use crate::leading_zeros::leading_zeros_u16; use core::mem; #[inline] pub(crate) const fn f32_to_bf16(value: f32) -> u16 { // TODO: Replace mem::transmute with to_bits() once to_bits is const-stabilized // Convert to raw bytes let x: u32 = unsafe { mem::transmute(value) }; // 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 } } #[inline] pub(crate) const fn f64_to_bf16(value: f64) -> u16 { // TODO: Replace mem::transmute with to_bits() once to_bits is const-stabilized // Convert to raw bytes, truncating the last 32-bits of mantissa; that precision will always // be lost on half-precision. let val: u64 = unsafe { mem::transmute(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; // 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 } } #[inline] pub(crate) const fn bf16_to_f32(i: u16) -> f32 { // TODO: Replace mem::transmute with from_bits() once from_bits is const-stabilized // If NaN, keep current mantissa but also set most significiant mantissa bit if i & 0x7FFFu16 > 0x7F80u16 { unsafe { mem::transmute((i as u32 | 0x0040u32) << 16) } } else { unsafe { mem::transmute((i as u32) << 16) } } } #[inline] pub(crate) const fn bf16_to_f64(i: u16) -> f64 { // TODO: Replace mem::transmute with from_bits() once from_bits is const-stabilized // Check for signed zero if i & 0x7FFFu16 == 0 { return unsafe { mem::transmute((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 unsafe { mem::transmute((half_sign << 48) | 0x7FF0_0000_0000_0000u64) }; } else { // NaN, keep current mantissa but also set most significiant mantissa bit return unsafe { mem::transmute((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 = leading_zeros_u16(half_man as u16) - 9; // Rebias and adjust exponent let exp = ((1023 - 127 - e) as u64) << 52; let man = (half_man << (46 + e)) & 0xF_FFFF_FFFF_FFFFu64; return unsafe { mem::transmute(sign | exp | man) }; } // Rebias exponent for a normalized normal let exp = ((unbiased_exp + 1023) as u64) << 52; let man = (half_man & 0x007Fu64) << 45; unsafe { mem::transmute(sign | exp | man) } }