Floating-Point Accuracy - 2024.1 English - UG1603

Floating-Point Accuracy

Depending on the chosen accuracy for floating-point operation (low | fast | safe) the precision in terms of Unit of Last Precision (ULP) (last correct bit) is different. The precision dictates the number of operations to be executed by the processor. The floating-point addition relies on the floating-point adder that exists in the hardware right after the bfloat16 vector multiplier.

Based on the precision of the floating-point operation, the table below specifies the ULP and the corresponding code that is executed.

VMUL.f bmh2, x4, x6, r1
VMAC.f bml3, bmh2, x7, x3, r1
VMAC.f bmh3, bml3, x7, x6, r1

VMUL.f bmh3, x7, x5, r1
VMAC.f bml4, bmh3, x3, x2, r1
VMAC.f bmh4, bml4, x8, x4, r1
VMAC.f bml5, bmh4, x3, x8, r1
VMAC.f bmh5, bml5, x7, x2, r1
VMAC.f bml6, bmh5, x7, x8, r1

VMUL.f bmh3, x4, x8, r1
VMAC.f bml4, bmh3, x4, x2, r1
VMAC.f bmh4, bml4, x3, x8, r1
VMAC.f bml5, bmh4, x5, x8, r1
VMAC.f bmh5, bml5, x3, x2, r1
VMAC.f bml8, bmh5, x7, x4, r1
VMAC.f bml6, bml8, x3, x7, r1
VMAC.f bml7, bml6, x5, x2, r1
VMAC.f bmh6, bml7, x5, x7, r1

The higher the precision, the greater the number of operations to be executed to achieve it, which can reduce the compute performance.