Module: Math
Relationships & Source Files | |
Namespace Children | |
Exceptions:
| |
Defined in: | math.c |
Overview
Module Math provides methods for basic trigonometric, logarithmic, and transcendental functions, and for extracting roots.
You can write its constants and method calls thus:
Math::PI # => 3.141592653589793
Math::E # => 2.718281828459045
Math.sin(0.0) # => 0.0
Math.cos(0.0) # => 1.0
If you include module Math, you can write simpler forms:
include Math
PI # => 3.141592653589793
E # => 2.718281828459045
sin(0.0) # => 0.0
cos(0.0) # => 1.0
For simplicity, the examples here assume:
include Math
INFINITY = Float::INFINITY
The domains and ranges for the methods are denoted by open or closed intervals, using, respectively, parentheses or square brackets:
-
An open interval does not include the endpoints:
(-INFINITY, INFINITY)
-
A closed interval includes the endpoints:
[-1.0, 1.0]
-
A half-open interval includes one endpoint, but not the other:
[1.0, INFINITY)
Many values returned by Math methods are numerical approximations. This is because many such values are, in mathematics, of infinite precision, while in numerical computation the precision is finite.
Thus, in mathematics, cos(π/2) is exactly zero, but in our computation cos(PI/2)
is a number very close to zero:
cos(PI/2) # => 6.123031769111886e-17
For very large and very small returned values, we have added formatted numbers for clarity:
tan(PI/2) # => 1.633123935319537e+16 # 16331239353195370.0
tan(PI) # => -1.2246467991473532e-16 # -0.0000000000000001
See class ::Float
for the constants that affect Ruby’s floating-point arithmetic.
What’s Here
Trigonometric Functions
-
.cos: Returns the cosine of the given argument.
-
.sin: Returns the sine of the given argument.
-
.tan: Returns the tangent of the given argument.
Inverse Trigonometric Functions
-
.acos: Returns the arc cosine of the given argument.
-
.asin: Returns the arc sine of the given argument.
-
.atan: Returns the arc tangent of the given argument.
-
.atan2: Returns the arg tangent of two given arguments.
Hyperbolic Trigonometric Functions
-
.cosh: Returns the hyperbolic cosine of the given argument.
-
.sinh: Returns the hyperbolic sine of the given argument.
-
.tanh: Returns the hyperbolic tangent of the given argument.
Inverse Hyperbolic Trigonometric Functions
-
.acosh: Returns the inverse hyperbolic cosine of the given argument.
-
.asinh: Returns the inverse hyperbolic sine of the given argument.
-
.atanh: Returns the inverse hyperbolic tangent of the given argument.
Exponentiation and Logarithmic Functions
-
.exp: Returns the value of a given value raised to a given power.
-
.log: Returns the logarithm of a given value in a given base.
-
.log10: Returns the base 10 logarithm of the given argument.
-
.log2: Returns the base 2 logarithm of the given argument.
Fraction and Exponent Functions
-
.frexp: Returns the fraction and exponent of the given argument.
-
.ldexp: Returns the value for a given fraction and exponent.
Root Functions
-
.cbrt: Returns the cube root of the given argument.
-
.sqrt: Returns the square root of the given argument.
Error Functions
-
.erf: Returns the value of the Gauss error function for the given argument.
-
.erfc: Returns the value of the complementary error function for the given argument.
Gamma Functions
-
.gamma: Returns the value of the gamma function for the given argument.
-
.lgamma: Returns the value of the logarithmic gamma function for the given argument.
Hypotenuse Function
-
.hypot: Returns
sqrt(a**2 + b**2)
for the givena
andb
.
