<![CDATA[size : 6883
uploaded_on : Sat Jun 20 00:00:00 1998
modified_on : Wed Dec 8 14:03:37 1999
title : Missing trigonometric functions
org_filename : Calc.pas
author : Unknown
authoremail :
description : Trigonometric, hyperbolic, logarithmic, power and root functions
keywords :
tested : Borland Pascal 7.0
submitted_by : The CKB Crew
submitted_by_email : ckb@netalive.org
uploaded_by : nobody
modified_by : nobody
owner : nobody
lang : pas
file-type : text/plain
category : pascal-alg-maths
__END_OF_HEADER__
{$O+}
{
F i l e I n f o r m a t i o n
* DESCRIPTION
Supplies missing trigonometric functions for Turbo Pascal 5.5. Also
provides hyperbolic, logarithmic, power, and root functions. All trig
functions accessibile by radians, decimal degrees, degrees-minutes-seconds
and a global DegreeType.
}
unit PTD_Calc;
(* PTD_Calc - Supplies missing trigonometric functions for Turbo Pascal 5.5
* Also provides hyperbolic, logarithmic, power, and root functions.
* All trig functions accessible by radians, decimal degrees,
* degrees-minutes-seconds, and a global DegreeType. Conversions
* between these are supplied.
*
*)
interface
type
DegreeType = record
Degrees, Minutes, Seconds : real;
end;
const
Infinity = 9.9999999999E+37;
{ Radians }
{ sin, cos, and arctan are predefined }
function Tan( Radians : real ) : real;
function ArcSin( InValue : real ) : real;
function ArcCos( InValue : real ) : real;
{ Degrees, expressed as a real number }
function DegreesToRadians( Degrees : real ) : real;
function RadiansToDegrees( Radians : real ) : real;
function Sin_Degree( Degrees : real ) : real;
function Cos_Degree( Degrees : real ) : real;
function Tan_Degree( Degrees : real ) : real;
function ArcSin_Degree( Degrees : real ) : real;
function ArcCos_Degree( Degrees : real ) : real;
function ArcTan_Degree( Degrees : real ) : real;
{ Degrees, in Degrees, Minutes, and Seconds, as real numbers }
function DegreePartsToDegrees( Degrees, Minutes, Seconds : real ) : real;
function DegreePartsToRadians( Degrees, Minutes, Seconds : real ) : real;
procedure DegreesToDegreeParts( DegreesIn : real;
var Degrees, Minutes, Seconds : real );
procedure RadiansToDegreeParts( Radians : real;
var Degrees, Minutes, Seconds : real );
function Sin_DegreeParts( Degrees, Minutes, Seconds : real ) : real;
function Cos_DegreeParts( Degrees, Minutes, Seconds : real ) : real;
function Tan_DegreeParts( Degrees, Minutes, Seconds : real ) : real;
function ArcSin_DegreeParts( Degrees, Minutes, Seconds : real ) : real;
function ArcCos_DegreeParts( Degrees, Minutes, Seconds : real ) : real;
function ArcTan_DegreeParts( Degrees, Minutes, Seconds : real ) : real;
{ Degrees, expressed as DegreeType ( reals in record ) }
function DegreeTypeToDegrees( DegreeVar : DegreeType ) : real;
function DegreeTypeToRadians( DegreeVar : DegreeType ) : real;
procedure DegreeTypeToDegreeParts( DegreeVar : DegreeType;
var Degrees, Minutes, Seconds : real );
procedure DegreesToDegreeType( Degrees : real; var DegreeVar : DegreeType );
procedure RadiansToDegreeType( Radians : real; var DegreeVar : DegreeType );
procedure DegreePartsToDegreeType( Degrees, Minutes, Seconds : real;
var DegreeVar : DegreeType );
function Sin_DegreeType( DegreeVar : DegreeType ) : real;
function Cos_DegreeType( DegreeVar : DegreeType ) : real;
function Tan_DegreeType( DegreeVar : DegreeType ) : real;
function ArcSin_DegreeType( DegreeVar : DegreeType ) : real;
