Modern Math CAbs

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CAbs

Returns the modulus, the distance from zero, without overflowing for large parts.

Syntax

CAbs( byref z as Complex ) as float64

Notes

• Factors out the larger component, so it does not overflow for operands near the type maximum where the naive sqr( x*x + y*y ) does. Identical in .NET and in AfxNova, and worth keeping.
• An infinite component makes the whole modulus infinite, NaN or not.
• For comparisons use CNorm instead: CAbs(a) < CAbs(b) costs two square roots for a question that needs none.
• vector.tiko used to spell this AbsValue. AfxNova spelled it CAbs, CMagnitude, CModulus and CMod; one name survives here.

Examples

#import "std/numeric"
using numeric

dim as Complex big_ = CSet( 1e200, 1e200 )

print CAbs( CSet( 3, 4 ) )                   '' 5   -- exact: the 3-4-5 triangle
print CAbs( big_ )                           '' 1.414213562373095e+200   -- the scaled form survives
print big_.re * big_.re + big_.im * big_.im  '' 1.#INF   -- the naive one does not
print CAbs( CSet( Infinity( ), 1.0 ) )       '' 1.#INF   -- one infinite part is enough

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