path: root/mu_instructions

## Mu's instructions and their table-driven translation

See http://akkartik.name/akkartik-convivial-20200607.pdf for the complete
story. In brief: Mu is a statement-oriented language. Blocks consist of flat
lists of instructions. Instructions can have inputs after the operation, and
outputs to the left of a '<-'. Inputs and outputs must be variables. They can't
include nested expressions. Variables can be literals ('n'), or live in a
register ('var/reg') or in memory ('var') at some 'stack-offset' from the 'ebp'
register. Outputs must be registers. To modify a variable in memory, pass it in
by reference as an input. (Inputs are more precisely called 'inouts'.)
Conversely, registers that are just read from must not be passed as outputs.

The following chart shows all the instruction forms supported by Mu, along with
the SubX instruction they're translated to.

## Integer instructions

These instructions use the general-purpose registers.

var/eax <- increment              => "40/increment-eax"
var/ecx <- increment              => "41/increment-ecx"
var/edx <- increment              => "42/increment-edx"
var/ebx <- increment              => "43/increment-ebx"
var/esi <- increment              => "46/increment-esi"
var/edi <- increment              => "47/increment-edi"
increment var                     => "ff 0/subop/increment *(ebp+" var.stack-offset ")"
increment *var/reg                => "ff 0/subop/increment *" reg

var/eax <- decrement              => "48/decrement-eax"
var/ecx <- decrement              => "49/decrement-ecx"
var/edx <- decrement              => "4a/decrement-edx"
var/ebx <- decrement              => "4b/decrement-ebx"
var/esi <- decrement              => "4e/decrement-esi"
var/edi <- decrement              => "4f/decrement-edi"
decrement var                     => "ff 1/subop/decrement *(ebp+" var.stack-offset ")"
decrement *var/reg                => "ff 1/subop/decrement *" reg

var/reg <- add var2/reg2          => "01/add-to %" reg " " reg2 "/r32"
var/reg <- add var2               => "03/add *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- add *var2/reg2         => "03/add *" reg2 " " reg "/r32"
add-to var1, var2/reg             => "01/add-to *(ebp+" var1.stack-offset ") " reg "/r32"
add-to *var1/reg1, var2/reg2      => "01/add-to *" reg1 " " reg2 "/r32"
var/eax <- add n                  => "05/add-to-eax " n "/imm32"
var/reg <- add n                  => "81 0/subop/add %" reg " " n "/imm32"
add-to var, n                     => "81 0/subop/add *(ebp+" var.stack-offset ") " n "/imm32"
add-to *var/reg, n                => "81 0/subop/add *" reg " " n "/imm32"

var/reg <- subtract var2/reg2     => "29/subtract-from %" reg " " reg2 "/r32"
var/reg <- subtract var2          => "2b/subtract *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- subtract *var2/reg2    => "2b/subtract *" reg2 " " reg1 "/r32"
subtract-from var1, var2/reg2     => "29/subtract-from *(ebp+" var1.stack-offset ") " reg2 "/r32"
subtract-from *var1/reg1, var2/reg2 => "29/subtract-from *" reg1 " " reg2 "/r32"
var/eax <- subtract n             => "2d/subtract-from-eax " n "/imm32"
var/reg <- subtract n             => "81 5/subop/subtract %" reg " " n "/imm32"
subtract-from var, n              => "81 5/subop/subtract *(ebp+" var.stack-offset ") " n "/imm32"
subtract-from *var/reg, n         => "81 5/subop/subtract *" reg " " n "/imm32"

