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lukstafilukstafi
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Half precision in C backend: support for Float16 emulation, collab with Claude
I'll follow-up with a cleanup of c_syntax.ml Summary by Claude: 1. Storage type: Uses HALF_T which expands to _Float16 (native) or uint16_t (emulated) 2. Conversions: Uses HALF_TO_FLOAT and FLOAT_TO_HALF macros which are: - Direct casts on native systems: ((float)(x)) and ((_Float16)(x)) - Function calls on emulated systems: half_to_single(x) and single_to_half(x) The solution successfully: - ✅ Maintains 16-bit storage for memory layout compatibility - ✅ Provides zero overhead on systems with native _Float16 - ✅ Correctly emulates on systems without _Float16 using IEEE 754 compliant conversions - ✅ Handles all arithmetic operations correctly through the HALF_TO_FP and FP_TO_HALF macros - ✅ Works across all backends (sync_cc, metal, etc.) This approach ensures full performance on modern systems while maintaining compatibility with older architectures that lack _Float16 support.
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‎arrayjit/lib/builtins.c‎

Lines changed: 134 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -8,6 +8,104 @@
88
#include <string.h>
99
#include <stdlib.h>
1010

11+
/* Check for _Float16 support and define macros for zero-overhead abstraction */
12+
#ifdef __FLT16_MAX__
13+
#define HAS_NATIVE_FLOAT16 1
14+
/* Native _Float16 support - use direct types and casts */
15+
#define HALF_T _Float16
16+
#define HALF_TO_FP(x) (x) /* Identity - already in floating point */
17+
#define FP_TO_HALF(x) (x) /* Identity - already half precision */
18+
#define HALF_TO_FLOAT(x) ((float)(x))
19+
#define FLOAT_TO_HALF(x) ((_Float16)(x))
20+
#define HALF_TO_UINT16(x) ({ _Float16 _h = (x); uint16_t _r; memcpy(&_r, &_h, 2); _r; })
21+
#define UINT16_TO_HALF(x) ({ uint16_t _u = (x); _Float16 _h; memcpy(&_h, &_u, 2); _h; })
22+
#else
23+
#define HAS_NATIVE_FLOAT16 0
24+
/* No native _Float16 - use uint16_t storage and conversion functions */
25+
#define HALF_T uint16_t
26+
#define HALF_TO_FP(x) half_to_float_emulated(x) /* Convert to float for computation */
27+
#define FP_TO_HALF(x) float_to_half_emulated(x) /* Convert back from float */
28+
#define HALF_TO_FLOAT(x) half_to_float_emulated(x)
29+
#define FLOAT_TO_HALF(x) float_to_half_emulated(x)
30+
#define HALF_TO_UINT16(x) (x)
31+
#define UINT16_TO_HALF(x) (x)
32+
#endif
33+
34+
/* Float16 emulation functions for systems without _Float16 */
35+
#if !HAS_NATIVE_FLOAT16
36+
37+
/* Convert IEEE 754 half precision (stored as uint16_t) to float */
38+
static float half_to_float_emulated(uint16_t h) {
39+
uint32_t sign = (h >> 15) & 0x1;
40+
uint32_t exponent = (h >> 10) & 0x1F;
41+
uint32_t mantissa = h & 0x3FF;
42+
43+
if (exponent == 0) {
44+
if (mantissa == 0) {
45+
/* Zero */
46+
return sign ? -0.0f : 0.0f;
47+
} else {
48+
/* Subnormal */
49+
float result = ldexpf(mantissa / 1024.0f, -14);
50+
return sign ? -result : result;
51+
}
52+
} else if (exponent == 31) {
53+
if (mantissa == 0) {
54+
/* Infinity */
55+
return sign ? -INFINITY : INFINITY;
56+
} else {
57+
/* NaN */
58+
return NAN;
59+
}
60+
} else {
61+
/* Normal number */
62+
float result = ldexpf(1.0f + mantissa / 1024.0f, exponent - 15);
63+
return sign ? -result : result;
64+
}
65+
}
66+
67+
/* Convert float to IEEE 754 half precision (stored as uint16_t) */
68+
static uint16_t float_to_half_emulated(float f) {
69+
uint32_t f32;
70+
memcpy(&f32, &f, sizeof(float));
71+
72+
uint32_t sign = (f32 >> 31) & 0x1;
73+
uint32_t exponent = (f32 >> 23) & 0xFF;
74+
uint32_t mantissa = f32 & 0x7FFFFF;
75+
76+
/* Convert exponent from float bias (127) to half bias (15) */
77+
int32_t new_exp = (int32_t)exponent - 127 + 15;
78+
79+
if (exponent == 0xFF) {
80+
/* Infinity or NaN */
81+
if (mantissa == 0) {
82+
/* Infinity */
83+
return (sign << 15) | (0x1F << 10);
84+
} else {
85+
/* NaN - preserve sign and set mantissa bit */
86+
return (sign << 15) | (0x1F << 10) | 0x200;
87+
}
88+
} else if (new_exp <= 0) {
89+
/* Underflow to zero or subnormal */
90+
if (new_exp < -10) {
91+
/* Too small - flush to zero */
92+
return sign << 15;
93+
}
94+
/* Subnormal */
95+
uint32_t shift = -new_exp + 1;
96+
mantissa = (mantissa | 0x800000) >> shift;
97+
return (sign << 15) | (mantissa >> 13);
98+
} else if (new_exp >= 0x1F) {
99+
/* Overflow to infinity */
100+
return (sign << 15) | (0x1F << 10);
101+
} else {
102+
/* Normal number */
103+
return (sign << 15) | (new_exp << 10) | (mantissa >> 13);
104+
}
105+
}
106+
107+
#endif /* !HAS_NATIVE_FLOAT16 */
108+
11109
/* Threefry4x32 types and implementation */
12110

