Math Module

ZPy provides a math module with mathematical functions and constants, similar to Python's math module.

Constants

Function	Value	Description
math_pi()	3.14159...	π (pi)
math_e()	2.71828...	Euler's number
math_tau()	6.28318...	τ (tau = 2π)
math_inf()	inf	Positive infinity
math_nan()	nan	Not a Number

print(math_pi())  # 3.141592653589793
print(math_e())   # 2.718281828459045
print(math_tau()) # 6.283185307179586

Power and Logarithmic Functions

math_sqrt(x)

Returns the square root of x.

print(math_sqrt(16))   # 4.0
print(math_sqrt(2))    # 1.4142135623730951

math_cbrt(x)

Returns the cube root of x.

print(math_cbrt(27))   # 3.0
print(math_cbrt(8))    # 2.0

math_exp(x)

Returns e raised to the power of x.

print(math_exp(1))     # 2.7182818284590455
print(math_exp(0))     # 1.0

math_expm1(x)

Returns e^x - 1. More accurate than math_exp(x) - 1 for small x.

print(math_expm1(0))   # 0.0
print(math_expm1(1))   # 1.7182818284590453

math_log(x)

Returns the natural logarithm of x.

print(math_log(math_e()))  # 1.0
print(math_log(1))         # 0.0

math_log2(x)

Returns the base-2 logarithm of x.

print(math_log2(8))    # 3.0
print(math_log2(1024)) # 10.0

math_log10(x)

Returns the base-10 logarithm of x.

print(math_log10(100)) # 2.0
print(math_log10(1000))# 3.0

math_log1p(x)

Returns ln(1 + x). More accurate than math_log(1 + x) for small x.

print(math_log1p(0))   # 0.0
print(math_log1p(1))   # 0.6931471805599453

Trigonometric Functions

All trigonometric functions use radians.

math_sin(x), math_cos(x), math_tan(x)

print(math_sin(math_pi() / 2))  # 1.0
print(math_cos(0))              # 1.0
print(math_tan(math_pi() / 4))  # 1.0

math_asin(x), math_acos(x), math_atan(x)

Inverse trigonometric functions. Return values in radians.

print(math_asin(1))   # 1.5707963267948966 (π/2)
print(math_acos(0))   # 1.5707963267948966 (π/2)
print(math_atan(1))   # 0.7853981633974483 (π/4)

math_atan2(y, x)

Returns the arc tangent of y/x in radians, using the signs of both arguments to determine the quadrant.

print(math_atan2(1, 1))   # 0.7853981633974483 (π/4)
print(math_atan2(1, -1))  # 2.356194490192345 (3π/4)

Hyperbolic Functions

math_sinh(x), math_cosh(x), math_tanh(x)

print(math_sinh(0))   # 0.0
print(math_cosh(0))   # 1.0
print(math_tanh(0))   # 0.0

math_asinh(x), math_acosh(x), math_atanh(x)

Inverse hyperbolic functions.

print(math_asinh(0))  # 0.0
print(math_acosh(1))  # 0.0
print(math_atanh(0))  # 0.0

Rounding Functions

math_floor(x)

Returns the largest integer less than or equal to x.

print(math_floor(3.7))   # 3.0
print(math_floor(-3.2))  # -4.0

math_ceil(x)

Returns the smallest integer greater than or equal to x.

print(math_ceil(3.2))    # 4.0
print(math_ceil(-3.7))   # -3.0

math_round(x)

Returns x rounded to the nearest integer.

print(math_round(3.5))   # 4.0
print(math_round(3.4))   # 3.0

math_trunc(x)

Returns x with the fractional part removed.

print(math_trunc(3.9))   # 3.0
print(math_trunc(-3.9))  # -3.0

Utility Functions

math_fabs(x)

Returns the absolute value of x as a float.

print(math_fabs(-5))     # 5.0
print(math_fabs(-3.14))  # 3.14

Note: The builtin abs(x) returns int for int input, float for float input. math_fabs always returns float.

math_fmod(x, y)

Returns the remainder of x / y.

print(math_fmod(10, 3))  # 1.0
print(math_fmod(7, 2.5)) # 2.0

math_modf(x)

Returns a list [fractional, integer] containing the fractional and integer parts of x.

result = math_modf(3.14)
print(result[0])  # 0.14 (fractional)
print(result[1])  # 3.0 (integer)

math_copysign(x, y)

Returns x with the sign of y.

print(math_copysign(5, -1))   # -5.0
print(math_copysign(-5, 1))   # 5.0

math_hypot(x, y)

Returns the Euclidean distance sqrt(x² + y²).

print(math_hypot(3, 4))  # 5.0
print(math_hypot(5, 12)) # 13.0

Example: Calculate Distance

# Distance between two points
def distance(x1, y1, x2, y2):
    dx = x2 - x1
    dy = y2 - y1
    return math_hypot(dx, dy)

print(distance(0, 0, 3, 4))  # 5.0

Example: Degrees to Radians

def degrees_to_radians(degrees):
    return degrees * math_pi() / 180

print(math_sin(degrees_to_radians(90)))  # 1.0

Summary Table

Function	Description
math_sqrt(x)	Square root
math_cbrt(x)	Cube root
math_exp(x)	e^x
math_expm1(x)	e^x - 1
math_log(x)	Natural log
math_log2(x)	Base-2 log
math_log10(x)	Base-10 log
math_log1p(x)	ln(1+x)
math_sin(x)	Sine
math_cos(x)	Cosine
math_tan(x)	Tangent
math_asin(x)	Arc sine
math_acos(x)	Arc cosine
math_atan(x)	Arc tangent
math_atan2(y, x)	Arc tangent of y/x
math_sinh(x)	Hyperbolic sine
math_cosh(x)	Hyperbolic cosine
math_tanh(x)	Hyperbolic tangent
math_asinh(x)	Inverse hyperbolic sine
math_acosh(x)	Inverse hyperbolic cosine
math_atanh(x)	Inverse hyperbolic tangent
math_floor(x)	Round down
math_ceil(x)	Round up
math_round(x)	Round to nearest
math_trunc(x)	Truncate
math_fabs(x)	Absolute value (float)
math_fmod(x, y)	Remainder
math_modf(x)	Fractional and integer parts
math_copysign(x, y)	Copy sign
math_hypot(x, y)	Euclidean distance
math_pi()	π constant
math_e()	e constant
math_tau()	τ constant
math_inf()	Infinity
math_nan()	NaN