Csc¶

Overview¶

The Csc expression calculates the cosecant of a numeric value. It returns the reciprocal of the sine function, mathematically equivalent to 1/sin(x), where x is the input value in radians.

Syntax¶

CSC(expr)

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

Arguments¶

Argument	Type	Description
child	Expression	The numeric expression to calculate the cosecant of (value in radians)

Return Type¶

DoubleType - Returns a double-precision floating-point number.

Supported Data Types¶

Numeric types (INT, LONG, FLOAT, DOUBLE, DECIMAL)
Any expression that can be implicitly cast to DOUBLE

Algorithm¶

Takes the input expression and evaluates it as a double value
Calculates the sine of the input value using math.sin(x)
Returns the reciprocal (1 / sin(x)) as the cosecant result
Leverages Java's Math.sin() function for the underlying sine calculation
Uses Spark's UnaryMathExpression framework for consistent null handling and type coercion

Partitioning Behavior¶

How this expression affects partitioning:

Preserves partitioning as it operates on individual rows without requiring data movement
Does not require shuffle operations
Can be pushed down to individual partitions for parallel execution

Edge Cases¶

Null handling: Returns null if the input expression evaluates to null
Zero and multiples of π: Returns positive or negative infinity when sin(x) equals zero (x = 0, π, 2π, etc.)
NaN input: Returns NaN (Not a Number) if input is NaN
Infinite input: Returns NaN if input is positive or negative infinity
Domain considerations: While mathematically defined for all real numbers except multiples of π, floating-point precision may cause unexpected results near these values

Code Generation¶

This expression supports Tungsten code generation for optimized performance. The doGenCode method generates Java code that directly calls java.lang.Math.sin() and computes the reciprocal, avoiding the overhead of interpreted execution.

Examples¶

-- Calculate cosecant of 1 radian
SELECT CSC(1);
-- Result: 1.1883951057781212

-- Calculate cosecant of π/2 (which equals 1)
SELECT CSC(PI()/2);
-- Result: 1.0

-- Handle null input
SELECT CSC(NULL);
-- Result: NULL

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

// Calculate cosecant of a column
df.select(expr("CSC(angle_column)"))

// Using with literal values
df.select(expr("CSC(1.0)").alias("csc_result"))

// Chaining with other math functions
df.select(expr("CSC(RADIANS(degrees_column))").alias("csc_from_degrees"))