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TRAINSCAN APPLICATIONS - WebScalp | |||||||||
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SHORT LINE: WebScalp is a web-based scientific calculator program. Your browser needs to have cookies enabled.
TRACKS:
WebScalp (web-based scientific calculator program) is a stack-based calculator that uses Reverse Polish Notation (RPN). This was popularlized by Hewlett Packard on their scientific calculators introduced starting in the 1970s. Ads at the time stated that this type of caculator "had no equal" because indeed they were without an "=" button. The RPN system of operation was more efficient for long calculations than the normal calculator wth an equals button.
In short, numbers entered into an RPN calculator like WebScalp get pushed onto a stack. Mathematical operations take place on the last number or the last two numbers pushed onto the stack. To add two numbers together, say 3 and 4, one would first push 3 onto the stack, then push 4 onto the stack, and finally add them together:
3 4 +
WebScalp adds the two numbers, pops the stack, and the result ends up on the top. A more complicated example is:
DEG 45 COS 2 SQRT *
...which is the sequence to calculate the cosine of 45 degrees multiplied by the square root of 2. The DEG ensures that angles are measured in degrees. Many functions are spelled out in words rather than assigning them to arbitrary and non-standard symbols. Some functions have more than one command that invoke them. For example:
RECIP and RECIPROCAL
... both calculate the reciprocal. Note that upper and lower case are not significant for commands.
WebScalp displays the complete stack which is ten numbers deep. The top of the stack is Z -- that's where the answers appear. Deeper numbers on the stack are stored in Y, X and so on, all the way back through Q. There are also ten memory locations numbered M0 through M9 in which numbers can be stored for later retrieval and use.
Numbers can be entered in fixed point:
e.g. 3.142857
Numbers can be entered in scientific notation:
e.g. 3e8 or -42e-22
Fixed point numbers can also use the suffixes "p" (pico; multiply by 10-9), "u" (micro; multiply by 10-6), "m" (milli; multiply by 10-3), "k" or "K" (kilo; multiply by 103), "M" (mega; multiply by 106), and "g" or "G" (giga; multiply by 109). Thus
3M
...produces 3000000.
Degrees, minutes, seconds (or hours, minutes, seconds) can be entered directly, separated by colons, as
30:32:22 for 30 degrees, 32 minutes, 22 seconds
...and they will be converted to decimal degrees (hours).
WebScalp can handle polynomials up to order 9 where the coefficients are stored in the memory locations M0 through M9. For example, f(z) = Az3 + Bz2 + Cz + D would be defined by the coefficients A, B, C, and D stored in memory locations M4 through M0. The coefficients can easily be entered on the stack and placed in memory. For example, the fourth-order polynomial F(z) = 2z3 + 9z2 + 4z + 1 can be defined using:
4 ORDER 2 9 4 1 POLYNOMIAL.
Assuming that the polynomial order has been set appropriately, then value of the polynomial for any value of Z can be evaluated using the commandF(Z).
The derivative of a defined polynomial for any value of Z can be calculated using
DF(Z).
A real root of a defined polynomial can be found by repeated applications of the
SOLVE
command, where Z is the initial estimate. This uses the Newton-Raphson method, one iteration per command. Different initial estimates and multiple uses of SOLVE may converge to different real roots where they exist. If no real root exists, repeated uses of SOLVE won't converge.
Webscalp can do limited manipulation of dates. A valid date is an integer of the form: yyyymmdd (year in four digits, month in two digits, and date in two digits). The command
TODAY CALENDAR
...will push the current date in valid format onto the top of the stack and display a three-month calendar with the current date highlighted. The calendar will remain as long as date manipulation commands are used.
Webscalp can also display the time as a four-digit integer (hhmm) using
NOW.
Note that the date and time are not necessarily local time of the user, but reflect the local time of the server where Webscalp is hosted.