var/reg <- and var2/reg2          => "21/and-with %" reg " " reg2 "/r32"
var/reg <- and var2               => "23/and *(ebp+" var2.stack-offset " " reg "/r32"
var/reg <- and *var2/reg2         => "23/and *" reg2 " " reg "/r32"
and-with var1, var2/reg           => "21/and-with *(ebp+" var1.stack-offset ") " reg "/r32"
and-with *var1/reg1, var2/reg2    => "21/and-with *" reg1 " " reg2 "/r32"
var/eax <- and n                  => "25/and-with-eax " n "/imm32"
var/reg <- and n                  => "81 4/subop/and %" reg " " n "/imm32"
and-with var, n                   => "81 4/subop/and *(ebp+" var.stack-offset ") " n "/imm32"
and-with *var/reg, n              => "81 4/subop/and *" reg " " n "/imm32"

var/reg <- or var2/reg2           => "09/or-with %" reg " " reg2 "/r32"
var/reg <- or var2                => "0b/or *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- or *var2/reg2          => "0b/or *" reg2 " " reg "/r32"
or-with var1, var2/reg2           => "09/or-with *(ebp+" var1.stack-offset " " reg2 "/r32"
or-with *var1/reg1, var2/reg2     => "09/or-with *" reg1 " " reg2 "/r32"
var/eax <- or n                   => "0d/or-with-eax " n "/imm32"
var/reg <- or n                   => "81 1/subop/or %" reg " " n "/imm32"
or-with var, n                    => "81 1/subop/or *(ebp+" var.stack-offset ") " n "/imm32"
or-with *var/reg, n               => "81 1/subop/or *" reg " " n "/imm32"

var/reg <- not                    => "f7 2/subop/not %" reg
not var                           => "f7 2/subop/not *(ebp+" var.stack-offset ")"
not *var/reg                      => "f7 2/subop/not *" reg

var/reg <- xor var2/reg2          => "31/xor-with %" reg " " reg2 "/r32"
var/reg <- xor var2               => "33/xor *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- xor *var2/reg2         => "33/xor *" reg2 " " reg "/r32"
xor-with var1, var2/reg           => "31/xor-with *(ebp+" var1.stack-offset ") " reg "/r32"
xor-with *var1/reg1, var2/reg2    => "31/xor-with *" reg1 " " reg2 "/r32"
var/eax <- xor n                  => "35/xor-with-eax " n "/imm32"
var/reg <- xor n                  => "81 6/subop/xor %" reg " " n "/imm32"
xor-with var, n                   => "81 6/subop/xor *(ebp+" var.stack-offset ") " n "/imm32"
xor-with *var/reg, n              => "81 6/subop/xor *" reg " " n "/imm32"

var/reg <- negate                 => "f7 3/subop/negate %" reg
negate var                        => "f7 3/subop/negate *(ebp+" var.stack-offset ")"
negate *var/reg                   => "f7 3/subop/negate *" reg

var/reg <- shift-left n           => "c1/shift 4/subop/left %" reg " " n "/imm32"
var/reg <- shift-right n          => "c1/shift 5/subop/right %" reg " " n "/imm32"
var/reg <- shift-right-signed n   => "c1/shift 7/subop/right-signed %" reg " " n "/imm32"
shift-left var, n                 => "c1/shift 4/subop/left *(ebp+" var.stack-offset ") " n "/imm32"
shift-left *var/reg, n            => "c1/shift 4/subop/left *" reg " " n "/imm32"
shift-right var, n                => "c1/shift 5/subop/right *(ebp+" var.stack-offset ") " n "/imm32"
shift-right *var/reg, n           => "c1/shift 5/subop/right *" reg " " n "/imm32"
shift-right-signed var, n         => "c1/shift 7/subop/right-signed *(ebp+" var.stack-offset ") " n "/imm32"
shift-right-signed *var/reg, n    => "c1/shift 7/subop/right-signed *" reg " " n "/imm32"

