# `addcx` — Add Carrying

> **Category:** [Integer ALU](../categories/alu.md) · **Form:** [XO](../forms/XO.md) · **Opcode:** `0x7c000014`

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## Assembler Mnemonics

| Mnemonic | XML entry | Flags | Description |
| --- | --- | --- | --- |
| `addc` | `addcx` | — | Add Carrying |
| `addco` | `addcx` | OE=1 | Add Carrying |
| `addc.` | `addcx` | Rc=1 | Add Carrying |
| `addco.` | `addcx` | OE=1, Rc=1 | Add Carrying |

## Syntax

```asm
addc[OE][Rc] [RD], [RA], [RB]
```

## Encoding

### `addcx` — form `XO`

- **Opcode word:** `0x7c000014`
- **Primary opcode (bits 0–5):** `31`
- **Extended opcode:** `10`
- **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` | addcx: read | Source GPR (`r0`–`r31`). |
| `RB` | addcx: read | Source GPR. |
| `RD` | addcx: write | Destination GPR. |
| `CA` | addcx: write | XER[CA] carry bit. Read by add-with-carry/subtract-with-borrow instructions, written by carrying instructions. |
| `OE` | addcx: write (conditional) | Overflow-enable bit. When 1, the instruction updates `XER[OV]` and stickies `XER[SO]` on signed overflow. |
| `CR` | addcx: write (conditional) | Condition-register update. When `Rc=1`, CR field 0 (or CR6 for vector compares, CR1 for FPU) is updated from the result. |

## Register Effects

### `addcx`

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

## Status-Register Effects

- `addcx`: **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)

```
RT <- (RA) + (RB)
CA <- carry_out_of_32_or_64_bit_add((RA), (RB))
```

## 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

**`addcx`**
- xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="addcx"`](../../xenia-canary/tools/ppc-instructions.xml)
- xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_alu.cc:64`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_alu.cc#L64)
- xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:8`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L8)
- xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:861`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L861)
- xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:190-205`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L190-L205)
<details><summary>xenia-rs interpreter body (frozen snapshot)</summary>

```rust
        PpcOpcode::addcx => {
            // PPCBUG-013+020: 32-bit truncation; CA from u32 unsigned compare.
            let ra32 = ctx.gpr[instr.ra()] as u32;
            let rb32 = ctx.gpr[instr.rb()] as u32;
            let result32 = ra32.wrapping_add(rb32);
            ctx.xer_ca = if result32 < ra32 { 1 } else { 0 };
            ctx.gpr[instr.rd()] = result32 as u64;
            if instr.oe() {
                let true_sum = (ra32 as i32 as i128) + (rb32 as i32 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

- **Carry-out is mandatory.** `XER[CA]` is updated unconditionally — `addcx` exists *to* produce the carry. It seeds a multi-word add chain that continues with [`addex`](addex.md) for middle words and [`addzex`](addzex.md)/[`addmex`](addmex.md) for the final word.
- **Carry detection by overflow comparison.** Xenia computes `CA = (result < RA)` — the standard unsigned-add overflow test. Equivalent to `CA = (RA + RB) >> 64` mathematically. This is correct for the 64-bit operand width that the Xenon implements; the spec also allows a 32-bit width selected by the implementation but the 970/Xenon use 64-bit add throughout.
- **No trap on signed overflow.** `addco`/`addco.` only set `XER[OV]` and sticky `XER[SO]`; they do not raise an exception. Xenia-rs leaves the `OE` branch as a `// TODO` (see [`addx`](addx.md) for the same gap).
- **64-bit CR update on Xenon, 32-bit in xenia-rs.** The `Rc=1` CR0 compare reads `result as i32 as i64` in [`interpreter.rs:97`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L97); spec demands the full 64-bit signed compare. Flag this as a xenia-rs quirk if you need bit-exact behaviour.
- **`XER[SO]` is sticky** — only `mcrxr` clears it. The `Rc=1` form folds it into `CR0[SO]`.
- **Operand aliasing is legal**, just like [`addx`](addx.md). `addc r3, r3, r3` simply doubles `r3` and records whether the result wrapped.

## Related Instructions

- [`addx`](addx.md) — same operation, but does **not** update `XER[CA]`.
- [`addex`](addex.md) — `RA + RB + XER[CA]`; chains a multi-word add after `addcx`.
- [`addmex`](addmex.md), [`addzex`](addzex.md) — terminate a carry chain by adding `−1` or `0` to `XER[CA]`.
- [`addic`](addic.md), [`addicx`](addicx.md) — D-form immediate variants that also write `XER[CA]`.
- [`subfcx`](subfcx.md) — the dual: produces a borrow-out in `XER[CA]`.

## IBM Reference

- [AIX 7.3 — `addc` (Add Carrying)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-addc-add-carrying-instruction)
- PowerISA v2.07B, Book I, §3.3.8 — Fixed-Point Add with Carry; defines `XER[CA]` semantics independent of operand width.