Constant Summary
-
E =
Definition of the mathematical constant
E
for Euler’s number (e) as a::Float
number.DBL2NUM(M_E)
-
PI =
Definition of the mathematical constant
PI
as a::Float
number.DBL2NUM(M_PI)
Class Method Summary
-
.acos(x) ⇒ Float
mod_func
Returns the arc cosine of
x
. -
.acosh(x) ⇒ Float
mod_func
Returns the inverse hyperbolic cosine of
x
. -
.asin(x) ⇒ Float
mod_func
Returns the arc sine of
x
. -
.asinh(x) ⇒ Float
mod_func
Returns the inverse hyperbolic sine of
x
. -
.atan(x) ⇒ Float
mod_func
Returns the arc tangent of
x
. -
.atan2(y, x) ⇒ Float
mod_func
Returns the arc tangent of
y
andx
in radians. -
.atanh(x) ⇒ Float
mod_func
Returns the inverse hyperbolic tangent of
x
. -
.cbrt(x) ⇒ Float
mod_func
Returns the cube root of
x
. - .cos(x) ⇒ Float mod_func
-
.cosh(x) ⇒ Float
mod_func
Returns the hyperbolic cosine of
x
in radians. -
.erf(x) ⇒ Float
mod_func
Returns the value of the Gauss error function for
x
. -
.erfc(x) ⇒ Float
mod_func
Returns the value of the complementary error function for
x
. -
.exp(x) ⇒ Float
mod_func
Returns
e
raised to thex
power. -
.frexp(x) ⇒ Array, exponent
mod_func
Returns a 2-element array containing the normalized signed float
fraction
and integerexponent
ofx
such that: -
.gamma(x) ⇒ Float
mod_func
Returns the value of the gamma function for
x
. -
.hypot(a, b) ⇒ Float
mod_func
Returns
sqrt(a**2 + b**2)
, which is the length of the longest sidec
(the hypotenuse) of the right triangle whose other sides have lengthsa
andb
. -
.ldexp(fraction, exponent) ⇒ Float
mod_func
Returns the value of
fraction * 2**exponent
. -
.lgamma(x) ⇒ Array, 1
mod_func
Returns a 2-element array equivalent to:
-
.log(x, base = Math::E) ⇒ Float
mod_func
Returns the base
base
logarithm ofx
. -
.log10(x) ⇒ Float
mod_func
Returns the base 10 logarithm of
x
. -
.log2(x) ⇒ Float
mod_func
Returns the base 2 logarithm of
x
. - .sin(x) ⇒ Float mod_func
-
.sinh(x) ⇒ Float
mod_func
Returns the hyperbolic sine of
x
in radians. -
.sqrt(x) ⇒ Float
mod_func
Returns the principal (non-negative) square root of
x
. - .tan(x) ⇒ Float mod_func
-
.tanh(x) ⇒ Float
mod_func
Returns the hyperbolic tangent of
x
in radians.
Class Method Details
.acos(x) ⇒ Float (mod_func)
Returns the arc cosine of x
.
-
Domain:
[-1, 1]
. -
Range:
[0, PI]
.
Examples:
acos(-1.0) # => 3.141592653589793 # PI
acos(0.0) # => 1.5707963267948966 # PI/2
acos(1.0) # => 0.0
# File 'math.c', line 196
static VALUE math_acos(VALUE unused_obj, VALUE x) { math_arc(x, acos) }
.acosh(x) ⇒ Float (mod_func)
Returns the inverse hyperbolic cosine of x
.
-
Domain:
[1, INFINITY]
. -
Range:
[0, INFINITY]
.
Examples:
acosh(1.0) # => 0.0
acosh(INFINITY) # => Infinity
# File 'math.c', line 371
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 (mod_func)
Returns the arc sine of x
.
-
Domain:
[-1, -1]
. -
Range:
[-PI/2, PI/2]
.
Examples:
asin(-1.0) # => -1.5707963267948966 # -PI/2
asin(0.0) # => 0.0
asin(1.0) # => 1.5707963267948966 # PI/2
# File 'math.c', line 219
static VALUE math_asin(VALUE unused_obj, VALUE x) { math_arc(x, asin) }
.asinh(x) ⇒ Float (mod_func)
Returns the inverse hyperbolic sine of x
.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[-INFINITY, INFINITY]
.
Examples:
asinh(-INFINITY) # => -Infinity
asinh(0.0) # => 0.0
asinh(INFINITY) # => Infinity
# File 'math.c', line 398
static VALUE math_asinh(VALUE unused_obj, VALUE x) { return DBL2NUM(asinh(Get_Double(x))); }
.atan(x) ⇒ Float (mod_func)
Returns the arc tangent of x
.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[-PI/2, PI/2]
.
