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

# `sradx` — Shift Right Algebraic Doubleword

> **Category:** [Integer ALU](../categories/alu.md) · **Form:** [X](../forms/X.md) · **Opcode:** `0x7c000634`

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## Assembler Mnemonics

| Mnemonic | XML entry | Flags | Description |
| --- | --- | --- | --- |
| `srad` | `sradx` | — | Shift Right Algebraic Doubleword |
| `srad.` | `sradx` | Rc=1 | Shift Right Algebraic Doubleword |

## Syntax

```asm
srad[Rc] [RA], [RS], [RB]
```

## Encoding

### `sradx` — form `X`

- **Opcode word:** `0x7c000634`
- **Primary opcode (bits 0–5):** `31`
- **Extended opcode:** `794`
- **Synchronising:** no

| Bits | Field | Meaning |
| --- | --- | --- |
| 0–5 | `OPCD` | primary opcode |
| 6–10 | `RT/FRT/VRT` | destination |
| 11–15 | `RA/FRA/VRA` | source A |
| 16–20 | `RB/FRB/VRB` | source B |
| 21–30 | `XO` | extended opcode (10 bits) |
| 31 | `Rc` | record-form flag |

## Operands

| Field | Role | Description |
| --- | --- | --- |
| `RS` | sradx: read | Source GPR (alias for RD in some stores). |
| `RB` | sradx: read | Source GPR. |
| `RA` | sradx: write | Source GPR (`r0`–`r31`). |
| `CR` | sradx: write (conditional) | Condition-register update. When `Rc=1`, CR field 0 (or CR6 for vector compares, CR1 for FPU) is updated from the result. |
| `CA` | sradx: write | XER[CA] carry bit. Read by add-with-carry/subtract-with-borrow instructions, written by carrying instructions. |

## Register Effects

### `sradx`

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

## Status-Register Effects

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

## Operation (pseudocode)

```
n <- (RB)[57:63]
RA <- ((RS) >>a n) sign-extended        if n < 64
CA <- (RS signed < 0) && any_bit_shifted_out
```

## 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

**`sradx`**
- xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="sradx"`](../../xenia-canary/tools/ppc-instructions.xml)
- xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_alu.cc:1201`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_alu.cc#L1201)
- xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:65`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L65)
- xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:841`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L841)
- xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:692-708`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L692-L708)
<details><summary>xenia-rs interpreter body (frozen snapshot)</summary>

```rust
        PpcOpcode::sradx => {
            let rs = ctx.gpr[instr.rs()] as i64;
            let sh = ctx.gpr[instr.rb()] & 0x7F;
            if sh == 0 {
                ctx.gpr[instr.ra()] = rs as u64;
                ctx.xer_ca = 0;
            } else if sh < 64 {
                let result = rs >> sh;
                ctx.xer_ca = if rs < 0 && (rs as u64) << (64 - sh) != 0 { 1 } else { 0 };
                ctx.gpr[instr.ra()] = result as u64;
            } else {
                ctx.gpr[instr.ra()] = if rs < 0 { u64::MAX } else { 0 };
                ctx.xer_ca = if rs < 0 { 1 } else { 0 };
            }
            if instr.rc_bit() { ctx.update_cr_signed(0, ctx.gpr[instr.ra()] as i64); }
            ctx.pc += 4;
        }
```
</details>

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## Special Cases & Edge Conditions

- **64-bit arithmetic (sign-propagating) right shift.** `RA ← (i64)RS >> (RB & 0x7F)` with bits shifted in matching the sign bit of `RS`. Counts ≥ 64 saturate: `RA` becomes all-ones if `RS < 0`, else zero.
- **`XER[CA]` is the "lost-ones" indicator.** `CA = 1` iff `RS` is negative AND any of the bits shifted out were `1`. This makes `srad` / `sradi` the standard idiom for "divide negative integer by power of 2 with round-toward-zero" — followed by `addze` to compensate when `CA = 1`.
- **Three branches in xenia.** `sh == 0` (no shift, `CA=0`), `sh < 64` (normal shift, `CA` per spec), and `sh ≥ 64` (saturate to `0` or `−1`, `CA` reflects sign). The `(rs as u64) << (64 - sh) != 0` check at [`interpreter.rs:486`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L486) extracts whether any non-zero bit was shifted out.
- **Shift count is 7 bits.** Same as [`sldx`](sldx.md): `RB[57:63]`.
- **`Rc=1` CR0 is correctly 64-bit.** [`interpreter.rs:489`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L489).
- **No `OE` bit.**
- **Used by signed-divide-by-power-of-2 idiom:** `srad rA, rS, n; addze rA, rA` produces `rS / 2^n` with truncation toward zero rather than toward `-∞`.

## Related Instructions

- [`sradix`](sradix.md) — immediate-shift form (`SH` 6-bit immediate).
- [`srawx`](srawx.md), [`srawix`](srawix.md) — 32-bit arithmetic right shifts.
- [`srdx`](srdx.md) — 64-bit *logical* right shift (no `XER[CA]`).
- [`addzex`](addzex.md) — companion for the divide-rounding idiom.
- [`sldx`](sldx.md) — left shift.

## IBM Reference

- [AIX 7.3 — `srad` (Shift Right Algebraic Doubleword)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-srad-shift-right-algebraic-double-word-instruction)