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Fix f64 to f16 subnormal boundary rounding #16

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Fix f64 to f16 subnormal boundary rounding #16

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41 changes: 17 additions & 24 deletions src/binary16/arch.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -622,33 +622,25 @@ pub(crate) const fn f32_to_f16_fallback(value: f32) -> u16 {

#[inline]
pub(crate) const fn f64_to_f16_fallback(value: f64) -> u16 {
// Convert to raw bytes, truncating the last 32-bits of mantissa; that precision
// will always be lost on half-precision.
// TODO: Replace mem::transmute with to_bits() once to_bits is const-stabilized
let val: u64 = unsafe { mem::transmute::<f64, u64>(value) };
let x = (val >> 32) as u32;

// Extract IEEE754 components
let sign = x & 0x8000_0000u32;
let exp = x & 0x7FF0_0000u32;
let man = x & 0x000F_FFFFu32;
// Extract IEEE754 components from full 64-bit representation
let sign = val & 0x8000_0000_0000_0000u64;
let exp = val & 0x7FF0_0000_0000_0000u64;
let man = val & 0x000F_FFFF_FFFF_FFFFu64;

// 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 {
0x0200u32
};
return ((sign >> 16) | 0x7C00u32 | nan_bit | (man >> 10)) as u16;
if exp == 0x7FF0_0000_0000_0000u64 {
// Set mantissa MSB for NaN (and also keep shifted mantissa bits)
let nan_bit = if man == 0 { 0u64 } else { 0x0200u64 };
return ((sign >> 48) | 0x7C00u64 | nan_bit | (man >> 42)) as u16;
}

// The number is normalized, start assembling half precision version
let half_sign = sign >> 16;
let half_sign = (sign >> 48) as u32;
// Unbias the exponent, then bias for half precision
let unbiased_exp = ((exp >> 20) as i64) - 1023;
let unbiased_exp = ((exp >> 52) as i64) - 1023;
let half_exp = unbiased_exp + 15;

// Check for exponent overflow, return +infinity
Expand All @@ -659,15 +651,16 @@ pub(crate) const fn f64_to_f16_fallback(value: f64) -> u16 {
// Check for underflow
if half_exp <= 0 {
// Check mantissa for what we can do
if 10 - half_exp > 21 {
if 14 - half_exp > 24 {
// 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 >> (11 - half_exp);
let man = man | 0x0010_0000_0000_0000u64;
let shift = 43 - half_exp; // shift amount to get to half mantissa position
let mut half_man = (man >> shift) as u32;
// Check for rounding (see comment above functions)
let round_bit = 1 << (10 - half_exp);
let round_bit = 1u64 << (shift - 1);
if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
half_man += 1;
}
Expand All @@ -677,9 +670,9 @@ pub(crate) const fn f64_to_f16_fallback(value: f64) -> u16 {

// Rebias the exponent
let half_exp = (half_exp as u32) << 10;
let half_man = man >> 10;
let half_man = (man >> 42) as u32;
// Check for rounding (see comment above functions)
let round_bit = 0x0000_0200u32;
let round_bit = 0x0000_0200_0000_0000u64;
if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
// Round it
((half_sign | half_exp | half_man) + 1) as u16
Expand Down