xenia-rs/migration/project-root/ppc-manual/fpu/fmaddx.md

fmaddx — Floating Multiply-Add

Category: Floating-Point · Form: A · Opcode: 0xfc00003a

Assembler Mnemonics

Mnemonic	XML entry	Flags	Description
fmadd	fmaddx	—	Floating Multiply-Add
fmadd.	fmaddx	Rc=1	Floating Multiply-Add

Syntax

fmadd[Rc] [FD], [FA], [FC], [FB]

Encoding

fmaddx — form A

• Opcode word: 0xfc00003a
• Primary opcode (bits 0–5): 63
• Extended opcode: 29
• 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
FA	fmaddx: read	Source A floating-point register (fr0–fr31).
FC	fmaddx: read	Source C floating-point register (for madd-style ops).
FB	fmaddx: read	Source B floating-point register.
FD	fmaddx: write	Destination floating-point register.
CR	fmaddx: 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	fmaddx: write	Floating-Point Status and Control Register.

Register Effects

fmaddx

• Reads (always): FA, FC, FB
• Reads (conditional): none
• Writes (always): FD, FPSCR
• Writes (conditional): CR

Status-Register Effects

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

Operation (pseudocode)

FRT <- (FRA × FRC) + FRB

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

fmaddx

• xenia-canary XML: tools/ppc-instructions.xml — search for mnem="fmaddx"
• xenia-canary emit: src/xenia/cpu/ppc/ppc_emit_fpu.cc:186
• xenia-rs opcode: crates/xenia-cpu/src/opcode.rs:28
• xenia-rs decoder: crates/xenia-cpu/src/decoder.rs:928
• xenia-rs interpreter: crates/xenia-cpu/src/interpreter.rs:2640-2652

xenia-rs interpreter body (frozen snapshot)

        PpcOpcode::fmaddx => {
            // PPCBUG-202: VXISI from input properties (not from `a*c` which has wrong sign on overflow).
            let a = ctx.fpr[instr.ra()];
            let c = ctx.fpr[instr.rc()];
            let b = ctx.fpr[instr.rb()];
            fpscr::check_invalid_mul(ctx, a, c);
            fpscr::check_invalid_fma_add(ctx, a, c, b, false);
            let result = a.mul_add(c, b);
            ctx.fpr[instr.rd()] = result;
            fpscr::update_after_op(ctx, result, a.is_finite() && b.is_finite() && c.is_finite());
            if instr.rc_bit() { update_cr1_from_fpscr(ctx); }
            ctx.pc += 4;
        }

Special Cases & Edge Conditions

• Single rounding step. fmadd computes (FRA × FRC) + FRB with one IEEE-754 rounding at the end — strictly more accurate than separate multiply + add. xenia-rs uses Rust's f64::mul_add, which guarantees a true FMA on hosts with hardware FMA (x86_64 with FMA3, ARM with NEON-FMA); on hosts without it, Rust's stdlib falls back to a software FMA so the semantic match is preserved.
• Operand layout. A-form: FRT, FRA, FRC, FRB. Note the assembler order — FRC (multiplier) comes before FRB (addend). Encoding bit fields are FRA (11–15), FRB (16–20), FRC (21–25).
• Invalid operations. 0×∞ + finite → VXIMZ; ∞×x + ∓∞ (after multiplication produces ±∞ that opposes addend sign) → VXISI. Quiet NaN result with FPSCR[VX, FX] set.
• FPSCR side effects. Hardware updates FPRF, FR, FI, FX, OX, UX, XX, VXIMZ, VXISI, VXSNAN. xenia-rs does not update FPSCR (xenia quirk).
• Rc=1 (fmadd.) copies FPSCR[FX, FEX, VX, OX] into CR1.
• NaN propagation. Quiet-NaN result for any NaN operand; signalling NaNs are quietened.
• Use case. Dot products, polynomial evaluation (Horner's method), matrix multiplies, Newton-Raphson divide/sqrt refinement. Hot-path PPC code is dense with fmadd.
• Denormal flush. Xenon boots with FPSCR[NI]=1; xenia uses host IEEE behavior.

Related Instructions

• fmaddsx — single-precision sibling.
• fmsubx, fnmaddx, fnmsubx — the other three fused multiply-add variants:
  • fmsub = (A×C) − B
  • fnmadd = −((A×C) + B)
  • fnmsub = −((A×C) − B)
• fmulx, faddx — non-fused decomposition (two rounding steps; less precise).
• fresx, frsqrtex — reciprocal helpers refined by fmadd/fnmsub.

IBM Reference

• AIX 7.3 — fmadd (Floating Multiply-Add)
• PowerISA v2.07B, Book I, Chapter 4 — Floating-Point Processor (single-rounding fused multiply-add definition).