var/eax <- copy n                 => "b8/copy-to-eax " n "/imm32"
var/ecx <- copy n                 => "b9/copy-to-ecx " n "/imm32"
var/edx <- copy n                 => "ba/copy-to-edx " n "/imm32"
var/ebx <- copy n                 => "bb/copy-to-ebx " n "/imm32"
var/esi <- copy n                 => "be/copy-to-esi " n "/imm32"
var/edi <- copy n                 => "bf/copy-to-edi " n "/imm32"
var/reg <- copy var2/reg2         => "89/<- %" reg " " reg2 "/r32"
copy-to var1, var2/reg            => "89/<- *(ebp+" var1.stack-offset ") " reg "/r32"
copy-to *var1/reg1, var2/reg2     => "89/<- *" reg1 " " reg2 "/r32"
var/reg <- copy var2              => "8b/-> *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- copy *var2/reg2        => "8b/-> *" reg2 " " reg "/r32"
var/reg <- copy n                 => "c7 0/subop/copy %" reg " " n "/imm32"
copy-to var, n                    => "c7 0/subop/copy *(ebp+" var.stack-offset ") " n "/imm32"
copy-to *var/reg, n               => "c7 0/subop/copy *" reg " " n "/imm32"

var/reg <- copy-byte var2/reg2    => "8a/byte-> %" reg2 " " reg "/r32"
                                     "81 4/subop/and %" reg " 0xff/imm32"
var/reg <- copy-byte *var2/reg2   => "8a/byte-> *" reg2 " " reg "/r32"
                                     "81 4/subop/and %" reg " 0xff/imm32"
copy-byte-to *var1/reg1, var2/reg2  => "88/byte<- *" reg1 " " reg2 "/r32"

compare var1, var2/reg2           => "39/compare *(ebp+" var1.stack-offset ") " reg2 "/r32"
compare *var1/reg1, var2/reg2     => "39/compare *" reg1 " " reg2 "/r32"
compare var1/reg1, var2           => "3b/compare<- *(ebp+" var2.stack-offset ") " reg1 "/r32"
compare var/reg, *var2/reg2       => "3b/compare<- *" reg " " n "/imm32"
compare var/eax, n                => "3d/compare-eax-with " n "/imm32"
compare var/reg, n                => "81 7/subop/compare %" reg " " n "/imm32"
compare var, n                    => "81 7/subop/compare *(ebp+" var.stack-offset ") " n "/imm32"
compare *var/reg, n               => "81 7/subop/compare *" reg " " n "/imm32"

var/reg <- multiply var2          => "0f af/multiply *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- multiply var2/reg2     => "0f af/multiply %" reg2 " " reg "/r32"
var/reg <- multiply *var2/reg2    => "0f af/multiply *" reg2 " " reg "/r32"

## Floating-point operations

These instructions operate on either floating-point registers (xreg) or
general-purpose registers (reg) in indirect mode.

var/xreg <- add var2/xreg2        => "f3 0f 58/add %" xreg2 " " xreg1 "/x32"
var/xreg <- add var2              => "f3 0f 58/add *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- add *var2/reg2        => "f3 0f 58/add *" reg2 " " xreg "/x32"

var/xreg <- subtract var2/xreg2   => "f3 0f 5c/subtract %" xreg2 " " xreg1 "/x32"
var/xreg <- subtract var2         => "f3 0f 5c/subtract *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- subtract *var2/reg2   => "f3 0f 5c/subtract *" reg2 " " xreg "/x32"

var/xreg <- multiply var2/xreg2   => "f3 0f 59/multiply %" xreg2 " " xreg1 "/x32"
var/xreg <- multiply var2         => "f3 0f 59/multiply *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- multiply *var2/reg2   => "f3 0f 59/multiply *" reg2 " " xreg "/x32"

var/xreg <- divide var2/xreg2     => "f3 0f 5e/divide %" xreg2 " " xreg1 "/x32"
var/xreg <- divide var2           => "f3 0f 5e/divide *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- divide *var2/reg2     => "f3 0f 5e/divide *" reg2 " " xreg "/x32"

