add

add(x1: array, x2: array, /) → array

Calculates the sum for each element x1_i of the input array x1 with the respective element x2_i of the input array x2.

Special cases

For floating-point operands,

  • If either x1_i or x2_i is NaN, the result is NaN.

  • If x1_i is +infinity and x2_i is -infinity, the result is NaN.

  • If x1_i is -infinity and x2_i is +infinity, the result is NaN.

  • If x1_i is +infinity and x2_i is +infinity, the result is +infinity.

  • If x1_i is -infinity and x2_i is -infinity, the result is -infinity.

  • If x1_i is +infinity and x2_i is a finite number, the result is +infinity.

  • If x1_i is -infinity and x2_i is a finite number, the result is -infinity.

  • If x1_i is a finite number and x2_i is +infinity, the result is +infinity.

  • If x1_i is a finite number and x2_i is -infinity, the result is -infinity.

  • If x1_i is -0 and x2_i is -0, the result is -0.

  • If x1_i is -0 and x2_i is +0, the result is +0.

  • If x1_i is +0 and x2_i is -0, the result is +0.

  • If x1_i is +0 and x2_i is +0, the result is +0.

  • If x1_i is either +0 or -0 and x2_i is a nonzero finite number, the result is x2_i.

  • If x1_i is a nonzero finite number and x2_i is either +0 or -0, the result is x1_i.

  • If x1_i is a nonzero finite number and x2_i is -x1_i, the result is +0.

  • In the remaining cases, when neither infinity, +0, -0, nor a NaN is involved, and the operands have the same mathematical sign or have different magnitudes, the sum must be computed and rounded to the nearest representable value according to IEEE 754-2019 and a supported round mode. If the magnitude is too large to represent, the operation overflows and the result is an infinity of appropriate mathematical sign.

Note

Floating-point addition is a commutative operation, but not always associative.

Parameters:

  • x1 (array) – first input array. Should have a numeric data type.

  • x2 (array) – second input array. Must be compatible with x1 (see Broadcasting). Should have a numeric data type.

Returns:

out (array) – an array containing the element-wise sums. The returned array must have a data type determined by Type Promotion Rules.