Inside Macintosh: PowerPC Numerics / Part 3 - Appendixes

Appendix E - MathLib Reference

Floating-Point Data Formats

Figure E-1

Table E-1 Interpreting floating-point values

If biased exponent e is:	And fraction f is:	Then value v is:	And class of v is:
	(any)	$v\; =\; (-1)s\times 2(e+-bias)\times (1.f)$ [73]	FP_NORMAL
$e\; =\; 0$	$f$ 0	$v\; =\; (-1)s\times 2minexp\times (0.f)$ [74]	FP_SUBNORMAL
$e\; =\; 0$	$f\; =\; 0$	$v\; =\; (-1)s\times 0$	FP_ZERO
$e\; =\; max$	$f\; =\; 0$	$v\; =\; (-1)s\times$	FP_INFINITE
$e\; =\; max$	$f$ 0	$v\; =\; NaN$	FP_SNAN (first bit is 0) FP_QNAN (first bit is 1)

Table E-2 Class and sign inquiry macros

fpclassify(x)

isnormal(x)

isfinite(x)

isnan(x)

signbit(x)

Floating-point data formats

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[72] max = 255 for float; 2047 for double and long double.

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[73] For long double both head and tail are evaluated this way and added together.

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[74] minexp = -126 for float; -1022 for double and long double.