BCX Run-time Mathematical Procedures

Most BCX mathematical functions return DOUBLE floating point values and expect DOUBLE floating point values for their arguments.

BCX LDOUBLE functions return LDOUBLE floating point values and expect LDOUBLE floating point values for their arguments.

PI mathematical constant

Purpose:

PI is a case-insensitive double precision numeric literal with a value of 3.141592653589793.

👉 Programs will need to be updated where a PI identifier has been used. That means removing your use of the PI identifier, regardless of case or data type. If you insist on having your definition of PI, you will need to change its name to something else like myPI.

DEGTORAD function

Purpose:

DEGTORAD converts angular units from degrees to radians.

AngleInRadians = DEGTORAD(AngleInDegrees AS DOUBLE)

Example:

$BCXVERSION "8.0.4"

DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE SineOfAngle
DIM AS STRING TheAnswer
   
DegreeAngle = 36.0
  
RadianAngle = DEGTORAD(DegreeAngle)
  
SineOfAngle = SIN(RadianAngle)
  
SPRINT TheAnswer, "The sine of", STR$(DegreeAngle), " degrees is", SineOfAngle
  
PRINT TheAnswer

Result:

The sine of 36 degrees is 0.587785252292464

RADTODEG function

Purpose:

RADTODEG converts angular units from radians to degrees.

AngleInDegrees = RADTODEG(AngleInRadians AS DOUBLE)

Example:

$BCXVERSION "8.0.4"

DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE SineOfAngle
DIM AS STRING TheAnswer

DegreeAngle = 36.0

RadianAngle = DEGTORAD(DegreeAngle)

SineOfAngle = SIN(RadianAngle)

SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a sine trigonometric ratio of", SineOfAngle

PRINT TheAnswer

RadianAngle = ASIN(SineOfAngle)

DegreeAngle = RADTODEG(RadianAngle)

SPRINT TheAnswer, "The sine trigonometric ratio of", SineOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."

PRINT TheAnswer

Result:

The angle of 36 degrees has a sine trigonometric ratio of 0.587785252292464
The sine trigonometric ratio of 0.587785252292464 corresponds to an angle of 35.9999999999994 degrees.

Trigonometric functions

Trigonometric functions are used to obtain an angle's trigonometric ratio from an angle.

All trigonometric functions use radians, not degrees, for their arguments and return values.

The inverse trigonometric functions return radian values.

SIN function

Purpose:

SIN returns the DOUBLE sine trigonometric ratio of a radian value angle.

SineOfAngle = SIN(RadianAngle AS DOUBLE)

Example:

DIM AS DOUBLE RadFromDeg
DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE SineOfAngle
DIM AS STRING TheAnswer

RadFromDeg = (PI / 180.0)

DegreeAngle = 36.0

RadianAngle = DegreeAngle * RadFromDeg

SineOfAngle = SIN(RadianAngle)

SPRINT TheAnswer, "The sine of", STR$(DegreeAngle), " degrees is", SineOfAngle

PRINT TheAnswer

Result:

The sine of 36 degrees is 0.587785252292473

SINL function

Purpose:

SINL returns the LDOUBLE sine trigonometric ratio of an angle.

SineOfAngle = SINL(RadianAngle AS LDOUBLE)

Example:

DIM LDbl_PI AS LDOUBLE
DIM RadFromDeg AS LDOUBLE
DIM DegreeAngle AS LDOUBLE
DIM RadianAngle AS LDOUBLE
DIM SineOfAngle AS LDOUBLE
DIM AS STRING TheAnswer
 
LDbl_PI = (4.0 * ATNL(1.0)) ' 1.0 is radians not degrees. 

RadFromDeg = (LDbl_PI / 180.0)
 
DegreeAngle = 36.0
 
RadianAngle = DegreeAngle * RadFromDeg
 
SineOfAngle = SINL(RadianAngle)
 
SPRINT TheAnswer, "The sine of", STR$(DegreeAngle), " degrees is", SineOfAngle
 
PRINT TheAnswer

Result:

The sine of 36 degrees is 0.5877852522924731292

COS function

Purpose:

COS returns the DOUBLE cosine trigonometric ratio of an angle.

