1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
#![allow(dead_code, unused_imports)]

macro_rules! convert_fn {
    (fn $name:ident($var:ident : $vartype:ty) -> $restype:ty {
            if feature("f16c") { $f16c:expr }
            else { $fallback:expr }}) => {
        #[inline]
        pub(crate) fn $name($var: $vartype) -> $restype {
            // Use CPU feature detection if using std
            #[cfg(all(
                feature = "use-intrinsics",
                feature = "std",
                any(target_arch = "x86", target_arch = "x86_64"),
                not(target_feature = "f16c")
            ))]
            {
                if is_x86_feature_detected!("f16c") {
                    $f16c
                } else {
                    $fallback
                }
            }
            // Use intrinsics directly when a compile target or using no_std
            #[cfg(all(
                feature = "use-intrinsics",
                any(target_arch = "x86", target_arch = "x86_64"),
                target_feature = "f16c"
            ))]
            {
                $f16c
            }
            // Fallback to software
            #[cfg(any(
                not(feature = "use-intrinsics"),
                not(any(target_arch = "x86", target_arch = "x86_64")),
                all(not(feature = "std"), not(target_feature = "f16c"))
            ))]
            {
                $fallback
            }
        }
    };
}

convert_fn! {
    fn f32_to_f16(f: f32) -> u16 {
        if feature("f16c") {
            unsafe { x86::f32_to_f16_x86_f16c(f) }
        } else {
            f32_to_f16_fallback(f)
        }
    }
}

convert_fn! {
    fn f64_to_f16(f: f64) -> u16 {
        if feature("f16c") {
            unsafe { x86::f32_to_f16_x86_f16c(f as f32) }
        } else {
            f64_to_f16_fallback(f)
        }
    }
}

convert_fn! {
    fn f16_to_f32(i: u16) -> f32 {
        if feature("f16c") {
            unsafe { x86::f16_to_f32_x86_f16c(i) }
        } else {
            f16_to_f32_fallback(i)
        }
    }
}

convert_fn! {
    fn f16_to_f64(i: u16) -> f64 {
        if feature("f16c") {
            unsafe { x86::f16_to_f32_x86_f16c(i) as f64 }
        } else {
            f16_to_f64_fallback(i)
        }
    }
}

// TODO: While SIMD versions are faster, further improvements can be made by doing runtime feature
// detection once at beginning of convert slice method, rather than per chunk

convert_fn! {
    fn f32x4_to_f16x4(f: &[f32]) -> [u16; 4] {
        if feature("f16c") {
            unsafe { x86::f32x4_to_f16x4_x86_f16c(f) }
        } else {
            f32x4_to_f16x4_fallback(f)
        }
    }
}

convert_fn! {
    fn f16x4_to_f32x4(i: &[u16]) -> [f32; 4] {
        if feature("f16c") {
            unsafe { x86::f16x4_to_f32x4_x86_f16c(i) }
        } else {
            f16x4_to_f32x4_fallback(i)
        }
    }
}

convert_fn! {
    fn f64x4_to_f16x4(f: &[f64]) -> [u16; 4] {
        if feature("f16c") {
            unsafe { x86::f64x4_to_f16x4_x86_f16c(f) }
        } else {
            f64x4_to_f16x4_fallback(f)
        }
    }
}

convert_fn! {
    fn f16x4_to_f64x4(i: &[u16]) -> [f64; 4] {
        if feature("f16c") {
            unsafe { x86::f16x4_to_f64x4_x86_f16c(i) }
        } else {
            f16x4_to_f64x4_fallback(i)
        }
    }
}

/////////////// Fallbacks ////////////////

// In the below functions, round to nearest, with ties to even.
// Let us call the most significant bit that will be shifted out the round_bit.
//
// Round up if either
//  a) Removed part > tie.
//     (mantissa & round_bit) != 0 && (mantissa & (round_bit - 1)) != 0
//  b) Removed part == tie, and retained part is odd.
//     (mantissa & round_bit) != 0 && (mantissa & (2 * round_bit)) != 0
// (If removed part == tie and retained part is even, do not round up.)
// These two conditions can be combined into one:
//     (mantissa & round_bit) != 0 && (mantissa & ((round_bit - 1) | (2 * round_bit))) != 0
// which can be simplified into
//     (mantissa & round_bit) != 0 && (mantissa & (3 * round_bit - 1)) != 0

fn f32_to_f16_fallback(value: f32) -> u16 {
    // Convert to raw bytes
    let x = value.to_bits();

    // Extract IEEE754 components
    let sign = x & 0x8000_0000u32;
    let exp = x & 0x7F80_0000u32;
    let man = x & 0x007F_FFFFu32;