Examples:
atan(-INFINITY) # => -1.5707963267948966 # -PI2
atan(-PI) # => -1.2626272556789115
atan(-PI/2) # => -1.0038848218538872
atan(0.0) # => 0.0
atan(PI/2) # => 1.0038848218538872
atan(PI) # => 1.2626272556789115
atan(INFINITY) # => 1.5707963267948966 # PI/2
# File 'math.c', line 246
static VALUE math_atan(VALUE unused_obj, VALUE x) { return DBL2NUM(atan(Get_Double(x))); }
.atan2(y, x) ⇒ Float (mod_func)
Returns the arc tangent of y
and x
in radians.
-
Domain of
y
:[-INFINITY, INFINITY]
. -
Domain of
x
:[-INFINITY, INFINITY]
. -
Range:
[-PI, PI]
.
Examples:
atan2(-1.0, -1.0) # => -2.356194490192345 # -3*PI/4
atan2(-1.0, 0.0) # => -1.5707963267948966 # -PI/2
atan2(-1.0, 1.0) # => -0.7853981633974483 # -PI/4
atan2(0.0, -1.0) # => 3.141592653589793 # PI
# File 'math.c', line 61
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 (mod_func)
Returns the inverse hyperbolic tangent of x
.
-
Domain:
[-1, 1]
. -
Range:
[-INFINITY, INFINITY]
.
Examples:
atanh(-1.0) # => -Infinity
atanh(0.0) # => 0.0
atanh(1.0) # => Infinity
# File 'math.c', line 421
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 (mod_func)
Returns the cube root of x
.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[-INFINITY, INFINITY]
.
Examples:
cbrt(-INFINITY) # => -Infinity
cbrt(-27.0) # => -3.0
cbrt(-8.0) # => -2.0
cbrt(-2.0) # => -1.2599210498948732
cbrt(1.0) # => 1.0
cbrt(0.0) # => 0.0
cbrt(1.0) # => 1.0
cbrt(2.0) # => 1.2599210498948732
cbrt(8.0) # => 2.0
cbrt(27.0) # => 3.0
cbrt(INFINITY) # => Infinity
# File 'math.c', line 741
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 (mod_func)
# File 'math.c', line 112
static VALUE math_cos(VALUE unused_obj, VALUE x) { return DBL2NUM(cos(Get_Double(x))); }
.cosh(x) ⇒ Float (mod_func)
Returns the hyperbolic cosine of x
in radians.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[1, INFINITY]
.
Examples:
cosh(-INFINITY) # => Infinity
cosh(0.0) # => 1.0
cosh(INFINITY) # => Infinity
# File 'math.c', line 278
static VALUE math_cosh(VALUE unused_obj, VALUE x) { return DBL2NUM(cosh(Get_Double(x))); }
.erf(x) ⇒ Float (mod_func)
Returns the value of the Gauss error function for x
.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[-1, 1]
.
Examples:
erf(-INFINITY) # => -1.0
erf(0.0) # => 0.0
erf(INFINITY) # => 1.0
Related: .erfc.
# File 'math.c', line 874
static VALUE math_erf(VALUE unused_obj, VALUE x) { return DBL2NUM(erf(Get_Double(x))); }
.erfc(x) ⇒ Float (mod_func)
Returns the value of the complementary error function for x
.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[0, 2]
.
Examples:
erfc(-INFINITY) # => 2.0
erfc(0.0) # => 1.0
erfc(INFINITY) # => 0.0
Related: .erf.
# File 'math.c', line 899
static VALUE math_erfc(VALUE unused_obj, VALUE x) { return DBL2NUM(erfc(Get_Double(x))); }
.exp(x) ⇒ Float (mod_func)
Returns e
raised to the x
power.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[0, INFINITY]
.
Examples:
exp(-INFINITY) # => 0.0
exp(-1.0) # => 0.36787944117144233 # 1.0/E
exp(0.0) # => 1.0
exp(0.5) # => 1.6487212707001282 # sqrt(E)
exp(1.0) # => 2.718281828459045 # E
exp(2.0) # => 7.38905609893065 # E**2
exp(INFINITY) # => Infinity
# File 'math.c', line 455
static VALUE math_exp(VALUE unused_obj, VALUE x) { return DBL2NUM(exp(Get_Double(x))); }
.frexp(x) ⇒ Array, exponent
(mod_func)
Returns a 2-element array containing the normalized signed float fraction
and integer exponent
of x
such that:
x = fraction * 2**exponent
See IEEE 754 double-precision binary floating-point format: binary64.
