Arithmetic Operators

The following table lists the arithmetic operators of the Fvec classes and generic syntax. The operators have been divided into standard and advanced operations, which are described in more detail later in this section.

Fvec Arithmetic Operators

Category	Operation	Operators	Generic Syntax
Standard	Addition	+ +=	`R = A + B;` `R += A;`
	Subtraction	- -=	`R = A - B;` `R -= A;`
	Multiplication	* *=	`R = A * B;` `R *= A;`
	Division	/ /=	`R = A / B;` `R /= A;`
Advanced	Square Root	sqrt	`R = sqrt(A);`
	Reciprocal (Newton-Raphson)	rcp rcp_nr	`R = rcp(A);` `R = rcp_nr(A);`
	Reciprocal Square Root (Newton-Raphson)	rsqrt rsqrt_nr	`R = rsqrt(A);` `R = rsqrt_nr(A);`

Standard Arithmetic Operator Usage

The following two tables show the return values for each class of the standard arithmetic operators, which use the syntax styles described earlier in the Return Value Notation section.

Standard Arithmetic Return Value Mapping

R	A	Operators				B	F32vec4	F64vec2	F32vec1
R0:=	A0	+	-	*	/	B0	X	X	X
R1:=	A1	+	-	*	/	B1	X	X	N/A
R2:=	A2	+	-	*	/	B2	X	N/A	N/A
R3:=	A3	+	-	*	/	B3	X	N/A	N/A

Arithmetic with Assignment Return Value Mapping

R	Operators				A	F32vec4	F64vec2	F32vec1
R0:=	+=	-=	*=	/=	A0	X	X	X
R1:=	+=	-=	*=	/=	A1	X	X	N/A
R2:=	+=	-=	*=	/=	A2	X	N/A	N/A
R3:=	+=	-=	*=	/=	A3	X	N/A	N/A

This table lists standard arithmetic operator syntax and intrinsics.

Standard Arithmetic Operations for Fvec Classes

Operation	Returns	Example Syntax Usage	Intrinsic
Addition	4 floats	`F32vec4 R = F32vec4 A + F32vec4 B;` `F32vec4 R += F32vec4 A;`	_mm_add_ps
	2 doubles	`F64vec2 R = F64vec2 A + F32vec2 B;` `F64vec2 R += F64vec2 A;`	_mm_add_pd
	1 float	`F32vec1 R = F32vec1 A + F32vec1 B;` `F32vec1 R += F32vec1 A;`	_mm_add_ss
Subtraction	4 floats	`F32vec4 R = F32vec4 A - F32vec4 B;` `F32vec4 R -= F32vec4 A;`	_mm_sub_ps
	2 doubles	`F64vec2 R - F64vec2 A + F32vec2 B;` `F64vec2 R -= F64vec2 A;`	_mm_sub_pd
	1 float	`F32vec1 R = F32vec1 A - F32vec1 B;` `F32vec1 R -= F32vec1 A;`	_mm_sub_ss
Multiplication	4 floats	`F32vec4 R = F32vec4 A * F32vec4 B;` `F32vec4 R *= F32vec4 A;`	_mm_mul_ps
	2 doubles	`F64vec2 R = F64vec2 A * F364vec2 B;` `F64vec2 R *= F64vec2 A;`	_mm_mul_pd
	1 float	`F32vec1 R = F32vec1 A * F32vec1 B;` `F32vec1 R *= F32vec1 A;`	_mm_mul_ss
Division	4 floats	`F32vec4 R = F32vec4 A / F32vec4 B;` `F32vec4 R /= F32vec4 A;`	_mm_div_ps
	2 doubles	`F64vec2 R = F64vec2 A / F64vec2 B;` `F64vec2 R /= F64vec2 A;`	_mm_div_pd
	1 float	`F32vec1 R = F32vec1 A / F32vec1 B;` `F32vec1 R /= F32vec1 A;`	_mm_div_ss

Advanced Arithmetic Operator Usage

The following table shows the return values classes of the advanced arithmetic operators, which use the syntax styles described earlier in the Return Value Notation section.

Advanced Arithmetic Return Value Mapping

R	Operators					A	F32vec4	F64vec2	F32vec1
R0:=	sqrt	rcp	rsqrt	rcp_nr	rsqrt_nr	A0	X	X	X
R1:=	sqrt	rcp	rsqrt	rcp_nr	rsqrt_nr	A1	X	X	N/A
R2:=	sqrt	rcp	rsqrt	rcp_nr	rsqrt_nr	A2	X	N/A	N/A
R3:=	sqrt	rcp	rsqrt	rcp_nr	rsqrt_nr	A3	X	N/A	N/A
`f :=`	add_horizontal			`(A0 + A1 + A2 + A3)`			X	N/A	N/A
d :=	add_horizontal			`(A0 + A1)`			N/A	X	N/A

This table shows examples for advanced arithmetic operators.

Advanced Arithmetic Operations for Fvec Classes

Returns	Example Syntax Usage	Intrinsic
Square Root
4 floats	`F32vec4 R = sqrt(F32vec4 A);`	_mm_sqrt_ps
2 doubles	`F64vec2 R = sqrt(F64vec2 A);`	_mm_sqrt_pd
1 float	`F32vec1 R = sqrt(F32vec1 A);`	_mm_sqrt_ss

Reciprocal
4 floats	`F32vec4 R = rcp(F32vec4 A);`	_mm_rcp_ps
2 doubles	`F64vec2 R = rcp(F64vec2 A);`	_mm_rcp_pd
1 float	`F32vec1 R = rcp(F32vec1 A);`	_mm_rcp_ss

Reciprocal Square Root
4 floats	`F32vec4 R = rsqrt(F32vec4 A);`	_mm_rsqrt_ps
2 doubles	`F64vec2 R = rsqrt(F64vec2 A);`	_mm_rsqrt_pd
1 float	`F32vec1 R = rsqrt(F32vec1 A);`	_mm_rsqrt_ss

Reciprocal Newton Raphson
4 floats	`F32vec4 R = rcp_nr(F32vec4 A);`	_mm_sub_ps _mm_add_ps _mm_mul_ps _mm_rcp_ps
2 doubles	`F64vec2 R = rcp_nr(F64vec2 A);`	_mm_sub_pd _mm_add_pd _mm_mul_pd _mm_rcp_pd
1 float	`F32vec1 R = rcp_nr(F32vec1 A);`	_mm_sub_ss _mm_add_ss _mm_mul_ss _mm_rcp_ss

Reciprocal Square Root Newton Raphson
4 float	`F32vec4 R = rsqrt_nr(F32vec4 A);`	_mm_sub_pd _mm_mul_pd _mm_rsqrt_ps
2 doubles	`F64vec2 R = rsqrt_nr(F64vec2 A);`	_mm_sub_pd _mm_mul_pd _mm_rsqrt_pd
1 float	`F32vec1 R = rsqrt_nr(F32vec1 A);`	_mm_sub_ss _mm_mul_ss _mm_rsqrt_ss

Horizontal Add
1 float	`float f = add_horizontal(F32vec4 A);`	_mm_add_ss _mm_shuffle_ss
1 double	`double d = add_horizontal(F64vec2 A);`	_mm_add_sd _mm_shuffle_sd