CosineOfAngle = COS(RadianAngle AS DOUBLE)

Example:

DIM AS DOUBLE RadFromDeg
DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE CosineOfAngle
DIM AS STRING TheAnswer

RadFromDeg = (PI / 180.0)

DegreeAngle = 36.0

RadianAngle = DegreeAngle * RadFromDeg

CosineOfAngle = COS(RadianAngle)

SPRINT TheAnswer, "The cosine of", STR$(DegreeAngle), " degrees is", CosineOfAngle

PRINT TheAnswer

Result:

The cosine of 36 degrees is 0.809016994374947

COSL function

Purpose:

COSL returns the LDOUBLE cosine trigonometric ratio of an angle.

CosineOfAngle = COSL(RadianAngleAS LDOUBLE)

Example:

DIM LDbl_PI AS LDOUBLE
DIM RadFromDeg AS LDOUBLE
DIM DegreeAngle AS LDOUBLE
DIM RadianAngle AS LDOUBLE
DIM CosineOfAngle AS LDOUBLE
DIM AS STRING TheAnswer
 
LDbl_PI = (4.0 * ATNL(1.0)) ' 1.0 is radians not degrees. 

RadFromDeg = (LDbl_PI / 180.0)
 
DegreeAngle = 36.0
 
RadianAngle = DegreeAngle * RadFromDeg
 
CosineOfAngle = COSL(RadianAngle)
 
SPRINT TheAnswer, "The cosine of", STR$(DegreeAngle), " degrees is", CosineOfAngle
 
PRINT TheAnswer

Result:

The cosine of 36 degrees is 0.8090169943749474241

TAN function

Purpose:

TAN returns the DOUBLE tangent trigonometric ratio of an angle.

TangentOfAngle = TAN(RadianAngle AS DOUBLE)

Example:

DIM AS DOUBLE RadFromDeg
DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE TangentOfAngle
DIM AS STRING TheAnswer

RadFromDeg = (PI / 180.0)
 
DegreeAngle = 36.0
 
RadianAngle = DegreeAngle * RadFromDeg
 
TangentOfAngle = TAN(RadianAngle)
 
SPRINT TheAnswer, "The tangent of", STR$(DegreeAngle), " degrees is", TangentOfAngle
 
PRINT TheAnswer

Result:

The tangent of 36 degrees is 0.726542528005361

TANL function

Purpose:

TANL returns the LDOUBLE tangent trigonometric ratio of an angle.

TangentOfAngle = TANL(RadianAngle AS LDOUBLE)

Example:

DIM LDbl_PI AS LDOUBLE
DIM RadFromDeg AS LDOUBLE
DIM DegreeAngle AS LDOUBLE
DIM RadianAngle AS LDOUBLE
DIM TangentOfAngle AS LDOUBLE
DIM AS STRING TheAnswer
  
LDbl_PI = (4.0 * ATNL(1.0)) ' 1.0 is radians not degrees. 

RadFromDeg = (LDbl_PI / 180.0)
  
DegreeAngle = 36.0
  
RadianAngle = DegreeAngle * RadFromDeg
  
TangentOfAngle = TANL(RadianAngle)
  
SPRINT TheAnswer, "The tangent of", STR$(DegreeAngle), " degrees is", TangentOfAngle
  
PRINT TheAnswer

Result:

The tangent of 36 degrees is 0.7265425280053608859

Inverse Trigonometric functions

Inverse trigonometric functions are used to obtain an angle from an angle's trigonometric ratio.

ASIN function

Purpose:

ASIN returns the DOUBLE radian angle of a sine trigonometric ratio.

RadianAngle = ASIN(SineOfAngle AS DOUBLE)

Example:

DIM AS DOUBLE RadFromDeg
DIM AS DOUBLE DegFromRad
DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE SineOfAngle
DIM AS STRING TheAnswer

DegFromRad# = (180.0 / PI)

RadFromDeg# = (PI / 180.0)

DegreeAngle# = 36.0

RadianAngle# = DegreeAngle * RadFromDeg

SineOfAngle# = SIN(RadianAngle)

SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a sine trigonometric ratio of", SineOfAngle

PRINT TheAnswer

RadianAngle = ASIN(SineOfAngle)

DegreeAngle# = RadianAngle * DegFromRad

SPRINT TheAnswer, "The sine trigonometric ratio of", SineOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."