There are also some exclusively floating-point instructions:

var/xreg <- reciprocal var2/xreg2 => "f3 0f 53/reciprocal %" xreg2 " " xreg1 "/x32"
var/xreg <- reciprocal var2       => "f3 0f 53/reciprocal *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- reciprocal *var2/reg2 => "f3 0f 53/reciprocal *" reg2 " " xreg "/x32"

var/xreg <- square-root var2/xreg2 => "f3 0f 51/square-root %" xreg2 " " xreg1 "/x32"
var/xreg <- square-root var2       => "f3 0f 51/square-root *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- square-root *var2/reg2 => "f3 0f 51/square-root *" reg2 " " xreg "/x32"

var/xreg <- inverse-square-root var2/xreg2 => "f3 0f 52/inverse-square-root %" xreg2 " " xreg1 "/x32"
var/xreg <- inverse-square-root var2       => "f3 0f 52/inverse-square-root *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- inverse-square-root *var2/reg2 => "f3 0f 52/inverse-square-root *" reg2 " " xreg "/x32"

var/xreg <- min var2/xreg2        => "f3 0f 5d/min %" xreg2 " " xreg1 "/x32"
var/xreg <- min var2              => "f3 0f 5d/min *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- min *var2/reg2        => "f3 0f 5d/min *" reg2 " " xreg "/x32"

var/xreg <- max var2/xreg2        => "f3 0f 5f/max %" xreg2 " " xreg1 "/x32"
var/xreg <- max var2              => "f3 0f 5f/max *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- max *var2/reg2        => "f3 0f 5f/max *" reg2 " " xreg "/x32"

Remember, when these instructions use indirect mode, they still use an integer
register. Floating-point registers can't hold addresses.

Most instructions operate exclusively on integer or floating-point operands.
The only exceptions are the instructions for converting between integers and
floating-point numbers.

var/xreg <- convert var2/reg2     => "f3 0f 2a/convert-to-float %" reg2 " " xreg "/x32"
var/xreg <- convert var2          => "f3 0f 2a/convert-to-float *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- convert *var2/reg2    => "f3 0f 2a/convert-to-float *" reg2 " " xreg "/x32"

Converting floats to ints performs rounding by default. (We don't mess with the
MXCSR control register.)

var/reg <- convert var2/xreg2     => "f3 0f 2d/convert-to-int %" xreg2 " " reg "/r32"
var/reg <- convert var2           => "f3 0f 2d/convert-to-int *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- convert *var2/reg2     => "f3 0f 2d/convert-to-int *" reg2 " " reg "/r32"

There's a separate instruction for truncating the fractional part.

var/reg <- truncate var2/xreg2     => "f3 0f 2c/truncate-to-int %" xreg2 " " reg "/r32"
var/reg <- truncate var2           => "f3 0f 2c/truncate-to-int *(ebp+" var2.stack-offset ") " reg "/r32"
var/reg <- truncate *var2/reg2     => "f3 0f 2c/truncate-to-int *" reg2 " " reg "/r32"

There are no instructions accepting floating-point literals. To obtain integer
literals in floating-point registers, copy them to general-purpose registers
and then convert them to floating-point.

One pattern you may have noticed above is that the floating-point instructions
above always write to registers. The only exceptions are `copy` instructions,
which can write to memory locations.

var/xreg <- copy var2/xreg2       => "f3 0f 11/<- %" xreg " " xreg2 "/x32"
copy-to var1, var2/xreg           => "f3 0f 11/<- *(ebp+" var1.stack-offset ") " xreg "/x32"
var/xreg <- copy var2             => "f3 0f 10/-> *(ebp+" var2.stack-offset ") " xreg "/x32"
var/xreg <- copy *var2/reg2       => "f3 0f 10/-> *" reg2 " " xreg "/x32"

Comparisons must always start with a register:

compare var1/xreg1, var2/xreg2    => "0f 2f/compare %" xreg2 " " xreg1 "/x32"
compare var1/xreg1, var2          => "0f 2f/compare *(ebp+" var2.stack-offset ") " xreg1 "/x32"

## Blocks

In themselves, blocks generate no instructions. However, if a block contains
variable declarations, they must be cleaned up when the block ends.

