The Math module contains module functions for basic trigonometric and transcendental functions. See class Float for a list of constants that define Rubyâs floating point accuracy.
Domains and codomains are given only for real (not complex) numbers.
ConstantsDefinition of the mathematical constant E for Eulerâs number (e) as a Float number.
Definition of the mathematical constant PI as a Float number.
acos(x) → Float click to toggle source
Computes the arc cosine of x. Returns 0..PI.
Domain: [-1, 1]
Codomain: [0, PI]
Math.acos(0) == Math::PI/2
static VALUE
math_acos(VALUE unused_obj, VALUE x)
{
double d;
d = Get_Double(x);
domain_check_range(d, -1.0, 1.0, "acos");
return DBL2NUM(acos(d));
}
acosh(x) → Float click to toggle source
Computes the inverse hyperbolic cosine of x.
Domain: [1, INFINITY)
Codomain: [0, INFINITY)
Math.acosh(1)
static VALUE
math_acosh(VALUE unused_obj, VALUE x)
{
double d;
d = Get_Double(x);
domain_check_min(d, 1.0, "acosh");
return DBL2NUM(acosh(d));
}
asin(x) → Float click to toggle source
Computes the arc sine of x. Returns -PI/2..PI/2.
Domain: [-1, -1]
Codomain: [-PI/2, PI/2]
Math.asin(1) == Math::PI/2
static VALUE
math_asin(VALUE unused_obj, VALUE x)
{
double d;
d = Get_Double(x);
domain_check_range(d, -1.0, 1.0, "asin");
return DBL2NUM(asin(d));
}
asinh(x) → Float click to toggle source
Computes the inverse hyperbolic sine of x.
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.asinh(1)
static VALUE
math_asinh(VALUE unused_obj, VALUE x)
{
return DBL2NUM(asinh(Get_Double(x)));
}
atan(x) → Float click to toggle source
Computes the arc tangent of x. Returns -PI/2..PI/2.
Domain: (-INFINITY, INFINITY)
Codomain: (-PI/2, PI/2)
Math.atan(0)
static VALUE
math_atan(VALUE unused_obj, VALUE x)
{
return DBL2NUM(atan(Get_Double(x)));
}
atan2(y, x) → Float click to toggle source
Computes the arc tangent given y and x. Returns a Float in the range -PI..PI. Return value is a angle in radians between the positive x-axis of cartesian plane and the point given by the coordinates (x, y) on it.
Domain: (-INFINITY, INFINITY)
Codomain: [-PI, PI]
Math.atan2(-0.0, -1.0) Math.atan2(-1.0, -1.0) Math.atan2(-1.0, 0.0) Math.atan2(-1.0, 1.0) Math.atan2(-0.0, 1.0) Math.atan2(0.0, 1.0) Math.atan2(1.0, 1.0) Math.atan2(1.0, 0.0) Math.atan2(1.0, -1.0) Math.atan2(0.0, -1.0) Math.atan2(INFINITY, INFINITY) Math.atan2(INFINITY, -INFINITY) Math.atan2(-INFINITY, INFINITY) Math.atan2(-INFINITY, -INFINITY)
static VALUE
math_atan2(VALUE unused_obj, VALUE y, VALUE x)
{
double dx, dy;
dx = Get_Double(x);
dy = Get_Double(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);
}
#ifndef ATAN2_INF_C99
if (isinf(dx) && isinf(dy)) {
/* optimization for FLONUM */
if (dx < 0.0) {
const double dz = (3.0 * M_PI / 4.0);
return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);
}
else {
const double dz = (M_PI / 4.0);
return (dy < 0.0) ? DBL2NUM(-dz) : DBL2NUM(dz);
}
}
#endif
return DBL2NUM(atan2(dy, dx));
}
atanh(x) → Float click to toggle source
Computes the inverse hyperbolic tangent of x.