PRINT TheAnswer

Result:

The angle of 36 degrees has a sine trigonometric ratio of 0.587785252292473
The sine trigonometric ratio of 0.587785252292473 corresponds to an angle of 36 degrees.

ASINL function

Purpose:

ASINL returns the LDOUBLE radian angle of a sine trigonometric ratio.

RadianAngle = ASINL(SineOfAngle AS LDOUBLE)

Example:

DIM LDbl_PI AS LDOUBLE
DIM RadFromDeg AS LDOUBLE
DIM DegFromRad AS LDOUBLE
DIM DegreeAngle AS LDOUBLE
DIM RadianAngle AS LDOUBLE
DIM SineOfAngle AS LDOUBLE
DIM AS STRING TheAnswer

LDbl_PI = (4.0 * ATNL(1.0)) ' 1.0 is radians not degrees. 

DegFromRad = (180.0 / LDbl_PI)

RadFromDeg = (LDbl_PI / 180.0)

DegreeAngle = 36.0

RadianAngle = DegreeAngle * RadFromDeg

SineOfAngle = SINL(RadianAngle)

SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a sine trigonometric ratio of", SineOfAngle

PRINT TheAnswer

RadianAngle = ASINL(SineOfAngle)

DegreeAngle = RadianAngle * DegFromRad

SPRINT TheAnswer, "The sine trigonometric ratio of", SineOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."

PRINT TheAnswer

Result:

The angle of 36 degrees has a sine trigonometric ratio of 0.5877852522924731292
The sine trigonometric ratio of 0.5877852522924731292 corresponds to an angle of 36 degrees.

ACOS function

Purpose:

ACOS returns the DOUBLE radian value angle of a cosine trigonometric ratio.

RadianAngle# = ACOS(CosineOfAngle AS DOUBLE)

Example:

DIM AS DOUBLE RadFromDeg
DIM AS DOUBLE DegFromRad
DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE CosineOfAngle
DIM AS STRING TheAnswer

DegFromRad = (180.0 / PI)

RadFromDeg = (PI / 180.0)

DegreeAngle = 36.0

RadianAngle = DegreeAngle * RadFromDeg

CosineOfAngle = COS(RadianAngle)

SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a cosine trigonometric ratio of", CosineOfAngle

PRINT TheAnswer

RadianAngle = ACOS(CosineOfAngle)

DegreeAngle = RadianAngle * DegFromRad

SPRINT TheAnswer, "The cosine trigonometric ratio of", CosineOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."

PRINT TheAnswer

Result:

The angle of 36 degrees has a cosine trigonometric ratio of 0.809016994374947
The cosine trigonometric ratio of 0.809016994374947 corresponds to an angle of 36 degrees.

ACOSL function

Purpose:

ACOSL returns the LDOUBLE precision value of the radian angle of a cosine trigonometric ratio.

RadianAngle = ACOSL(CosineOfAngle AS LDOUBLE)

Example:

DIM LDbl_PI AS LDOUBLE
DIM RadFromDeg AS LDOUBLE
DIM DegFromRad AS LDOUBLE
DIM DegreeAngle AS LDOUBLE
DIM RadianAngle AS LDOUBLE
DIM CosineOfAngle AS LDOUBLE
DIM AS STRING TheAnswer

LDbl_PI = (4.0 * ATNL(1.0)) ' 1.0 is radians not degrees. 

DegFromRad = (180.0 / LDbl_PI)

RadFromDeg = (LDbl_PI / 180.0)

DegreeAngle = 36.0

RadianAngle = DegreeAngle * RadFromDeg

CosineOfAngle = COSL(RadianAngle)

SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a cosine trigonometric ratio of", CosineOfAngle

PRINT TheAnswer

RadianAngle = ACOSL(CosineOfAngle)

DegreeAngle = RadianAngle * DegFromRad

SPRINT TheAnswer, "The cosine trigonometric ratio of", CosineOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."

