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

SQRT() returns the square root of a number. A perfect square comes back exact, and any other root is correct to the last digit a REAL holds. The square root of a negative number raises an error -- give it as a complex number, sqrt(-4 + 0i), for the complex root. SQR() is an older name for the same function.

print sqrt(64) // Returns: 8 print sqrt(2) // Returns: 1.414213562373095 print sqrt(-4 + 0i) // Returns: 0+2i

SGN() returns the sign of a number: -1 for a negative number, 0 for zero, and 1 for a positive number.

print sgn(-238) // Returns: -1 print sgn(0) // Returns: 0 print sgn(238) // Returns: 1

EPS is the smallest step a REAL value can take in its exact range: 0.0000000000000001, one unit of the 16-decimal grid (see the REAL data type page). Use it as the tolerance for "close enough" comparisons of computed decimals -- abs(a - b) <= eps -- instead of a magic number.

print eps // Returns: 0.0000000000000001 print abs(0.1 + 0.2 - 0.3) <= eps // Returns: 1

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

DIV0INF() divides two numbers by the IEEE rules: a nonzero number over 0 is Inf or -Inf, 0 / 0 is NaN, anything else is the ordinary exact division. The companion of div0() for when a hole or an infinity is the honest answer (the plain / raises DIVBY0).

print div0inf(6, 3) // Returns: 2 print div0inf(6, 0) // Returns: Inf print div0inf(-6, 0) // Returns: -Inf print div0inf(0, 0) // Returns: NaN

DIVR() divides and keeps the exact fraction when the quotient does not terminate: divr(1, 3) * 3 is exactly 1, where 1 / 3 * 3 is 0.9999999999999999. Its operands are whole numbers, fractions, or decimals of up to nine places (divr(0.05, 12) is 1/240); a quotient that terminates is an ordinary decimal (divr(1, 4) is 0.25), and a zero divisor raises DIVBY0 as / does. How fractions behave in arithmetic, in comparison and in print is on the REAL internals page (Internals: REAL and String Data Types).

print divr(1, 3) * 3 // Returns: 1 print fraction$(divr(0.05, 12)) // Returns: 1/240 print divr(1, 4) // Returns: 0.25

NUMERATOR() and DENOMINATOR() take a fraction apart (a decimal gives its reduced fraction's parts, a value in scientific form too, and a whole number itself and 1), and DECIMAL() rounds a fraction to its sixteen-place decimal.

print numerator(divr(22, 7)) // Returns: 22 print denominator(divr(22, 7)) // Returns: 7 print denominator(0.25) // Returns: 4 print decimal(divr(2, 3)) // Returns: 0.6666666666666667

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)

SEC() returns the secant of an angle in radians, which is 1 / cos().

print sec(0) // Returns: 1

CSC() returns the cosecant of an angle in radians, which is 1 / sin().

print csc(pi / 2) // Returns: 1

COT() returns the cotangent of an angle in radians, which is 1 / tan().

print cot(pi / 4) // Returns: 1

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. ATN() is an older name for the same function.

print atan(0) // Returns: 0 print atan(1) // Returns: 0.7854 (pi/4) print atn(1) // Returns: 0.785398163397448 (the same as atan(1))

ATAN() also returns the arctangent of a number.

print atan(33) // Returns: 1.5405

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

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

DEG() converts an angle in radians to degrees.

print deg(pi) // Returns: 180 print deg(pi / 4) // Returns: 45

RAD() converts an angle in degrees to radians, the unit sin(), cos() and tan() take.

print rad(180) // Returns: 3.1415926535897932 print sin(rad(90)) // Returns: 1

SINH() returns the hyperbolic sine of a number.

print sinh(0) // Returns: 0 print sinh(1) // Returns: 1.1752011936438

COSH() returns the hyperbolic cosine of a number.

print cosh(0) // Returns: 1 print cosh(1) // Returns: 1.54308063481524

TANH() returns the hyperbolic tangent of a number, always between -1 and 1.

print tanh(0) // Returns: 0 print tanh(1) // Returns: 0.761594155955765

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, ROUNDING it to the nearest whole number (a half goes away from zero), where INT() drops the fraction. The result must fit an integer, -2,147,483,648 to 2,147,483,647; a value outside that range raises the catchable exception INTERR ("Integer overflow").

print int(2.7); integer(2.7) // Returns: 2 3 print integer(2.5); integer(-2.5) // Returns: 3 -3 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.

RANDOMIZE starts the random numbers over from an unpredictable point taken from the clock -- the same thing every program run does when it starts, so a program never needs it for that. Its use is to leave a set seed sequence: set seed NN makes rnd() give the same numbers on every run (handy while testing), and randomize goes back to numbers nobody can predict.

set seed 7 print rnd(1000); rnd(1000); rnd(1000) // Returns: 598 300 332 set seed 7 print rnd(1000); rnd(1000); rnd(1000) // Returns: 598 300 332 (the same three) randomize print rnd(1000); rnd(1000); rnd(1000) // Returns: 954 333 830 (different on every run)

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

LOG2() returns the base-2 logarithm of a number.

print log2(8) // Returns: 3 print log2(1024) // Returns: 10

LOG10() returns the base-10 (common) logarithm of a number.

print log10(1000) // Returns: 3 print log10(0.001) // Returns: -3

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.

Common Math Functions

Core Math Functions

Trigonometric Functions

Rounding and Integer Functions

Random Number Functions

Conversion and Utility Functions

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