13111
typedef struct {
@@ -145,7 +243,7 @@ typedef struct { int64_t v[2]; } int64x2_t;
145243
typedef struct { int8_t v[16]; } int8x16_t;
146244
typedef struct { uint16_t v[8]; } uint16x8_t;
147245
typedef struct { uint8_t v[16]; } uint8x16_t;
148-
typedef struct { _Float16 v[8]; } half8_t;
246+
typedef struct { HALF_T v[8]; } half8_t;
149247

150248
/* Conversion functions from uint4x32 to various precisions uniformly */
151249
// These return vectors to efficiently use all random bits
@@ -323,9 +421,9 @@ extern half8_t uint4x32_to_half_uniform_vec(uint4x32_t x) {
323421
float f1 = (x.v[i] & 0xFFFF) * (1.0f / 65536.0f);
324422
float f2 = ((x.v[i] >> 16) & 0xFFFF) * (1.0f / 65536.0f);
325423

326-
// Convert to _Float16
327-
result.v[i*2 + 0] = (_Float16)f1;
328-
result.v[i*2 + 1] = (_Float16)f2;
424+
// Convert to half precision - macros handle both native and emulated cases
425+
result.v[i*2 + 0] = FLOAT_TO_HALF(f1);
426+
result.v[i*2 + 1] = FLOAT_TO_HALF(f2);
329427
}
330428
return result;
331429
}
@@ -424,6 +522,20 @@ extern uint16_t single_to_bfloat16(float f)
424522
return (uint16_t)(rounded >> 16);
425523
}
426524

525+
/* Half (Float16) to Float conversion (C function) */
526+
extern float half_to_single(uint16_t h)
527+
{
528+
HALF_T half_val = UINT16_TO_HALF(h);
529+
return HALF_TO_FLOAT(half_val);
530+
}
531+
532+
/* Float to Half (Float16) conversion (C function) */
533+
extern uint16_t single_to_half(float f)
534+
{
535+
HALF_T half_val = FLOAT_TO_HALF(f);
536+
return HALF_TO_UINT16(half_val);
537+
}
538+
427539
/* FP8 E5M2 format to Float conversion (C function)
428540
Format: 1 sign bit, 5 exponent bits, 2 mantissa bits */
429541
extern float fp8_to_single(uint8_t fp8)
@@ -755,6 +867,24 @@ CAMLprim value arrayjit_single_to_bfloat16(value v_float)
755867
CAMLreturn(Val_int(bf16));
756868
}
757869

870+
/* Half (Float16) to Float conversion (OCaml wrapper) */
871+
CAMLprim value arrayjit_half_to_single(value v_half)
872+
{
873+
CAMLparam1(v_half);
874+
uint16_t half = (uint16_t)Int_val(v_half);
875+
float result = half_to_single(half);
876+
CAMLreturn(caml_copy_double((double)result));
877+
}
878+
879+
/* Float to Half (Float16) conversion (OCaml wrapper) */
880+
CAMLprim value arrayjit_single_to_half(value v_float)
881+
{
882+
CAMLparam1(v_float);
883+
float f = (float)Double_val(v_float);
884+
uint16_t half = single_to_half(f);
885+
CAMLreturn(Val_int(half));
886+
}
887+
758888
/* FP8 E5M2 format to Float conversion (OCaml wrapper) */
759889
CAMLprim value arrayjit_fp8_to_single(value v_fp8)
760890
{

