# 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
+=
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
R1:= A1 + - * / B1     N/A
R2:= A2 + - * / B2   N/A N/A
R3:= A3 + - * / B3   N/A N/A

### Arithmetic with Assignment Return Value Mapping

R Operators A F32vec4 F64vec2 F32vec1
R0:= += -= *= /= A0
R1:= += -= *= /= A1     N/A
R2:= += -= *= /= A2   N/A N/A
R3:= += -= *= /= A3   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;
2 doubles F64vec2 R = F64vec2 A + F32vec2 B;
F64vec2 R += F64vec2 A;
1 float F32vec1 R = F32vec1 A + F32vec1 B;
F32vec1 R += F32vec1 A;
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

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
R1:= sqrt rcp rsqrt rcp_nr rsqrt_nr A1     N/A
R2:= sqrt rcp rsqrt rcp_nr rsqrt_nr A2   N/A N/A
R3:= sqrt rcp rsqrt rcp_nr rsqrt_nr A3   N/A N/A
f := add_horizontal     (A0 + A1 + A2 + A3)       N/A N/A
d := add_horizontal     (A0 + A1)     N/A   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_mul_ps
_mm_rcp_ps
2 doubles F64vec2 R = rcp_nr(F64vec2 A); _mm_sub_pd
_mm_mul_pd
_mm_rcp_pd
1 float F32vec1 R = rcp_nr(F32vec1 A); _mm_sub_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