hex.sub.init

This is where the sub “truth” tables are. must be called once if you want to use hex.sub (hex.init calls it).
Its 9-bits are expected to be {carry&lt;<8 | src&lt;<4 | dst} at the jump to it (for the src,dst hexes, and the carry bit, of the sub operation).
Its 9-bits are expected to be {new_carry&lt;<8} after the jump to it.

Signature

def init @ switch__without_carry, switch__with_carry, flip_carry, clean_table_entry, end < ..tables.res > dst { ... }

Defined in hex/math.fj — lines 260–289 (view on GitHub).

Complexity

  • Time: 8 (when jumping to dst, until finished)

  • Space: 1570

See the complexity glossary for what @, w, dw, dbit, n mean.

Requires init

The following must be initialised before this macro is invoked:

  • hex.tables.init_shared (or hex.init)

Output labels

This macro exposes labels into the caller’s scope via >:

  • dst — This variable is an 9-bit variable (in a single op, [dbit,dbit+9)).

Source

Click to view the macro body

def init @ switch__without_carry, switch__with_carry, flip_carry, clean_table_entry, end < ..tables.res > dst {
    ;end
  dst: ;.switch__without_carry

    pad 512
    // The next lines are the subtraction flipping-tables.
    // The [carry<<8 | src<<4 | dst] entry sets hex.tables.res (assumed to be 0) to (dst - src - carry) ^ dst,
    //   so that xoring it with dst will update it to the sub-result.
    //   also, it updates the carry (.dst+dbit+8) to the next carry. (subtraction's carry is also known as the borrow).
    // Upon entering here, .dst was xored with the correct table-entry, and was jumped into.
  switch__without_carry:
    // Space Complexity / total table ops: 528.
    rep(256, d) stl.wflip_macro ..tables.res+w, \
        ((((d&0xf)-(d>>4)  )&0xf)^(d&0xf))*dw, \
        (((d&0xf)-(d>>4)   < 0) ? (flip_carry+d*dw) : (clean_table_entry+d*dw))
  switch__with_carry:
    // Space Complexity / total table ops: 528.
    rep(256, d) stl.wflip_macro ..tables.res+w, \
        ((((d&0xf)-(d>>4)-1)&0xf)^(d&0xf))*dw, \
        (((d&0xf)-(d>>4)-1 < 0) ? (clean_table_entry+d*dw) : (flip_carry+d*dw))

  flip_carry:
    // if got here - flip the carry; then clean the table-entry.
    // in about half of the times, we'll get here.
    rep(256, i) stl.fj .dst+dbit+8, clean_table_entry+i*dw
  clean_table_entry:
    // xors back the table-entry from .dst
    ..tables.clean_table_entry__table .dst
  end:
}

Depends on

Used by

Example uses

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