***************************************************************************
 ***************************************************************************
 modules/Utility_Constants.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 36 Custom Constants Are Defined

 CLIGHT = "299792458"
 G_STD = "9.80665"
 G_UNIV = "0.000000000066742"
 M_PER_A = "0.0000000001"
 M_PER_NM = "0.000000001"
 M_PER_UM = "0.000001"
 M_PER_MM = "0.001"
 M_PER_CM = "0.01"
 M_PER_IN = "0.0254"
 M_PER_FT = "0.3048"
 M_PER_YD = "0.9144"
 M_PER_M = "1"
 M_PER_KM = "1000"
 M_PER_MI = "1609.344"
 M_PER_NMI = "1852"
 M_PER_LS = "299792458"
 KM_PER_NMI = "1.852"
 KM_PER_MI = "1.609344"
 M_PER_AU = "149597870691"
 KM_PER_AU = "149597870.691"
 KM_PER_IAU = "149597871"
 M_PER_LY = "9460730472580800"
 M_PER_PC = "30856775813057289.532915512381557"
 AU_PER_LY = "63241.0770880709446742"
 AU_PER_PC = "206264.8062470963551565"
 LY_PER_PC = "3.2615637769712137"
 LT_1AU = "0.00577551830441213"
 KG_PER_OZ = "0.028349523125"
 KG_PER_LB = "0.45959237"
 G_PER_OZ = "28.349523125"
 N_PER_LB = "4.4482216152605"
 S_PER_JYR = "31557600"
 S_PER_GYR = "31556952"
 Planck_h = "0.000000000000000000000000000000000662606896"
 sigma = "0.00000005670373"
 k = "0.000000000000000000000013806504"



 --------------------------------------------------------------
 No Custom Functions Are Defined

 

 ***************************************************************************
 ***************************************************************************
 modules/Angular_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 14 Custom Functions Are Defined

 DMS_To_Deg ($DMSStr)
 Deg_To_DMS ($AngleDeg, $ssDecimals=0, $PosSymbol='')
 Deg_To_HMS ($AngleDeg, $ssDecimals=0, $PosSymbol='')
 DegHrs_To_DHMS ($DegHrs, $ssDecimals=0)
 Attach_DHMS_Symbols ($DHMSStr, $DHSymbolMode='D')
 Deg_Mod_360 ($DegStr)
 Compass_Symbol ($AzimDeg, $ZeroModeSymbol='N')
 sin_($AngDeg)
 cos_($AngDeg)
 tan_($AngDeg)
 asin_($x)
 acos_($x)
 atan_($x)
 atan2_($y, $x)

 ***************************************************************************
 ***************************************************************************
 modules/Astronomy_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 178 Custom Functions Are Defined