Domain: (-1, 1)
Codomain: (-INFINITY, INFINITY)
Math.atanh(1)
static VALUE
math_atanh(VALUE unused_obj, VALUE x)
{
double d;
d = Get_Double(x);
domain_check_range(d, -1.0, +1.0, "atanh");
/* check for pole error */
if (d == -1.0) return DBL2NUM(-HUGE_VAL);
if (d == +1.0) return DBL2NUM(+HUGE_VAL);
return DBL2NUM(atanh(d));
}
cbrt(x) → Float click to toggle source
Returns the cube root of x.
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
-9.upto(9) {|x|
p [x, Math.cbrt(x), Math.cbrt(x)**3]
}
static VALUE
math_cbrt(VALUE unused_obj, VALUE x)
{
double f = Get_Double(x);
double r = cbrt(f);
#if defined __GLIBC__
if (isfinite(r) && !(f == 0.0 && r == 0.0)) {
r = (2.0 * r + (f / r / r)) / 3.0;
}
#endif
return DBL2NUM(r);
}
cos(x) → Float click to toggle source
Computes the cosine of x (expressed in radians). Returns a Float in the range -1.0..1.0.
Domain: (-INFINITY, INFINITY)
Codomain: [-1, 1]
Math.cos(Math::PI)
static VALUE
math_cos(VALUE unused_obj, VALUE x)
{
return DBL2NUM(cos(Get_Double(x)));
}
cosh(x) → Float click to toggle source
Computes the hyperbolic cosine of x (expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: [1, INFINITY)
Math.cosh(0)
static VALUE
math_cosh(VALUE unused_obj, VALUE x)
{
return DBL2NUM(cosh(Get_Double(x)));
}
erf(x) → Float click to toggle source
Calculates the error function of x.
Domain: (-INFINITY, INFINITY)
Codomain: (-1, 1)
Math.erf(0)
static VALUE
math_erf(VALUE unused_obj, VALUE x)
{
return DBL2NUM(erf(Get_Double(x)));
}
erfc(x) → Float click to toggle source
Calculates the complementary error function of x.
Domain: (-INFINITY, INFINITY)
Codomain: (0, 2)
Math.erfc(0)
static VALUE
math_erfc(VALUE unused_obj, VALUE x)
{
return DBL2NUM(erfc(Get_Double(x)));
}
exp(x) → Float click to toggle source
Returns e**x.
Domain: (-INFINITY, INFINITY)
Codomain: (0, INFINITY)
Math.exp(0) Math.exp(1) Math.exp(1.5)
static VALUE
math_exp(VALUE unused_obj, VALUE x)
{
return DBL2NUM(exp(Get_Double(x)));
}
frexp(x) → [fraction, exponent] click to toggle source
Returns a two-element array containing the normalized fraction (a Float) and exponent (an Integer) of x.
fraction, exponent = Math.frexp(1234) fraction * 2**exponent
static VALUE
math_frexp(VALUE unused_obj, VALUE x)
{
double d;
int exp;
d = frexp(Get_Double(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 the 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)] }
static VALUE
math_gamma(VALUE unused_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. */
};
enum {NFACT_TABLE = numberof(fact_table)};
double d;
d = Get_Double(x);
/* check for domain error */
if (isinf(d)) {
if (signbit(d)) domain_error("gamma");
return DBL2NUM(HUGE_VAL);
}
if (d == 0.0) {
return signbit(d) ? DBL2NUM(-HUGE_VAL) : DBL2NUM(HUGE_VAL);
}
if (d == floor(d)) {
domain_check_min(d, 0.0, "gamma");
if (1.0 <= d && d <= (double)NFACT_TABLE) {
return DBL2NUM(fact_table[(int)d - 1]);
}
}
return DBL2NUM(tgamma(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)
static VALUE
math_hypot(VALUE unused_obj, VALUE x, VALUE y)
{
return DBL2NUM(hypot(Get_Double(x), Get_Double(y)));
}
ldexp(fraction, exponent) → float click to toggle source
Returns the value of fraction*(2**exponent).
fraction, exponent = Math.frexp(1234) Math.ldexp(fraction, exponent)
static VALUE
math_ldexp(VALUE unused_obj, VALUE x, VALUE n)
{
return DBL2NUM(ldexp(Get_Double(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.
Math.lgamma(x) is the same as
[Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
but avoids overflow by Math.gamma(x) for large x.
