructions.
+//      s2 is not guaranteed to be aligned, so 1 byte. (But all we are doing is subtracting multiples of 16 from s1... not sure how this helps)