# `vrefp` — Vector Reciprocal Estimate Floating Point > **Category:** [VMX (Altivec)](../categories/vmx.md) · **Form:** [VX](../forms/VX.md) · **Opcode:** `0x1000010a` ## Assembler Mnemonics | Mnemonic | XML entry | Flags | Description | | --- | --- | --- | --- | | `vrefp` | `vrefp` | — | Vector Reciprocal Estimate Floating Point | | `vrefp128` | `vrefp128` | — | Vector128 Reciprocal Estimate Floating Point | ## Syntax ```asm vrefp [VD], [VB] vrefp128 [VD], [VB] ``` ## Encoding ### `vrefp` — form `VX` - **Opcode word:** `0x1000010a` - **Primary opcode (bits 0–5):** `4` - **Extended opcode:** `266` - **Synchronising:** no | Bits | Field | Meaning | | --- | --- | --- | | 0–5 | `OPCD` | primary opcode (4) | | 6–10 | `VRT/VD` | destination vector register | | 11–15 | `VRA/VA` | source A vector register | | 16–20 | `VRB/VB` | source B vector register | | 21–31 | `XO` | extended opcode (11 bits) | ### `vrefp128` — form `VX128_3` - **Opcode word:** `0x18000630` - **Primary opcode (bits 0–5):** `6` - **Extended opcode:** `1584` - **Synchronising:** no | Bits | Field | Meaning | | --- | --- | --- | | 0–5 | `OPCD` | primary opcode (6) | | 6–10 | `VD128l` | destination low 5 bits | | 11–15 | `IMM` | 5-bit immediate | | 16–20 | `VB128l` | source B low 5 bits | | 21–27 | `XO` | extended opcode | | 28–29 | `VD128h` | destination high 2 bits | | 30–31 | `VB128h` | source B high 2 bits | ## Operands | Field | Role | Description | | --- | --- | --- | | `VB` | vrefp: read; vrefp128: read | Source B vector register. | | `VD` | vrefp: write; vrefp128: write | Destination vector register. | ## Register Effects ### `vrefp` - **Reads (always):** `VB` - **Reads (conditional):** _none_ - **Writes (always):** `VD` - **Writes (conditional):** _none_ ### `vrefp128` - **Reads (always):** `VB` - **Reads (conditional):** _none_ - **Writes (always):** `VD` - **Writes (conditional):** _none_ ## Status-Register Effects _No condition-register or status-register effects._ ## 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 **`vrefp`** - xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="vrefp"`](../../xenia-canary/tools/ppc-instructions.xml) - xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_altivec.cc:1227`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_altivec.cc#L1227) - xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:117`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L117) - xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:457`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L457) - xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:2153-2161`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L2153-L2161)
xenia-rs interpreter body (frozen snapshot) ```rust PpcOpcode::vrefp | PpcOpcode::vrefp128 => { let vb = if matches!(instr.opcode, PpcOpcode::vrefp128) { instr.vb128() } else { instr.rb() }; let vd = if matches!(instr.opcode, PpcOpcode::vrefp128) { instr.vd128() } else { instr.rd() }; let b = ctx.vr[vb].as_f32x4(); let mut r = [0f32; 4]; for i in 0..4 { r[i] = 1.0 / b[i]; } ctx.vr[vd] = xenia_types::Vec128::from_f32x4_array(r); ctx.pc += 4; } ```
**`vrefp128`** - xenia-canary XML: [`tools/ppc-instructions.xml` — search for `mnem="vrefp128"`](../../xenia-canary/tools/ppc-instructions.xml) - xenia-canary emit: [`src/xenia/cpu/ppc/ppc_emit_altivec.cc:1230`](../../xenia-canary/src/xenia/cpu/ppc/ppc_emit_altivec.cc#L1230) - xenia-rs opcode: [`crates/xenia-cpu/src/opcode.rs:117`](../../xenia-rs/crates/xenia-cpu/src/opcode.rs#L117) - xenia-rs decoder: [`crates/xenia-cpu/src/decoder.rs:664`](../../xenia-rs/crates/xenia-cpu/src/decoder.rs#L664) - xenia-rs interpreter: [`crates/xenia-cpu/src/interpreter.rs:2153-2161`](../../xenia-rs/crates/xenia-cpu/src/interpreter.rs#L2153-L2161)
xenia-rs interpreter body (frozen snapshot) ```rust PpcOpcode::vrefp | PpcOpcode::vrefp128 => { let vb = if matches!(instr.opcode, PpcOpcode::vrefp128) { instr.vb128() } else { instr.rb() }; let vd = if matches!(instr.opcode, PpcOpcode::vrefp128) { instr.vd128() } else { instr.rd() }; let b = ctx.vr[vb].as_f32x4(); let mut r = [0f32; 4]; for i in 0..4 { r[i] = 1.0 / b[i]; } ctx.vr[vd] = xenia_types::Vec128::from_f32x4_array(r); ctx.pc += 4; } ```
## Special Cases & Edge Conditions - **Lane-wise reciprocal *estimate*.** Each 32-bit float lane of `VB` is approximated by `1.0 / VB[i]`. The PowerPC spec permits an **estimate** accurate to about 1/4096 (≈12 bits); xenia-rs produces the *exact* IEEE-754 reciprocal by dividing, trading accuracy for simplicity. Game code that cares about bit-reproducible behaviour should Newton-iterate with [`vnmsubfp`](vnmsubfp.md) regardless of which backend computes the seed. - **Standard Newton iteration.** `x₁ = x₀ * (2 − VB * x₀)`, expressible as `vnmsubfp x₁, x₀, VB, 2.0f` followed by `vmaddfp x₁, x₀, x₁, 0.0f` (or similar). One iteration roughly doubles the valid bit count. - **IEEE-754 binary32 lanes; `VSCR[NJ]` honoured** (denormals flush to zero when `NJ = 1`). - **No VSCR[SAT] update, no FPSCR update, no exception.** Division by zero yields ±∞; division of zero yields ±∞ too (same sign convention). - **Big-endian lane indexing.** - **VMX128 sibling [`vrefp128`](vrefp128.md).** ## Related Instructions - [`vrsqrtefp`](vrsqrtefp.md) — reciprocal *square root* estimate, used with the same Newton scheme. - [`vmaddfp`](vmaddfp.md), [`vnmsubfp`](vnmsubfp.md) — the building blocks of the Newton iteration. - [`vexptefp`](vexptefp.md), [`vlogefp`](vlogefp.md) — other "estimate"-style transcendentals. - [`vaddfp`](vaddfp.md), [`vsubfp`](vsubfp.md) — the float add/sub. ## IBM Reference - [AIX 7.3 — `vrefp` (Vector Reciprocal Estimate Floating Point)](https://www.ibm.com/docs/en/aix/7.3.0?topic=set-vrefp-vector-reciprocal-estimate-floating-point-instruction) - [IBM AltiVec Technology Programmer's Interface Manual, Chapter 5 — Floating-Point Arithmetic](https://www.nxp.com/docs/en/reference-manual/ALTIVECPIM.pdf)