half/bfloat/
convert.rs

Help
1use crate::leading_zeros::leading_zeros_u16;
2use core::mem;
3
4#[inline]
5pub(crate) const fn f32_to_bf16(value: f32) -> u16 {
6    // TODO: Replace mem::transmute with to_bits() once to_bits is const-stabilized
7    // Convert to raw bytes
8    let x: u32 = unsafe { mem::transmute::<f32, u32>(value) };
9
10    // check for NaN
11    if x & 0x7FFF_FFFFu32 > 0x7F80_0000u32 {
12        // Keep high part of current mantissa but also set most significiant mantissa bit
13        return ((x >> 16) | 0x0040u32) as u16;
14    }
15
16    // round and shift
17    let round_bit = 0x0000_8000u32;
18    if (x & round_bit) != 0 && (x & (3 * round_bit - 1)) != 0 {
19        (x >> 16) as u16 + 1
20    } else {
21        (x >> 16) as u16
22    }
23}
24
25#[inline]
26pub(crate) const fn f64_to_bf16(value: f64) -> u16 {
27    // TODO: Replace mem::transmute with to_bits() once to_bits is const-stabilized
28    // Convert to raw bytes, truncating the last 32-bits of mantissa; that precision will always
29    // be lost on half-precision.
30    let val: u64 = unsafe { mem::transmute::<f64, u64>(value) };
31    let x = (val >> 32) as u32;
32
33    // Extract IEEE754 components
34    let sign = x & 0x8000_0000u32;
35    let exp = x & 0x7FF0_0000u32;
36    let man = x & 0x000F_FFFFu32;
37
38    // Check for all exponent bits being set, which is Infinity or NaN
39    if exp == 0x7FF0_0000u32 {
40        // Set mantissa MSB for NaN (and also keep shifted mantissa bits).
41        // We also have to check the last 32 bits.
42        let nan_bit = if man == 0 && (val as u32 == 0) {
43            0
44        } else {
45            0x0040u32
46        };
47        return ((sign >> 16) | 0x7F80u32 | nan_bit | (man >> 13)) as u16;
48    }
49
50    // The number is normalized, start assembling half precision version
51    let half_sign = sign >> 16;
52    // Unbias the exponent, then bias for bfloat16 precision
53    let unbiased_exp = ((exp >> 20) as i64) - 1023;
54    let half_exp = unbiased_exp + 127;
55
56    // Check for exponent overflow, return +infinity
57    if half_exp >= 0xFF {
58        return (half_sign | 0x7F80u32) as u16;
59    }
60
61    // Check for underflow
62    if half_exp <= 0 {
63        // Check mantissa for what we can do
64        if 7 - half_exp > 21 {
65            // No rounding possibility, so this is a full underflow, return signed zero
66            return half_sign as u16;
67        }
68        // Don't forget about hidden leading mantissa bit when assembling mantissa
69        let man = man | 0x0010_0000u32;
70        let mut half_man = man >> (14 - half_exp);
71        // Check for rounding
72        let round_bit = 1 << (13 - half_exp);
73        if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
74            half_man += 1;
75        }
76        // No exponent for subnormals
77        return (half_sign | half_man) as u16;
78    }
79
80    // Rebias the exponent
81    let half_exp = (half_exp as u32) << 7;
82    let half_man = man >> 13;
83    // Check for rounding
84    let round_bit = 0x0000_1000u32;
85    if (man & round_bit) != 0 && (man & (3 * round_bit - 1)) != 0 {
86        // Round it
87        ((half_sign | half_exp | half_man) + 1) as u16
88    } else {
89        (half_sign | half_exp | half_man) as u16
90    }
91}
92
93#[inline]
94pub(crate) const fn bf16_to_f32(i: u16) -> f32 {
95    // TODO: Replace mem::transmute with from_bits() once from_bits is const-stabilized
96    // If NaN, keep current mantissa but also set most significiant mantissa bit
97    if i & 0x7FFFu16 > 0x7F80u16 {
98        unsafe { mem::transmute::<u32, f32>((i as u32 | 0x0040u32) << 16) }
99    } else {
100        unsafe { mem::transmute::<u32, f32>((i as u32) << 16) }
101    }
102}
103
104#[inline]
105pub(crate) const fn bf16_to_f64(i: u16) -> f64 {
106    // TODO: Replace mem::transmute with from_bits() once from_bits is const-stabilized
107    // Check for signed zero
108    if i & 0x7FFFu16 == 0 {
109        return unsafe { mem::transmute::<u64, f64>((i as u64) << 48) };
110    }
111
112    let half_sign = (i & 0x8000u16) as u64;
113    let half_exp = (i & 0x7F80u16) as u64;
114    let half_man = (i & 0x007Fu16) as u64;
115
116    // Check for an infinity or NaN when all exponent bits set
117    if half_exp == 0x7F80u64 {
118        // Check for signed infinity if mantissa is zero
119        if half_man == 0 {
120            return unsafe {
121                mem::transmute::<u64, f64>((half_sign << 48) | 0x7FF0_0000_0000_0000u64)
122            };
123        } else {
124            // NaN, keep current mantissa but also set most significiant mantissa bit
125            return unsafe {
126                mem::transmute::<u64, f64>(
127                    (half_sign << 48) | 0x7FF8_0000_0000_0000u64 | (half_man << 45),
128                )
129            };
130        }
131    }
132
133    // Calculate double-precision components with adjusted exponent
134    let sign = half_sign << 48;
135    // Unbias exponent
136    let unbiased_exp = ((half_exp as i64) >> 7) - 127;
137
138    // Check for subnormals, which will be normalized by adjusting exponent
139    if half_exp == 0 {
140        // Calculate how much to adjust the exponent by
141        let e = leading_zeros_u16(half_man as u16) - 9;
142
143        // Rebias and adjust exponent
144        let exp = ((1023 - 127 - e) as u64) << 52;
145        let man = (half_man << (46 + e)) & 0xF_FFFF_FFFF_FFFFu64;
146        return unsafe { mem::transmute::<u64, f64>(sign | exp | man) };
147    }
148    // Rebias exponent for a normalized normal
149    let exp = ((unbiased_exp + 1023) as u64) << 52;
150    let man = (half_man & 0x007Fu64) << 45;
151    unsafe { mem::transmute::<u64, f64>(sign | exp | man) }
152}
half/bfloat/convert.rs

half/bfloat/
convert.rs
