# `fsqrtsx` — Floating Square Root Single

> **Category:** [Floating-Point](../categories/fpu.md) · **Form:** [A](../forms/A.md) · **Opcode:** `0xec00002c`

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## Assembler Mnemonics

| Mnemonic | XML entry | Flags | Description |
| --- | --- | --- | --- |
| `fsqrts` | `fsqrtsx` | — | Floating Square Root Single |
| `fsqrts.` | `fsqrtsx` | Rc=1 | Floating Square Root Single |

## Syntax

```asm
fsqrts[Rc] [FD], [FB]
```

## Encoding

### `fsqrtsx` — form `A`

- **Opcode word:** `0xec00002c`
- **Primary opcode (bits 0–5):** `59`
- **Extended opcode:** `22`
- **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 |
| --- | --- | --- |
| `FB` | fsqrtsx: read | Source B floating-point register. |
| `FD` | fsqrtsx: write | Destination floating-point register. |
| `CR` | fsqrtsx: 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` | fsqrtsx: write | Floating-Point Status and Control Register. |

## Register Effects

### `fsqrtsx`

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

## Status-Register Effects

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

## 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

**`fsqrtsx`**
- xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="fsqrtsx"`](../../xenia-canary/tools/ppc-instructions.xml)
- xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_fpu.cc:168`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_fpu.cc#L168)
- xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:30`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L30)
- xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:389`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L389)
- xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:2801-2814`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L2801-L2814)
<details><summary>xenia-rs interpreter body (frozen snapshot)</summary>

```rust
        PpcOpcode::fsqrtsx => {
            let b = ctx.fpr[instr.rb()];
            if b.is_sign_negative() && b != 0.0 && !b.is_nan() {
                fpscr::set_exception(ctx, fpscr::VXSQRT);
            }
            if fpscr::is_snan(b) {
                fpscr::set_exception(ctx, fpscr::VXSNAN);
            }
            let result = to_single(ctx, b.sqrt());
            ctx.fpr[instr.rd()] = result;
            fpscr::update_after_op(ctx, result, b.is_finite());
            if instr.rc_bit() { update_cr1_from_fpscr(ctx); }
            ctx.pc += 4;
        }
```
</details>

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## Special Cases & Edge Conditions

- **Single precision.** Result is rounded to IEEE-754 binary32 then re-encoded into the destination 64-bit FPR. xenia computes `to_single(b.sqrt())`.
- **Negative inputs are invalid.** `sqrt(x < 0)` (other than `-0`) sets `FPSCR[VXSQRT, VX, FX]` and yields a quiet NaN. `sqrt(-0) = -0` per IEEE-754.
- **`sqrt(+∞) = +∞`**, exact.
- **FPSCR side effects.** Hardware updates `FPRF`, `FR`, `FI`, `FX` plus exception bits `XX` (very common — sqrt is rarely exact in single precision), `VXSQRT`, `VXSNAN`. xenia-rs does not update FPSCR (xenia quirk).
- **`Rc=1` (`fsqrts.`)** copies `FPSCR[FX, FEX, VX, OX]` into CR1.
- **NaN propagation.** Quiet-NaN result for any NaN operand; signalling NaNs are quietened.
- **Performance.** `fsqrts` is a multi-cycle, non-pipelined operation on Xenon. Hot-path code commonly uses `frsqrte` + Newton-Raphson + `fmul`.
- **Encoding.** A-form, primary 59, XO 22; reads `FRB` only.
- **Rounding mode** uses `FPSCR[RN]` (default nearest-even).

## Related Instructions

- [`fsqrtx`](fsqrtx.md) — double-precision square root.
- [`frsqrtex`](frsqrtex.md) — reciprocal-square-root estimate; combined with `fmuls` to compute `1/sqrt(x)` cheaply.
- [`fresx`](fresx.md) — reciprocal estimate; pairs with `fsqrts` to compute `1/sqrt(x)`.
- [`fmulsx`](fmulsx.md), [`fmaddsx`](fmaddsx.md) — used in Newton-Raphson refinement of `frsqrte` outputs.
- [`frspx`](frspx.md) — explicit double→single rounding.

## IBM Reference

- [AIX 7.3 — `fsqrts` (Floating Square Root Single)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-fsqrts-floating-square-root-single-instruction)
- [PowerISA v2.07B, Book I, Chapter 4 — Floating-Point Processor](https://openpowerfoundation.org/specifications/isa/).