Module: Math

Defined in:
math.c

Overview

Document-class: 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.

Defined Under Namespace

Classes: DomainError

Constant Summary collapse

PI = 
DBL2NUM(atan(1.0)*4.0)
E = 
DBL2NUM(exp(1.0))

Class Method Summary collapse

Class Method Details

.acos(x) ⇒ Float

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

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 < -1.0 || 1.0 < d0) domain_error("acos");
    d = acos(d0);
    return DBL2NUM(d);
}

.acosh(x) ⇒ Float

Computes the inverse hyperbolic cosine of x.

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 < 1.0) domain_error("acosh");
    d = acosh(d0);
    return DBL2NUM(d);
}

.asin(x) ⇒ Float

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

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 < -1.0 || 1.0 < d0) domain_error("asin");
    d = asin(d0);
    return DBL2NUM(d);
}

.asinh(x) ⇒ Float

Computes the inverse hyperbolic sine of x.

Returns:




# File 'math.c'

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

.atan(x) ⇒ Float

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

Returns:




# File 'math.c'

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

.atan2(y, x) ⇒ Float

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

Math.atan2(-0.0, -1.0) #=> -3.141592653589793
Math.atan2(-1.0, -1.0) #=> -2.356194490192345
Math.atan2(-1.0, 0.0)  #=> -1.5707963267948966
Math.atan2(-1.0, 1.0)  #=> -0.7853981633974483
Math.atan2(-0.0, 1.0)  #=> -0.0
Math.atan2(0.0, 1.0)   #=> 0.0
Math.atan2(1.0, 1.0)   #=> 0.7853981633974483
Math.atan2(1.0, 0.0)   #=> 1.5707963267948966
Math.atan2(1.0, -1.0)  #=> 2.356194490192345
Math.atan2(0.0, -1.0)  #=> 3.141592653589793

Returns:




# File 'math.c'

static VALUE
math_atan2(VALUE obj, VALUE y, VALUE x)
{
#ifndef M_PI
# define M_PI 3.14159265358979323846
#endif
double dx, dy;
Need_Float2(y, x);
dx = RFLOAT_VALUE(x);
dy = RFLOAT_VALUE(y);
if (dx == 0.0 && dy == 0.0) {
if (!signbit(dx))
    return DBL2NUM(dy);
    if (!signbit(dy))
    return DBL2NUM(M_PI);
return DBL2NUM(-M_PI);
}

.atanh(x) ⇒ Float

Computes the inverse hyperbolic tangent of x.

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 <  -1.0 || +1.0 <  d0) domain_error("atanh");
    /* check for pole error */
    if (d0 == -1.0) return DBL2NUM(-INFINITY);
    if (d0 == +1.0) return DBL2NUM(+INFINITY);
    d = atanh(d0);
    return DBL2NUM(d);
}

.cbrt(numeric) ⇒ Float

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]

Returns:




# File 'math.c'

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

.cos(x) ⇒ Float

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

Returns:




# File 'math.c'

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

.cosh(x) ⇒ Float

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

Returns:




# File 'math.c'

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

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

.erf(x) ⇒ Float

Calculates the error function of x.

Returns:




# File 'math.c'

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

.erfc(x) ⇒ Float

Calculates the complementary error function of x.

Returns:




# File 'math.c'

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

.exp(x) ⇒ Float

Returns e**x.

Math.exp(0)       #=> 1.0
Math.exp(1)       #=> 2.718281828459045
Math.exp(1.5)     #=> 4.4816890703380645

Returns:




# File 'math.c'

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

.frexp(numeric) ⇒ Array

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

Returns:




# File 'math.c'

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

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 can be an approximation.

 def fact(n) (1..n).inject(1) {|r,i| r*i } end
 1.upto(26) {|i| p [i, Math.gamma(i), fact(i-1)] }
 #=> [1, 1.0, 1]
 #   [2, 1.0, 1]
 #   [3, 2.0, 2]
 #   [4, 6.0, 6]
 #   [5, 24.0, 24]
 #   [6, 120.0, 120]
 #   [7, 720.0, 720]
 #   [8, 5040.0, 5040]
 #   [9, 40320.0, 40320]
 #   [10, 362880.0, 362880]
 #   [11, 3628800.0, 3628800]
 #   [12, 39916800.0, 39916800]
 #   [13, 479001600.0, 479001600]
 #   [14, 6227020800.0, 6227020800]
 #   [15, 87178291200.0, 87178291200]
 #   [16, 1307674368000.0, 1307674368000]
 #   [17, 20922789888000.0, 20922789888000]
 #   [18, 355687428096000.0, 355687428096000]
 #   [19, 6.402373705728e+15, 6402373705728000]
 #   [20, 1.21645100408832e+17, 121645100408832000]
 #   [21, 2.43290200817664e+18, 2432902008176640000]
 #   [22, 5.109094217170944e+19, 51090942171709440000]
 #   [23, 1.1240007277776077e+21, 1124000727777607680000]
 #   [24, 2.5852016738885062e+22, 25852016738884976640000]
 #   [25, 6.204484017332391e+23, 620448401733239439360000]
 #   [26, 1.5511210043330954e+25, 15511210043330985984000000]

