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pub(crate) fn f32_to_bf16(value: f32) -> u16 {
// Convert to raw bytes
let x = value.to_bits();
// check for NaN
if x & 0x7FFF_FFFFu32 > 0x7F80_0000u32 {
// Keep high part of current mantissa but also set most significiant mantissa bit
return ((x >> 16) | 0x0040u32) as u16;
}
// round and shift
let round_bit = 0x0000_8000u32;
if (x & round_bit) != 0 && (x & (3 * round_bit - 1)) != 0 {
(x >> 16) as u16 + 1
} else {
(x >> 16) as u16
}
}
pub(crate) fn f64_to_bf16(value: f64) -> u16 {
// Convert to raw bytes, truncating the last 32-bits of mantissa; that precision will always
// be lost on half-precision.
let val = value.to_bits();
let x = (val >> 32) as u32;
// Extract IEEE754 components
let sign = x & 0x8000_0000u32;
let exp = x & 0x7FF0_0000u32;
let man = x & 0x000F_FFFFu32;
// Check for all exponent bits being set, which is Infinity or NaN
if exp == 0x7FF0_0000u32 {
// Set mantissa MSB for NaN (and also keep shifted mantissa bits).
// We also have to check the last 32 bits.
let nan_bit = if man == 0 && (val as u32 == 0) {
0
} else {
0x0040u32
};
return ((sign >> 16) | 0x7F80u32 | nan_bit | (man >> 13)) as u16;
}
// The number is normalized, start assembling half precision version
let half_sign = sign >> 16;
// Unbias the exponent, then bias for bfloat16 precision
let unbiased_exp = ((exp >> 20) as i64) - 1023;
let half_exp = unbiased_exp + 127;
// Check for exponent overflow, return +infinity
if half_exp >= 0xFF {
return (half_sign | 0x7F80u32) as u16;
}
// Check for underflow
if half_exp <= 0 {
// Check mantissa for what we can do
if 7 - half_exp > 21 {
// No rounding possibility, so this is a full underflow, return signed zero
return half_sign as u16;
}
// Don't forget about hidden leading mantissa bit when assembling mantissa
let man = man | 0x0010_0000u32;
let mut half_man = man >> (14 - half_exp);
// Check for rounding
let round_bit = 1 << (13 - half_exp);
if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
half_man += 1;
}
// No exponent for subnormals
return (half_sign | half_man) as u16;
}
// Rebias the exponent
let half_exp = (half_exp as u32) << 7;
let half_man = man >> 13;
// Check for rounding
let round_bit = 0x0000_1000u32;
if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
// Round it
((half_sign | half_exp | half_man) + 1) as u16
} else {
(half_sign | half_exp | half_man) as u16
}
}
pub(crate) fn bf16_to_f32(i: u16) -> f32 {
// If NaN, keep current mantissa but also set most significiant mantissa bit
if i & 0x7FFFu16 > 0x7F80u16 {
f32::from_bits((i as u32 | 0x0040u32) << 16)
} else {
f32::from_bits((i as u32) << 16)
}
}
pub(crate) fn bf16_to_f64(i: u16) -> f64 {
// Check for signed zero
if i & 0x7FFFu16 == 0 {
return f64::from_bits((i as u64) << 48);
}
let half_sign = (i & 0x8000u16) as u64;
let half_exp = (i & 0x7F80u16) as u64;
let half_man = (i & 0x007Fu16) as u64;
// Check for an infinity or NaN when all exponent bits set
if half_exp == 0x7F80u64 {
// Check for signed infinity if mantissa is zero
if half_man == 0 {
return f64::from_bits((half_sign << 48) | 0x7FF0_0000_0000_0000u64);
} else {
// NaN, keep current mantissa but also set most significiant mantissa bit
return f64::from_bits((half_sign << 48) | 0x7FF8_0000_0000_0000u64 | (half_man << 45));
}
}
// Calculate double-precision components with adjusted exponent
let sign = half_sign << 48;
// Unbias exponent
let unbiased_exp = ((half_exp as i64) >> 7) - 127;
// Check for subnormals, which will be normalized by adjusting exponent
if half_exp == 0 {
// Calculate how much to adjust the exponent by
let e = (half_man as u16).leading_zeros() - 9;
// Rebias and adjust exponent
let exp = ((1023 - 127 - e) as u64) << 52;
let man = (half_man << (46 + e)) & 0xF_FFFF_FFFF_FFFFu64;
return f64::from_bits(sign | exp | man);
}
// Rebias exponent for a normalized normal
let exp = ((unbiased_exp + 1023) as u64) << 52;
let man = (half_man & 0x007Fu64) << 45;
f64::from_bits(sign | exp | man)
}
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