+ - * / Y^Z Z^X RECIP SQR SQRT CHS ABS INT FRAC TAX TAX2
COS SIN TAN ACOS ASIN ATAN ATAN2 LN LOG EXP EXP10 MOD % DIST AZ POLAR RECT
ORDER POLY F(Z) DF(Z) SOLVE QUADRATIC
NOW TODAY CAL
YR YEAR MON MONTH MOY
JULIAN DOY DOW
DDAY DDAYS DDATE DDATES
+D +M +W +Y
D+ M+ W+ Y+
PI TWOPI
C G
KM_MI MI_KM M_FT FT_M
GIMP_L L_GIMP GUS_L L_GUS OZ_L L_OZ
KT_MPH MPH_KT KT_KPH KPH_KT
MPS_KPH KPH_MPS FPS_MPH MPH_FPS
OZ_GR GR_OZ LB_KG KG_LB
FT2_M2 M2_FT2 FT2_ACRE ACRE_FT2 M2_ACRE ACRE_M2
FT3_M3 M3_FT3 YD3_M3 M3_YD3
F_C C_F
DMS HMS
DB _DB
R_P P_R
STOn STO+n STO-n STO*n STO/n RCLn
CL CLS CLM CLA CLEAR SWAP PUSH POP
RADS MILS DEGS LAT LONG LOWER UPPER MODULUS ORDER RESET EXIT HELP VER TAX1% TAX2%
LEFT CENTER CENTRE RIGHT FORMAT FLEX FIX DISPLAY INPUT
_DB : decibels to ratio : units
- : minus : Z = Y - Z
! : factorial : Z = Z!
* : times : Z = Y * Z
/ : divide : Z = Y / Z
+ : plus : Z = Y + Z
+D : date plus day : Z = Y + Z where Y is valid date and Z is offset in days
+M : date plus week : Z = Y + Z where Y is valid date and Z is offset in months (actually 30 days)
+W : date plus week : Z = Y + Z where Y is valid date and Z is offset in weeks
+Y : date plus week : Z = Y + Z where Y is valid date and Z is offset in years (actually 365 days)
% : calculate modulus (residue) : Z = Z % Modulus
< : pop stack : Z = Y ; Y = X ; ... R = Q
> : push stack : Q = R ; R = S ; ...Y = Z
ABS : absolute value : Z = |Z|
ACOS : arc cosine : Z = acos(Z)
ACRE->FT2 : acres to square feet : units
ACRE_FT2 : acres to square feet : units
ACRE->M2 : acres to square metres : units
ACRE_M2 : acres to square metres : units
ASIN : arc sine : Z = asin(Z)
ATAN : arc tangent : Z = atan(Z)
ATAN2 : 4 quadrant arc tan : Z = atan(Z/Y)
AZ : calculate azimuth of bearing from one point to another : Z = azimuth, assuming points have been pushed onto stack in order x1, y1, x2, y2
AZIMUTH : calculate azimuth of bearing from one point to another : Z = azimuth, assuming points have been pushed onto stack in order x1, y1, x2, y2
C : c : speed of light, metres/second
C->F : degrees C to degrees F : units
C_F : degrees C to degrees F : units
CAL : calendar : calendar of Z if it's a valid date
CENTER : center display of Z : presentation
CENTRE : centre display of Z : presentation
CHS : change sign : Z = -1 * Z
CL : clear Z : Z = 0
CLA : clear all stack and memory : Z=Y=...Q = 0 ; M0=M1=...M9 = 0
CLEAR : clear all stack and memory : Z=Y=...Q = 0 ; M0=M1=...M9 = 0
CLM : clear memory : M0=M1=...M9 = 0
CLS : clear stack : Z=Y=...Q = 0
COS : cosine : Z = cos(Z)
D+ : date plus day : Z = Y + Z where Y is valid date and Z is offset in days
DB : ratio to decibels : units
DDAY : difference in days : Z = days between date in Z and date in Y assuming they both contain valid date
DDAYS : difference in days : Z = days between date in Z and date in Y assuming they both contain valid date
DDATE : difference in days : Z = days between date in Z and date in Y assuming they both contain valid date
DDATES : difference in days : Z = days between date in Z and date in Y assuming they both contain valid date
DEG : assume angles are in degrees : setting
DEGREE : assume angles are in degrees : setting
DEGREES : assume angles are in degrees : setting
DF(X) : calculate derivative of polynomial function : Z = F'(Z)
DF(Z) : calculate derivative of polynomial function : Z = F'(Z)
DFX : calculate derivative of polynomial function : Z = F'(Z)
DFZ : calculate derivative of polynomial function : Z = F'(Z)
DISPLAY : diplay type, depending on Z : text if Z=0; small graphics if Z=1; large graphics if Z=2
DIST : calculate distance between two points : Z = distance, assuming points have been pushed onto stack in order x1, y1, x2, y2
DISTANCE : calculate distance between two points : Z = distance, assuming points have been pushed onto stack in order x1, y1, x2, y2
DMS : show degrees:minutes:seconds from decimal degrees in Z : units
DONE : exit program : control
DOW : day of week : Z = day(Z) 1..7 (Sunday..Sat) if Z contains valid date
DOY : day of year : Z = day(Z) 1..366 if Z contains valid date
EXIT : exit program : control
EXP : natural exponential : Z = e^Z
EXP10 : base 10 exponential : Z = 10^Z
F->C : degrees F to degrees C : units
F_C : degrees F to degrees C : units
F(X) : calculate polynomial function : Z = F(Z)
F(Z) : calculate polynomial function : Z = F(Z)
FACT : factorial : Z = Z!