function ArcCos_DegreeType( DegreeVar : DegreeType ) : real;
function ArcTan_DegreeType( DegreeVar : DegreeType ) : real;
{ Hyperbolic functions }
function Sinh( Invalue : real ) : real;
function Cosh( Invalue : real ) : real;
function Tanh( Invalue : real ) : real;
function Coth( Invalue : real ) : real;
function Sech( Invalue : real ) : real;
function Csch( Invalue : real ) : real;
function ArcSinh( Invalue : real ) : real;
function ArcCosh( Invalue : real ) : real;
function ArcTanh( Invalue : real ) : real;
function ArcCoth( Invalue : real ) : real;
function ArcSech( Invalue : real ) : real;
function ArcCsch( Invalue : real ) : real;
{ Logarithms, Powers, and Roots }
{ e to the x is exp() }
{ natural log is ln() }
function Log10( InNumber : real ) : real;
function Log( Base, InNumber : real ) : real; { log of any base }
function Power( InNumber, Exponent : real ) : real;
function Root( InNumber, TheRoot : real ) : real;
{----------------------------------------------------------------------}
implementation
const
RadiansPerDegree = 0.017453292520;
DegreesPerRadian = 57.295779513;
MinutesPerDegree = 60.0;
SecondsPerDegree = 3600.0;
SecondsPerMinute = 60.0;
LnOf10 = 2.3025850930;
{-----------}
{ Radians }
{-----------}
{ sin, cos, and arctan are predefined }
function Tan { ( Radians : real ) : real };
{ note: returns Infinity where appropriate }
var
CosineVal : real;
TangentVal : real;
begin
CosineVal := cos( Radians );
if CosineVal = 0.0 then
Tan := Infinity
else
begin
TangentVal := sin( Radians ) / CosineVal;
if ( TangentVal < -Infinity ) or ( TangentVal > Infinity ) then
Tan := Infinity
else
Tan := TangentVal;
end;
end;
function ArcSin{ ( InValue : real ) : real };
{ notes: 1) exceeding input range of -1 through +1 will cause runtime error }
{ 2) only returns principal values }
{ ( -pi/2 through pi/2 radians ) ( -90 through +90 degrees ) }
begin
if abs( InValue ) = 1.0 then
ArcSin := pi / 2.0
else
ArcSin := arctan( InValue / sqrt( 1 - InValue * InValue ) );
end;
function ArcCos{ ( InValue : real ) : real };
{ notes: 1) exceeding input range of -1 through +1 will cause runtime error }
{ 2) only returns principal values }
{ ( 0 through pi radians ) ( 0 through +180 degrees ) }
var
Result : real;
begin
if InValue = 0.0 then
ArcCos := pi / 2.0
else
begin
Result := arctan( sqrt( 1 - InValue * InValue ) / InValue );
if InValue < 0.0 then
ArcCos := Result + pi
else
ArcCos := Result;
end;
end;
{---------------------------------------}
{ Degrees, expressed as a real number }
{---------------------------------------}
function DegreesToRadians{ ( Degrees : real ) : real };
begin
DegreesToRadians := Degrees * RadiansPerDegree;
end;
function RadiansToDegrees{ ( Radians : real ) : real };
begin
RadiansToDegrees := Radians * DegreesPerRadian;
end;
function Sin_Degree{ ( Degrees : real ) : real };
begin
Sin_Degree := sin( DegreesToRadians( Degrees ) );
end;
function Cos_Degree{ ( Degrees : real ) : real };
begin
Cos_Degree := cos( DegreesToRadians( Degrees ) );
end;
function Tan_Degree{ ( Degrees : real ) : real };
begin
Tan_Degree := Tan( DegreesToRadians( Degrees ) );
<ORIGINAL MESSAGE OVER 200 LINES, SPLIT IN 2 OR MORE>
==============================================================================
BBS: «« The Information and Technology Exchan
To: JEFFREY HUNTSMAN Date: 11-27─91 (09:08)
From: FLOOR NAAIJKENS Number: 3163 [101] PASCAL
Subj: CALC (1) <CONT> Status: Publ
]]>