xenia-rs/migration/project-root/ppc-manual/alu/mulhdx.md

# `mulhdx` — Multiply High Doubleword

> **Category:** [Integer ALU](../categories/alu.md) · **Form:** [XO](../forms/XO.md) · **Opcode:** `0x7c000092`

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## Assembler Mnemonics

| Mnemonic | XML entry | Flags | Description |
| --- | --- | --- | --- |
| `mulhd` | `mulhdx` | — | Multiply High Doubleword |
| `mulhd.` | `mulhdx` | Rc=1 | Multiply High Doubleword |

## Syntax

```asm
mulhd[Rc] [RD], [RA], [RB]
```

## Encoding

### `mulhdx` — form `XO`

- **Opcode word:** `0x7c000092`
- **Primary opcode (bits 0–5):** `31`
- **Extended opcode:** `73`
- **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` | mulhdx: read | Source GPR (`r0`–`r31`). |
| `RB` | mulhdx: read | Source GPR. |
| `RD` | mulhdx: write | Destination GPR. |
| `CR` | mulhdx: 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

### `mulhdx`

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

## Status-Register Effects

- `mulhdx`: **CR0** ← signed-compare(result, 0) with `SO ← XER[SO]`, when `Rc=1`.

## Operation (pseudocode)

```
RT <- ((RA) * (RB))[0:63]                 ; high 64 of signed 64×64
```

## 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

**`mulhdx`**
- xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="mulhdx"`](../../xenia-canary/tools/ppc-instructions.xml)
- xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_alu.cc:297`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_alu.cc#L297)
- xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:57`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L57)
- xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:864`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L864)
- xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:445-453`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L445-L453)
<details><summary>xenia-rs interpreter body (frozen snapshot)</summary>

```rust
        PpcOpcode::mulhdx => {
            let ra = ctx.gpr[instr.ra()] as i64 as i128;
            let rb = ctx.gpr[instr.rb()] as i64 as i128;
            ctx.gpr[instr.rd()] = (ra.wrapping_mul(rb) >> 64) as u64;
            if instr.rc_bit() {
                ctx.update_cr_signed(0, ctx.gpr[instr.rd()] as i64);
            }
            ctx.pc += 4;
        }
```
</details>

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## Special Cases & Edge Conditions

- **Returns the high 64 bits of a signed 64×64 product.** Pair with [`mulldx`](mulldx.md) (which returns the low 64 bits) to obtain the full 128-bit product. Both must be issued separately; PowerPC has no fused multiply-double-wide instruction.
- **No `OE` bit.** This XO-form instruction has no overflow-enable variant — there is no "high half overflow" because the high half is always defined.
- **Xenia widens to `i128` natively.** [`interpreter.rs:275`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L275) does the multiply in 128 bits then extracts the high 64. The `i64 as i128` casts ensure signed extension on both sides.
- **`Rc=1` CR0 update is correctly 64-bit.** [`interpreter.rs:278`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L278) uses `as i64` directly. CR0 reflects the sign of the high half: `LT` if the product is negative, `GT` if positive and large enough to overflow into the high half, `EQ` if the product fits in 64 bits *signed* (so the high half is the sign-extension of the low half — but xenia's check uses raw signed-zero compare, which equates only when the high half is exactly zero, i.e. the product is in `[0, 2^63)`).
- **Use [`mulhdux`](mulhdux.md) for the unsigned high half.** The two instructions differ in whether the operands are sign- or zero-extended before the multiply.
- **Slow.** 64-bit multiply is multi-cycle on Xenon; combining `mulhd` with `mulld` for a full 128-bit product roughly doubles the cost.

## Related Instructions

- [`mulldx`](mulldx.md) — low 64 bits of the same signed product.
- [`mulhdux`](mulhdux.md) — high 64 bits, unsigned interpretation.
- [`mullwx`](mullwx.md), [`mulhwx`](mulhwx.md), [`mulhwux`](mulhwux.md) — 32-bit family.
- [`divdx`](divdx.md), [`divdux`](divdux.md) — 64-bit division.

## IBM Reference

- [AIX 7.3 — `mulhd` (Multiply High Doubleword)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-mulhd-multiply-high-double-word-instruction)