TCMMRLFP16PS

TCMMRLFP16PS multiplies two tiles of complex numbers as matrices and adds the real parts of the result to a tile of singles: C += Re(A × B). Each dword of A and B is one complex number, its real part in the low FP16 half and its imaginary part in the high half, the layout VFMULCPH uses in vector registers. Element C[m][n] gains the sum over k of Ar × Br - Ai × Bi, taking A[m][k] and B[k][n]. TCMMIMFP16PS adds the imaginary parts, Ai × Br + Ar × Bi, so a complex matrix product takes the two instructions and two accumulator tiles. Both came with AMX-COMPLEX, which Intel’s extensions reference lists for Granite Rapids D and Diamond Rapids.

No interleaving in B#

The real AMX multiplies, such as TDPFP16PS, read each dword of B as two values from consecutive rows, so B must be repacked first. Here a dword of B is a single complex number, and B is an ordinary row-major matrix of K rows of N complex numbers, as is A. With full tiles of 16 rows of 64 bytes, one instruction makes 16 × 16 sums of 16 complex products each. The shapes are checked as for the other AMX multiplies: A’s dwords per row must equal B’s rows, C must have A’s rows and B’s row width, and #UD follows if they do not fit.

Two sums, then one subtraction#

The SDM’s Operation keeps two single-precision sums for each element of C: one of the products of the real parts and one of the products of the imaginary parts, the latter with A’s imaginary part negated. Each product of two FP16 values fits a single exactly, so each step of a sum rounds once, to nearest even. The two sums are added at the end of the row, and the total is added to C. MXCSR is neither read nor written, no exception is raised, FP16 denormals count as the numbers they are, and a denormal single result becomes zero.

In our builds#

With -mamx-complex, GCC 14 and Clang 23 at -O2 compile _tile_cmmrlfp16ps(3, 4, 5) to tcmmrlfp16ps tmm3, tmm4, tmm5, the bytes C4 E2 50 6C DC, VEX opcode 6Ch with no prefix bits. Clang 23 also has __tile_cmmrlfp16ps for its __tile1024i type. Zen 5 has no AMX, and this site’s recorded cases include none of TCMMRLFP16PS.

Forms

Operation

What the forms do, in pseudocode that our tests run against results recorded on real processors. How to read.

on = xcr0 if cr4 >> 18 & 1 else 0    # XCR0, where CR4.OSXSAVE is set
if on >> 17 & 3 != 3:                # TILECFG and TILEDATA
    fault(UD)
if palette != 1:                     # 0: no tiles configured; ACE's
    fault(UD)                        # palette 2 multiplies no tiles
t = tmm1.number                      # three different tiles
if t == tmm2.number or t == tmm3.number:
    fault(UD)
if tmm2.number == tmm3.number:
    fault(UD)
if 0 in (tmm1.rows, tmm2.rows, tmm3.rows):
    fault(UD)                        # one TILECFG leaves out
if tmm1.colsb % 4 or tmm2.colsb % 4:
    fault(UD)                        # rows of whole dwords
if tmm2.rows != tmm1.rows:           # A: M rows, as C
    fault(UD)
if tmm2.colsb // 4 != tmm3.rows:     # A: K dwords, B: K rows
    fault(UD)
if tmm3.colsb != tmm1.colsb:         # B: N dwords, as C
    fault(UD)
# K and N within the TMUL unit's 16 and 64 bytes (CPUID leaf
# 1EH): true of every tile of palette 1
if xfd >> 18 & 1:                    # the OS keeps the tiles from
    fault(NM)                        # this thread
for m in range(tmm1.rows):
    x = tmm2.row[m]                  # row m of A
    for n in range(tmm1.colsb // 4):
        e = o = cvt_f32_ne(0)        # two sums, from +0
        for k in range(tmm2.colsb // 4):
            y = tmm3.row[k]          # row k of B
            # re * re, and -im * im
            a = x.f16[2 * k]
            b = y.f16[2 * n]
            e = fmadd_ne(a, b, e)
            a = neg(x.f16[2 * k + 1])
            b = y.f16[2 * n + 1]
            o = fmadd_ne(a, b, o)
        c = tmm1.row[m].f32[n]
        r = add_ne(e, o)
        tmm1.row[m].f32[n] = add_ne(c, r)
start_row = 0
# tmm1 is zeroed past its rows and colsb

Operands

Flags

None: XED records no flag that the forms test or change.

Exceptions

The exception class is XED's name for the set of exception conditions that a form follows. How to read.

All forms

AMX-E4

Attributes

What else XED records about the forms. How to read.

All forms

may abort a TSX transaction

Intrinsics

The C intrinsics of Clang 23.1.2 that compile to TCMMRLFP16PS, each with the form it compiles to and the Clang options it needs. The forms come from compiling every intrinsic and decoding the result with Intel XED; all intrinsics A–Z explains the method.

CPUID and processors

Each form belongs to an XED ISA set. A form can be used when the processor reports every CPUID bit of one of its ISA set's alternatives.

More AMX-COMPLEX instructions

• TCMMIMFP16PS