Math

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Latest revision as of 08:23, 18 May 2012

ROBOTC has a powerful collection of useful math functions for the NXT, TETRIX, VEX CORTEX, and Arduino MEGA-based platforms. The RCX, VEX PIC and Arduino 328P-based platforms do not have enough memory to store these more advanced math functions or support floating point numbers.

abs

float abs(const float input)

(float) Returns the absolute value of a number.

Parameter	Explanation	Data Type
input	The number to take the absolute value of (can be: int, long, short, float).	float

float G = -9.81;           // create a variable 'G' and set it equal to -9.81
float downForce = abs(G);  // create and set variable 'downForce' to the absolute value of 'G' (9.81)

acos

float acos(const float Cosine)

(float) Returns the arc-cosine of a number in radians.

Parameter	Explanation	Data Type
Cosine	The number to take the arc-cosine of (in radians).	float

float param = 0.5;                        // create and set floating point variable 'param' to 0.5
float result = acos(param) * 180.0 / PI;  // create floating point variable 'result' and
                                          // set it equal to the arc-cosine of 'param' in degrees (60)

asin

float asin(const float Sine)

(float) Returns the arc-sine of a number in radians.

Parameter	Explanation	Data Type
Sine	The number to take the arc-sine of (in radians).	float

float param = 0.5;                        // create and set floating point variable 'param' to 0.5
float result = asin(param) * 180.0 / PI;  // create floating point variable 'result' and
                                          // set it equal to the arc-sine of 'param' in degrees (30)

atan

float atan(const float Tangent)

(float) Returns the arc-tangent of a number in radians.

Parameter	Explanation	Data Type
Tangent	The number to take the arc-tangent of (in radians).	float

float param = 0.5;                        // create and set floating point variable 'param' to 0.5
float result = asin(param) * 180.0 / PI;  // create floating point variable 'result' and
                                          // set it equal to the arc-sine of 'param' in degrees (26.565)

atof

float atof ( string str )

(float) Returns a float representation of the string, str.

Parameter	Explanation	Data Type
str	The string to convert to a float.	string

task main()
{
  string strPI = "3.14";    // string 'strPI' is set equal to "3.14"
  float test = atof(strPI); // convert the string value of 'strPI' to a float and set 'test' to that number (3.14)
  while(true);              // keep the ROBOTC debugger alive so we can see the result
}

atoi

long atoi ( string str )

(long) Returns a long representation of the string, str.

Parameter	Explanation	Data Type
str	The string to convert to a long.	string

task main()
{
  string strPI = "3.14";    // string 'strPI' is set equal to "3.14"
  long test = atoi(strPI);  // convert the string value of 'strPI' to a long and set 'test' to that number (3)
  while(true);              // keep the ROBOTC debugger alive so we can see the result
}

ceil

float ceil(const float input)

(float) Returns the smallest integer value that is greater than or equal to input.

Parameter	Explanation	Data Type
input	The floating point number to take the ceiling value of.	float

float E = 2.72;           // create a variable 'E' and set it equal to 2.72
float ceiling = ceil(E);  // create and set variable 'ceiling' to the ceiling value of 'E' (3)

cos

float cos(const float fRadians)

(float) Returns the cosine of a number of radians.

Parameter	Explanation	Data Type
fRadians	The number to take the cosine of (in radians).	float

float result = cos(PI);  // create a floating point variable 'result' and 
                         // set it equal to the cosine of PI (-1)

cosDegrees

float cosDegrees(const float fDegrees)

(float) Returns the cosine of a number of degrees.

Parameter	Explanation	Data Type
fDegrees	The number to take the cosine of (in degrees).	float

float result = cosDegrees(180);  // create a floating point variable 'result' and
                                 // set it equal to the cosine of 180 degrees (-1)

degreesToRadians

float degreesToRadians(const float fDegrees)

(float) Returns the radian equivalent of fDegrees.

Parameter	Explanation	Data Type
fDegrees	The number of degrees to convert into radians.	float

float radiansPerDegree = degreesToRadians(1.0);  // create a floating point variable 'radiansPerDegree ' 
                                                 // and set it equal to the amount of radians in 1.0 degrees (0.017)

exp

float exp(const float input)

(float) Returns the number 'e' rasied to the power of input.

