rontolisp:bfloat16-bits

(rontolisp:bfloat16-bits real)

Returns the bfloat16 bit pattern of a real, an integer 0-65535. A bfloat16 is the top sixteen bits of an IEEE 754 single float: one sign bit, the same eight exponent bits an f32 has, and seven mantissa bits. It therefore covers the whole f32 range and trades precision for width, which is what makes it the storage format published machine-learning checkpoints use.

The narrowing rounds to nearest, ties to even. Truncating the low sixteen bits instead would answer the same value for most inputs and bias every sum downward, so the two exact midpoints below round in opposite directions.

rontolisp:bits-bfloat16 takes the pattern back. Widening is exact and total -- every one of the 65536 patterns is a float, infinities and NaNs included -- so the pair is an involution on patterns, and the round trip through a value is the bfloat16-rounded value.