Acosh¶

Overview¶

The Acosh expression computes the inverse hyperbolic cosine (hyperbolic arccosine) of a numeric value. It implements the mathematical function acosh(x) = ln(x + √(x² - 1)) for input values x ≥ 1, returning NaN for invalid inputs.

Syntax¶

ACOSH(expr)

// DataFrame API
import org.apache.spark.sql.functions._
df.select(acosh(col("value")))

Arguments¶

Argument	Type	Description
expr	Numeric	The input expression for which to calculate the inverse hyperbolic cosine

Return Type¶

Double - Returns a double-precision floating-point number representing the inverse hyperbolic cosine.

Supported Data Types¶

All numeric types (Int, Long, Float, Double, Decimal)
Input values are cast to Double for computation

Algorithm¶

Accepts a single numeric expression as input (child)
Applies the mathematical formula: ln(x + √(x² - 1))
Uses StrictMath.log() for logarithmic computation and Math.sqrt() for square root
Returns NaN for inputs less than 1.0 (mathematically undefined domain)
Inherits standard null propagation from UnaryMathExpression

Partitioning Behavior¶

How this expression affects partitioning:

Preserves partitioning as it's a deterministic unary transformation
Does not require shuffle operations
Can be pushed down to individual partitions

Edge Cases¶

Returns NaN for null inputs (standard null propagation)
Returns NaN for inputs < 1.0 (outside mathematical domain)
Returns 0.0 for input value 1.0 (acosh(1) = 0)
Returns positive infinity for positive infinity input
Handles negative infinity and negative values by returning NaN

Code Generation¶

This expression supports Tungsten code generation with a custom doGenCode implementation that generates efficient Java code using StrictMath.log() and Math.sqrt() operations directly in the generated bytecode.

Examples¶

-- Basic usage
SELECT ACOSH(1.0);    -- Returns 0.0
SELECT ACOSH(2.0);    -- Returns ~1.317
SELECT ACOSH(0.5);    -- Returns NaN
SELECT ACOSH(NULL);   -- Returns NULL

-- With table data
SELECT value, ACOSH(value) as acosh_value 
FROM VALUES (1.0), (2.0), (5.0) AS t(value);

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

// Basic computation
df.select(acosh(col("measurement")))

// With column alias
df.select(acosh(col("input")).alias("acosh_result"))

// Combined with other expressions
df.select(col("id"), acosh(col("value") + 1))