PRINT TheAnswer

Result:

The angle of 36 degrees has a cosine trigonometric ratio of 0.8090169943749474241
The cosine trigonometric ratio of 0.8090169943749474241 corresponds to an angle of 36 degrees.

ATN function

Purpose:

ATN returns the DOUBLE radian value angle of a tangent trigonometric ratio.

RadianAngle = ATN(TangentOfAngle AS DOUBLE)

Example:

DIM AS DOUBLE RadFromDeg
DIM AS DOUBLE DegFromRad
DIM AS DOUBLE DegreeAngle
DIM AS DOUBLE RadianAngle
DIM AS DOUBLE TangentOfAngle
DIM AS STRING TheAnswer

DegFromRad = (180.0 / PI)

RadFromDeg = (PI / 180.0)

DegreeAngle = 36.0

RadianAngle = DegreeAngle * RadFromDeg

TangentOfAngle = TAN(RadianAngle)

SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a tangent trigonometric ratio of", TangentOfAngle

PRINT TheAnswer

RadianAngle = ATN(TangentOfAngle)

DegreeAngle = RadianAngle * DegFromRad

SPRINT TheAnswer, "The tangent trigonometric ratio of", TangentOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."

PRINT TheAnswer

Result:

The angle of 36 degrees has a tangent trigonometric ratio of 0.726542528005361
The tangent trigonometric ratio of 0.726542528005361 corresponds to an angle of 36 degrees.

ATNL function

Purpose:

ATNL returns the LDOUBLE precision value of the radian angle of a tangent trigonometric ratio.

RadianAngle = ATNL(TangentOfAngle AS LDOUBLE)

Example 1:

DIM LDbl_PI AS LDOUBLE
DIM RadFromDeg AS LDOUBLE
DIM DegFromRad AS LDOUBLE
DIM DegreeAngle AS LDOUBLE
DIM RadianAngle AS LDOUBLE
DIM TangentOfAngle AS LDOUBLE
DIM AS STRING TheAnswer
 
LDbl_PI = (4.0 * ATNL(1.0)) ' 1.0 is radians not degrees. 

DegFromRad = (180.0 / LDbl_PI)
 
RadFromDeg = (LDbl_PI / 180.0)
 
DegreeAngle = 36.0
 
RadianAngle = DegreeAngle * RadFromDeg
 
TangentOfAngle = TANL(RadianAngle)
 
SPRINT TheAnswer, "The angle of", STR$(DegreeAngle), " degrees has a tangent trigonometric ratio of", TangentOfAngle
 
PRINT TheAnswer
 
RadianAngle = ATNL(TangentOfAngle)
 
DegreeAngle = RadianAngle * DegFromRad
 
SPRINT TheAnswer, "The tangent trigonometric ratio of", TangentOfAngle, " corresponds to an angle of", DegreeAngle, " degrees."
 
PRINT TheAnswer

Result:

The angle of 36 degrees has a tangent trigonometric ratio of 0.7265425280053608859
The tangent trigonometric ratio of 0.7265425280053608859 corresponds to an angle of 36 degrees.

Example 2:

DIM DBL_Pi AS DOUBLE
DIM LDBL_Pi AS LDOUBLE
DBL_Pi = 4.0 * ATAN(1.0)
LDBL_Pi = 4.0 * ATANL(1.0)
PRINT "DOUBLE Pi  =", DBL_Pi
PRINT "LDOUBLE Pi =", LDBL_Pi
PAUSE

Result:

DOUBLE Pi  = 3.14159265358979
LDOUBLE Pi = 3.141592653589793239

Press any key to continue . . .

Hyperbolic Trigonometric functions

SINH function

Purpose:

SINH returns the DOUBLE hyperbolic sine trigonometric ratio of a radian value angle.

HypeSineOfAngle = SINH(RadianAngle AS DOUBLE)

Example:

DIM HalfPi AS DOUBLE
DIM DBLSinh AS DOUBLE

HalfPi = 2.0 * ATAN(1.0)
DBLSinh = SINH(HalfPi)
PRINT DBLSinh

Result:

2.30129890230729

COSH function

Purpose:

COSH returns the DOUBLE hyperbolic cosine trigonometric ratio of an angle.