-
Domain:
[-INFINITY, INFINITY]
. -
::Range
[-INFINITY, INFINITY]
.
Examples:
frexp(-INFINITY) # => [-Infinity, -1]
frexp(-2.0) # => [-0.5, 2]
frexp(-1.0) # => [-0.5, 1]
frexp(0.0) # => [0.0, 0]
frexp(1.0) # => [0.5, 1]
frexp(2.0) # => [0.5, 2]
frexp(INFINITY) # => [Infinity, -1]
Related: .ldexp (inverse of frexp
).
# File 'math.c', line 782
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 (mod_func)
Returns the value of the gamma function for x
.
-
Domain:
(-INFINITY, INFINITY]
excluding negative integers. -
Range:
[-INFINITY, INFINITY]
.
Examples:
gamma(-2.5) # => -0.9453087204829431
gamma(-1.5) # => 2.3632718012073513
gamma(-0.5) # => -3.5449077018110375
gamma(0.0) # => Infinity
gamma(1.0) # => 1.0
gamma(2.0) # => 1.0
gamma(3.0) # => 2.0
gamma(4.0) # => 6.0
gamma(5.0) # => 24.0
Related: .lgamma.
# File 'math.c', line 930
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(a, b) ⇒ Float (mod_func)
Returns sqrt(a**2 + b**2)
, which is the length of the longest side c
(the hypotenuse) of the right triangle whose other sides have lengths a
and b
.
-
Domain of
a
:[-INFINITY, INFINITY]
. -
Domain of +ab:
[-INFINITY, INFINITY]
. -
Range:
[0, INFINITY]
.
Examples:
hypot(0.0, 1.0) # => 1.0
hypot(1.0, 1.0) # => 1.4142135623730951 # sqrt(2.0)
hypot(3.0, 4.0) # => 5.0
hypot(5.0, 12.0) # => 13.0
hypot(1.0, sqrt(3.0)) # => 1.9999999999999998 # Near 2.0
Note that if either argument is INFINITY
or -INFINITY
, the result is Infinity
.
# File 'math.c', line 849
static VALUE math_hypot(VALUE unused_obj, VALUE x, VALUE y) { return DBL2NUM(hypot(Get_Double(x), Get_Double(y))); }
.ldexp(fraction, exponent) ⇒ Float (mod_func)
Returns the value of fraction * 2**exponent
.
-
Domain of
fraction
:[0.0, 1.0)
. -
Domain of
exponent
:[0, 1024]
(larger values are equivalent to 1024).
See IEEE 754 double-precision binary floating-point format: binary64.
Examples:
ldexp(-INFINITY, -1) # => -Infinity
ldexp(-0.5, 2) # => -2.0
ldexp(-0.5, 1) # => -1.0
ldexp(0.0, 0) # => 0.0
ldexp(-0.5, 1) # => 1.0
ldexp(-0.5, 2) # => 2.0
ldexp(INFINITY, -1) # => Infinity
Related: .frexp (inverse of ldexp
).
# File 'math.c', line 818
static VALUE math_ldexp(VALUE unused_obj, VALUE x, VALUE n) { return DBL2NUM(ldexp(Get_Double(x), NUM2INT(n))); }
.lgamma(x) ⇒ Array, 1
(mod_func)
Returns a 2-element array equivalent to:
[Math.log(Math.gamma(x).abs), Math.gamma(x) < 0 ? -1 : 1]
See logarithmic gamma function.
-
Domain:
(-INFINITY, INFINITY]
. -
::Range
of first element:(-INFINITY, INFINITY]
. -
Second element is -1 or 1.
Examples:
lgamma(-4.0) # => [Infinity, -1]
lgamma(-3.0) # => [Infinity, -1]
lgamma(-2.0) # => [Infinity, -1]
lgamma(-1.0) # => [Infinity, -1]
lgamma(0.0) # => [Infinity, 1]
lgamma(1.0) # => [0.0, 1]
lgamma(2.0) # => [0.0, 1]
lgamma(3.0) # => [0.6931471805599436, 1]
lgamma(4.0) # => [1.7917594692280545, 1]
lgamma(-2.5) # => [-0.05624371649767279, -1]
lgamma(-1.5) # => [0.8600470153764797, 1]
lgamma(-0.5) # => [1.265512123484647, -1]
lgamma(0.5) # => [0.5723649429247004, 1]
lgamma(1.5) # => [-0.12078223763524676, 1]
lgamma(2.5) # => [0.2846828704729205, 1]
Related: .gamma.
