Math

The Math module contains module functions for basic trigonometric and transcendental functions. See class Float for a list of constants that define Ruby’s floating point accuracy.

Constants

E
PI

Public Class Methods

acos(x) => float click to toggle source

Computes the arc cosine of x. Returns 0..PI.

 
               static VALUE
math_acos(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = acos(d0);
    domain_check(d0, d, "acos");
    return DBL2NUM(d);
}

acosh(x) => float click to toggle source

Computes the inverse hyperbolic cosine of x.

 
               static VALUE
math_acosh(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = acosh(d0);
    domain_check(d0, d, "acosh");
    return DBL2NUM(d);
}

asin(x) => float click to toggle source

Computes the arc sine of x. Returns -{PI/2} .. {PI/2}.

 
               static VALUE
math_asin(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = asin(d0);
    domain_check(d0, d, "asin");
    return DBL2NUM(d);
}

asinh(x) => float click to toggle source

Computes the inverse hyperbolic sine of x.

 
               static VALUE
math_asinh(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(asinh(RFLOAT_VALUE(x)));
}

atan(x) => float click to toggle source

Computes the arc tangent of x. Returns -{PI/2} .. {PI/2}.

 
               static VALUE
math_atan(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(atan(RFLOAT_VALUE(x)));
}

atan2(y, x) => float click to toggle source

Computes the arc tangent given y and x. Returns -PI..PI.

 
               static VALUE
math_atan2(VALUE obj, VALUE y, VALUE x)
{
    Need_Float2(y, x);
    return DBL2NUM(atan2(RFLOAT_VALUE(y), RFLOAT_VALUE(x)));
}

atanh(x) => float click to toggle source

Computes the inverse hyperbolic tangent of x.

 
               static VALUE
math_atanh(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = atanh(d0);
    domain_check(d0, d, "atanh");
    infinity_check(x, d, "atanh");
    return DBL2NUM(d);
}

cbrt(numeric) => float click to toggle source

Returns the cube root of numeric.

-9.upto(9) {|x|
  p [x, Math.cbrt(x), Math.cbrt(x)**3]
}
#=>
[-9, -2.0800838230519, -9.0]
[-8, -2.0, -8.0]
[-7, -1.91293118277239, -7.0]
[-6, -1.81712059283214, -6.0]
[-5, -1.7099759466767, -5.0]
[-4, -1.5874010519682, -4.0]
[-3, -1.44224957030741, -3.0]
[-2, -1.25992104989487, -2.0]
[-1, -1.0, -1.0]
[0, 0.0, 0.0]
[1, 1.0, 1.0]
[2, 1.25992104989487, 2.0]
[3, 1.44224957030741, 3.0]
[4, 1.5874010519682, 4.0]
[5, 1.7099759466767, 5.0]
[6, 1.81712059283214, 6.0]
[7, 1.91293118277239, 7.0]
[8, 2.0, 8.0]
[9, 2.0800838230519, 9.0]

 
               static VALUE
math_cbrt(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(cbrt(RFLOAT_VALUE(x)));
}

cos(x) => float click to toggle source

Computes the cosine of x (expressed in radians). Returns -1..1.

 
               static VALUE
math_cos(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(cos(RFLOAT_VALUE(x)));
}

cosh(x) => float click to toggle source

Computes the hyperbolic cosine of x (expressed in radians).

 
               static VALUE
math_cosh(VALUE obj, VALUE x)
{
    Need_Float(x);
    
    return DBL2NUM(cosh(RFLOAT_VALUE(x)));
}

erf(x) => float click to toggle source

Calculates the error function of x.

 
               static VALUE
math_erf(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(erf(RFLOAT_VALUE(x)));
}

erfc(x) => float click to toggle source

Calculates the complementary error function of x.

 
               static VALUE
math_erfc(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(erfc(RFLOAT_VALUE(x)));
}

exp(x) => float click to toggle source

Returns e**x.

 
               static VALUE
math_exp(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(exp(RFLOAT_VALUE(x)));
}

frexp(numeric) => [ fraction, exponent ] click to toggle source

Returns a two-element array containing the normalized fraction (a Float) and exponent (a Fixnum) of numeric.

fraction, exponent = Math.frexp(1234)   #=> [0.6025390625, 11]
fraction * 2**exponent                  #=> 1234.0

 
               static VALUE
math_frexp(VALUE obj, VALUE x)
{
    double d;
    int exp;

    Need_Float(x);
    
    d = frexp(RFLOAT_VALUE(x), &exp);
    return rb_assoc_new(DBL2NUM(d), INT2NUM(exp));
}

gamma(x) => float click to toggle source

Calculates the gamma function of x.