HypeCosineOfAngle = COSH(RadianAngle AS DOUBLE)

Example:

DIM HalfPi AS DOUBLE
DIM DBLCosh AS DOUBLE

HalfPi = 2.0 * ATAN(1.0)
DBLCosh = COSH(HalfPi)
PRINT DBLCosh

Result:

2.50917847865806

TANH function

Purpose:

TANH returns the DOUBLE tangent trigonometric ratio of an angle.

HypeTangentOfAngle = TANH(RadianAngle AS DOUBLE)

Example:

DIM QrtrPi AS DOUBLE
DIM DBLTan AS DOUBLE
DIM DBLTanh AS DOUBLE

QrtrPi = ATAN(1.0)
DBLTan = TAN(QrtrPi)
DBLTanh = TANH(DBLTan)
PRINT DBLTan
PRINT DBLTanh

Result:

1
0.761594155955765

Inverse Hyperbolic Trigonometric functions

Inverse hyperbolic trigonometric functions are used to obtain a radian angle from a hyperbolic trigonometric ratio.

ASINH function

Purpose:

ASINH returns the DOUBLE radian value angle of a hyperbolic sine trigonometric ratio.

RadianAngle = ASINH(HypeSineOfAngle AS DOUBLE)

Example:

DIM QrtrPi AS DOUBLE
DIM DBLSinh AS DOUBLE
DIM DBLASinh AS DOUBLE

QrtrPi = ATAN(1.0)
DBLSinh = SINH(QrtrPi)
DBLASinh = ASINH(DBLSinh)
PRINT DBLSinh
PRINT DBLASinh

Result:

0.86867096148601
0.785398163397448

ACOSH function

Purpose:

ACOSH returns the DOUBLE radian value angle of a hyperbolic cosine trigonometric ratio.

RadianAngle = ACOSH(HypeCosineOfAngle AS DOUBLE)

Example:

DIM QrtrPi AS DOUBLE
DIM DBLCosh AS DOUBLE
DIM DBLACosh AS DOUBLE

QrtrPi = ATAN(1.0)
DBLCosh = COSH(QrtrPi)
DBLACosh = ACOSH(DBLCosh)
PRINT DBLCosh
PRINT DBLACosh

Result:

1.32460908925201
0.785398163397448

ATANH function

Purpose:

ATANH returns the DOUBLE radian value angle of a hyperbolic tangent trigonometric ratio.

RadianAngle = ATANH(HypeTangentOfAngle AS DOUBLE)

Example:

DIM QrtrPi AS DOUBLE
DIM DBLTanh AS DOUBLE
DIM DBLATanh AS DOUBLE

QrtrPi = ATAN(1.0)
DBLTanh = TANH(QrtrPi)
DBLATanh = ATANH(DBLTanh)
PRINT DBLTanh
PRINT DBLATanh

Result:

0.655794202632672
0.785398163397448

LOG function

Purpose:

LOG returns the natural logarithmic DOUBLE value of a number.

NatLogNum = LOG(TheNumber AS DOUBLE)

LOGL function

Purpose:

LOGL returns the natural logarithmic LDOUBLE value of a number.

NatLogNum = LOGL(TheNumber AS LDOUBLE)

Example 1:

DIM RetDBL#
DIM RetLDBL AS LDOUBLE

RetDBL# = LOG(9000.0)
PRINT RetDBL#

RetLDBL = LOGL(9000.0)
PRINT RetLDBL

Result:

9.10497985631836
9.104979856318356435

Example 2:

The following routine uses LOG to calculate the length of a number.

DIM Number#
DIM LengthOfNumber#

Number# = 1234567890
LengthOfNumber# = INT(LOG(Number#) / LOG(10)) + 1
PRINT LengthOfNumber#

Result:

10

EXP natural exponential function

Purpose:

EXP raises Euler's number, 2.718281828459, to a specified exponent. EXP is the inverse of the natural logarithmic LOG function.

