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Mar 28, 2022
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Add dot product to overview #69

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85 changes: 62 additions & 23 deletions proposals/relaxed-simd/Overview.md
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Original file line number Diff line number Diff line change
Expand Up @@ -248,6 +248,42 @@ def q15mulr(a, b):
return result
```

### Relaxed integer dot product

- `i16x8.dot_i8x16_i7x16_s(a: v128, b: v128) -> v128`
- `i16x8.dot_i8x16_i7x16_u(a: v128, b: v128) -> v128`
- `i32x4.dot_i8x16_i7x16_add_s(a: v128, b:v128, c:v128) -> v128`
- `i32x4.dot_i8x16_i7x16_add_u(a: v128, b:v128, c:v128) -> v128`

Returns the multiplication of 8-bit elements (signed or unsigned) by 7-bit
elements (unsigned) with accumulation of adjacent products. The `i32x4` versions
allows for accumulation into another vector.

When the second operand of the product has the high bit set in a lane, that
lane's result is implementation defined.

```python
def dot_product(signed, elements, a, b, c):
intermediate = []
result = []
for i in range(16):
if (b[i] & 0x80):
lhs = as_signed(a[i]) if signed else a[i]
rhs = IMPLEMENTATION_DEFINED_ONE_OF(as_signed(b[i]), b[i])
intermediate[i] = lhs + rhs
else:
intermediate[i] = (as_signed(a[i]) if signed else a[i]) * b[i]
for i in range(0, 16, elements):
result[i/elements] == sum(intermediate[i:i+elements])
result[i/elements] += c[i/elements] if c else 0

i16x8_dot_i8x16_i7x16_s(a, b) = dot_product(signed=True, elements=2, a, b)
i16x8_dot_i8x16_i7x16_u(a, b) = dot_product(signed=False, elements=2, a, b)
i32x4.dot_i8x16_i7x16_add_s(a, b, c) = dot_product(signed=True, elements=4, a, b, c)
i32x4.dot_i8x16_i7x16_add_s(a, b, c) = dot_product(signed=False, elements=4, a, b, c)
```


## Binary format

All opcodes have the `0xfd` prefix (same as SIMD proposal), which are omitted in the table below.
Expand All @@ -258,29 +294,32 @@ 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 |
| Reserved for dot product | 0x112 - 0x115 | unimplemented |
| Reserved for bfloat16 dot product | 0x116 | unimplemented |
| Reserved | 0x117 - 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 |
| `i16x8.dot_i8x16_i7x16_u` | 0x113 | unimplemented |
| `i32x4.dot_i8x16_i7x16_add_s` | 0x114 | unimplemented |
| `i32x4.dot_i8x16_i7x16_add_u` | 0x115 | unimplemented |
| Reserved for bfloat16 | 0x116 | unimplemented |
| Reserved | 0x117 - 0x12F | |

## References

Expand Down