FACTORIAL : factorial : Z = Z!
FIX : fixed point display : setting
FIXED : fixed point display : setting
FLEX : flexible display format : setting
FLEXIBLE : flexible display format : setting
FORMAT : set fixed diplay format width.decimals : setting
FPS->MPH : feet per second to miles per hour : units
FPS_MPH : feet per second to miles per hour : units
FRAC : fractional portion : Z = Z - int(Z)
FT->M : feet to metres : units
FT_M : feet to metres : units
FT2->ACRE : square feet to acres : units
FT2_ACRE : square feet to acres : units
FT2->M2 : square feet to square metres : units
FT2_M2 : square feet to square metres : units
FT3->M3 : cubic feet to cubic metres : units
FT3_M3 : cubic feet to cubic metres : units
FX : calculate polynomial function : Z = F(Z)
FZ : calculate polynomial function : Z = F(Z)
G : g : gravitational constant, m/second2
GIMP->L : imperial gallons to litres : units
GIMP_L : imperial gallons to litres : units
GR->OZ : grams to ounces : units
GR_OZ : grams to ounces : units
GST : calculate tax 1 : Y = Z; Z = tax1(Z)
GST% : set tax rate 1 : Tax1 = Z
GUS->L : US gallons to litres : units
GUS_L : US gallons to litres : units
HELP : display help file : control
HMS : show hours:minutes:seconds from decimal hours in Z : units
INPUT : size of command line space, depending on Z : if Z is 1 or less, single command line; otherwise Z lines to a maximum of 20
INT : integer portion : Z = int(Z)
JULIAN : day of year : Z = day(Z) 1..366 if Z contains valid date
KG->LB : kilograms to pounds : units
KG->LB : kilograms to pounds : units
KM->MI : kilometres to miles : units
KM_MI : kilometres to miles : units
KPH->KT : kilometres per hour to knots : units
KPH_KT : kilometres per hour to knots : units
KT->KPH : knots to kilometres per hour : units
KT_KPH : knots to kilometres per hour : units
KT->MPH : knots to miles per hour : units
KT_MPH : knots to miles per hour : units
L->GIMP : litres to imperial gallons : units
L_GIMP : litres to imperial gallons : units
L->GUS : litres to US gallons : units
L_GUS : litres to US gallons : units
L->OZ : litres to fluid ounces : units
L_OZ : litres to fluid ounces : units
LAT : set latitude : Latitude = Z (not currently used by any function)
LATITUDE : set latitude : Latitude = Z (not currently used by any function)
LB->KG : pounds to kilograms : units
LB_KG : pounds to kilograms : units
LEFT : left justify display of Z : presentation
LN : natural log : Z = ln(Z)
LOG : base 10 log : Z = log10(Z)
LONG : set longitude : Longitude = Z (not currently used by any function)
LONGITUDE : set longitude : Longitude = Z (not currently used by any function)
LOWER : set lower limit for fixed point presentation (anything smaller than this value is not shown in fixed point) : presentation
M+ : date plus week : Z = Y + Z where Y is valid date and Z is offset in months (actually 30 days)
M->FT : metres to feet : units
M_FT : metres to feet : units
M2->ACRE : square metres to acres : units
M2_ACRE : square metres to acres : units
M2->FT2 : square metres to square feet : units
M2_FT2 : square metres to square feet : units
M3->FT3 : cubic metres to cubic feet : units
M3_FT3 : cubic metres to cubic feet : units
M3->YD3 : cubic metres to cubic yards : units
M3_YD3 : cubic metres to cubic yards : units
MI->KM : miles to kilometres : units
MI_KM : miles to kilometres : units
MIL : assume angles are in mils : setting
MILS : assume angles are in mils : setting
MOD : calculate modulus (residue) : Z = Z % Modulus
MODULUS : set modulus : Modulus = Z
MON : month : Z = month(Z) 1..12 if Z contains valid date
MONTH : month : Z = month(Z) 1..12 if Z contains valid date
MOY : month of year : Z = month(Z) 1..12 if Z contains valid date
MPH->FPS : miles per hour to feet per second : units
MPH_FPS : miles per hour to feet per second : units
MPH->KT : miles per hour to knots : units
MPH_KT : miles per hour to knots : units
NOW : current time : Z = hhhhmm
ORDER : set polynomial order : order = Z
OZ->GR : ounces to grams : units
OZ_GR : ounces to grams : units
OZ->L : fluid ounces to litres : units
OZ_L : fluid ounces to litres : units
P_R : convert polar to rectangular coordinates : Z = y-coord, Y = x-coord, assuming that Y=magnitude, Z=argument
PI : pi : Z = 3.14...