DBLNatExp = EXP(ExpNumber AS DOUBLE)

Example:

DIM DBLExponent AS DOUBLE
DIM DBLNatExp AS DOUBLE

DBLExponent = 2.30258509299405
DBLNatExp = EXP(DBLExponent)
PRINT DBLNatExp

Result:

10

LOG10 function

Purpose:

LOG10 returns the DOUBLE common, base-10, logarithm of a number.

ComLogNum = LOG10(TheNumber AS DOUBLE)

Example:

DIM Number#
DIM LengthOfNumber#

Number# = 1234567890
LengthOfNumber# = INT(LOG10(Number#) / LOG10(10)) + 1
PRINT LengthOfNumber#

Result:

10

LOG10L function

Purpose:

LOG10L returns the LDOUBLE common, base-10, logarithm of a number.

ComLogLDBL = LOG10L(LDBLNumber AS LDOUBLE)

Example:

DIM RetDBL#
DIM RetLDBL AS LDOUBLE

RetDBL# = LOG10(9000.0)
PRINT RetDBL#

RetLDBL = LOG10L(9000.0)
PRINT RetLDBL

Result:

3.95424250943932
3.954242509439324875

SQR and SQRT functions

Purpose:

SQR and SQRT return the square root DOUBLE value of a DOUBLE number.

RetDBL = SQR(DBLNumber AS DOUBLE)

RetDBL = SQRT(DBLNumber AS DOUBLE)

SQRL and SQRTL functions

Purpose:

SQRL and SQRTL return the square root LDOUBLE value of an LDOUBLE number.

RetLDBL = SQRL(LDBLNumber AS DOUBLE)

RetLDBL = SQRTL(LDBLNumber AS LDOUBLE)

Example:

DIM RetDBL#
DIM RetLDBL AS LDOUBLE

RetDBL# = SQRT(3.14159265358979)
PRINT RetDBL#

RetLDBL = SQRTL(3.141592653589793239L)
PRINT RetLDBL

Result:

1.77245385090552
1.772453850905516027

HYPOT function

Purpose:

HYPOT returns, as a DOUBLE value, the length of the hypotenuse of a right angled triangle given the lengths, as DOUBLE numbers, of the adjacent sides.

DBLHypot = HYPOT(DBLSideA AS DOUBLE, DBLSideB AS DOUBLE)

HYPOTL function

Purpose:

HYPOTL returns, as an LDOUBLE value, the length of the hypotenuse of a right angled triangle given the lengths, as LDOUBLE numbers, of the adjacent sides.

LDBLHypot = HYPOTL(LDBLSideA AS LDOUBLE, LDBLSideB AS LDOUBLE)

Example:

DIM DBLSideA#
DIM DBLSideB#
DIM DBLHypot#
DBLSideA# = 3.1
DBLSideB# = 4.1
DBLHypot# = HYPOT(DBLSideA#, DBLSideB#)
PRINT DBLHypot#


DIM LDBLSideA AS LDOUBLE
DIM LDBLSideB AS LDOUBLE
DIM LDBLHypot AS LDOUBLE
LDBLSideA = 3.1
LDBLSideB = 4.1
LDBLHypot = HYPOTL(LDBLSideA, LDBLSideB)
PRINT LDBLHypot

Result:

5.14003891035856
5.140038910358558525

POW function

Purpose:

POW returns, as a DOUBLE, the result of a DOUBLE value base raised to the power of a DOUBLE value exponent.

DBLPowered = POW(DBLBase AS DOUBLE, DBLExponent AS DOUBLE)

Example:

DIM DBLPowered AS DOUBLE
DIM DBLBase AS DOUBLE
DIM DBLExponent AS DOUBLE

DBLBase = 2

FOR INTEGER i = 2 TO 16
 DBLExponent#  = i
 DBLPowered# = POW(DBLBase#, DBLExponent#)
 PRINT DBLPowered#
NEXT i

Result:

4
8
16
32
64
128
256
512
1024
2048
4096
8192
16384
32768
65536

POWL function

Purpose:

POWL returns, as an LDOUBLE value, the result of an LDOUBLE value base raised to the power of an LDOUBLE value exponent.

