Common Math Functions

For transcendental functions like sin(), cos(), exp(), and log(), Sheerpower temporarily converts its internal REAL number to a standard DOUBLE, performs the operation, and then converts the result back to a REAL. This is acceptable because the results of these functions are irrational and cannot be represented exactly by any finite-precision data type.

For all other math operations, Sheerpower maintains its high-precision REAL data type throughout the calculation, ensuring maximum numeric accuracy wherever mathematically possible.

Core Math Functions

ABS() returns the absolute value of a number.

print abs(-10) // Returns: 10 print abs(10) // Returns: 10

DIV0() divides two numbers and returns 0 if the divisor is 0.

print div0(0.8, 0.000004) // Returns: 200000 print div0(0.8, 0.0) // Returns: 0 print div0(6, 3) // Returns: 2 print div0(6, 0) // Returns: 0

FP() returns the fractional part of a number.

print fp(238.304) // Returns: 0.304

MOD() returns the remainder of one number divided by another.

print mod(36, 13) // Returns: 10

REMAINDER() returns the remainder of a division operation.

print remainder(-4, 3) // Returns: -1

Trigonometric Functions

SIN() returns the sine of an angle.

print sin(0) // Returns: 0 print sin(1.5708) // Returns: 1 (approximately)

COS() returns the cosine of an angle.

print cos(0) // Returns: 1 print cos(1.5708) // Returns: 0 (approximately)

TAN() returns the tangent of an angle.

print tan(0) // Returns: 0 print tan(0.7854) // Returns: 1 (approximately, pi/4)

ASIN() returns the arcsine of a number.

print asin(0) // Returns: 0 print asin(1) // Returns: 1.5708 (pi/2)

ACOS() returns the arccosine of a number.

print acos(1) // Returns: 0 print acos(0) // Returns: 1.5708 (pi/2)

ATAN() returns the arctangent of a number.

print atan(0) // Returns: 0 print atan(1) // Returns: 0.7854 (pi/4)

ATN() also returns the arctangent of a number.

print atn(33) // Returns: 1.5405

ANGLE() returns the angle from (0,0) to (x,y) in radians.

print angle(4, 9) // Returns: 1.15257

Rounding and Integer Functions

CEIL() returns the smallest integer greater than or equal to a number.

print ceil(2.3) // Returns: 3 print ceil(-2.3) // Returns: -2

FLOOR() returns the largest integer less than or equal to a number.

print floor(2.7) // Returns: 2 print floor(-2.7) // Returns: -3

INT() returns the whole portion of a REAL number as a REAL.

print int(148.8432) // Returns: 148

INTEGER() converts a numeric expression to an integer.

z = integer(4 + (993 * 35)) print z // Returns: 34759

IP() truncates the decimal portion of a number.

print ip(1234.56) // Returns: 1234

ROUND() rounds a number to a specified number of decimal places.

print round(21.83492, 2) // Returns: 21.83

TRUNCATE() cuts off digits after a specified decimal place.

print truncate(123.45678, 2) // Returns: 123.45 print truncate(123.45678, 4) // Returns: 123.4567

Random Number Functions

RND() generates a random number.

print rnd // Returns: 0.94097 (example) print rnd(100) // Returns: 56 (example)

Note: The rnd() function returns a fraction between 0 and 1 when used without parameters. If a numeric argument is provided, it returns a whole number between 1 and that number. Use set seed NN to specify a repeatable sequence.

Conversion and Utility Functions

REAL() converts a numeric expression to a REAL value.

input 'Your age': age% let decimal_age = real(age%) print 'Your number is'; decimal_age // Your age? 31 → Your number is 31

EXP() returns e raised to the power of a number.

print exp(1) // Returns: 2.7183 print exp(0) // Returns: 1

LOG() returns the natural logarithm (base e) of a number.

print log(1) // Returns: 0 print log(2.7183) // Returns: 1

MIN() returns the smaller of two values.

print min(3, 2) // Returns: 2 print min(-1, -5) // Returns: -5

MAX() returns the larger of two values.

print max(5, 9) // Returns: 9

CLAMP() restricts a value to a given range.

print clamp(15, 1, 10) // Returns: 10 print clamp(5, 1, 10) // Returns: 5 print clamp(-3, 1, 10) // Returns: 1

Sheerpower provides a wide range of additional built-in math functions. Most operate directly on its REAL data type to preserve precision throughout. For a complete reference, see the documentation here.

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