Parameter	Explanation	Data Type
input	The floating point number to raise the constant 'e' to.	float

float result = exp(4);  // create floating point variable 'result' and 
                        // set it equal to e raised to the 4th power (e^4 = 54.598)

floor

float floor(const float input)

(float) Returns the largest integer value that is less than or equal to input.

Parameter	Explanation	Data Type
input	The floating point number to take the floor value of.	float

float E = 2.72;              // create a variable 'E' and set it equal to 2.72
float floorValue = ceil(E);  // create and set variable 'floorValue' to the ceiling value of 'E' (2)

log

float log(const float input)

(float) Returns the natural logarithm (ln) of input.

Parameter	Explanation	Data Type
input	The floating point number to take the natural logarithm of.	float

float E = 2.72;     // create a variable 'E' and set it equal to 2.72
float ln = log(E);  // create and set variable 'ln' to the natural log of 'E' (1.00)

log10

float log10(const float input)

(float) Returns the base-10 logarithm of input.

Parameter	Explanation	Data Type
input	The floating point number to take the base-10 logarithm of.	float

float E = 2.72;            // create a variable 'E' and set it equal to 2.72
float logBTen = log10(E);  // create and set variable 'logBTen' to the base-10 log of 'E' (0.43)

PI

const float PI = 3.14159265358979323846264338327950288419716939937510

(float) The constant π.

float y = 0.0;                // create and set 'y' to 0.0
float LCD_width = 100.0;      // create and set 'LCD_width' to 100.0 (width of NXT LCD in pixels)
 
nxtDrawLine(0, 31, 99, 31);   // draw a line across the center of the LCD
 
for(int x = 0; x < 100; x++)  // loop from 0 to 99
{
  y = sin(x * (2.0 * PI) / LCD_width) * 25; // calculate y-coordinate of pixel to draw
  nxtSetPixel(x, y + 31);                   // draw pixel at (x, y+31)
  wait1Msec(100);                           // wait 100 milliseconds
}

pow

float pow(const float base, const float exponent)

(float) Returns base to the power of exponent.

Parameter	Explanation	Data Type
base	The floating point base to raise to the power of 'power'.	float
exponent	The floating point exponent to raise 'base' to.	float

float kilobyte = pow(10, 3);  // create floating point variable 'kilobyte' and
                              // set it equal to 10^3 or 1000

radiansToDegrees

short radiansToDegrees(const float fRadians)

(short) Returns the degree equivalent of fRadians.

Parameter	Explanation	Data Type
fRadians	The number of radians to convert into degrees.	float

float degrees = radiansToDegrees(PI);  // create a floating point variable 'degrees' 
                                       // and set it equal to the amount of degrees in PI (180)

rand

word rand()

(word) Returns a pseudo-random integral number in the range 0 to at least 32,767 (depending on platform).

A typical way to generate pseudo-random numbers in a determined range using rand is to use the modulo of the returned value by the range span and add the initial value of the range:

( value % 100 ) is in the range 0 to 99 ( value % 100 + 1 ) is in the range 1 to 100 ( value % 30 + 1985 ) is in the range 1985 to 2014

Notice though that this modulo operation does not generate a truly uniformly distributed random number in the span (since in most cases lower numbers are slightly more likely), but it is generally a good approximation for short spans.

task main()
{
  int min = -100;   // create int variable 'min' and set it to -100
  int max = 100;    // create int variable 'max' and set it to 100
 
  srand(nSysTime);  // generate seed for rand() from current system time
 
  while(true)       // infinite loop:
  {
    motor[rightMotor] = (rand() % (max-min)) + min; // set 'rightMotor' to a random number in the range: [min, max]
    motor[leftMotor]  = (rand() % (max-min)) + min; // set 'leftMotor' to a random number in the range: [min, max]
    wait1Msec(500); // wait 500 milliseconds
  }
}

randLong

long randLong()

(long) Returns a pseudo-random integral number in the range 0 to at least 2,147,483,647 (depending on platform).