LDBLPowered = POWL(LDBLBase AS LDOUBLE, LDBLExponent AS LDOUBLE)

Example:

DIM LDBLPowered AS LDOUBLE
DIM LDBLBase AS LDOUBLE
DIM LDBLExponent AS LDOUBLE
 
LDBLBase = 2.1
 
FOR INTEGER i = 1.1 TO 16.1 STEP 1
 LDBLExponent  = i
 LDBLPowered = POWL(LDBLBase, LDBLExponent)
 PRINT LDBLPowered
NEXT i

Result:

2.100000000000000089
4.410000000000000373
9.261000000000001175
19.44810000000000329
40.84101000000000864
85.76612100000002176
180.1088541000000533
378.2285936100001279
794.2800465810003022
1667.988097820100705
3502.775005422211629
7355.827511386644732
15447.23777391195459
32439.19932521510601
68122.3185829517255
143056.8690241986296

MOD function

Purpose:

MOD returns, as a DOUBLE value, the remainder of a division operation.

👉 Unlike most other BASIC implementations of MOD, which return an INTEGER, BCX MOD returns a DOUBLE, including any remaining fraction. For a procedure which returns, as an INTEGER value, the remainder of a division operation, see the below IMOD function.

Syntax 1: As Function Remainder = MOD(Dividend AS DOUBLE, Divisor AS DOUBLE) Return Value: Data type: DOUBLE Remainder The remainder of the division operation. Parameters: Data type: DOUBLE Dividend The value to be divided. Data type: DOUBLE Divisor The value dividing Dividend. Example 1: DIM Remainder# DIM Dividend# DIM Divisor# Dividend# = 5.3 Divisor# = 2.0 Remainder# = MOD(Dividend#, Divisor#) PRINT Remainder# Result: 1.3 Syntax 2: As Operator Remainder = Dividend AS DOUBLE MOD Divisor AS DOUBLE Return Value: Data type: DOUBLE Remainder The remainder of the division operation. Parameters: Data type: DOUBLE Dividend The value to be divided. Data type: DOUBLE Divisor The value dividing Dividend. Example 2: DIM Remainder# DIM Dividend# DIM Divisor# Dividend# = 5.3 Divisor# = 2.0 Remainder# = Dividend# MOD Divisor# PRINT Remainder# Result: 1.3

Remarks:

👉 In QuickBASIC, the MOD remainder operator uses integer division with rounding in calculations. Keep this in mind if you are porting some old QuickBASIC code that uses the MOD remainder operator.

Example:

The QuickBASIC MOD calculation

19.0 MOD 6.7

BCX equivalent result, can be had using the technique shown in this BCX example.

DIM AS INTEGER RetInt

RetInt = QB_MOD(19.0, 6.7)

PRINT RetInt

FUNCTION QB_MOD (dividend AS DOUBLE, divisor AS DOUBLE) AS INTEGER
  '******************************************************** 
  ' Replicates the QBasic modulus function algorithm 
  '******************************************************** 
  DIM AS INTEGER idividend, idivisor
  idividend = INT(ROUND(dividend, 0))
  idivisor = INT(ROUND(divisor, 0))
  FUNCTION = IMOD(idividend, idivisor)
END FUNCTION

Result:

5

IMOD function

Purpose:

IMOD returns, as an INTEGER value, the remainder of a division operation.

Remainder = IMOD(Dividend AS INTEGER, Divisor AS INTEGER)

Example:

DIM Remainder%
DIM Dividend%
DIM Divisor%

Dividend% = 5
Divisor%  = 2

Remainder% = IMOD(Dividend%, Divisor%)
PRINT Remainder%

Result:

1

% modulus operator

Functionally equivalent to the BCX IMOD function, the C language modulus operator % is accepted by BCX in BASIC expressions.

👉 When using the % modulus operator, a space must be to the left and right of of the % symbol.

Example:

 DIM Remainder AS INTEGER
 DIM Dividend AS INTEGER
 DIM Divisor AS INTEGER

 Dividend = 5
 Divisor  = 2

 Remainder = Dividend % Divisor
 PRINT Remainder

Result:

1