cosh function

Synopsis

$cosh(number)

Technical

Returns the hyperbolic cosine of number, equivalent mathematically to (exp(number) + exp(-number)) / 2. Every finite real number is in its domain; successful real results are at least 1. The corresponding principal inverse is acosh().

The normal rules about number arguments apply. The first argument word is converted with atof(), accepting decimal fractions and scientific notation; additional words are ignored. Missing input returns an empty string. Nonnumeric input converts to zero, and a numeric prefix can be accepted even when followed by nonnumeric text.

Returns and restrictions

The calculation uses the C library's cosh() and a C double. Results are formatted with %.50g, not limited to six decimal places. The floating_point_math and floating_point_precision settings do not change the calculation or formatting. Extra displayed digits do not imply 50 digits of accuracy.

Large-magnitude finite inputs can overflow. EPIC returns RANGE if the library reports the overflow through errno; platforms that report it only through floating-point exception flags can instead return the library's overflow value, commonly infinity. Positive or negative infinite input produces positive infinity, and NaN input ordinarily produces NaN. The shared wrapper returns DOM for a reported domain error and an empty string for another reported error. It checks errno, not floating-point exception flags, and clears errno after argument conversion and before calculating the hyperbolic cosine.

Examples

The approximate examples describe numeric values; the returned strings may contain more digits.

Source

source/functions.c registers cosh and implements it through the shared math-function and error-return macros. include/functions.h defines argument conversion and formatting. The C/POSIX hyperbolic cosine specification defines special inputs, overflow, and library error reporting.