A typical way to generate pseudo-random numbers in a determined range using rand is to use the modulo of the returned value by the range span and add the initial value of the range:

( value % 100 ) is in the range 0 to 99 ( value % 100 + 1 ) is in the range 1 to 100 ( value % 30 + 1985 ) is in the range 1985 to 2014

Notice though that this modulo operation does not generate a truly uniformly distributed random number in the span (since in most cases lower numbers are slightly more likely), but it is generally a good approximation for short spans.

task main()
{
  long min = -100;   // create long variable 'min' and set it to -100
  long max = 100;    // create long variable 'max' and set it to 100
 
  srand(nSysTime);  // generate seed for rand() from current system time
 
  while(true)       // infinite loop:
  {
    motor[rightMotor] = (randLong() % (max-min)) + min; // set 'rightMotor' to a random number in the range: [min, max]
    motor[leftMotor]  = (randLong() % (max-min)) + min; // set 'leftMotor' to a random number in the range: [min, max]
    wait1Msec(500); // wait 500 milliseconds
  }
}

sgn

short sgn(const float input)

(short) Returns a value less than 0 if input is negative, and a value greater than 0 if input is positive.

Parameter	Explanation	Data Type
input	The number to test the sign of	float

int res1 = sgn(-9.81);  // returns -1 to 'res1'
int res2 = sgn(3.14);   // returns 1 to 'res2'
int res3 = sgn(0);      // returns 0 to 'res3'

sin

float sin(const float fRadians)

(float) Returns the sine of a number of radians.

Parameter	Explanation	Data Type
fRadians	The number to take the sine of (in radians).	float

float result = sin(PI);  // create a floating point variable 'result' and
                         // set it equal to the cosine of PI (0)

sinDegrees

float sinDegrees(const float fDegrees)

(float) Returns the sine of a number of degrees.

Parameter	Explanation	Data Type
fDegrees	The number to take the sine of (in degrees).	float

float result = sinDegrees(180);  // create a floating point variable 'result' and 
                                 // set it equal to the sine of 180 degrees (0)

srand

void srand(const long nSeedValue)

(void) The pseudo-random number generator is initialized using the argument passed as nSeedValue.

For every different seed value used in a call to srand, the pseudo-random number generator can be expected to generate a different succession of results in the subsequent calls to rand. Two different initializations with the same seed, instructs the pseudo-random generator to generate the same succession of results for the subsequent calls to rand in both cases.

Parameter	Explanation	Data Type
nSeedValue	The seed for the pseudo-random number generator, rand()	long

task main()
{
  int min = -100;   // create int variable 'min' and set it to -100
  int max = 100;    // create int variable 'max' and set it to 100
 
  srand(nSysTime);  // generate seed for rand() from current system time
 
  while(true)       // infinite loop:
  {
    motor[rightMotor] = (rand() % (max-min)) + min; // set 'rightMotor' to a random number in the range: [min, max]
    motor[leftMotor]  = (rand() % (max-min)) + min; // set 'leftMotor' to a random number in the range: [min, max]
    wait1Msec(500); // wait 500 milliseconds
  }
}

sqrt

float sqrt(const float input)

(float) Returns the square-root of input.

Parameter	Explanation	Data Type
input	The number to take the square-root of.	float

float result = sqrt(1764);  // create a floating point variable 'result' and 
                            // set it equal to the square-root of 1764 (42)

@@ Line 614: / Line 614: @@
 {| style="color:black;" width="100%" cellpadding="5%" cellspacing="0" border="0"
 |-
-| class="functionType"| <span class="bigKeywordBI">long </span><span class="bigKeywordB">srand</span><span class="bigCodePunc">()</span>
+| class="functionType"| <span class="bigKeywordBI">long </span><span class="bigKeywordB">randLong</span><span class="bigCodePunc">()</span>
 |-
 | style="font-family:Verdana, Geneva, sans-serif; color:black; background-color:#FFFFFF; text-align:left; font-size:100%;"|([[Data_Types#dataType_long|long]]) Returns a pseudo-random integral number in the range 0 to at least 2,147,483,647 (depending on platform).

Math

Latest revision as of 08:23, 18 May 2012

Contents

abs

acos

asin

atan

atof

atoi

ceil

cos

cosDegrees

degreesToRadians

exp

floor

log

log10

PI

pow

radiansToDegrees

rand

randLong

sgn

sin

sinDegrees

srand

sqrt

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