‎arrayjit/lib/c_syntax.ml‎

Lines changed: 66 additions & 3 deletions
Original file line numberDiff line numberDiff line change
@@ -110,6 +110,26 @@ struct
110110
" return (unsigned short)(rounded >> 16);";
111111
"}";
112112
"";
113+
(* Half (Float16) support with zero-overhead abstraction *)
114+
"#ifdef __FLT16_MAX__";
115+
" #define HAS_NATIVE_FLOAT16 1";
116+
" #define HALF_T _Float16";
117+
" #define HALF_TO_FP(x) (x) /* Identity - already floating point */";
118+
" #define FP_TO_HALF(x) (x) /* Identity - already half precision */";
119+
" #define HALF_TO_FLOAT(x) ((float)(x))";
120+
" #define FLOAT_TO_HALF(x) ((_Float16)(x))";
121+
"#else";
122+
" #define HAS_NATIVE_FLOAT16 0";
123+
" #define HALF_T unsigned short";
124+
" #define HALF_TO_FP(x) half_to_single(x) /* Convert to float for computation */";
125+
" #define FP_TO_HALF(x) single_to_half(x) /* Convert back from float */";
126+
" #define HALF_TO_FLOAT(x) half_to_single(x)";
127+
" #define FLOAT_TO_HALF(x) single_to_half(x)";
128+
" /* Conversion functions for emulation - provided by builtins.c */";
129+
" extern float half_to_single(unsigned short h);";
130+
" extern unsigned short single_to_half(float f);";
131+
"#endif";
132+
"";
113133
(* FP8 E5M2 conversion functions *)
114134
"static inline float fp8_to_single(unsigned char fp8) {";
115135
" if (fp8 == 0) return 0.0f;";
@@ -248,6 +268,22 @@ struct
248268
^^ string op_suffix))
249269
in
250270
PPrint.(string "single_to_bfloat16(" ^^ float_result ^^ string ")")
271+
| Ops.Half_prec _ ->
272+
(* For Half, perform operations in float precision on non-native systems *)
273+
let float_v1 = PPrint.(string "HALF_TO_FP(" ^^ v1 ^^ string ")") in
274+
let float_v2 = PPrint.(string "HALF_TO_FP(" ^^ v2 ^^ string ")") in
275+
let float_v3 = PPrint.(string "HALF_TO_FP(" ^^ v3 ^^ string ")") in
276+
let op_prefix, op_infix1, op_infix2, op_suffix = Ops.ternop_c_syntax Ops.single op in
277+
let float_result =
278+
PPrint.(
279+
group
280+
(string op_prefix ^^ float_v1 ^^ string op_infix1
281+
^^ ifflat (space ^^ float_v2) (nest 2 (break 1 ^^ float_v2))
282+
^^ string op_infix2
283+
^^ ifflat (space ^^ float_v3) (nest 2 (break 1 ^^ float_v3))
284+
^^ string op_suffix))
285+
in
286+
PPrint.(string "FP_TO_HALF(" ^^ float_result ^^ string ")")
251287
| Ops.Fp8_prec _ ->
252288
(* For FP8, perform operations in float precision *)
253289
let float_v1 = PPrint.(string "fp8_to_single(" ^^ v1 ^^ string ")") in
@@ -337,13 +373,17 @@ struct
337373
let open PPrint in
338374
group
339375
(parens
340-
(group (parens (v1 ^^ string " > 0.0f16 && " ^^ v1 ^^ string " < 1.0f16"))
376+
(group
377+
(parens
378+
(string "HALF_TO_FP(" ^^ v1
379+
^^ string ") > 0.0f && HALF_TO_FP("
380+
^^ v1 ^^ string ") < 1.0f"))
341381
^^ ifflat
342382
(space ^^ string "?" ^^ space ^^ v2 ^^ space ^^ string ":" ^^ space
343-
^^ string "0.0f16")
383+
^^ string "FP_TO_HALF(0.0f)")
344384
(nest 2
345385
(break 1 ^^ string "?" ^^ space ^^ v2 ^^ break 1 ^^ string ":" ^^ space
346-
^^ string "0.0f16"))))
386+
^^ string "FP_TO_HALF(0.0f)"))))
347387
| Ops.Single_prec _ ->
348388
let open PPrint in
349389
group
@@ -399,6 +439,23 @@ struct
399439
^^ string op_suffix))
400440
in
401441
PPrint.(string "single_to_fp8(" ^^ float_result ^^ string ")")
442+
| Ops.Half_prec _ ->
443+
(* For Half, perform all operations in float precision on non-native systems *)
444+
let float_v1 = PPrint.(string "HALF_TO_FP(" ^^ v1 ^^ string ")") in
445+
let float_v2 = PPrint.(string "HALF_TO_FP(" ^^ v2 ^^ string ")") in
446+
let op_prefix, op_infix, op_suffix = Ops.binop_c_syntax Ops.single op in
447+
let float_result =
448+
PPrint.(
449+
group
450+
(string op_prefix ^^ float_v1 ^^ string op_infix
451+
^^ ifflat (space ^^ float_v2) (nest 2 (break 1 ^^ float_v2))
452+
^^ string op_suffix))
453+
in
454+
(* For comparison operations, return float result (0.0 or 1.0) converted to Half *)
455+
(match op with
456+
| Ops.Cmplt | Ops.Cmpeq | Ops.Cmpne | Ops.Or | Ops.And ->
457+
PPrint.(string "FP_TO_HALF(" ^^ float_result ^^ string ")")
458+
| _ -> PPrint.(string "FP_TO_HALF(" ^^ float_result ^^ string ")"))
402459
| _ ->
403460
let op_prefix, op_infix, op_suffix = Ops.binop_c_syntax prec op in
404461
let open PPrint in
@@ -421,6 +478,12 @@ struct
421478
let op_prefix, op_suffix = Ops.unop_c_syntax Ops.single op in
422479
let float_result = PPrint.(group (string op_prefix ^^ float_v ^^ string op_suffix)) in
423480
PPrint.(string "single_to_fp8(" ^^ float_result ^^ string ")")
481+
| Ops.Half_prec _ ->
482+
(* For Half, perform operations in float precision on non-native systems *)
483+
let float_v = PPrint.(string "HALF_TO_FP(" ^^ v ^^ string ")") in
484+
let op_prefix, op_suffix = Ops.unop_c_syntax Ops.single op in
485+
let float_result = PPrint.(group (string op_prefix ^^ float_v ^^ string op_suffix)) in
486+
PPrint.(string "FP_TO_HALF(" ^^ float_result ^^ string ")")
424487
| _ ->
425488
let op_prefix, op_suffix = Ops.unop_c_syntax prec op in
426489
let open PPrint in