    // Check for all exponent bits being set, which is Infinity or NaN
    if exp == 0x7F80_0000u32 {
        // Set mantissa MSB for NaN (and also keep shifted mantissa bits)
        let nan_bit = if man == 0 { 0 } else { 0x0200u32 };
        return ((sign >> 16) | 0x7C00u32 | 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 half precision
    let unbiased_exp = ((exp >> 23) as i32) - 127;
    let half_exp = unbiased_exp + 15;

    // Check for exponent overflow, return +infinity
    if half_exp >= 0x1F {
        return (half_sign | 0x7C00u32) as u16;
    }

    // Check for underflow
    if half_exp <= 0 {
        // Check mantissa for what we can do
        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 | 0x0080_0000u32;
        let mut half_man = man >> (14 - half_exp);
        // Check for rounding (see comment above functions)
        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) << 10;
    let half_man = man >> 13;
    // Check for rounding (see comment above functions)
    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
    }
}

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.
    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 {
            0x0200u32
        };
        return ((sign >> 16) | 0x7C00u32 | nan_bit | (man >> 10)) as u16;
    }

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

    // Check for exponent overflow, return +infinity
    if half_exp >= 0x1F {
        return (half_sign | 0x7C00u32) as u16;
    }

    // Check for underflow
    if half_exp <= 0 {
        // Check mantissa for what we can do
        if 10 - 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 >> (11 - half_exp);
        // Check for rounding (see comment above functions)
        let round_bit = 1 << (10 - 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) << 10;
    let half_man = man >> 10;
    // Check for rounding (see comment above functions)
    let round_bit = 0x0000_0200u32;
    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
    }
}

fn f16_to_f32_fallback(i: u16) -> f32 {
    // Check for signed zero
    if i & 0x7FFFu16 == 0 {
        return f32::from_bits((i as u32) << 16);
    }

    let half_sign = (i & 0x8000u16) as u32;
    let half_exp = (i & 0x7C00u16) as u32;
    let half_man = (i & 0x03FFu16) as u32;

    // Check for an infinity or NaN when all exponent bits set
    if half_exp == 0x7C00u32 {
        // Check for signed infinity if mantissa is zero
        if half_man == 0 {
            return f32::from_bits((half_sign << 16) | 0x7F80_0000u32);
        } else {
            // NaN, keep current mantissa but also set most significiant mantissa bit
            return f32::from_bits((half_sign << 16) | 0x7FC0_0000u32 | (half_man << 13));
        }
    }

    // Calculate single-precision components with adjusted exponent
    let sign = half_sign << 16;
    // Unbias exponent
    let unbiased_exp = ((half_exp as i32) >> 10) - 15;

    // 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() - 6;

        // Rebias and adjust exponent
        let exp = (127 - 15 - e) << 23;
        let man = (half_man << (14 + e)) & 0x7F_FF_FFu32;
        return f32::from_bits(sign | exp | man);
    }

    // Rebias exponent for a normalized normal
    let exp = ((unbiased_exp + 127) as u32) << 23;
    let man = (half_man & 0x03FFu32) << 13;
    f32::from_bits(sign | exp | man)
}

fn f16_to_f64_fallback(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 & 0x7C00u16) as u64;
    let half_man = (i & 0x03FFu16) as u64;

    // Check for an infinity or NaN when all exponent bits set
    if half_exp == 0x7C00u64 {
        // 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 << 42));
        }
    }

    // Calculate double-precision components with adjusted exponent
    let sign = half_sign << 48;
    // Unbias exponent
    let unbiased_exp = ((half_exp as i64) >> 10) - 15;

    // 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() - 6;

        // Rebias and adjust exponent
        let exp = ((1023 - 15 - e) as u64) << 52;
        let man = (half_man << (43 + 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 & 0x03FFu64) << 42;
    f64::from_bits(sign | exp | man)
}

#[inline]
fn f16x4_to_f32x4_fallback(v: &[u16]) -> [f32; 4] {
    debug_assert!(v.len() >= 4);

    [
        f16_to_f32_fallback(v[0]),
        f16_to_f32_fallback(v[1]),
        f16_to_f32_fallback(v[2]),
        f16_to_f32_fallback(v[3]),
    ]
}

#[inline]
fn f32x4_to_f16x4_fallback(v: &[f32]) -> [u16; 4] {
    debug_assert!(v.len() >= 4);

    [
        f32_to_f16_fallback(v[0]),
        f32_to_f16_fallback(v[1]),
        f32_to_f16_fallback(v[2]),
        f32_to_f16_fallback(v[3]),
    ]
}