Clean up var on the stack         => "81 0/subop/add %esp " size-of(var) "/imm32"
Clean up var/reg                  => "8f 0/subop/pop %" reg

Clean up var/xreg                 => "f3 0f 10/-> *esp " xreg "/x32"
                                     "81 0/subop/add %esp 4/imm32"

## Jumps

Besides having to clean up any variable declarations (see above) between
themselves and their target, jumps translate like this:

break                             => "e9/jump break/disp32"
break label                       => "e9/jump " label ":break/disp32"
loop                              => "e9/jump loop/disp32"
loop label                        => "e9/jump " label ":loop/disp32"

break-if-=                        => "0f 84/jump-if-= break/disp32"
break-if-= label                  => "0f 84/jump-if-= " label ":break/disp32"
loop-if-=                         => "0f 84/jump-if-= loop/disp32"
loop-if-= label                   => "0f 84/jump-if-= " label ":loop/disp32"

break-if-!=                       => "0f 85/jump-if-!= break/disp32"
break-if-!= label                 => "0f 85/jump-if-!= " label ":break/disp32"
loop-if-!=                        => "0f 85/jump-if-!= loop/disp32"
loop-if-!= label                  => "0f 85/jump-if-!= " label ":loop/disp32"

break-if-<                        => "0f 8c/jump-if-< break/disp32"
break-if-< label                  => "0f 8c/jump-if-< " label ":break/disp32"
loop-if-<                         => "0f 8c/jump-if-< loop/disp32"
loop-if-< label                   => "0f 8c/jump-if-< " label ":loop/disp32"

break-if->                        => "0f 8f/jump-if-> break/disp32"
break-if-> label                  => "0f 8f/jump-if-> " label ":break/disp32"
loop-if->                         => "0f 8f/jump-if-> loop/disp32"
loop-if-> label                   => "0f 8f/jump-if-> " label ":loop/disp32"

break-if-<=                       => "0f 8e/jump-if-<= break/disp32"
break-if-<= label                 => "0f 8e/jump-if-<= " label ":break/disp32"
loop-if-<=                        => "0f 8e/jump-if-<= loop/disp32"
loop-if-<= label                  => "0f 8e/jump-if-<= " label ":loop/disp32"

break-if->=                       => "0f 8d/jump-if->= break/disp32"
break-if->= label                 => "0f 8d/jump-if->= " label ":break/disp32"
loop-if->=                        => "0f 8d/jump-if->= loop/disp32"
loop-if->= label                  => "0f 8d/jump-if->= " label ":loop/disp32"

break-if-addr<                    => "0f 82/jump-if-addr< break/disp32"
break-if-addr< label              => "0f 82/jump-if-addr< " label ":break/disp32"
loop-if-addr<                     => "0f 82/jump-if-addr< loop/disp32"
loop-if-addr< label               => "0f 82/jump-if-addr< " label ":loop/disp32"

break-if-addr>                    => "0f 87/jump-if-addr> break/disp32"
break-if-addr> label              => "0f 87/jump-if-addr> " label ":break/disp32"
loop-if-addr>                     => "0f 87/jump-if-addr> loop/disp32"
loop-if-addr> label               => "0f 87/jump-if-addr> " label ":loop/disp32"

break-if-addr<=                   => "0f 86/jump-if-addr<= break/disp32"
break-if-addr<= label             => "0f 86/jump-if-addr<= " label ":break/disp32"
loop-if-addr<=                    => "0f 86/jump-if-addr<= loop/disp32"
loop-if-addr<= label              => "0f 86/jump-if-addr<= " label ":loop/disp32"

break-if-addr>=                   => "0f 83/jump-if-addr>= break/disp32"
break-if-addr>= label             => "0f 83/jump-if-addr>= " label ":break/disp32"
loop-if-addr>=                    => "0f 83/jump-if-addr>= loop/disp32"
loop-if-addr>= label              => "0f 83/jump-if-addr>= " label ":loop/disp32"

Similar float variants like `break-if-float<` are aliases for the corresponding
`addr` equivalents. The x86 instruction set stupidly has floating-point
operations only update a subset of flags.

