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Mojo function

decode_e2m1_to_bf16

def decode_e2m1_to_bf16[width: SIMDLength, //](nibble: SIMD[DType.uint16, width]) -> SIMD[DType.bfloat16, width]

Decodes E2M1 nibbles to bfloat16 with branch-free bit arithmetic.

Maps each 4-bit E2M1 value (s e1 e0 m0: bit3 sign, bits2:1 exponent, bit0 mantissa) directly to a bfloat16 bit pattern using shifts / masks / select, with no data-dependent table gather. This is the vectorizable equivalent of indexing E2M1_TO_FLOAT32 and is bit-identical to it: all 16 E2M1 values ({+-0, +-0.5, +-1, +-1.5, +-2, +-3, +-4, +-6}) are exactly representable in bfloat16, so the constructed bit pattern equals the table entry exactly.

Construction (bf16 layout s | 8-bit exp (bias 127) | 7-bit mantissa): let E = bits2:1 and m = bit0.

Normal (E >= 1): value 2^(E-1) * (1 + m/2), so exponent field E + 126 and mantissa MSB m (mantissa field m << 6).
Subnormal-class (E == 0): value 0.5 * m, i.e. bf16 0x3F00 (+0.5) when m == 1, else 0x0000 (+0.0). Selected branch-free.
Sign bit (s) is OR'd into bit 15, so -0 (nibble 8) maps to bf16 0x8000 exactly as the table's -0.0 entry.

Parameters:

width (SIMDLength): SIMD width (lane count) of the nibble vector.

Args:

nibble (SIMD[DType.uint16, width]): One E2M1 nibble per lane in the low 4 bits (0..15).

Returns:

SIMD[DType.bfloat16, width]: The decoded values as SIMD[DType.bfloat16, width], bit-identical to casting E2M1_TO_FLOAT32[nibble] to bfloat16.