# File 'math.c', line 1019
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, base = Math::E) ⇒ Float (mod_func)
Returns the base base
logarithm of x
.
-
Domain:
[0, INFINITY]
. -
Range:
[-INFINITY, INFINITY)]
.
Examples:
log(0.0) # => -Infinity
log(1.0) # => 0.0
log(E) # => 1.0
log(INFINITY) # => Infinity
log(0.0, 2.0) # => -Infinity
log(1.0, 2.0) # => 0.0
log(2.0, 2.0) # => 1.0
log(0.0, 10.0) # => -Infinity
log(1.0, 10.0) # => 0.0
log(10.0, 10.0) # => 1.0
# File 'math.c', line 505
static VALUE math_log(int argc, const VALUE *argv, VALUE unused_obj) { return rb_math_log(argc, argv); }
.log10(x) ⇒ Float (mod_func)
Returns the base 10 logarithm of x
.
-
Domain:
[0, INFINITY]
. -
Range:
[-INFINITY, INFINITY]
.
Examples:
log10(0.0) # => -Infinity
log10(1.0) # => 0.0
log10(10.0) # => 1.0
log10(INFINITY) # => Infinity
# File 'math.c', line 637
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 (mod_func)
Returns the base 2 logarithm of x
.
-
Domain:
[0, INFINITY]
. -
Range:
[-INFINITY, INFINITY]
.
Examples:
log2(0.0) # => -Infinity
log2(1.0) # => 0.0
log2(2.0) # => 1.0
log2(INFINITY) # => Infinity
# File 'math.c', line 606
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 (mod_func)
# File 'math.c', line 139
static VALUE math_sin(VALUE unused_obj, VALUE x) { return DBL2NUM(sin(Get_Double(x))); }
.sinh(x) ⇒ Float (mod_func)
Returns the hyperbolic sine of x
in radians.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[-INFINITY, INFINITY]
.
Examples:
sinh(-INFINITY) # => -Infinity
sinh(0.0) # => 0.0
sinh(INFINITY) # => Infinity
# File 'math.c', line 310
static VALUE math_sinh(VALUE unused_obj, VALUE x) { return DBL2NUM(sinh(Get_Double(x))); }
.sqrt(x) ⇒ Float (mod_func)
Returns the principal (non-negative) square root of x
.
-
Domain:
[0, INFINITY]
. -
Range:
[0, INFINITY]
.
Examples:
sqrt(0.0) # => 0.0
sqrt(0.5) # => 0.7071067811865476
sqrt(1.0) # => 1.0
sqrt(2.0) # => 1.4142135623730951
sqrt(4.0) # => 2.0
sqrt(9.0) # => 3.0
sqrt(INFINITY) # => Infinity
# File 'math.c', line 673
static VALUE math_sqrt(VALUE unused_obj, VALUE x) { return rb_math_sqrt(x); }
.tan(x) ⇒ Float (mod_func)
Returns the tangent of x
in radians.
-
Domain:
(-INFINITY, INFINITY)
. -
Range:
(-INFINITY, INFINITY)
.
Examples:
tan(-PI) # => 1.2246467991473532e-16 # -0.0000000000000001
tan(-PI/2) # => -1.633123935319537e+16 # -16331239353195370.0
tan(0.0) # => 0.0
tan(PI/2) # => 1.633123935319537e+16 # 16331239353195370.0
tan(PI) # => -1.2246467991473532e-16 # -0.0000000000000001
# File 'math.c', line 167
static VALUE math_tan(VALUE unused_obj, VALUE x) { return DBL2NUM(tan(Get_Double(x))); }
.tanh(x) ⇒ Float (mod_func)
Returns the hyperbolic tangent of x
in radians.
-
Domain:
[-INFINITY, INFINITY]
. -
Range:
[-1, 1]
.
Examples:
tanh(-INFINITY) # => -1.0
tanh(0.0) # => 0.0
tanh(INFINITY) # => 1.0
# File 'math.c', line 349
static VALUE math_tanh(VALUE unused_obj, VALUE x) { return DBL2NUM(tanh(Get_Double(x))); }