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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));

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