IMCOSH

What it does

IMCOSH(inumber)

IMCOSH(inumber) returns the complex hyperbolic cosine. Real and imaginary coefficients use radians where a circular angle is involved. A pure imaginary input has the real cosine as its mathematical result.

Try it

=IMCOSH("i") gives real text about "0.54030230586814", since the mathematical value is cos(1). =IMCOSH("0") returns "1". The pure imaginary example distinguishes hyperbolic cosine from IMCOS.

Quirks

The result is text, including for a real-only answer. Malformed complex text gives #NUM! in the current parser and a logical argument gives #VALUE! in the wrapper.

On the real axis the current direct function applies the public EXP overflow domain to abs(real), then calls the runtime hyperbolic primitive. It explicitly keeps the imaginary coordinate zero. IMSECH, its reciprocal companion, retains a wider runtime route, so computing the reciprocal of a separately formatted IMCOSH result need not reproduce it at the domain edge.

How to implement

Parse the two coefficients and suffix before doing arithmetic; use the common complex formatter afterward. Retain suffix consistency, suppress a zero component and omit the coefficient one before the imaginary unit. Formatting and parsing have their own fifteen-significant-digit rules, so testing only the algebra misses observable behaviour.

For z=a+bi, the mathematical component formula is cosh(a)*cos(b) + i*sinh(a)*sin(b). The current real-axis direct hyperbolic route enforces the exponential overflow domain and avoids an infinity-times-zero imaginary component. The formula is a derivation aid; the named runtime leaves and stores in the current source define its implementation candidate. Validate text output as well as numeric components, and keep unmeasured rounding stages open.

Rust code

37 imcosh "IMCOSH" (1, 1) [V "inumber"] |s, a, sv| { unary_complex(s, a, |z| { z.check_real_hyperbolic_domain()?; Ok(z.cosh()) }) }

No implementation has been published with a Handbook test suite for this function.

Version differences

The recorded environments below distinguish a reading from a same-input comparison. Counts describe captured inputs in each environment; overlapping captures and comparisons are not totals of unique worksheet calls.

The record contains no same-input comparison between these environments. Reading different inputs on different builds does not establish either a version change or cross-build agreement.

Recorded environments and comparison details.

Alternatives

IMSECH is the reciprocal hyperbolic function. IMCOS and IMSIN are the circular companions. COMPLEX constructs an input from two numeric coefficients.

Named variants

No named variants are recorded yet.