Type Promotion

For operations that involve two (or more) input arguments, kernel_float will first convert the inputs into a common type before applying the operation. For example, when adding vec<int, N> to vec<float, N>, both arguments must first be converted into a vec<float, N>.

This procedure is called “type promotion” and is implemented as follows. Initially, every argument is transformed into a vector using the into_vec function Next, all arguments must have length N or length 1, where vectors of length 1 are repeated to become length N. Finally, the vector element types are promoted into a shared type.

The rules for element type promotion in kernel_float are slightly different than in regular C++. In a nutshell, for two element types, the promotion rules can be summarized as follows:

If one of the types is bool, the result is the other type.
If one type is a floating-point and the other is an integer (signed or unsigned), the outcome is the floating-point type.
If both are floating-point types, the largest of the two is chosen. An exception is combining half and bfloat16, which results in float.
If both types are integer types of the same signedness, the largest of the two is chosen.
Combining a signed integer and unsigned integer type is not allowed.

Overview

The type promotion rules are shown in the table below. The labels are as follows:

b: boolean
iN: signed integer of N bits (e.g., int, long)
uN: unsigned integer of N bits (e.g., unsigned int, size_t)
fN: floating-point type of N bits (e.g., float, double)
bf16: bfloat16 floating-point format.

Type Promotion Rules.
	b	i8	i16	i32	i64	u8	u16	u32	u64	f8	f16	bf16	f32	f64
b	b	i8	i16	i32	i64	u8	u16	u32	u64	f8	f16	bf16	f32	f64
i8	i8	i8	i16	i32	i64	x	x	x	x	f8	f16	bf16	f32	f64
i16	i16	i16	i16	i32	i64	x	x	x	x	f8	f16	bf16	f32	f64
i32	i32	i32	i32	i32	i64	x	x	x	x	f8	f16	bf16	f32	f64
i64	i64	i64	i64	i64	i64	x	x	x	x	f8	f16	bf16	f32	f64
u8	u8	x	x	x	x	u8	u16	u32	u64	f8	f16	bf16	f32	f64
u16	u16	x	x	x	x	u16	u16	u32	u64	f8	f16	bf16	f32	f64
u32	u32	x	x	x	x	u32	u32	u32	u64	f8	f16	bf16	f32	f64
u64	u64	x	x	x	x	u64	u64	u64	u64	f8	f16	bf16	f32	f64
f8	f8	f8	f8	f8	f8	f8	f8	f8	f8	f8	f16	bf16	f32	f64
f16	f16	f16	f16	f16	f16	f16	f16	f16	f16	f16	f16	f32	f32	f64
bf16	bf16	bf16	bf16	bf16	bf16	bf16	bf16	bf16	bf16	bf16	f32	bf16	f32	f64
f32	f32	f32	f32	f32	f32	f32	f32	f32	f32	f32	f32	f32	f32	f64
f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64	f64