TanD(deg.d) Compute the tangent of an angle given in degrees.

[ehowington]

;------------------------------------------------------------------------------
; Procedure: TanD(deg.d)
; Purpose: Compute the tangent of an angle given in degrees.
;
; Input:
; - deg.d: Angle in degrees (any real value). Large magnitudes are allowed.
;
; Processing:
; - Performs range reduction modulo 180° to improve numerical stability.
; - Maps the reduced angle to the principal interval (-90°, 90°].
; - Converts degrees to radians, then computes the tangent.
;
; Return:
; - Result.d: The tangent of the input angle (unitless).
;
; Notes / Edge cases:
; - At odd multiples of 90° (e.g., 90°, 270°, ...), Tan is undefined and may
; overflow to +/-Infinity depending on platform/IEEE behavior.
; - If 'deg' is NaN, the result will be NaN.
; - This function does not allocate memory or modify global state.
;------------------------------------------------------------------------------
EnableExplicit

ProcedureDLL.d TanD(deg.d)
; Reduce the angle modulo 180° to improve numeric stability for large |deg|
Protected.d a = deg - 180.0 * Int(deg / 180.0) ; range-reduction to [0, 180)

; Shift to principal range (-90°, 90°] for best Tan accuracy
If a > 90.0
a = a - 180.0 ; e.g., 135° -> -45°
ElseIf a <= -90.0
a = a + 180.0 ; e.g., -135° -> 45°
EndIf

; Convert to radians and return tangent
ProcedureReturn Tan(Radian(a))
EndProcedure

; Helper: reduce any degree input to principal range (-90°, 90°]
Procedure.d ReduceAngle180(deg.d)
Protected.d a = deg - 180.0 * Int(deg / 180.0)
If a > 90.0
a = a - 180.0
ElseIf a <= -90.0
a = a + 180.0
EndIf
ProcedureReturn a
EndProcedure

; Helper: detect undefined tan (cos ~ 0 after range reduction)
Procedure.b IsTanUndefined(deg.d)
Protected.d a = ReduceAngle180(deg)
Protected.d c = Cos(Radian(a))
If Abs(c) < 1.0e-15
ProcedureReturn #True
EndIf
ProcedureReturn #False
EndProcedure

;------------------------------------------------------------------------------
; Runnable examples (Debug output only; no windows, no console)
;------------------------------------------------------------------------------
CompilerIf #PB_Compiler_IsMainFile
Define.d deg, reducedA, got, expected, eps
Define.s verdict$

eps = 1.0e-12

Debug "TanD examples (degrees -> result) with expected values"
Debug "------------------------------------------------------"

; 0°
deg = 0.0 : got = TanD(deg) : expected = 0.0
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "CLOSE" : EndIf
Debug "TanD(0.0) = " + StrD(got, 16) + " ; should be 0 -> " + verdict$

; 30°
deg = 30.0 : got = TanD(deg) : expected = 1.0 / Sqr(3.0)
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "CLOSE" : EndIf
Debug "TanD(30.0) = " + StrD(got, 16) + " ; should be ~0.5773502691896257 (1/sqrt(3)) -> " + verdict$

; 45°
deg = 45.0 : got = TanD(deg) : expected = 1.0
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "CLOSE" : EndIf
Debug "TanD(45.0) = " + StrD(got, 16) + " ; should be 1 -> " + verdict$

; 60°
deg = 60.0 : got = TanD(deg) : expected = Sqr(3.0)
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "CLOSE" : EndIf
Debug "TanD(60.0) = " + StrD(got, 16) + " ; should be ~1.7320508075688772 (sqrt(3)) -> " + verdict$

; 90° (asymptote, undefined)
deg = 90.0 : got = TanD(deg)
If IsTanUndefined(deg)
Debug "TanD(90.0) = undefined (+/-Infinity)"
Else
Debug "TanD(90.0) = " + StrD(got, 16) + " ; near asymptote"
EndIf

; 135°
deg = 135.0 : got = TanD(deg) : expected = -1.0
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "CLOSE" : EndIf
Debug "TanD(135.0) = " + StrD(got, 16) + " ; should be -1 -> " + verdict$

; -45°
deg = -45.0 : got = TanD(deg) : expected = -1.0
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "CLOSE" : EndIf
Debug "TanD(-45.0) = " + StrD(got, 16) + " ; should be -1 -> " + verdict$

; -90° and 270° (asymptotes)
deg = -90.0 : got = TanD(deg)
If IsTanUndefined(deg)
Debug "TanD(-90.0) = undefined (+/-Infinity)"
Else
Debug "TanD(-90.0) = " + StrD(got, 16) + " ; near asymptote"
EndIf

deg = 270.0 : got = TanD(deg)
If IsTanUndefined(deg)
Debug "TanD(270.0) = undefined (+/-Infinity)"
Else
Debug "TanD(270.0) = " + StrD(got, 16) + " ; near asymptote"
EndIf

; Near-asymptote behavior (sign check)
Debug "TanD(89.999) = " + StrD(TanD(89.999), 16) + " ; should be very large positive"
Debug "TanD(90.001) = " + StrD(TanD(90.001), 16) + " ; should be very large negative"

; Large input with range reduction demonstration
deg = 1000000.0 : got = TanD(deg)
reducedA = ReduceAngle180(deg)
expected = TanD(reducedA)
If Abs(got-expected) <= eps : verdict$ = "PASS" : Else : verdict$ = "FAIL" : EndIf
Debug "TanD(1000000) = " + StrD(got, 16) + " ; should be same as TanD(" + StrD(reducedA, 6) + ") = " + StrD(expected, 16) + " -> " + verdict$

CompilerEndIf