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.
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);
}
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);
}
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);
}
Computes the inverse hyperbolic sine of x.
static VALUE
math_asinh(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(asinh(RFLOAT_VALUE(x)));
}
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)));
}
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)
{
double dx, dy;
Need_Float2(y, x);
dx = RFLOAT_VALUE(x);
dy = RFLOAT_VALUE(y);
if (dx == 0.0 && dy == 0.0) domain_error("atan2");
if (isinf(dx) && isinf(dy)) domain_error("atan2");
return DBL2NUM(atan2(dy, dx));
}
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);
}
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)));
}
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)));
}
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)));
}
Calculates the error function of x.
static VALUE
math_erf(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(erf(RFLOAT_VALUE(x)));
}
Calculates the complementary error function of x.
static VALUE
math_erfc(VALUE obj, VALUE x)
{
Need_Float(x);
return DBL2NUM(erfc(RFLOAT_VALUE(x)));
}
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)));
}
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));
}
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);
}
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)));
}
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)));
}
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.
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));
}
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);
}
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);
}
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);
}
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)));
}
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)));
}
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);
}