# `subfmex` — Subtract From Minus One Extended

> **Category:** [Integer ALU](../categories/alu.md) · **Form:** [XO](../forms/XO.md) · **Opcode:** `0x7c0001d0`

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## Assembler Mnemonics

| Mnemonic | XML entry | Flags | Description |
| --- | --- | --- | --- |
| `subfme` | `subfmex` | — | Subtract From Minus One Extended |
| `subfmeo` | `subfmex` | OE=1 | Subtract From Minus One Extended |
| `subfme.` | `subfmex` | Rc=1 | Subtract From Minus One Extended |
| `subfmeo.` | `subfmex` | OE=1, Rc=1 | Subtract From Minus One Extended |

## Syntax

```asm
subfme[OE][Rc] [RD], [RA]
```

## Encoding

### `subfmex` — form `XO`

- **Opcode word:** `0x7c0001d0`
- **Primary opcode (bits 0–5):** `31`
- **Extended opcode:** `232`
- **Synchronising:** no

| Bits | Field | Meaning |
| --- | --- | --- |
| 0–5 | `OPCD` | primary opcode (31) |
| 6–10 | `RT` | destination GPR |
| 11–15 | `RA` | source A |
| 16–20 | `RB` | source B |
| 21 | `OE` | overflow-enable flag |
| 22–30 | `XO` | extended opcode (9 bits) |
| 31 | `Rc` | record-form flag |

## Operands

| Field | Role | Description |
| --- | --- | --- |
| `RA` | subfmex: read | Source GPR (`r0`–`r31`). |
| `CA` | subfmex: read; subfmex: write | XER[CA] carry bit. Read by add-with-carry/subtract-with-borrow instructions, written by carrying instructions. |
| `RD` | subfmex: write | Destination GPR. |
| `CR` | subfmex: write (conditional) | Condition-register update. When `Rc=1`, CR field 0 (or CR6 for vector compares, CR1 for FPU) is updated from the result. |
| `OE` | subfmex: write (conditional) | Overflow-enable bit. When 1, the instruction updates `XER[OV]` and stickies `XER[SO]` on signed overflow. |

## Register Effects

### `subfmex`

- **Reads (always):** `RA`, `CA`
- **Reads (conditional):** _none_
- **Writes (always):** `RD`, `CA`
- **Writes (conditional):** `CR`, `OE`

## Status-Register Effects

- `subfmex`: **CR0** ← signed-compare(result, 0) with `SO ← XER[SO]`, when `Rc=1`.; **XER[OV]** ← signed-overflow(result); **XER[SO]** stickies, when `OE=1`.; **XER[CA]** ← carry-out of the add / borrow-in of the subtract (always).

## Operation (pseudocode)

```
; Pseudocode derives directly from the xenia-rs interpreter
; arm (see Implementation References). Operation semantics:
;   - Read source operands from the fields listed under Operands.
;   - Apply the arithmetic / logical / memory action described
;     in the Description field above.
;   - Write results to the destination register(s); update any
;     status bits enumerated under Status-Register Effects.
; Consult the IBM AIX reference link under IBM Reference for
; canonical PPC-style pseudocode where xenia's expression is
; terse.
```

## C Translation Example

```c
/* C translation: the xenia-rs interpreter arm below in           */
/* Implementation References is the authoritative semantic        */
/* snapshot. Translate it line-by-line:                            */
/*   - ctx.gpr[N]  -> r[N]       (or f[]/v[] for FPRs/VRs)        */
/*   - mem.read_u*/write_u* -> mem_read_u*_be / mem_write_u*_be   */
/*   - ctx.update_cr_signed(fld, v) -> update_cr_signed(fld, v)   */
/*   - ctx.xer_ca / xer_ov / xer_so -> xer.CA / xer.OV / xer.SO   */
/* The Register Effects and Status-Register Effects tables above  */
/* enumerate every side effect a faithful translation must emit.  */
```

## Implementation References

**`subfmex`**
- xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="subfmex"`](../../xenia-canary/tools/ppc-instructions.xml)
- xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_alu.cc:486`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_alu.cc#L486)
- xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:83`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L83)
- xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:871`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L871)
- xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:325-341`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L325-L341)
<details><summary>xenia-rs interpreter body (frozen snapshot)</summary>

```rust
        PpcOpcode::subfmex => {
            // PPCBUG-019: also fixes the always-true CA edge — `!ra` on u64
            // is non-zero when ra32==0xFFFFFFFF and ca==0, so CA was stuck at 1.
            let ra32 = ctx.gpr[instr.ra()] as u32;
            let ca = ctx.xer_ca as u32;
            let result32 = (!ra32).wrapping_add(ca).wrapping_sub(1);
            ctx.xer_ca = if (!ra32) != 0 || ca != 0 { 1 } else { 0 };
            ctx.gpr[instr.rd()] = result32 as u64;
            if instr.oe() {
                let true_sum = -(ra32 as i32 as i128) - 2 + (ca as i128);
                overflow::apply(ctx, true_sum != (result32 as i32) as i128);
            }
            if instr.rc_bit() {
                ctx.update_cr_signed(0, result32 as i32 as i64);
            }
            ctx.pc += 4;
        }
```
</details>

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## Special Cases & Edge Conditions

- **`RT ← ~RA + (−1) + XER[CA]` ≡ `~RA − 1 + CA`.** Terminator for a multi-word subtract chain when the high "minuend" word is implicitly all-ones (e.g. when computing `~x` style negation across many words).
- **`RB` field unused.** XO-form but only `RA` is read.
- **Carry-out predicate.** `CA' = (~RA != 0) || (CA != 0)` ([`interpreter.rs:191`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L191)). Only when `RA == ~0` (all ones) AND `CA == 0` does `CA'` become 0 — every other case produces no borrow on this final word.
- **`OE=1`** should set `XER[OV]` on signed overflow; xenia-rs ignores it.
- **64-bit CR update on Xenon, 32-bit in xenia-rs.** [`interpreter.rs:194`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L194).
- **`XER[CA]` must be initialised** (typically by a [`subfcx`](subfcx.md) or [`subfex`](subfex.md) earlier in the chain).
- **Symmetric with [`addmex`](addmex.md)**, the add-side terminator.

## Related Instructions

- [`subfzex`](subfzex.md) — terminate with `~RA + 0 + CA` instead.
- [`subfex`](subfex.md) — middle-of-chain.
- [`subfcx`](subfcx.md) — chain seed.
- [`addmex`](addmex.md) — dual.

## IBM Reference

- [AIX 7.3 — `subfme` (Subtract From Minus One Extended)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-subfme-subtract-from-minus-one-extended-instruction)