Returns:




# File 'math.c'

static VALUE
math_gamma(VALUE obj, VALUE x)
{
static const double fact_table[] = {
    /* fact(0) */ 1.0,
    /* fact(1) */ 1.0,
    /* fact(2) */ 2.0,
    /* fact(3) */ 6.0,
    /* fact(4) */ 24.0,
    /* fact(5) */ 120.0,
    /* fact(6) */ 720.0,
    /* fact(7) */ 5040.0,
    /* fact(8) */ 40320.0,
    /* fact(9) */ 362880.0,
    /* fact(10) */ 3628800.0,
    /* fact(11) */ 39916800.0,
    /* fact(12) */ 479001600.0,
    /* fact(13) */ 6227020800.0,
    /* fact(14) */ 87178291200.0,
    /* fact(15) */ 1307674368000.0,
    /* fact(16) */ 20922789888000.0,
    /* fact(17) */ 355687428096000.0,
    /* fact(18) */ 6402373705728000.0,
    /* fact(19) */ 121645100408832000.0,
    /* fact(20) */ 2432902008176640000.0,
    /* fact(21) */ 51090942171709440000.0,
    /* fact(22) */ 1124000727777607680000.0,
    /* fact(23)=25852016738884976640000 needs 56bit mantissa which is
     * impossible to represent exactly in IEEE 754 double which have
     * 53bit mantissa. */
}

.hypot(x, y) ⇒ Float

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

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

Returns:




# File 'math.c'

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

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

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

Returns:




# File 'math.c'

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

.lgamma(x) ⇒ Array, ...

Calculates the logarithmic gamma of x and

the sign of gamma of x.

Math.lgamma(x) is same as
 [Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
but avoid overflow by Math.gamma(x) for large x.

Returns ].

Returns:




# File 'math.c'

static VALUE
math_lgamma(VALUE obj, VALUE x)
{
double d0, d;
int sign=1;
VALUE v;
Need_Float(x);
d0 = RFLOAT_VALUE(x);
/* check for domain error */
if (isinf(d0)) {
if (signbit(d0)) domain_error("lgamma");
return rb_assoc_new(DBL2NUM(INFINITY), INT2FIX(1));
}

.log(numeric) ⇒ Float .log(num, base) ⇒ Float

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

Math.log(1)          #=> 0.0
Math.log(Math::E)    #=> 1.0
Math.log(Math::E**3) #=> 3.0
Math.log(12,3)       #=> 2.2618595071429146

Overloads:




# File 'math.c'

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);
d0 = RFLOAT_VALUE(x);
/* check for domain error */
if (d0 < 0.0) domain_error("log");
/* check for pole error */
if (d0 == 0.0) return DBL2NUM(-INFINITY);
d = log(d0);
if (argc == 2) {
Need_Float(base);
d /= log(RFLOAT_VALUE(base));
}

.log10(numeric) ⇒ Float

Returns the base 10 logarithm of numeric.

Math.log10(1)       #=> 0.0
Math.log10(10)      #=> 1.0
Math.log10(10**100) #=> 100.0

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 < 0.0) domain_error("log10");
    /* check for pole error */
    if (d0 == 0.0) return DBL2NUM(-INFINITY);
    d = log10(d0);
    return DBL2NUM(d);
}

.log2(numeric) ⇒ Float

Returns the base 2 logarithm of numeric.

Math.log2(1)      #=> 0.0
Math.log2(2)      #=> 1.0
Math.log2(32768)  #=> 15.0
Math.log2(65536)  #=> 16.0

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 < 0.0) domain_error("log2");
    /* check for pole error */
    if (d0 == 0.0) return DBL2NUM(-INFINITY);
    d = log2(d0);
    return DBL2NUM(d);
}

.sin(x) ⇒ Float

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

Returns:




# File 'math.c'

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

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

.sinh(x) ⇒ Float

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

Returns:




# File 'math.c'

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

.sqrt(numeric) ⇒ Float

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]

Returns:




# File 'math.c'

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

    Need_Float(x);
    d0 = RFLOAT_VALUE(x);
    /* check for domain error */
    if (d0 < 0.0) domain_error("sqrt");
    if (d0 == 0.0) return DBL2NUM(0.0);
    d = sqrt(d0);
    return DBL2NUM(d);
}

.tan(x) ⇒ Float

Returns the tangent of x (expressed in radians).

Returns:




# File 'math.c'

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

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

.tanh ⇒ Float

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

Returns:




# File 'math.c'

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