Note that gamma(n) is same as fact(n-1) for integer n >= 0. However gamma(n) returns float and possibly has error in calculation.

def fact(n) (1..n).inject(1) {|r,i| r*i } end
0.upto(25) {|i| p [i, Math.gamma(i+1), fact(i)] }
#=>
[0, 1.0, 1]
[1, 1.0, 1]
[2, 2.0, 2]
[3, 6.0, 6]
[4, 24.0, 24]
[5, 120.0, 120]
[6, 720.0, 720]
[7, 5040.0, 5040]
[8, 40320.0, 40320]
[9, 362880.0, 362880]
[10, 3628800.0, 3628800]
[11, 39916800.0, 39916800]
[12, 479001599.999999, 479001600]
[13, 6227020800.00001, 6227020800]
[14, 87178291199.9998, 87178291200]
[15, 1307674368000.0, 1307674368000]
[16, 20922789888000.0, 20922789888000]
[17, 3.55687428096001e+14, 355687428096000]
[18, 6.40237370572799e+15, 6402373705728000]
[19, 1.21645100408832e+17, 121645100408832000]
[20, 2.43290200817664e+18, 2432902008176640000]
[21, 5.10909421717094e+19, 51090942171709440000]
[22, 1.12400072777761e+21, 1124000727777607680000]
[23, 2.58520167388851e+22, 25852016738884976640000]
[24, 6.20448401733239e+23, 620448401733239439360000]
[25, 1.5511210043331e+25, 15511210043330985984000000]

 
               static VALUE
math_gamma(VALUE obj, VALUE x)
{
    double d0, d;
    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = tgamma(d0);
    domain_check(d0, d, "gamma");
    return DBL2NUM(d);
}

hypot(x, y) => float click to toggle source

Returns sqrt(x**2 + y**2), the hypotenuse of a right-angled triangle with sides x and y.

Math.hypot(3, 4)   #=> 5.0

 
               static VALUE
math_hypot(VALUE obj, VALUE x, VALUE y)
{
    Need_Float2(x, y);
    return DBL2NUM(hypot(RFLOAT_VALUE(x), RFLOAT_VALUE(y)));
}

ldexp(flt, int) → float click to toggle source

Returns the value of flt*(2**int).

fraction, exponent = Math.frexp(1234)
Math.ldexp(fraction, exponent)   #=> 1234.0

 
               static VALUE
math_ldexp(VALUE obj, VALUE x, VALUE n)
{
    Need_Float(x);
    return DBL2NUM(ldexp(RFLOAT_VALUE(x), NUM2INT(n)));
}

lgamma(x) => [float, -1 or 1] click to toggle source

Calculates the logarithmic gamma of x and the sign of gamma of x.

::lgamma is same as

[Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]

but avoid overflow by ::gamma for large x.

 
               static VALUE
math_lgamma(VALUE obj, VALUE x)
{
    double d0, d;
    int sign;
    VALUE v;
    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = lgamma_r(d0, &sign);
    domain_check(d0, d, "lgamma");
    v = DBL2NUM(d);
    return rb_assoc_new(v, INT2FIX(sign));
}

log(numeric) => float click to toggle source

log(num,base) => float

Returns the natural logarithm of numeric. If additional second argument is given, it will be the base of logarithm.

 
               static VALUE
math_log(int argc, VALUE *argv)
{
    VALUE x, base;
    double d0, d;

    rb_scan_args(argc, argv, "11", &x, &base);
    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = log(d0);
    if (argc == 2) {
        Need_Float(base);
        d /= log(RFLOAT_VALUE(base));
    }
    domain_check(d0, d, "log");
    infinity_check(x, d, "log");
    return DBL2NUM(d);
}

log10(numeric) => float click to toggle source

Returns the base 10 logarithm of numeric.

 
               static VALUE
math_log10(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = log10(d0);
    domain_check(d0, d, "log10");
    infinity_check(x, d, "log10");
    return DBL2NUM(d);
}

log2(numeric) => float click to toggle source

Returns the base 2 logarithm of numeric.

 
               static VALUE
math_log2(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = log2(d0);
    domain_check(d0, d, "log2");
    infinity_check(x, d, "log2");
    return DBL2NUM(d);
}

sin(x) => float click to toggle source

Computes the sine of x (expressed in radians). Returns -1..1.

 
               static VALUE
math_sin(VALUE obj, VALUE x)
{
    Need_Float(x);

    return DBL2NUM(sin(RFLOAT_VALUE(x)));
}

sinh(x) => float click to toggle source

Computes the hyperbolic sine of x (expressed in radians).

 
               static VALUE
math_sinh(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(sinh(RFLOAT_VALUE(x)));
}

sqrt(numeric) => float click to toggle source

Returns the non-negative square root of numeric.

0.upto(10) {|x|            
  p [x, Math.sqrt(x), Math.sqrt(x)**2]
}
#=>
[0, 0.0, 0.0]
[1, 1.0, 1.0]
[2, 1.4142135623731, 2.0]
[3, 1.73205080756888, 3.0]
[4, 2.0, 4.0]
[5, 2.23606797749979, 5.0]
[6, 2.44948974278318, 6.0]
[7, 2.64575131106459, 7.0]
[8, 2.82842712474619, 8.0]
[9, 3.0, 9.0]
[10, 3.16227766016838, 10.0]

 
               static VALUE
math_sqrt(VALUE obj, VALUE x)
{
    double d0, d;

    Need_Float(x);
    errno = 0;
    d0 = RFLOAT_VALUE(x);
    d = sqrt(d0);
    domain_check(d0, d, "sqrt");
    return DBL2NUM(d);
}

tan(x) => float click to toggle source

Returns the tangent of x (expressed in radians).

 
               static VALUE
math_tan(VALUE obj, VALUE x)
{
    Need_Float(x);

    return DBL2NUM(tan(RFLOAT_VALUE(x)));
}

tanh() => float click to toggle source

Computes the hyperbolic tangent of x (expressed in radians).

 
               static VALUE
math_tanh(VALUE obj, VALUE x)
{
    Need_Float(x);
    return DBL2NUM(tanh(RFLOAT_VALUE(x)));
}

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