xenia-rs/migration/project-root/ppc-manual/vmx/vrsqrtefp.md

vrsqrtefp — Vector Reciprocal Square Root Estimate Floating Point

Category: VMX (Altivec) · Form: VX · Opcode: 0x1000014a

Assembler Mnemonics

Mnemonic	XML entry	Flags	Description
vrsqrtefp	vrsqrtefp	—	Vector Reciprocal Square Root Estimate Floating Point
vrsqrtefp128	vrsqrtefp128	—	Vector128 Reciprocal Square Root Estimate Floating Point

Syntax

vrsqrtefp [VD], [VB]
vrsqrtefp128 [VD], [VB]

Encoding

vrsqrtefp — form VX

• Opcode word: 0x1000014a
• Primary opcode (bits 0–5): 4
• Extended opcode: 330
• 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)

vrsqrtefp128 — form VX128_3

• Opcode word: 0x18000670
• Primary opcode (bits 0–5): 6
• Extended opcode: 1648
• 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	vrsqrtefp: read; vrsqrtefp128: read	Source B vector register.
VD	vrsqrtefp: write; vrsqrtefp128: write	Destination vector register.

Register Effects

vrsqrtefp

• Reads (always): VB
• Reads (conditional): none
• Writes (always): VD
• Writes (conditional): none

vrsqrtefp128

• 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 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

vrsqrtefp

• xenia-canary XML: tools/ppc-instructions.xml — search for mnem="vrsqrtefp"
• xenia-canary emit: src/xenia/cpu/ppc/ppc_emit_altivec.cc:1371
• xenia-rs opcode: crates/xenia-cpu/src/opcode.rs:120
• xenia-rs decoder: crates/xenia-cpu/src/decoder.rs:463
• xenia-rs interpreter: crates/xenia-cpu/src/interpreter.rs:2162-2170

xenia-rs interpreter body (frozen snapshot)

        PpcOpcode::vrsqrtefp | PpcOpcode::vrsqrtefp128 => {
            let vb = if matches!(instr.opcode, PpcOpcode::vrsqrtefp128) { instr.vb128() } else { instr.rb() };
            let vd = if matches!(instr.opcode, PpcOpcode::vrsqrtefp128) { 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].sqrt(); }
            ctx.vr[vd] = xenia_types::Vec128::from_f32x4_array(r);
            ctx.pc += 4;
        }

vrsqrtefp128

• xenia-canary XML: tools/ppc-instructions.xml — search for mnem="vrsqrtefp128"
• xenia-canary emit: src/xenia/cpu/ppc/ppc_emit_altivec.cc:1374
• xenia-rs opcode: crates/xenia-cpu/src/opcode.rs:120
• xenia-rs decoder: crates/xenia-cpu/src/decoder.rs:665
• xenia-rs interpreter: crates/xenia-cpu/src/interpreter.rs:2162-2170

xenia-rs interpreter body (frozen snapshot)

        PpcOpcode::vrsqrtefp | PpcOpcode::vrsqrtefp128 => {
            let vb = if matches!(instr.opcode, PpcOpcode::vrsqrtefp128) { instr.vb128() } else { instr.rb() };
            let vd = if matches!(instr.opcode, PpcOpcode::vrsqrtefp128) { 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].sqrt(); }
            ctx.vr[vd] = xenia_types::Vec128::from_f32x4_array(r);
            ctx.pc += 4;
        }

Special Cases & Edge Conditions

• Lane-wise reciprocal-square-root estimate. Each 32-bit float lane of VB is approximated by 1.0 / sqrt(VB[i]). The PowerPC spec permits a 12-bit estimate; xenia-rs computes the exact IEEE-754 result. Games that depend on Xenon's low-precision estimate may need a helper to truncate bits to match hardware.
• Standard Newton iteration (Quake-style): x₁ = x₀ * (1.5 − 0.5 * VB * x₀²). One pass produces ~24 bits of precision — essentially indistinguishable from a true 1/sqrt.
• Negative input is a trap in math terms but not in ISA terms: the hardware returns a QNaN. sqrt(−x) for x > 0 → QNaN. Zero produces +∞ (and may sticky-set no bits).
• IEEE-754 binary32; VSCR[NJ] honoured.
• No VSCR[SAT], no FPSCR update, no exception.
• Big-endian lane indexing.
• VMX128 sibling vrsqrtefp128.

Related Instructions

• vrefp — plain reciprocal estimate.
• vmaddfp, vnmsubfp — the Newton iteration primitives.
• vexptefp, vlogefp — the other transcendental estimates.

IBM Reference

• AIX 7.3 — vrsqrtefp (Vector Reciprocal Square Root Estimate Floating Point)
• IBM AltiVec Technology Programmer's Interface Manual, Chapter 5 — Floating-Point Arithmetic