Sec¶

Overview¶

The Sec expression computes the secant of a numeric value. The secant function is defined as the reciprocal of the cosine function (1/cos(x)), where the input is expected to be in radians.

Syntax¶

SEC(expr)

// DataFrame API
import org.apache.spark.sql.functions._
df.select(expr("sec(column_name)"))

Arguments¶

Argument	Type	Description
child	Expression	A numeric expression representing the angle in radians

Return Type¶

Returns a DoubleType value representing the secant of the input.

Supported Data Types¶

Numeric types (converted to Double internally)
Any expression that can be cast to a numeric value

Algorithm¶

Takes the input numeric value as an angle in radians
Computes the cosine of the input using math.cos(x)
Returns the reciprocal (1/cosine) to get the secant value
Uses standard Java Math library functions for the underlying calculation
Supports Catalyst code generation for optimized execution

Partitioning Behavior¶

This expression preserves partitioning behavior:

Does not require data shuffle
Operates on individual rows independently
Maintains existing data partitioning scheme

Edge Cases¶

Returns null when input is null
Returns Double.POSITIVE_INFINITY or Double.NEGATIVE_INFINITY when cosine of input equals zero (at π/2 + nπ)
Input values that cause cosine to be very close to zero may result in very large values
NaN input produces NaN output

Code Generation¶

This expression supports Tungsten code generation through the doGenCode method, which generates optimized Java code using java.lang.Math.cos() for better performance in tight loops.

Examples¶

-- Basic usage
SELECT SEC(0);
-- Result: 1.0

-- Using with column data
SELECT SEC(angle_column) FROM trigonometry_table;

-- Using with mathematical constants
SELECT SEC(PI()/3);
-- Result: 2.0 (secant of 60 degrees)

// DataFrame API usage
import org.apache.spark.sql.functions._

val df = spark.range(1).select(lit(0).as("angle"))
df.select(expr("sec(angle)")).show()

// Using with existing columns
val trigDF = spark.table("angles_table")
trigDF.select(col("*"), expr("sec(radians)").as("secant_value"))