Modern Math CTan

Home › Math Library › Math Library › CTan

CTan

Returns the tangent of a complex number, finite even for a large imaginary part.

Syntax

CTan( byref z as Complex ) as Complex

Notes

• The stabilised form, from .NET. CSin( z ) / CCos( z ) is inf/inf — that is, NaN — for an imaginary part above about 710, because cosh overflows there while the tangent itself is heading calmly for ±i. This uses the double-angle identity, and above |im| = 4 divides through by cosh so that neither operand can overflow.
• Both axes are answered directly, which is both exact and correct about the sign of a zero: CTan( 1 - 0i ) is tan(1) - 0i, and the general path gives the last digit of tan(1) wrong and the zero the wrong sign.
• Spelled with the C prefix because, when this library was a header in namespace FB, a function of the unprefixed name shadowed the intrinsic for every later header — measured, it broke what is now random.tiko — after which the intrinsic could not be called back. The name stayed when the header became std/numeric.

Examples

#import "std/numeric"
using numeric

dim as Complex z = CSet( 3, 4 )

print CToString( CTan( z ) )                                     '' -0.00018734620462947842+0.9993559873814732i
print CToString( CTan( CSet( 1, 750 ) ) )                        '' 0+1i   -- still finite -- heading for i
print CIsNaN( CSin( CSet( 1, 750 ) ) / CCos( CSet( 1, 750 ) ) )  '' true   -- the naive route, for comparison
print CToString( CTan( CSet( 1, 0 ) ) )                          '' 1.5574077246549023+0i   -- exactly the real tangent

---

Library: Math Library
Category: Math Library
Documented under: Members