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std.math.traits

This is a submodule of std.math.

It contains several functions for introspection on numerical values.

License:

Boost License 1.0.

Authors:

Walter Bright, Don Clugston, Conversion of CEPHES math library to D by Iain Buclaw and David Nadlinger

Source std/math/traits.d

pure nothrow @nogc @trusted bool isNaN(X)(X x) if (isFloatingPoint!X);

Determines if x is NaN.

Parameters:

X x a floating point number.

Returns:

true if x is Nan.

Examples:

assert( isNaN(float.init));
assert( isNaN(-double.init));
assert( isNaN(real.nan));
assert( isNaN(-real.nan));
assert(!isNaN(cast(float) 53.6));
assert(!isNaN(cast(real)-53.6));

pure nothrow @nogc @trusted bool isFinite(X)(X x);

Determines if x is finite.

Parameters:

X x a floating point number.

Returns:

true if x is finite.

Examples:

assert( isFinite(1.23f));
assert( isFinite(float.max));
assert( isFinite(float.min_normal));
assert(!isFinite(float.nan));
assert(!isFinite(float.infinity));

pure nothrow @nogc @trusted bool isNormal(X)(X x);

Determines if x is normalized.

A normalized number must not be zero, subnormal, infinite nor NAN.

Parameters:

X x a floating point number.

Returns:

true if x is normalized.

Examples:

float f = 3;
double d = 500;
real e = 10e+48;

assert(isNormal(f));
assert(isNormal(d));
assert(isNormal(e));
f = d = e = 0;
assert(!isNormal(f));
assert(!isNormal(d));
assert(!isNormal(e));
assert(!isNormal(real.infinity));
assert(isNormal(-real.max));
assert(!isNormal(real.min_normal/4));

pure nothrow @nogc @trusted bool isSubnormal(X)(X x);

Determines if x is subnormal.

Subnormals (also known as "denormal number"), have a 0 exponent and a 0 most significant mantissa bit.

Parameters:

X x a floating point number.

Returns:

true if x is a denormal number.

Examples:

import std.meta : AliasSeq;

static foreach (T; AliasSeq!(float, double, real))
{{
    T f;
    for (f = 1.0; !isSubnormal(f); f /= 2)
        assert(f != 0);
}}

pure nothrow @nogc @trusted bool isInfinity(X)(X x) if (isFloatingPoint!X);

Determines if x is ±∞.

Parameters:

X x a floating point number.

Returns:

true if x is ±∞.

Examples:

assert(!isInfinity(float.init));
assert(!isInfinity(-float.init));
assert(!isInfinity(float.nan));
assert(!isInfinity(-float.nan));
assert(isInfinity(float.infinity));
assert(isInfinity(-float.infinity));
assert(isInfinity(-1.0f / 0.0f));

pure nothrow @nogc @trusted bool isIdentical(real x, real y);

Is the binary representation of x identical to y?

Examples:

assert( isIdentical(0.0, 0.0));
assert( isIdentical(1.0, 1.0));
assert( isIdentical(real.infinity, real.infinity));
assert( isIdentical(-real.infinity, -real.infinity));

assert(!isIdentical(0.0, -0.0));
assert(!isIdentical(real.nan, -real.nan));
assert(!isIdentical(real.infinity, -real.infinity));

pure nothrow @nogc @trusted int signbit(X)(X x);

Return 1 if sign bit of e is set, 0 if not.

Examples:

assert(!signbit(float.nan));
assert(signbit(-float.nan));
assert(!signbit(168.1234f));
assert(signbit(-168.1234f));
assert(!signbit(0.0f));
assert(signbit(-0.0f));
assert(signbit(-float.max));
assert(!signbit(float.max));

assert(!signbit(double.nan));
assert(signbit(-double.nan));
assert(!signbit(168.1234));
assert(signbit(-168.1234));
assert(!signbit(0.0));
assert(signbit(-0.0));
assert(signbit(-double.max));
assert(!signbit(double.max));

assert(!signbit(real.nan));
assert(signbit(-real.nan));
assert(!signbit(168.1234L));
assert(signbit(-168.1234L));
assert(!signbit(0.0L));
assert(signbit(-0.0L));
assert(signbit(-real.max));
assert(!signbit(real.max));

pure nothrow @nogc @trusted R copysign(R, X)(R to, X from) if (isFloatingPoint!R && isFloatingPoint!X); pure nothrow @nogc @trusted R copysign(R, X)(X to, R from) if (isIntegral!X && isFloatingPoint!R);

Parameters:

R `to`	the numeric value to use
X `from`	the sign value to use

Returns:

a value composed of to with from's sign bit.

Examples:

writeln(copysign(1.0, 1.0)); // 1.0
writeln(copysign(1.0, -0.0)); // -1.0
writeln(copysign(1UL, -1.0)); // -1.0
writeln(copysign(-1.0, -1.0)); // -1.0

writeln(copysign(real.infinity, -1.0)); // -real.infinity
assert(copysign(real.nan, 1.0) is real.nan);
assert(copysign(-real.nan, 1.0) is real.nan);
assert(copysign(real.nan, -1.0) is -real.nan);

pure nothrow @nogc @safe F sgn(F)(F x) if (isFloatingPoint!F || isIntegral!F);

Returns -1 if x < 0, x if x == 0, 1 if x > 0, and NAN if x==NAN.

Examples:

writeln(sgn(168.1234)); // 1
writeln(sgn(-168.1234)); // -1
writeln(sgn(0.0)); // 0
writeln(sgn(-0.0)); // 0

pure nothrow @nogc @safe bool isPowerOf2(X)(const X x) if (isNumeric!X);

Check whether a number is an integer power of two.

Note that only positive numbers can be integer powers of two. This function always return false if x is negative or zero.

Parameters:

X x the number to test

Returns:

true if x is an integer power of two.

Examples:

import std.math.exponential : pow;

assert( isPowerOf2(1.0L));
assert( isPowerOf2(2.0L));
assert( isPowerOf2(0.5L));
assert( isPowerOf2(pow(2.0L, 96)));
assert( isPowerOf2(pow(2.0L, -77)));

assert(!isPowerOf2(-2.0L));
assert(!isPowerOf2(-0.5L));
assert(!isPowerOf2(0.0L));
assert(!isPowerOf2(4.315));
assert(!isPowerOf2(1.0L / 3.0L));

assert(!isPowerOf2(real.nan));
assert(!isPowerOf2(real.infinity));

Examples:

assert( isPowerOf2(1));
assert( isPowerOf2(2));
assert( isPowerOf2(1uL << 63));

assert(!isPowerOf2(-4));
assert(!isPowerOf2(0));
assert(!isPowerOf2(1337u));

Library Reference

std.math.traits