POLAR : convert rectangular to polar coordinates : Z = magnitude, Y = argument, assuming that Y=x-coord, Z=y-coord
POLY : define polynomial : copy stack to memory to define the coefficients of a polynomial to level defined by ORDER, i.e. Mem[0] = Z, Mem[1] = Y... Mem[order]
POLYNOMIAL : define polynomial : copy stack to memory to define the coefficients of a polynomial to level defined by ORDER i.e. Mem[0] = Z, Mem[1] = Y... Mem[order]
POP : pop stack : Z = Y ; Y = X ; ... R = Q
PST : calculate tax 2 : Y = Z; Z = tax2(Z)
PST2% : set tax rate 2 : Tax2 = Z
PUSH : push stack : Q = R ; R = S ; ...Y = Z
QUAD : calculate real roots of a second-order polynomial using quadratic equation : Z = first real root, second one displayed if it exists
QUADRATIC : calculate real roots of a second-order polynomial using quadratic equation : Z = first real root, second one displayed if it exists
R_P : convert rectangular to polar coordinates : Z = magnitude, Y = argument, assuming that Y=x-coord, Z=y-coord
RAD : assume angles are in radians : setting
RADIANS : assume angles are in radians : setting
RADS : assume angles are in radians : setting
RCLn : recall from memory : Z = Mem[n]
RECIP : reciprocal : Z = 1/Z
RECIPROCAL : reciprocal : Z = 1/Z
RECT : convert polar to rectangular coordinates : Z = y-coord, Y = x-coord, assuming that Y=magnitude, Z=argument
RECTANGULAR : convert polar to rectangular coordinates : Z = y-coord, Y = x-coord, assuming that Y=magnitude, Z=argument
RESET : reset all settings to defaults : setting
RIGHT : right justify display of Z : presentation
SIN : sine : Z = sin(Z)
SOLVE : calculate one Newton-Raphson iteration to solve polynomial function : Z = Z - F(Z) / F'(Z)
SQR : square : Z = Z*Z
SQRT : square root : Z = sqrt(Z)
STO-n : subtract from memory : Mem[n] = Mem[n] - Z
STO*n : multiply by memory : Mem[n] = Mem[n] * Z
STO/n : divide into memory : Mem[n] = Mem[n] / Z
STO+n : add to memory : Mem[n] = Mem[n] + Z
STOn : store to memory : Mem[n] = Z
SWAP : swap bottom two elements of stack : Z = Y ; Y = Z
TAN : tangent : Z = tan(Z)
TAX : calculate tax 1 : Y = Z; Z = tax1(Z)
TAX1 : calculate tax 1 : Y = Z; Z = tax1(Z)
TAX2 : calculate tax 2 : Y = Z; Z = tax2(Z)
TAX% : set tax rate 1 : Tax1 = Z
TAX1% : set tax rate 1 : Tax1 = Z
TAX2% : set tax rate 2 : Tax2 = Z
TODAY : current date : Z = yyyymmdd
TWOPI : pi times two : Z = 6.28...
UPPER : set upper limit for fixed point presentation (anything larger than this value is not shown in fixed point) : presentation
VAT : calculate tax 1 : Y = Z; Z = tax1(Z)
VAT% : set tax rate 1 : Tax1 = Z
VER : display software version : control
VERSION : display software version : control
W+ : date plus week : Z = Y + Z where Y is valid date and Z is offset in weeks
Y^Z : power : Z = Y ^ Z
Y+ : date plus week : Z = Y + Z where Y is valid date and Z is offset in years (actually 365 days)
YD3->M3 : cubic yards to cubic metres : units
YD3_M3 : cubic yards to cubic metres : units
YEAR : year : Z = year(Z) if Z contains valid date
YR : year : Z = year(Z) if Z contains valid date
Z^Y : power : Z = Z ^ Y