Math.lgamma(0)
static VALUE
math_lgamma(VALUE unused_obj, VALUE x)
{
double d;
int sign=1;
VALUE v;
d = Get_Double(x);
/* check for domain error */
if (isinf(d)) {
if (signbit(d)) domain_error("lgamma");
return rb_assoc_new(DBL2NUM(HUGE_VAL), INT2FIX(1));
}
if (d == 0.0) {
VALUE vsign = signbit(d) ? INT2FIX(-1) : INT2FIX(+1);
return rb_assoc_new(DBL2NUM(HUGE_VAL), vsign);
}
v = DBL2NUM(lgamma_r(d, &sign));
return rb_assoc_new(v, INT2FIX(sign));
}
log(x) → Float click to toggle source
log(x, base) → Float
Returns the logarithm of x. If additional second argument is given, it will be the base of logarithm. Otherwise it is e (for the natural logarithm).
Domain: (0, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.log(0) Math.log(1) Math.log(Math::E) Math.log(Math::E**3) Math.log(12, 3)
static VALUE
math_log(int argc, const VALUE *argv, VALUE unused_obj)
{
return rb_math_log(argc, argv);
}
log10(x) → Float click to toggle source
Returns the base 10 logarithm of x.
Domain: (0, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.log10(1) Math.log10(10) Math.log10(10**100)
static VALUE
math_log10(VALUE unused_obj, VALUE x)
{
size_t numbits;
double d = get_double_rshift(x, &numbits);
domain_check_min(d, 0.0, "log10");
/* check for pole error */
if (d == 0.0) return DBL2NUM(-HUGE_VAL);
return DBL2NUM(log10(d) + numbits * log10(2)); /* log10(d * 2 ** numbits) */
}
log2(x) → Float click to toggle source
Returns the base 2 logarithm of x.
Domain: (0, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.log2(1) Math.log2(2) Math.log2(32768) Math.log2(65536)
static VALUE
math_log2(VALUE unused_obj, VALUE x)
{
size_t numbits;
double d = get_double_rshift(x, &numbits);
domain_check_min(d, 0.0, "log2");
/* check for pole error */
if (d == 0.0) return DBL2NUM(-HUGE_VAL);
return DBL2NUM(log2(d) + numbits); /* log2(d * 2 ** numbits) */
}
sin(x) → Float click to toggle source
Computes the sine of x (expressed in radians). Returns a Float in the range -1.0..1.0.
Domain: (-INFINITY, INFINITY)
Codomain: [-1, 1]
Math.sin(Math::PI/2)
static VALUE
math_sin(VALUE unused_obj, VALUE x)
{
return DBL2NUM(sin(Get_Double(x)));
}
sinh(x) → Float click to toggle source
Computes the hyperbolic sine of x (expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.sinh(0)
static VALUE
math_sinh(VALUE unused_obj, VALUE x)
{
return DBL2NUM(sinh(Get_Double(x)));
}
sqrt(x) → Float click to toggle source
Returns the non-negative square root of x.
Domain: [0, INFINITY)
Codomain:[0, INFINITY)
0.upto(10) {|x|
p [x, Math.sqrt(x), Math.sqrt(x)**2]
}
Note that the limited precision of floating point arithmetic might lead to surprising results:
Math.sqrt(10**46).to_i
See also BigDecimal#sqrt and Integer.sqrt.
static VALUE
math_sqrt(VALUE unused_obj, VALUE x)
{
return rb_math_sqrt(x);
}
tan(x) → Float click to toggle source
Computes the tangent of x (expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: (-INFINITY, INFINITY)
Math.tan(0)
static VALUE
math_tan(VALUE unused_obj, VALUE x)
{
return DBL2NUM(tan(Get_Double(x)));
}
tanh(x) → Float click to toggle source
Computes the hyperbolic tangent of x (expressed in radians).
Domain: (-INFINITY, INFINITY)
Codomain: (-1, 1)
Math.tanh(0)
static VALUE
math_tanh(VALUE unused_obj, VALUE x)
{
return DBL2NUM(tanh(Get_Double(x)));
}
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