 Perihelion_Ymd_TZHM ($Y, $TZHM="00:00", $DateOutMode=0)
 Aphelion_Ymd_TZHM ($Y, $TZHM="00:00", $DateOutMode=0)
 Aphelion_Ymd_TZhm ($yArg, $TZhm="00:00:00", $CalMode=1)
 Mean_Sidereal_Time ($JD, $LngDeg=0)
 Mean_Epsilon ($JD)
 AU_To_AU_Km_Mi ($AUs, $AUDecimals=10)
 Mag1_Dist1_Dist2_To_Mag2 ($Mag1, $Dist1, $Dist2)
 Vis_Mag_Diff_To_b ($m1, $m2)
 Delta_Epsilon_2000B($JD)
 Delta_Psi_2000B($JD)
 Delta_Equinox_2000B($JD)
 Delta_T_Estimate ($yNum, $mNum=1)
 March_Equinox ($YGreg, $TZhm="+00:00")
 June_Solstice ($YGreg, $TZhm="+00:00")
 September_Equinox ($YGreg, $TZhm="+00:00")
 December_Solstice ($YGreg, $TZhm="+00:00")
 Seasonal_Statistics ($Y, $TZhm="+00:00")
 Mercury_hXYZ($JD)
 Venus_hXYZ($JD)
 Earth_hXYZ($JD)
 Mars_hXYZ($JD)
 Jupiter_hXYZ($JD)
 Saturn_hXYZ($JD)
 Uranus_hXYZ($JD)
 Neptune_hXYZ($JD)
 Geocentric_Sun($JD)
 Geocentric_Mercury($JD)
 Geocentric_Venus($JD)
 Geocentric_Mars($JD)
 Geocentric_Jupiter($JD)
 Geocentric_Saturn($JD)
 Geocentric_Uranus($JD)
 Geocentric_Neptune($JD)
 Geocentric_Moon ($JD)
 Mercury_X0($t) // 1853 terms of order 0
 Mercury_X1($t) // 1023 terms of order 1
 Mercury_X2($t) // 413 terms of order 2
 Mercury_X3($t) // 135 terms of order 3
 Mercury_X4($t) // 42 terms of order 4
 Mercury_X5($t) // 16 terms of order 5
 Mercury_Y0($t) // 1853 terms of order 0
 Mercury_Y1($t) // 1023 terms of order 1
 Mercury_Y2($t) // 413 terms of order 2
 Mercury_Y3($t) // 135 terms of order 3
 Mercury_Y4($t) // 42 terms of order 4
 Mercury_Y5($t) // 16 terms of order 5
 Mercury_Z0($t) // 598 terms of order 0
 Mercury_Z1($t) // 360 terms of order 1
 Mercury_Z2($t) // 167 terms of order 2
 Mercury_Z3($t) // 47 terms of order 3
 Mercury_Z4($t) // 12 terms of order 4
 Mercury_Z5($t) // 7 terms of order 5
 Venus_X0($t) // 685 terms of order 0
 Venus_X1($t) // 406 terms of order 1
 Venus_X2($t) // 133 terms of order 2
 Venus_X3($t) // 25 terms of order 3
 Venus_X4($t) // 12 terms of order 4
 Venus_X5($t) // 4 terms of order 5
 Venus_Y0($t) // 685 terms of order 0
 Venus_Y1($t) // 406 terms of order 1
 Venus_Y2($t) // 133 terms of order 2
 Venus_Y3($t) // 25 terms of order 3
 Venus_Y4($t) // 12 terms of order 4
 Venus_Y5($t) // 4 terms of order 5
 Venus_Z0($t) // 190 terms of order 0
 Venus_Z1($t) // 117 terms of order 1
 Venus_Z2($t) // 49 terms of order 2
 Venus_Z3($t) // 12 terms of order 3
 Venus_Z4($t) // 3 terms of order 4
 Venus_Z5($t) // 3 terms of order 5
 Earth_X0($t) // 1007 terms of order 0
 Earth_X1($t) //  600 terms of order 1
 Earth_X2($t) //  248 terms of order 2
 Earth_X3($t) //   46 terms of order 3
 Earth_X4($t) //   20 terms of order 4
 Earth_X5($t) //    7 terms of order 5
 Earth_Y0($t) // 1007 terms of order 0
 Earth_Y1($t) //  600 terms of order 1
 Earth_Y2($t) //  248 terms of order 2
 Earth_Y3($t) //   46 terms of order 3
 Earth_Y4($t) //   20 terms of order 4
 Earth_Y5($t) //    7 terms of order 5
 Earth_Z0($t) //  178 terms of order 0
 Earth_Z1($t) //   97 terms of order 1
 Earth_Z2($t) //   47 terms of order 2
 Earth_Z3($t) //   11 terms of order 3
 Earth_Z4($t) //    5 terms of order 4
 Earth_Z5($t) //    1 term  of order 5
 Mars_X0($t) // 1907 terms of order 0
 Mars_X1($t) // 1023 terms of order 1
 Mars_X2($t) // 511 terms of order 2
 Mars_X3($t) // 192 terms of order 3
 Mars_X4($t) // 81 terms of order 4