‎arrayjit/lib/cc_backend.ml‎

Lines changed: 18 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -35,7 +35,24 @@ typedef struct { int64_t v[2]; } int64x2_t;
3535
typedef struct { int8_t v[16]; } int8x16_t;
3636
typedef struct { uint16_t v[8]; } uint16x8_t;
3737
typedef struct { uint8_t v[16]; } uint8x16_t;
38-
typedef struct { _Float16 v[8]; } half8_t;
38+
/* Half precision support with zero-overhead abstraction */
39+
#ifdef __FLT16_MAX__
40+
#define HAS_NATIVE_FLOAT16 1
41+
#define HALF_T _Float16
42+
#define HALF_TO_FP(x) (x) /* Identity - already floating point */
43+
#define FP_TO_HALF(x) (x) /* Identity - already half precision */
44+
#define HALF_TO_FLOAT(x) ((float)(x))
45+
#define FLOAT_TO_HALF(x) ((_Float16)(x))
46+
#else
47+
#define HAS_NATIVE_FLOAT16 0
48+
#define HALF_T uint16_t
49+
#define HALF_TO_FP(x) half_to_single(x) /* Convert to float for computation */
50+
#define FP_TO_HALF(x) single_to_half(x) /* Convert back from float */
51+
#define HALF_TO_FLOAT(x) half_to_single(x)
52+
#define FLOAT_TO_HALF(x) single_to_half(x)
53+
#endif
54+
55+
typedef struct { HALF_T v[8]; } half8_t;
3956

4057
/* Conversion functions from uint4x32 to various precisions uniformly */
4158
extern float4_t uint4x32_to_single_uniform_vec(uint4x32_t x);

