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  • math.c

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

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

 
 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);
 }
 if (isinf(dx) && isinf(dy)) domain_error("atan2");
 return DBL2NUM(atan2(dy, dx));
}
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);
 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 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.

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

 
 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 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]

 
 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. */
 };
 double d0, d;
 double intpart, fracpart;
 Need_Float(x);
 d0 = RFLOAT_VALUE(x);
 /* check for domain error */
 if (isinf(d0) && signbit(d0)) domain_error("gamma");
 fracpart = modf(d0, &intpart);
 if (fracpart == 0.0) {
 if (intpart < 0) domain_error("gamma");
 if (0 < intpart &&
 intpart - 1 < (double)numberof(fact_table)) {
 return DBL2NUM(fact_table[(int)intpart - 1]);
 }
 }
 d = tgamma(d0);
 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=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));
 }
 d = lgamma_r(d0, &sign);
 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.

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

 
 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));
 }
 return DBL2NUM(d);
}
log10(numeric) → float click to toggle source

Returns the base 10 logarithm of numeric.

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

 
 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 click to toggle source

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

 
 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 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);
 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 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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