 Mars_X5($t) // 26 terms of order 5
 Mars_Y0($t) // 1907 terms of order 0
 Mars_Y1($t) // 1023 terms of order 1
 Mars_Y2($t) // 511 terms of order 2
 Mars_Y3($t) // 192 terms of order 3
 Mars_Y4($t) // 81 terms of order 4
 Mars_Y5($t) // 26 terms of order 5
 Mars_Z0($t) // 355 terms of order 0
 Mars_Z1($t) // 252 terms of order 1
 Mars_Z2($t) // 133 terms of order 2
 Mars_Z3($t) // 56 terms of order 3
 Mars_Z4($t) // 20 terms of order 4
 Mars_Z5($t) // 7 terms of order 5
 Jupiter_X0($t) // 1272 terms of order 0
 Jupiter_X1($t) // 638 terms of order 1
 Jupiter_X2($t) // 358 terms of order 2
 Jupiter_X3($t) // 190 terms of order 3
 Jupiter_X4($t) // 73 terms of order 4
 Jupiter_X5($t) // 15 terms of order 5
 Jupiter_Y0($t) // 1272 terms of order 0
 Jupiter_Y1($t) // 638 terms of order 1
 Jupiter_Y2($t) // 358 terms of order 2
 Jupiter_Y3($t) // 190 terms of order 3
 Jupiter_Y4($t) // 73 terms of order 4
 Jupiter_Y5($t) // 15 terms of order 5
 Jupiter_Z0($t) // 216 terms of order 0
 Jupiter_Z1($t) // 124 terms of order 1
 Jupiter_Z2($t) // 68 terms of order 2
 Jupiter_Z3($t) // 39 terms of order 3
 Jupiter_Z4($t) // 11 terms of order 4
 Jupiter_Z5($t) // 5 terms of order 5
 Saturn_X0($t) // 2047 terms of order 0
 Saturn_X1($t) // 1023 terms of order 1
 Saturn_X2($t) // 511 terms of order 2
 Saturn_X3($t) // 250 terms of order 3
 Saturn_X4($t) // 110 terms of order 4
 Saturn_X5($t) // 40 terms of order 5
 Saturn_Y0($t) // 2047 terms of order 0
 Saturn_Y1($t) // 1023 terms of order 1
 Saturn_Y2($t) // 511 terms of order 2
 Saturn_Y3($t) // 250 terms of order 3
 Saturn_Y4($t) // 110 terms of order 4
 Saturn_Y5($t) // 40 terms of order 5
 Saturn_Z0($t) // 420 terms of order 0
 Saturn_Z1($t) // 234 terms of order 1
 Saturn_Z2($t) // 91 terms of order 2
 Saturn_Z3($t) // 45 terms of order 3
 Saturn_Z4($t) // 22 terms of order 4
 Saturn_Z5($t) // 9 terms of order 5
 Uranus_X0($t) // 1926 terms of order 0
 Uranus_X1($t) // 856 terms of order 1
 Uranus_X2($t) // 341 terms of order 2
 Uranus_X3($t) // 106 terms of order 3
 Uranus_X4($t) // 23 terms of order 4
 Uranus_X5($t) // 2 terms of order 5
 Uranus_Y0($t) // 1926 terms of order 0
 Uranus_Y1($t) // 856 terms of order 1
 Uranus_Y2($t) // 341 terms of order 2
 Uranus_Y3($t) // 106 terms of order 3
 Uranus_Y4($t) // 23 terms of order 4
 Uranus_Y5($t) // 2 terms of order 5
 Uranus_Z0($t) // 235 terms of order 0
 Uranus_Z1($t) // 159 terms of order 1
 Uranus_Z2($t) // 65 terms of order 2
 Uranus_Z3($t) // 18 terms of order 3
 Uranus_Z4($t) // 6 terms of order 4
 Uranus_Z5($t) // 1 term of order 5
 Neptune_X0($t) // 821 terms of order 0
 Neptune_X1($t) // 342 terms of order 1
 Neptune_X2($t) // 113 terms of order 2
 Neptune_X3($t) // 37 terms of order 3
 Neptune_X4($t) // 14 terms of order 4
 Neptune_X5($t) // 1 term of order 5
 Neptune_Y0($t) // 821 terms of order 0
 Neptune_Y1($t) // 342 terms of order 1
 Neptune_Y2($t) // 113 terms of order 2
 Neptune_Y3($t) // 37 terms of order 3
 Neptune_Y4($t) // 14 terms of order 4
 Neptune_Y5($t) // 1 term of order 5
 Neptune_Z0($t) // 133 terms of order 0
 Neptune_Z1($t) // 61 terms of order 1
 Neptune_Z2($t) // 20 terms of order 2
 Neptune_Z3($t) // 8 terms of order 3
 Neptune_Z4($t) // 1 term of order 4
 Neptune_Z5($t) // 1 term of order 5

