xenia-rs/migration/project-root/ppc-manual/fpu/fmulx.md

# `fmulx` — Floating Multiply

> **Category:** [Floating-Point](../categories/fpu.md) · **Form:** [A](../forms/A.md) · **Opcode:** `0xfc000032`

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## Assembler Mnemonics

| Mnemonic | XML entry | Flags | Description |
| --- | --- | --- | --- |
| `fmul` | `fmulx` | — | Floating Multiply |
| `fmul.` | `fmulx` | Rc=1 | Floating Multiply |

## Syntax

```asm
fmul[Rc] [FD], [FA], [FC]
```

## Encoding

### `fmulx` — form `A`

- **Opcode word:** `0xfc000032`
- **Primary opcode (bits 0–5):** `63`
- **Extended opcode:** `25`
- **Synchronising:** no

| Bits | Field | Meaning |
| --- | --- | --- |
| 0–5 | `OPCD` | primary opcode (59 or 63) |
| 6–10 | `FRT` | destination FPR |
| 11–15 | `FRA` | source A FPR |
| 16–20 | `FRB` | source B FPR |
| 21–25 | `FRC` | source C FPR (multiplier for madd-style ops) |
| 26–30 | `XO` | extended opcode (5 bits) |
| 31 | `Rc` | record-form flag (updates CR1) |

## Operands

| Field | Role | Description |
| --- | --- | --- |
| `FA` | fmulx: read | Source A floating-point register (`fr0`–`fr31`). |
| `FC` | fmulx: read | Source C floating-point register (for madd-style ops). |
| `FD` | fmulx: write | Destination floating-point register. |
| `CR` | fmulx: write (conditional) | Condition-register update. When `Rc=1`, CR field 0 (or CR6 for vector compares, CR1 for FPU) is updated from the result. |
| `FPSCR` | fmulx: write | Floating-Point Status and Control Register. |

## Register Effects

### `fmulx`

- **Reads (always):** `FA`, `FC`
- **Reads (conditional):** _none_
- **Writes (always):** `FD`, `FPSCR`
- **Writes (conditional):** `CR`

## Status-Register Effects

- `fmulx`: **CR1** ← FPSCR[FX, FEX, VX, OX] when `Rc=1`.; **FPSCR** updated per IEEE-754 flags (FX, FEX, FPRF, FR, FI, exceptions).

## Operation (pseudocode)

```
FRT <- FRA × FRC
```

## 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

**`fmulx`**
- xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="fmulx"`](../../xenia-canary/tools/ppc-instructions.xml)
- xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_fpu.cc:89`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_fpu.cc#L89)
- xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:28`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L28)
- xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:925`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L925)
- xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:2595-2605`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L2595-L2605)
<details><summary>xenia-rs interpreter body (frozen snapshot)</summary>

```rust
        PpcOpcode::fmulx => {
            // A-form: frD = frA * frC (frC is at rc() field, bits 21-25)
            let a = ctx.fpr[instr.ra()];
            let c = ctx.fpr[instr.rc()];
            fpscr::check_invalid_mul(ctx, a, c);
            let result = a * c;
            ctx.fpr[instr.rd()] = result;
            fpscr::update_after_op(ctx, result, a.is_finite() && c.is_finite());
            if instr.rc_bit() { update_cr1_from_fpscr(ctx); }
            ctx.pc += 4;
        }
```
</details>

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## Special Cases & Edge Conditions

- **A-form quirk: multiplier is `FRC`, not `FRB`.** `fmul` reads operands from the `FRA` (bits 11–15) and `FRC` (bits 21–25) fields, bridging the multiply and fused-multiply-add families. xenia decodes this as `instr.rc()` (the FRC field, distinct from `rc_bit()` for the record bit).
- **Double precision.** Operates on IEEE-754 binary64; [`fmulsx`](fmulsx.md) rounds to binary32.
- **`0 × ±∞` is invalid.** Sets `FPSCR[VXIMZ, VX, FX]` and yields a quiet NaN.
- **FPSCR side effects.** Hardware updates `FPRF`, `FR`, `FI`, `FX` plus exception bits `OX` (overflow), `UX` (underflow), `XX` (inexact), `VXIMZ` (0×∞), `VXSNAN` (signalling NaN). xenia-rs does **not** update FPSCR in the interpreter snapshot — xenia quirk.
- **`Rc=1` (`fmul.`)** copies `FPSCR[FX, FEX, VX, OX]` into CR1.
- **NaN propagation.** Any NaN operand yields a quiet NaN; signalling NaNs are quietened.
- **Sign of result.** Standard IEEE: `sign(a) XOR sign(c)`. `+0 × −0 = −0` and `−x × +∞ = −∞`.
- **Denormal flush.** Xenon boots with `FPSCR[NI]=1` (flush-to-zero); xenia inherits host IEEE behavior, so multiplications that produce subnormal results may differ subtly from hardware.
- **Rounding mode** uses `FPSCR[RN]` (default nearest-even).

## Related Instructions

- [`fmulsx`](fmulsx.md) — single-precision multiply.
- [`fmaddx`](fmaddx.md), [`fmsubx`](fmsubx.md), [`fnmaddx`](fnmaddx.md), [`fnmsubx`](fnmsubx.md) — fused multiply-add family; share the same `FRA × FRC` core but add/subtract `FRB` with a single rounding step. Prefer fused forms for dot products and polynomial evaluation.
- [`faddx`](faddx.md), [`fsubx`](fsubx.md), [`fdivx`](fdivx.md) — sibling double-precision arithmetic.
- [`fresx`](fresx.md), [`frsqrtex`](frsqrtex.md) — reciprocal helpers commonly paired with `fmul` for reciprocal divides.
- [`mffsx`](mffsx.md), [`mtfsfx`](mtfsfx.md) — FPSCR control.

## IBM Reference

- [AIX 7.3 — `fmul` (Floating Multiply)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-fm-fmul-floating-multiply-instruction)
- [PowerISA v2.07B, Book I, Chapter 4 — Floating-Point Processor](https://openpowerfoundation.org/specifications/isa/).