# Module: Math

Defined in:
math.c

## Constant Summary collapse

PI =
`rb_float_new(atan(1.0)*4.0)`
E =
`rb_float_new(exp(1.0))`

## Class Method Summary collapse

• Computes the arc cosine of x.

• Computes the inverse hyperbolic cosine of x.

• Computes the arc sine of x.

• Computes the inverse hyperbolic sine of x.

• Computes the arc tangent of x.

• Computes the arc tangent given y and x.

• Computes the inverse hyperbolic tangent of x.

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

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

• Calculates the error function of x.

• Calculates the complementary error function of x.

• Returns e**x.

• Returns a two-element array containing the normalized fraction (a `Float`) and exponent (a `Fixnum`) of numeric.

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

• Returns the value of flt*(2**int).

• Returns the natural logarithm of numeric.

• Returns the base 10 logarithm of numeric.

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

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

• Returns the non-negative square root of numeric.

• Returns the tangent of x (expressed in radians).

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

## Class Method Details

### .acos(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.acos(x) => float * * Computes the arc cosine of x. Returns 0..PI. */ static VALUE math_acos(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = acos(RFLOAT(x)->value); domain_check(d, "acos"); return rb_float_new(d); }```

### .acosh(x) ⇒ Float

Computes the inverse hyperbolic cosine of x.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.acosh(x) => float * * Computes the inverse hyperbolic cosine of x. */ static VALUE math_acosh(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = acosh(RFLOAT(x)->value); domain_check(d, "acosh"); return rb_float_new(d); }```

### .asin(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.asin(x) => float * * Computes the arc sine of x. Returns -{PI/2} .. {PI/2}. */ static VALUE math_asin(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = asin(RFLOAT(x)->value); domain_check(d, "asin"); return rb_float_new(d); }```

### .asinh(x) ⇒ Float

Computes the inverse hyperbolic sine of x.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.asinh(x) => float * * Computes the inverse hyperbolic sine of x. */ static VALUE math_asinh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(asinh(RFLOAT(x)->value)); }```

### .atan(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.atan(x) => float * * Computes the arc tangent of x. Returns -{PI/2} .. {PI/2}. */ static VALUE math_atan(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(atan(RFLOAT(x)->value)); }```

### .atan2(y, x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.atan2(y, x) => float * * Computes the arc tangent given y and x. Returns * -PI..PI. * */ static VALUE math_atan2(obj, y, x) VALUE obj, x, y; { Need_Float2(y, x); return rb_float_new(atan2(RFLOAT(y)->value, RFLOAT(x)->value)); }```

### .atanh(x) ⇒ Float

Computes the inverse hyperbolic tangent of x.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.atanh(x) => float * * Computes the inverse hyperbolic tangent of x. */ static VALUE math_atanh(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = atanh(RFLOAT(x)->value); domain_check(d, "atanh"); return rb_float_new(d); }```

### .cos(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.cos(x) => float * * Computes the cosine of x (expressed in radians). Returns * -1..1. */ static VALUE math_cos(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(cos(RFLOAT(x)->value)); }```

### .cosh(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.cosh(x) => float * * Computes the hyperbolic cosine of x (expressed in radians). */ static VALUE math_cosh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(cosh(RFLOAT(x)->value)); }```

### .erf(x) ⇒ Float

Calculates the error function of x.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.erf(x) => float * * Calculates the error function of x. */ static VALUE math_erf(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(erf(RFLOAT(x)->value)); }```

### .erfc(x) ⇒ Float

Calculates the complementary error function of x.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.erfc(x) => float * * Calculates the complementary error function of x. */ static VALUE math_erfc(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(erfc(RFLOAT(x)->value)); }```

### .exp(x) ⇒ Float

Returns e**x.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.exp(x) => float * * Returns e**x. */ static VALUE math_exp(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(exp(RFLOAT(x)->value)); }```

### .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' /* * call-seq: * Math.frexp(numeric) => [ fraction, exponent ] * * 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(obj, x) VALUE obj, x; { double d; int exp; Need_Float(x); d = frexp(RFLOAT(x)->value, &exp); return rb_assoc_new(rb_float_new(d), INT2NUM(exp)); }```

### .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' /* * call-seq: * Math.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 */ static VALUE math_hypot(obj, x, y) VALUE obj, x, y; { Need_Float2(x, y); return rb_float_new(hypot(RFLOAT(x)->value, RFLOAT(y)->value)); }```

### .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' /* * call-seq: * Math.ldexp(flt, int) -> float * * Returns the value of flt*(2**int). * * fraction, exponent = Math.frexp(1234) * Math.ldexp(fraction, exponent) #=> 1234.0 */ static VALUE math_ldexp(obj, x, n) VALUE obj, x, n; { Need_Float(x); return rb_float_new(ldexp(RFLOAT(x)->value, NUM2INT(n))); }```

### .log(numeric) ⇒ Float

Returns the natural logarithm of numeric.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.log(numeric) => float * * Returns the natural logarithm of numeric. */ static VALUE math_log(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = log(RFLOAT(x)->value); domain_check(d, "log"); return rb_float_new(d); }```

### .log10(numeric) ⇒ Float

Returns the base 10 logarithm of numeric.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.log10(numeric) => float * * Returns the base 10 logarithm of numeric. */ static VALUE math_log10(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = log10(RFLOAT(x)->value); domain_check(d, "log10"); return rb_float_new(d); }```

### .sin(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.sin(x) => float * * Computes the sine of x (expressed in radians). Returns * -1..1. */ static VALUE math_sin(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(sin(RFLOAT(x)->value)); }```

### .sinh(x) ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.sinh(x) => float * * Computes the hyperbolic sine of x (expressed in * radians). */ static VALUE math_sinh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(sinh(RFLOAT(x)->value)); }```

### .sqrt(numeric) ⇒ Float

Returns the non-negative square root of numeric.

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.sqrt(numeric) => float * * Returns the non-negative square root of numeric. */ static VALUE math_sqrt(obj, x) VALUE obj, x; { double d; Need_Float(x); errno = 0; d = sqrt(RFLOAT(x)->value); domain_check(d, "sqrt"); return rb_float_new(d); }```

### .tan(x) ⇒ Float

Returns the tangent of x (expressed in radians).

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.tan(x) => float * * Returns the tangent of x (expressed in radians). */ static VALUE math_tan(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(tan(RFLOAT(x)->value)); }```

### .tanh ⇒ Float

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

Returns:

 ``` ``` ```# File 'math.c' /* * call-seq: * Math.tanh() => float * * Computes the hyperbolic tangent of x (expressed in * radians). */ static VALUE math_tanh(obj, x) VALUE obj, x; { Need_Float(x); return rb_float_new(tanh(RFLOAT(x)->value)); }```