 ***************************************************************************
 ***************************************************************************
 modules/bcMath_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 18 Custom Functions Are Defined

 bcNth_Root_Of_X ($N, $X, $NumDecimals=16)
 bcN_Factorial ($N=0)
 bcPerm_N_R ($IntN, $IntR)
 bcComb_N_R ($N, $R)
 bcGCD ($IntAStr, $IntBStr)
 bcAdd_Frac ($A_B, $C_D)
 bcSub_Frac ($A_B, $C_D)
 bcMul_Frac ($A_B, $C_D)
 bcDiv_Frac ($A_B, $C_D)
 bcReduce_Frac ($E_F)
 bcInt_Frac_Sum ($IntFraxStr, $ReduceFlag=TRUE)
 bcInt_Frac_Mul ($IntFraxStr, $ReduceFlag=TRUE)
 bcBase10_To_BaseB ($X10, $BaseB, $TruncationLimit=0)
 bcX_Base_B_To_Base_10 ($BaseBNumStr, $BaseB)
 bcInt_Frac_To_Decimal ($IntFracA_B, $NumDecimals=1000)
 bcIs_Base_B ($XBaseBString, $BaseB)
 bcBaseB_Int_To_Base10 ($XBaseBString, $BaseB)
 bcBase10_Int_To_BaseB ($X10IntStr, $BaseB)

 ***************************************************************************
 ***************************************************************************
 modules/Calendrical_Date_and_Time_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 26 Custom Functions Are Defined

 GYmd_HMS_To_JD ($Ymd_HMS)
 Ymd_HMS_To_JD ($Ymd_HMS, $CalMode=1)
 JD_To_Ymd_HMS ($JD, $ssDecimals=0, $CalMode=1)
 Ymd_HMS_To_Date_HMS ($YmdHMS)
 HMS_To_Hrs ($HMSStr)
 Hrs_To_HMS ($hours, $ssDecimals=0, $PosSymbol='')
 JD_To_DoW_Num($JD)
 JD_To_DoW_Name($JD)
 DoW_Num_To_Name ($DoW)
 Month_Num_To_Name ($mNum)
 Month_Name_To_Num ($mName)
 Days_In_Month ($Ym, $CalMode=1)
 Nth_Sunday_In_Ym ($N, $Ym, $CalMode=1)
 Nth_DoW_In_Ym ($N, $DoW, $Ym, $CalMode=1)
 Ymd_N_Days_Hence ($YmdStart, $NDays, $CalMode=1)
 DoW_N_Days_Hence($DoWStart, $N)
 Ymd_HMS_UT_PlusMin_HMS ($Ymd_HMS_UT, $ZZhms="00:00:00", $CalMode=1)
 Seconds_To_HMS ($SecondsArg, $NumDecimals=0, $PosSign='')
 Days_To_Days_HMS ($days=0, $ssDecimals=0)
 Date_Time_Diff ($YmdA_hmsA, $YmdB_hmsB, $CalMode=1)
 Calendar_Text ($Ym, $CalMode=1)
 Calendar_Table ($ISOymd, $HiColor="cyan", $CalMode=1)
 Calendar_Matrix ($DoW1, $MDays, $HiliteDay, $CalTitle ="", $TitleColor="cyan")
 USA_Daylight_Saving_Time_Span ($year)
 EU_Summer_Time_Span ($year)
 Greg_Easter_Date ($Y, $DateModeOut=0)

 ***************************************************************************
 ***************************************************************************
 modules/Extended_Math_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 3 Custom Functions Are Defined

 LaGrange_Interpolate ($XYDataTable, $xArg)
 Swap_LaGrange_Data_Pairs ($XYDataStr)
 Extremum5 ($DataTableStr)

 ***************************************************************************
 ***************************************************************************
 modules/Metric_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 2 Custom Functions Are Defined

 Temp_To_Temp ($FromTempStr, $ToScaleStr)
 Length_To_Length ($LengthAndUnits, $ToUnits)

 ***************************************************************************
 ***************************************************************************
 modules/Randomizing_Functions.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 4 Custom Functions Are Defined

 Random_Digits_BaseB ($NumDigits=1, $BaseB=10, $LZeroSuppressed=FALSE)
 Random_DHMS ($DHMode = 'D',  $NumDecimals = 0)
 Random_Ymd ($YmdA=16000101, $YmdB=22001231, $CalMode=1)
 Random_Ymd_HMS ($YmdA=16000101, $YmdB=22001231, $CalMode=1)

 ***************************************************************************
 ***************************************************************************
 modules/Testing_Module.php

 Quick Reference Synopsis of Constants, Functions and Arguments

 --------------------------------------------------------------
 No Custom Constants Are Defined

 



 --------------------------------------------------------------
 1 Custom Function Is Defined

 GJD_To_Ymd_HMS ($JD, $ssDecimals=0)