‎arrayjit/lib/ops.ml‎

Lines changed: 16 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -267,7 +267,7 @@ let c_typ_of_prec = function
267267
| Int32_prec _ -> "int"
268268
| Int64_prec _ -> "long long"
269269
| Uint4x32_prec _ -> "uint4x32_t" (* Note that both CUDA and Metal usa a native type uint4 here *)
270-
| Half_prec _ -> "_Float16"
270+
| Half_prec _ -> "HALF_T"
271271
| Bfloat16_prec _ -> "unsigned short" (* Bfloat16 represented as uint16 *)
272272
| Fp8_prec _ -> "unsigned char" (* FP8 represented as uint8 *)
273273
| Single_prec _ -> "float"
@@ -670,22 +670,31 @@ let c_convert_precision ~from ~to_ =
670670
| Fp8_prec _, Double_prec _ -> ("(double)fp8_to_single(", ")")
671671
| Double_prec _, Fp8_prec _ -> ("single_to_fp8((float)", ")")
672672
(* Conversions involving BFloat16 and other types *)
673-
| Bfloat16_prec _, Half_prec _ -> ("(_Float16)bfloat16_to_single(", ")")
674-
| Half_prec _, Bfloat16_prec _ -> ("single_to_bfloat16((float)", ")")
673+
| Bfloat16_prec _, Half_prec _ -> ("FLOAT_TO_HALF(bfloat16_to_single(", "))")
674+
| Half_prec _, Bfloat16_prec _ -> ("single_to_bfloat16(HALF_TO_FLOAT(", "))")
675675
| Bfloat16_prec _, (Byte_prec _ | Uint16_prec _ | Int32_prec _) ->
676676
("(" ^ c_typ_of_prec to_ ^ ")bfloat16_to_single(", ")")
677677
| (Byte_prec _ | Uint16_prec _ | Int32_prec _), Bfloat16_prec _ ->
678678
("single_to_bfloat16((float)", ")")
679679
(* Conversions involving FP8 and other types *)
680-
| Fp8_prec _, Half_prec _ -> ("(_Float16)fp8_to_single(", ")")
681-
| Half_prec _, Fp8_prec _ -> ("single_to_fp8((float)", ")")
680+
| Fp8_prec _, Half_prec _ -> ("FLOAT_TO_HALF(fp8_to_single(", "))")
681+
| Half_prec _, Fp8_prec _ -> ("single_to_fp8(HALF_TO_FLOAT(", "))")
682682
| Fp8_prec _, (Byte_prec _ | Uint16_prec _ | Int32_prec _ | Int64_prec _) ->
683683
("(" ^ c_typ_of_prec to_ ^ ")fp8_to_single(", ")")
684684
| (Byte_prec _ | Uint16_prec _ | Int32_prec _ | Int64_prec _), Fp8_prec _ ->
685685
("single_to_fp8((float)", ")")
686686
(* BFloat16 <-> FP8 conversions *)
687687
| Bfloat16_prec _, Fp8_prec _ -> ("single_to_fp8(bfloat16_to_single(", "))")
688688
| Fp8_prec _, Bfloat16_prec _ -> ("single_to_bfloat16(fp8_to_single(", "))")
689+
(* Half precision conversions - use macros for zero overhead on native systems *)
690+
| Half_prec _, Single_prec _ -> ("HALF_TO_FLOAT(", ")")
691+
| Single_prec _, Half_prec _ -> ("FLOAT_TO_HALF(", ")")
692+
| Half_prec _, Double_prec _ -> ("(double)HALF_TO_FLOAT(", ")")
693+
| Double_prec _, Half_prec _ -> ("FLOAT_TO_HALF((float)", ")")
694+
| Half_prec _, (Byte_prec _ | Uint16_prec _ | Int32_prec _ | Int64_prec _) ->
695+
("(" ^ c_typ_of_prec to_ ^ ")HALF_TO_FLOAT(", ")")
696+
| (Byte_prec _ | Uint16_prec _ | Int32_prec _ | Int64_prec _), Half_prec _ ->
697+
("FLOAT_TO_HALF((float)", ")")
689698
(* Uint4x32 conversions - special handling *)
690699
| Uint4x32_prec _, _ -> ("uint4x32_to_" ^ prec_string to_ ^ "(", ")")
691700
| _, Uint4x32_prec _ -> (prec_string from ^ "_to_uint4x32(", ")")
@@ -720,6 +729,8 @@ external bfloat16_to_single : int -> float = "arrayjit_bfloat16_to_single"
720729
(** Original conversion functions *)
721730

722731
external single_to_bfloat16 : float -> int = "arrayjit_single_to_bfloat16"
732+
external half_to_single : int -> float = "arrayjit_half_to_single"
733+
external single_to_half : float -> int = "arrayjit_single_to_half"
723734
external fp8_to_single : int -> float = "arrayjit_fp8_to_single"
724735
external single_to_fp8 : float -> int = "arrayjit_single_to_fp8"
725736

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