Four sets of conditional jumps are useful for detecting overflow.

break-if-carry                    => "0f 82/jump-if-carry break/disp32"
break-if-carry label              => "0f 82/jump-if-carry " label "/disp32"
loop-if-carry                     => "0f 82/jump-if-carry break/disp32"
loop-if-carry label               => "0f 82/jump-if-carry " label "/disp32"

break-if-not-carry                => "0f 83/jump-if-not-carry break/disp32"
break-if-not-carry label          => "0f 83/jump-if-not-carry " label "/disp32"
loop-if-not-carry                 => "0f 83/jump-if-not-carry break/disp32"
loop-if-not-carry label           => "0f 83/jump-if-not-carry " label "/disp32"

break-if-overflow                 => "0f 80/jump-if-overflow break/disp32"
break-if-overflow label           => "0f 80/jump-if-overflow " label ":break/disp32"
loop-if-overflow                  => "0f 80/jump-if-overflow loop/disp32"
loop-if-overflow label            => "0f 80/jump-if-overflow " label ":loop/disp32"

break-if-not-overflow             => "0f 81/jump-if-not-overflow break/disp32"
break-if-not-overflow label       => "0f 81/jump-if-not-overflow " label ":break/disp32"
loop-if-not-overflow              => "0f 81/jump-if-not-overflow loop/disp32"
loop-if-not-overflow label        => "0f 81/jump-if-not-overflow " label ":loop/disp32"

All this relies on a convention that every `{}` block is delimited by labels
ending in `:loop` and `:break`.

## Returns

The `return` instruction cleans up variable declarations just like an unconditional
`jump` to end of function, but also emits a series of copies before the final
`jump`, copying each argument of `return` to the register appropriate to the
respective function output. This doesn't work if a function output register
contains a later `return` argument (e.g. if the registers for two outputs are
swapped in `return`), so you can't do that.

return                            => "c3/return"

---

In the following instructions types are provided for clarity even if they must
be provided in an earlier 'var' declaration.

# Address operations

var/reg: (addr T) <- address var2: T
  => "8d/copy-address *(ebp+" var2.stack-offset ") " reg "/r32"

# Array operations

var/reg: (addr T) <- index arr/rega: (addr array T), idx/regi: int
  | if size-of(T) is 1, 2, 4 or 8
      => "81 7/subop/compare %" rega " 0/imm32"
         "0f 84/jump-if-= __mu-abort-null-index-base-address/disp32"
         "(__check-mu-array-bounds *" rega " %" regi " " size-of(T) ")"
         "8d/copy-address *(" rega "+" regi "<<" log2(size-of(T)) "+4) " reg "/r32"
var/reg: (addr T) <- index arr: (array T len), idx/regi: int
  => "(__check-mu-array-bounds *(ebp+" arr.stack-offset ") %" regi " " size-of(T) ")"
     "8d/copy-address *(ebp+" regi "<<" log2(size-of(T)) "+" (arr.stack-offset + 4) ") " reg "/r32"
var/reg: (addr T) <- index arr/rega: (addr array T), n
  => "81 7/subop/compare %" rega " 0/imm32"
     "0f 84/jump-if-= __mu-abort-null-index-base-address/disp32"
     "(__check-mu-array-bounds *" rega " " n " " size-of(T) ")"
     "8d/copy-address *(" rega "+" (n*size-of(T)+4) ") " reg "/r32"
var/reg: (addr T) <- index arr: (array T len), n
  => "(__check-mu-array-bounds *(ebp+" arr.stack-offset ") " n " " size-of(T) ")"
     "8d/copy-address *(ebp+" (arr.stack-offset+4+n*size-of(T)) ") " reg "/r32"

