The math extensions provide mathematical functions such as trigonometry, logarithms, rounding and related utilities. These extensions may or may not be present depending on the platform and configuration of LispBM.

Trigonometry

sin

Computes the sine of a given angle (in radians). The form of a sin expression is (sin expr).

(sin 0.500000f32)

0.479426f32

(sin 3.141593f32)

0.000000f32

(sin (* 0.500000f32 3.141592f32))

1.000000f32

cos

Computes the cosine of a given angle (in radians). The form of a cos expression is (cos expr).

(cos 0.500000f32)

0.877583f32

(cos 3.141593f32)

-1.000000f32

(cos (* 0.500000f32 3.141592f32))

0.000000f32

tan

Computes the tangent of a given angle (in radians). The form of a tan expression is (tan expr).

(tan 0.500000f32)

0.546302f32

(tan 3.141593f32)

-0.000000f32

(tan (* 0.500000f32 3.141592f32))

3185560.750000f32

asin

Computes the arcsine of a value, returning an angle in radians. The form of an asin expression is (asin expr). The argument should be in the range [-1, 1].

(asin 0.000000f32)

0.000000f32

(asin 1.000000f32)

1.570796f32

(asin 0.500000f32)

0.523599f32

acos

Computes the arccosine of a value, returning an angle in radians. The form of an acos expression is (acos expr). The argument should be in the range [-1, 1].

(acos 0.000000f32)

1.570796f32

(acos 1.000000f32)

0.000000f32

(acos 0.500000f32)

1.047198f32

atan

Computes the arctangent of a value, returning an angle in radians. The form of an atan expression is (atan expr).

(atan 0.000000f32)

0.000000f32

(atan 1.000000f32)

0.785398f32

(atan -1.000000f32)

-0.785398f32

atan2

Computes the arctangent of y/x, using the signs of both arguments to determine the correct quadrant. Returns an angle in radians in the range [-pi, pi]. The form of an atan2 expression is (atan2 y x).

(atan2 1.000000f32 1.000000f32)

0.785398f32

(atan2 0.000000f32 -1.000000f32)

3.141593f32

(atan2 -1.000000f32 0.000000f32)

-1.570796f32

Exponential and Logarithm

pow

Raises a base to a given exponent. The form of a pow expression is (pow base exponent).

(pow 2.000000f32 10.000000f32)

1024.000000f32

(pow 3.000000f32 3.000000f32)

27.000000f32

(pow 2.000000f32 0.500000f32)

1.414214f32

exp

Computes the exponential function e raised to the power of the argument. The form of an exp expression is (exp expr).

(exp 0.000000f32)

1.000000f32

(exp 1.000000f32)

2.718282f32

(exp -1.000000f32)

0.367879f32

sqrt

Computes the square root of a number. The form of a sqrt expression is (sqrt expr).

(sqrt 4.000000f32)

2.000000f32

(sqrt 2.000000f32)

1.414214f32

(sqrt 0.000000f32)

0.000000f32

log

Computes the natural logarithm (base e) of a number. The form of a log expression is (log expr).

(log 1.000000f32)

0.000000f32

(log 2.718282f32)

1.000000f32

(log 10.000000f32)

2.302585f32

log10

Computes the base-10 logarithm of a number. The form of a log10 expression is (log10 expr).

(log10 1.000000f32)

0.000000f32

(log10 10.000000f32)

1.000000f32

(log10 100.000000f32)

2.000000f32

Rounding

floor

Rounds a number down to the nearest integer, returning a float. The form of a floor expression is (floor expr).

(floor 1.600000f32)

1.000000f32

(floor -1.600000f32)

-2.000000f32

(floor 2.000000f32)

2.000000f32

ceil

Rounds a number up to the nearest integer, returning a float. The form of a ceil expression is (ceil expr).

(ceil 1.200000f32)

2.000000f32

(ceil -1.200000f32)

-1.000000f32

(ceil 2.000000f32)

2.000000f32

round

Rounds a number to the nearest integer, returning a float. Halfway cases are rounded away from zero. The form of a round expression is (round expr).

(round 1.400000f32)

1.000000f32

(round 1.500000f32)

2.000000f32

(round -1.500000f32)

-2.000000f32

Angle Conversion

deg2rad

Converts degrees to radians. When called with a single argument the form is (deg2rad expr). When called with multiple arguments, each is converted and the results are returned as a list.

(deg2rad 180.000000f32)

3.141593f32

(deg2rad 90.000000f32)

1.570796f32

(deg2rad 0.000000f32 90.000000f32 180.000000f32 270.000000f32 360.000000f32)

(0.000000f32 1.570796f32 3.141593f32 4.712389f32 6.283185f32)

rad2deg

Converts radians to degrees. When called with a single argument the form is (rad2deg expr). When called with multiple arguments, each is converted and the results are returned as a list.

(rad2deg 3.141592f32)

179.999969f32

(rad2deg 1.570796f32)

90.000000f32

(rad2deg 0.000000f32 1.570796f32 3.141592f32)

(0.000000f32 90.000000f32 179.999969f32)

Floating-point Predicates

is-nan

is-nan checks whether a floating-point value is NaN (not a number). Returns t if the value is NaN and nil otherwise. The form of an is-nan expression is (is-nan expr). Only float and double values can be NaN; any other number type returns nil. NaN can arise from operations such as (sqrt -1.0) or (asin 2.0). Note that division by zero is an error in LispBM and does not produce NaN.

(is-nan (sqrt -1.000000f32))

t

(is-nan (asin 2.000000f32))

t

(is-nan 1.000000f32)

nil

is-inf

is-inf checks whether a floating-point value is infinite. Returns t if the value is positive or negative infinity, nil otherwise. The form of an is-inf expression is (is-inf expr). Only float and double values can be infinite; any other number type returns nil. Infinity can arise from operations such as (exp 1000.0) or (log 0.0). Note that division by zero is an error in LispBM and does not produce infinity.

(is-inf (exp 1000.000000f32))

t

(is-inf (log 0.000000f32))

t

(is-inf 1.000000f32)

nil

This document was generated by LispBM version 0.36.0