Module: BigMathR::Hyperb

Defined in:
ext/bigdecimal/math_r/hyperb.c,
ext/bigdecimal/math_r/math_r.c

Overview

A module that provides a hyperbolic functions. It is used internally.
It handle the real number solutions. The algorithm is implemented according to the references, when |x| < 3 computes to series expansion, otherwise computes by exponent identity.

Synopsis

The function names defined are the same as those in the C/C++ standard.

  • Hyperbolic Sine: :sinh
  • Hyperbolic Cosine: :cosh
  • Hyperbolic Tangent: :tanh
    Follow, those reciprocals of not defined in C/C++ standard.

- Hyperbolic Cosecant: +:csch+
- Hyperbolic Secant: +:sech+
- Hyperbolic Cotangent: +:coth+
Reference:: C-gengo ni yoru hyoujun alkgorithm jiten (Japanese) - Hasruhiko Okumura (Gijutsu hyouron-sha)

Class Method Summary collapse

Class Method Details

.cosh(x, prec) ⇒ BigDecimal

Computes hyperbolic cosine of x.

Examples:

BigMathR::Hyperb.cosh(1, 20) # Series expansion
#=> 0.15430806348152437785e1
BigMathR::Hyperb.cosh(4, 20) # Formula
#=> 0.27308232836016486629e2

Parameters:

  • x (Numeric) —

    Numerical argument

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Real solution

Raises:

  • (ArgumentError) —

    Occurs when prec is not a positive integer.

  • (TypeError) —

    Occurs when x is not a numeric class.

Since:

  • 0.1.0



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# File 'ext/bigdecimal/math_r/hyperb.c', line 50

static VALUE
__impl_hyperb_cosh(VALUE unused_obj, VALUE x, VALUE prec)
{
	return cosh_branch(x, prec, cosh_formula);
}

.coth(x, prec) ⇒ BigDecimal

Computes hyperbolic cotangent of x.

Examples:

BigMathR::Hyperb.coth(1, 20) # Series expansion
#=> 0.13130352854993313036e1
BigMathR::Hyperb.coth(4, 20) # Formula
#=> 0.10006711504016824899e1

Parameters:

  • x (Numeric) —

    Numerical argument

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Real solution

Raises:

  • (ArgumentError) —

    Occurs when prec is not a positive integer.

  • (TypeError) —

    Occurs when x is not a numeric class.

Since:

  • 0.1.0



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# File 'ext/bigdecimal/math_r/hyperb.c', line 134

static VALUE
__impl_hyperb_coth(VALUE unused_obj, VALUE x, VALUE prec)
{
	return coth_branch(x, prec, coth_formula);
}

.csch(x, prec) ⇒ BigDecimal

Computes hyperbolic cosecant of x.

Examples:

BigMathR::Hyperb.csch(1, 20) # Series expansion
#=> 0.85091812823932154512e0
BigMathR::Hyperb.csch(4, 20) # Formula
#=> 0.36643570325865605966e-1

Parameters:

  • x (Numeric) —

    Numerical argument

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Real solution

Raises:

  • (ArgumentError) —

    Occurs when prec is not a positive integer.

  • (TypeError) —

    Occurs when x is not a numeric class.

Since:

  • 0.1.0



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# File 'ext/bigdecimal/math_r/hyperb.c', line 92

static VALUE
__impl_hyperb_csch(VALUE unused_obj, VALUE x, VALUE prec)
{
	return csch_branch(x, prec, csch_formula);
}

.sech(x, prec) ⇒ BigDecimal

Computes hyperbolic secant of x.

Examples:

BigMathR::Hyperb.sech(1, 20) # Series expansion
#=> 0.64805427366388539957e0
BigMathR::Hyperb.sech(4, 20) # Formula
#=> 0.36618993473686532773e-1

Parameters:

  • x (Numeric) —

    Numerical argument

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Real solution

Raises:

  • (ArgumentError) —

    Occurs when prec is not a positive integer.

  • (TypeError) —

    Occurs when x is not a numeric class.

Since:

  • 0.1.0



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# File 'ext/bigdecimal/math_r/hyperb.c', line 113

static VALUE
__impl_hyperb_sech(VALUE unused_obj, VALUE x, VALUE prec)
{
	return sech_branch(x, prec, sech_formula);
}

.tanh(x, prec) ⇒ BigDecimal

Computes hyperbolic tangent of x.

Examples:

BigMathR::Hyperb.tanh(1, 20) # Series expansion
#=> 0.76159415595576488812e0
BigMathR::Hyperb.tanh(4, 20) # Formula
#=> 0.99932929973906704379e0

Parameters:

  • x (Numeric) —

    Numerical argument

  • prec (Integer) —

    Arbitrary precision

Returns:

  • (BigDecimal) —

    Real solution

Raises:

  • (ArgumentError) —

    Occurs when prec is not a positive integer.

  • (TypeError) —

    Occurs when x is not a numeric class.

Since:

  • 0.1.0



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# File 'ext/bigdecimal/math_r/hyperb.c', line 71

static VALUE
__impl_hyperb_tanh(VALUE unused_obj, VALUE x, VALUE prec)
{
	return tanh_branch(x, prec, tanh_formula);
}