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Add BFloat16 dot product #88

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Sep 15, 2022
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Add BFloat16 dot product #88

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76 changes: 51 additions & 25 deletions proposals/relaxed-simd/Overview.md
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Original file line number Diff line number Diff line change
Expand Up @@ -180,7 +180,7 @@ All the instructions take 3 operands, `a`, `b`, `c`, perform `a * b + c` or `-(a
where:

- the intermediate `b * c` is be rounded first, and the final result rounded again (for a total of 2 roundings), or
- the the entire expression evaluated with higher precision and then only rounded once (if supported by hardware).
- the entire expression evaluated with higher precision and then only rounded once (if supported by hardware).

### Relaxed laneselect

Expand Down Expand Up @@ -279,6 +279,32 @@ i16x8_dot_i8x16_i7x16_s(a, b) = dot_product(signed=True, elements=2, a, b
i32x4.dot_i8x16_i7x16_add_s(a, b, c) = dot_product(signed=False, elements=2, a, b, c)
```

### Relaxed BFloat16 dot product

- `f32x4.relaxed_dot_bf16x8_add_f32x4(a: v128, b: v128, c: v128) -> v128`

BFloat16 is a 16-bit floating-point format that represents the IEEE FP32 numbers
truncated to the high 16 bits. This instruction computes a FP32 dot product of 2
BFloat16 with accumulation into another FP32.

```python
def bfloat16_dot_product(a, b, c):
for i in range(8):
y.fp32[i] =
y.fp32[i] +
cast<fp32>(a.bf16[2*i]) * cast<fp32>(b.bf16[2*i]) +
cast<fp32>(a.bf16[2*i+1]) * cast<fp32>(b.bf16[2*i+1])
```

This instruction is implementation defined in the following ways:

- evaluation order
- can compute dot product in one step, then accumulation in another, or
- accumulate first product in one step, then accumulate second product in
another step
- fusion, the steps described above can be both fused or both unfused
- the intermediate results can be Round-to-Nearest-Even or Round-to-Odd.


## Binary format

Expand All @@ -290,30 +316,30 @@ where chosen to fit into the holes in the opcode space of SIMD proposal. Going
forward, the opcodes for relaxed-simd specification will be the ones in the
"opcode" column, and it will take some time for tools and engines to update.

| instruction | opcode | prototype opcode |
| ---------------------------------- | -------------- | ---------------- |
| `i8x16.relaxed_swizzle` | 0x100 | 0xa2 |
| `i32x4.relaxed_trunc_f32x4_s` | 0x101 | 0xa5 |
| `i32x4.relaxed_trunc_f32x4_u` | 0x102 | 0xa6 |
| `i32x4.relaxed_trunc_f64x2_s_zero` | 0x103 | 0xc5 |
| `i32x4.relaxed_trunc_f64x2_u_zero` | 0x104 | 0xc6 |
| `f32x4.relaxed_fma` | 0x105 | 0xaf |
| `f32x4.relaxed_fms` | 0x106 | 0xb0 |
| `f64x2.relaxed_fma` | 0x107 | 0xcf |
| `f64x2.relaxed_fms` | 0x108 | 0xd0 |
| `i8x16.relaxed_laneselect` | 0x109 | 0xb2 |
| `i16x8.relaxed_laneselect` | 0x10a | 0xb3 |
| `i32x4.relaxed_laneselect` | 0x10b | 0xd2 |
| `i64x2.relaxed_laneselect` | 0x10c | 0xd3 |
| `f32x4.relaxed_min` | 0x10d | 0xb4 |
| `f32x4.relaxed_max` | 0x10e | 0xe2 |
| `f64x2.relaxed_min` | 0x10f | 0xd4 |
| `f64x2.relaxed_max` | 0x110 | 0xee |
| `i16x8.relaxed_q15mulr_s` | 0x111 | unimplemented |
| `i16x8.dot_i8x16_i7x16_s` | 0x112 | unimplemented |
| `i32x4.dot_i8x16_i7x16_add_s` | 0x113 | unimplemented |
| Reserved for bfloat16 | 0x114 | unimplemented |
| Reserved | 0x115 - 0x12F | |
| instruction | opcode | prototype opcode |
| ------------------------------------ | -------------- | ---------------- |
| `i8x16.relaxed_swizzle` | 0x100 | 0xa2 |
| `i32x4.relaxed_trunc_f32x4_s` | 0x101 | 0xa5 |
| `i32x4.relaxed_trunc_f32x4_u` | 0x102 | 0xa6 |
| `i32x4.relaxed_trunc_f64x2_s_zero` | 0x103 | 0xc5 |
| `i32x4.relaxed_trunc_f64x2_u_zero` | 0x104 | 0xc6 |
| `f32x4.relaxed_fma` | 0x105 | 0xaf |
| `f32x4.relaxed_fms` | 0x106 | 0xb0 |
| `f64x2.relaxed_fma` | 0x107 | 0xcf |
| `f64x2.relaxed_fms` | 0x108 | 0xd0 |
| `i8x16.relaxed_laneselect` | 0x109 | 0xb2 |
| `i16x8.relaxed_laneselect` | 0x10a | 0xb3 |
| `i32x4.relaxed_laneselect` | 0x10b | 0xd2 |
| `i64x2.relaxed_laneselect` | 0x10c | 0xd3 |
| `f32x4.relaxed_min` | 0x10d | 0xb4 |
| `f32x4.relaxed_max` | 0x10e | 0xe2 |
| `f64x2.relaxed_min` | 0x10f | 0xd4 |
| `f64x2.relaxed_max` | 0x110 | 0xee |
| `i16x8.relaxed_q15mulr_s` | 0x111 | unimplemented |
| `i16x8.dot_i8x16_i7x16_s` | 0x112 | unimplemented |
| `i32x4.dot_i8x16_i7x16_add_s` | 0x113 | unimplemented |
| `f32x4.relaxed_dot_bf16x8_add_f32x4` | 0x114 | unimplemented |
| Reserved | 0x115 - 0x12F | |

## References

Expand Down