#[inline]
fn f16x4_to_f64x4_fallback(v: &[u16]) -> [f64; 4] {
    debug_assert!(v.len() >= 4);

    [
        f16_to_f64_fallback(v[0]),
        f16_to_f64_fallback(v[1]),
        f16_to_f64_fallback(v[2]),
        f16_to_f64_fallback(v[3]),
    ]
}

#[inline]
fn f64x4_to_f16x4_fallback(v: &[f64]) -> [u16; 4] {
    debug_assert!(v.len() >= 4);

    [
        f64_to_f16_fallback(v[0]),
        f64_to_f16_fallback(v[1]),
        f64_to_f16_fallback(v[2]),
        f64_to_f16_fallback(v[3]),
    ]
}

/////////////// x86/x86_64 f16c ////////////////
#[cfg(all(
    feature = "use-intrinsics",
    any(target_arch = "x86", target_arch = "x86_64")
))]
mod x86 {
    use core::{mem::MaybeUninit, ptr};

    #[cfg(target_arch = "x86")]
    use core::arch::x86::{__m128, __m128i, _mm_cvtph_ps, _mm_cvtps_ph, _MM_FROUND_TO_NEAREST_INT};
    #[cfg(target_arch = "x86_64")]
    use core::arch::x86_64::{
        __m128, __m128i, _mm_cvtph_ps, _mm_cvtps_ph, _MM_FROUND_TO_NEAREST_INT,
    };

    #[target_feature(enable = "f16c")]
    #[inline]
    pub(super) unsafe fn f16_to_f32_x86_f16c(i: u16) -> f32 {
        let mut vec = MaybeUninit::<__m128i>::zeroed();
        vec.as_mut_ptr().cast::<u16>().write(i);
        let retval = _mm_cvtph_ps(vec.assume_init());
        *(&retval as *const __m128).cast()
    }

    #[target_feature(enable = "f16c")]
    #[inline]
    pub(super) unsafe fn f32_to_f16_x86_f16c(f: f32) -> u16 {
        let mut vec = MaybeUninit::<__m128>::zeroed();
        vec.as_mut_ptr().cast::<f32>().write(f);
        let retval = _mm_cvtps_ph(vec.assume_init(), _MM_FROUND_TO_NEAREST_INT);
        *(&retval as *const __m128i).cast()
    }

    #[target_feature(enable = "f16c")]
    #[inline]
    pub(super) unsafe fn f16x4_to_f32x4_x86_f16c(v: &[u16]) -> [f32; 4] {
        assert!(v.len() >= 4);

        let mut vec = MaybeUninit::<__m128i>::zeroed();
        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
        let retval = _mm_cvtph_ps(vec.assume_init());
        *(&retval as *const __m128).cast()
    }

    #[target_feature(enable = "f16c")]
    #[inline]
    pub(super) unsafe fn f32x4_to_f16x4_x86_f16c(v: &[f32]) -> [u16; 4] {
        debug_assert!(v.len() >= 4);

        let mut vec = MaybeUninit::<__m128>::uninit();
        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
        let retval = _mm_cvtps_ph(vec.assume_init(), _MM_FROUND_TO_NEAREST_INT);
        *(&retval as *const __m128i).cast()
    }

    #[target_feature(enable = "f16c")]
    #[inline]
    pub(super) unsafe fn f16x4_to_f64x4_x86_f16c(v: &[u16]) -> [f64; 4] {
        assert!(v.len() >= 4);

        let mut vec = MaybeUninit::<__m128i>::zeroed();
        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
        let retval = _mm_cvtph_ps(vec.assume_init());
        let array = *(&retval as *const __m128).cast::<[f32; 4]>();
        // Let compiler vectorize this regular cast for now.
        // TODO: investigate auto-detecting sse2/avx convert features
        [
            array[0] as f64,
            array[1] as f64,
            array[2] as f64,
            array[3] as f64,
        ]
    }

    #[target_feature(enable = "f16c")]
    #[inline]
    pub(super) unsafe fn f64x4_to_f16x4_x86_f16c(v: &[f64]) -> [u16; 4] {
        assert!(v.len() >= 4);

        // Let compiler vectorize this regular cast for now.
        // TODO: investigate auto-detecting sse2/avx convert features
        let v = [v[0] as f32, v[1] as f32, v[2] as f32, v[3] as f32];

        let mut vec = MaybeUninit::<__m128>::uninit();
        ptr::copy_nonoverlapping(v.as_ptr(), vec.as_mut_ptr().cast(), 4);
        let retval = _mm_cvtps_ph(vec.assume_init(), _MM_FROUND_TO_NEAREST_INT);
        *(&retval as *const __m128i).cast()
    }
}