# `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) ``` ; No hand-written pseudocode for this instruction yet. ; The authoritative semantics are the Canary emitter snapshot under ; Implementation References; about half of Canary's emitters open ; with the PPC-style definition as a comment (`RD <- (RA) + (RB)`). ; Every side effect is also enumerated in the Register Effects and ; Status-Register Effects tables above. ``` ## C Translation Example ```c /* No hand-written C yet. Translate the Canary emitter snapshot */ /* under Implementation References; its HIR maps directly: */ /* f.LoadGPR(n) / f.StoreGPR(n, v) -> r[n] / r[n] = v */ /* f.LoadFPR / StoreFPR, f.LoadVR / StoreVR -> f[n], v[n] */ /* f.Load(ea, T), f.Store(ea, v) -> raw read / write; emitters */ /* wrap them in f.ByteSwap for the big-endian guest value */ /* f.UpdateCR(n, v) -> CR field n from v's LOW 32 BITS vs 0 */ /* f.LoadCA / f.StoreCA -> xer.CA; f.StoreSAT -> vscr.SAT */ /* i.XO.RA, i.D.DS, ... -> the bit-fields listed under Operands */ /* The Register Effects and Status-Register Effects tables above */ /* enumerate every side effect a faithful translation must emit. */ ``` ## Implementation References **`vrefp`** - Canary XML: [`tools/ppc-instructions.xml` — search for `mnem="vrefp"`](https://github.com/xenia-canary/xenia-canary/blob/f21ebd49e979e44f081f474df78c3fbfee9cb3f2/tools/ppc-instructions.xml) - Canary emitter: [`src/xenia/cpu/ppc/ppc_emit_altivec.cc:1203`](https://github.com/xenia-canary/xenia-canary/blob/f21ebd49e979e44f081f474df78c3fbfee9cb3f2/src/xenia/cpu/ppc/ppc_emit_altivec.cc#L1203) - Sylpheed opcode: [`crates/sylpheed-ppc/src/opcode.rs:421`](../../../crates/sylpheed-ppc/src/opcode.rs#L421) - Sylpheed decoder: [`crates/sylpheed-ppc/src/decoder.rs:572`](../../../crates/sylpheed-ppc/src/decoder.rs#L572)
Canary emitter (frozen snapshot @ f21ebd49e9) ```cpp int InstrEmit_vrefp(PPCHIRBuilder& f, const InstrData& i) { return InstrEmit_vrefp_(f, i.VX.VD, i.VX.VB); } // ── delegates to (src/xenia/cpu/ppc/ppc_emit_altivec.cc:1197) ── int InstrEmit_vrefp_(PPCHIRBuilder& f, uint32_t vd, uint32_t vb) { // (VD) <- 1/(VB) Value* v = f.Recip(f.LoadVR(vb)); f.StoreVR(vd, v); return 0; } ```
**`vrefp128`** - Canary XML: [`tools/ppc-instructions.xml` — search for `mnem="vrefp128"`](https://github.com/xenia-canary/xenia-canary/blob/f21ebd49e979e44f081f474df78c3fbfee9cb3f2/tools/ppc-instructions.xml) - Canary emitter: [`src/xenia/cpu/ppc/ppc_emit_altivec.cc:1206`](https://github.com/xenia-canary/xenia-canary/blob/f21ebd49e979e44f081f474df78c3fbfee9cb3f2/src/xenia/cpu/ppc/ppc_emit_altivec.cc#L1206) - Sylpheed opcode: [`crates/sylpheed-ppc/src/opcode.rs:422`](../../../crates/sylpheed-ppc/src/opcode.rs#L422) - Sylpheed decoder: [`crates/sylpheed-ppc/src/decoder.rs:779`](../../../crates/sylpheed-ppc/src/decoder.rs#L779)
Canary emitter (frozen snapshot @ f21ebd49e9) ```cpp int InstrEmit_vrefp128(PPCHIRBuilder& f, const InstrData& i) { return InstrEmit_vrefp_(f, VX128_3_VD128, VX128_3_VB128); } // ── delegates to (src/xenia/cpu/ppc/ppc_emit_altivec.cc:1197) ── int InstrEmit_vrefp_(PPCHIRBuilder& f, uint32_t vd, uint32_t vb) { // (VD) <- 1/(VB) Value* v = f.Recip(f.LoadVR(vb)); f.StoreVR(vd, v); return 0; } ```
## 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); Canary divides exactly (`vdivps` into `1.0`) — its comment notes that AVX `rcpps` misses that 1/4096 bound and broke gameplay in one title. 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`.** ## 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)