Title: Mathematical Functions

Contents:

  1. Mathematical Constants
  2. Infinities and Not-a-number
    1. Constants
    2. Module functions
  3. Elementary Functions
  4. Small Integer Powers
  5. Testing the Sign of Numbers
  6. Testing for Odd and Even Numbers
  7. Maximum and Minimum functions
  8. Approximate Comparison of Floating Point Numbers

1 Mathematical Constants

GSL::M_E
The base of exponentials, e
GSL::M_LOG2E
The base-2 logarithm of e, log_2(e)
GSL::M_LOG10E
The base-10 logarithm of e, log_10(e)
GSL::M_SQRT2
The square root of two, sqrt(2)
GSL::M_SQRT1_2
The square root of one-half, sqrt(1/2)
GSL::M_SQRT3
The square root of three, sqrt(3)
GSL::M_PI
The constant pi
GSL::M_PI_2
Pi divided by two
GSL::M_PI_4
Pi divided by four
GSL::M_SQRTPI
The square root of pi
GSL::M_2_SQRTPI
Two divided by the square root of pi
GSL::M_1_PI
The reciprocal of pi, 1/pi
GSL::M_2_PI
Twice the reciprocal of pi, 2/pi
GSL::M_LN10
The natural logarithm of ten, ln(10)
GSL::M_LN2
The natural logarithm of ten, ln(2)
GSL::M_LNPI
The natural logarithm of ten, ln(pi)
GSL::M_EULER
Euler's constant

2 Infinities and Not-a-number

2.1 Constants

GSL::POSINF
The IEEE representation of positive infinity, computed from the expression +1.0/0.0.
GSL::NEGINF
The IEEE representation of negative infinity, computed from the expression -1.0/0.0.
GSL::NAN
The IEEE representation of the Not-a-Number symbol, computed from the ratio 0.0/0.0.

2.2 Module functions

GSL::isnan(x)
This returns 1 if x is not-a-number.
GSL::isnan?(x)
This returns true if x is not-a-number, and false otherwise.
GSL::isinf(x)
This returns +1 if x is positive infinity, -1 if x is negative infinity and 0 otherwise. NOTE: In Darwin9.5.0-gcc4.0.1, this method returns 1 for -inf.
GSL::isinf?(x)
This returns true if x is positive or negative infinity, and false otherwise.
GSL::finite(x)
This returns 1 if x is a real number, and 0 if it is infinite or not-a-number.
GSL::finite?(x)
This returns true if x is a real number, and false if it is infinite or not-a-number.

3 Elementary Functions

GSL::log1p(x)
This method computes the value of log(1+x) in a way that is accurate for small x. It provides an alternative to the BSD math function log1p(x).
GSL::expm1(x)
This method computes the value of exp(x)-1 in a way that is accurate for small x. It provides an alternative to the BSD math function expm1(x).
GSL::hypot(x, y)
This method computes the value of sqrt{x^2 + y^2} in a way that avoids overflow.
GSL::hypot3(x, y, z)
Computes the value of sqrt{x^2 + y^2 + z^2} in a way that avoids overflow.
GSL::acosh(x)
This method computes the value of arccosh(x).
GSL::asinh(x)
This method computes the value of arcsinh(x).
GSL::atanh(x)

This method computes the value of arctanh(x).

These methods above can take argument x of Integer, Float, Array, Vector or Matrix.

GSL::ldexp(x)
This method computes the value of x * 2^e.
GSL::frexp(x)
This method splits the number x into its normalized fraction f and exponent e, such that x = f * 2^e and 0.5 <= f < 1. The method returns f and the exponent e as an array, [f, e]. If x is zero, both f and e are set to zero.

4 Small Integer Powers

GSL::pow_int(x, n)
This routine computes the power x^n for integer n. The power is computed efficiently -- for example, x^8 is computed as ((x^2)^2)^2, requiring only 3 multiplications.
GSL::pow_2(x)
GSL::pow_3(x)
GSL::pow_4(x)
GSL::pow_5(x)
GSL::pow_6(x)
GSL::pow_7(x)
GSL::pow_8(x)
GSL::pow_9(x)
These methods can be used to compute small integer powers x^2, x^3, etc. efficiently.

5 Testing the Sign of Numbers

GSL::SIGN(x)
GSL::sign(x)
Return the sign of x. It is defined as ((x) >= 0 ? 1 : -1). Note that with this definition the sign of zero is positive (regardless of its IEEE sign bit).

6 Testing for Odd and Even Numbers

GSL::is_odd(n)
GSL::IS_ODD(n)
Evaluate to 1 if n is odd and 0 if n is even. The argument n must be of Fixnum type.
GSL::is_odd?(n)
GSL::IS_ODD?(n)
Return true if n is odd and false if even.
GSL::is_even(n)
GSL::IS_EVEN(n)
Evaluate to 1 if n is even and 0 if n is odd. The argument n must be of Fixnum type.
GSL::is_even?(n)
GSL::IS_even?(n)
Return true if n is even and false if odd.

7 Maximum and Minimum functions

GSL::max(a, b)
GSL::MAX(a, b)
GSL::min(a, b)
GSL::MIN(a, b)

8 Approximate Comparison of Floating Point Numbers

GSL::fcmp(a, b, epsilon = 1e-10)
This method determines whether x and y are approximately equal to a relative accuracy epsilon.
GSL::equal?(a, b, epsilon = 1e-10)

9 Module Constants

GSL::VERSION
GSL version
GSL::RB_GSL_VERSION
GSL::RUBY_GSL_VERSION
Ruby/GSL version

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