var/reg: (offset T) <- compute-offset arr: (addr array T), idx/regi: int  # arr can be in reg or mem
  => "69/multiply %" regi " " size-of(T) "/imm32 " reg "/r32"
var/reg: (offset T) <- compute-offset arr: (addr array T), idx: int       # arr can be in reg or mem
  => "69/multiply *(ebp+" idx.stack-offset ") " size-of(T) "/imm32 " reg "/r32"
var/reg: (addr T) <- index arr/rega: (addr array T), o/rego: (offset T)
  => "81 7/subop/compare %" rega " 0/imm32"
     "0f 84/jump-if-= __mu-abort-null-index-base-address/disp32"
     "(__check-mu-array-bounds %" rega " %" rego " 1 \"" function-name "\")"
     "8d/copy-address *(" rega "+" rego "+4) " reg "/r32"

Computing the length of an array is complex.

var/reg: int <- length arr/reg2: (addr array T)
  | if T is byte (TODO)
      => "8b/-> *" reg2 " " reg "/r32"
  | if size-of(T) is 4 or 8 or 16 or 32 or 64 or 128
      => "8b/-> *" reg2 " " reg "/r32"
         "c1/shift 5/subop/logic-right %" reg " " log2(size-of(T)) "/imm8"
  | otherwise
      x86 has no instruction to divide by a literal, so
      we need up to 3 extra registers! eax/edx for division and say ecx
      => if reg is not eax
          "50/push-eax"
         if reg is not ecx
          "51/push-ecx"
         if reg is not edx
          "52/push-edx"
         "8b/-> *" reg2 " eax/r32"
         "31/xor %edx 2/r32/edx"  # sign-extend, but array size can't be negative
         "b9/copy-to-ecx " size-of(T) "/imm32"
         "f7 7/subop/idiv-eax-edx-by %ecx"
         if reg is not eax
           "89/<- %" reg " 0/r32/eax"
         if reg is not edx
          "5a/pop-to-edx"
         if reg is not ecx
          "59/pop-to-ecx"
         if reg is not eax
          "58/pop-to-eax"

# User-defined types

If a record (product) type T was defined to have elements a, b, c, ... of
types T_a, T_b, T_c, ..., then accessing one of those elements f of type T_f:

var/reg: (addr T_f) <- get var2/reg2: (addr T), f
  => "81 7/subop/compare %" reg2 " 0/imm32"
     "0f 84/jump-if-= __mu-abort-null-get-base-address/disp32"
     "8d/copy-address *(" reg2 "+" offset(f) ") " reg "/r32"
var/reg: (addr T_f) <- get var2: T, f
  => "8d/copy-address *(ebp+" var2.stack-offset "+" offset(f) ") " reg "/r32"

When the base is an address we perform a null check.

# Allocating memory

allocate in: (addr handle T)
  => "(allocate Heap " size-of(T) " " in ")"

populate in: (addr handle array T), num  # can be literal or variable on stack or register
  => "(allocate-array2 Heap " size-of(T) " " num " " in ")"

populate-stream in: (addr handle stream T), num  # can be literal or variable on stack or register
  => "(new-stream Heap " size-of(T) " " num " " in ")"

# Some miscellaneous helpers to avoid error-prone size computations

clear x: (addr T)
  => "(zero-out " s " " size-of(T) ")"

read-from-stream s: (addr stream T), out: (addr T)
  => "(read-from-stream " s " " out " " size-of(T) ")"

write-to-stream s: (addr stream T), in: (addr T)
  => "(write-to-stream " s " " in " " size-of(T) ")"

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