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fnormal

floating-point normalization

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

fnormal(e)

fnormal(e, digits)

fnormal(e, digits, epsilon)

Parameters

e

-

algebraic expression, or a list, set, relation, series, or range of algebraic expressions

digits

-

(optional) number of digits for floating-point evaluation (defaults to the value of the global variable Digits)

epsilon

-

(optional) error tolerance for ``fuzzy zero'' (defaults to the value Float(1,-digits+2))

Description

• 

The value returned by fnormal is an expression equivalent to e under the assumption that all numeric values with magnitude less than epsilon may be considered to be zero.

• 

In addition, all floats in e which remain nonzero are converted to floats with digits precision.

• 

fnormal preserves numeric type and sign information as much as possible.  Thus, for example, fnormal(1e-20*I, 10) = 0.*I not 0. .  This ensures that branching behavior is generally not affected by fnormal.  Use simplify(expr, zero) to remove 0 real or imaginary parts of complex floating point numbers.

• 

If e is a list, set, range, series, equation, or relation, then fnormal is applied recursively to the components of e.

Examples

fnormal1.10-10

0.

(1)

fnormal1+1.10-10I

1.+0.I

(2)

fnormal1010,109,108

0.,0.,1100000000

(3)

e2x2+0.00001xπ

e:=2x2+0.00001xπ

(4)

fnormale

2x2+0.00001xπ

(5)

fnormale,4

2x23.141592654

(6)

fevalfe

f:=2.x2+0.00001x3.141592654

(7)

fnormalf,4

2.x23.142

(8)

ln1.1.10-15I,lnfnormal1.1.10-15I,10,lnsimplifyfnormal1.1.10-15I,10,zero

5.10-313.141592654I,0.3.141592654I,0.+3.141592654I

(9)

See Also

evalf

evalhf

simplify/zero

type/embedded_axis

 


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