how to calculate (A*B*C)%10000007 where A,B,C can be maximum 10^18
Let I = 10000007, so
A = n1 * I + X1
B = n2 * I + X2
C = n3 * I + X3
A * B => (n1 * I + X1) (n2 * I + X2) => n1 * n2 * I^2 + n1 * X2 * I + n2 * X1 * I + X1 * X2
Only X1 * X2 can't div by I
Hence, A * B % I === X1 * X2 % I === (A % I) * (B % I) % I
Therefore (A * B * C) % I === [(A % I) * (B % I) % I] * (C % I) % I
Related
I am not able to compute the Barrier Option, because it shows me an error in the first line (where I wrote function). The code is as following. Thank you in advance.
Function UOBarrierOption(S As Double, q As Double, T As Double, X As Double, r As Double, _
sigma As Double, CallPutFlag As String, H As Double, K As Double, phi As Double, eta As Double)
Dim x1 As Double, x2 As Double
Dim y1 As Double, y2 As Double
Dim z As Double, mu As Double, lambda As Double
Dim AA As Double, BB As Double, CC As Double, DD As Double, EE As Double, FF As Double
mu = (r - q - sigma ^ 2 / 2) / (sigma ^ 2)
lambda = Sqr(mu ^ 2 + 2 * r / sigma ^ 2)
x1 = Log(S / X) / (sigma * Sqr(T)) + (1 + mu) * sigma * Sqr(T)
x2 = Log(S / H) / (sigma * Sqr(T)) + (1 + mu) * sigma * Sqr(T)
y1 = (Log(H ^ 2) / S / S) / (sigma * Sqr(T)) + (1 + mu) * sigma * Sqr(T)
y2 = (Log(H / S)) / (sigma * Sqr(T)) + (1 + mu) * sigma * Sqr(T)
z = Log(H / S) / (sigma * Sqr(T)) + lambda * sigma * Sqr(T)
AA = phi * S * Exp(-q * T) * Application.NormSDist(phi * x1) - phi * X * Exp(-r * T) * Application.NormSDist(phi * x1 - phi * sigma * Sqr(T))
BB = phi * S * Exp(-q * T) * Application.NormSDist(phi * x2) - phi * X * Exp(-r * T) * Application.NormSDist(phi * x2 - phi * sigma * Sqr(T))
CC = phi * S * Exp(-q * T) * (H / S) ^ (2 * (mu + 1)) * Application.NormSDist(eta * y1) - phi * X * Exp(-r * T) * (H / S) ^ (2 * mu) * Application.NormSDist(eta * y1 - eta * sigma * Sqr(T))
DD = phi * S * Exp(-q * T) * (H / S) ^ (2 * (mu + 1)) * Application.NormSDist(eta * y2) - phi * X * Exp(-r * T) * (H / S) ^ (2 * mu) * Application.NormSDist(eta * y2 - eta * sigma * Sqr(T))
EE = K * Exp(-r * T) * (Application.NormSDist(eta * x2 - eta * sigma * Sqr(T)) - (H / S) ^ (2 * mu) * Application.NormSDist(eta * y2 - eta * sigma * Sqr(T)))
FF = K * Exp(-r * T) * (Application.NormSDist(-eta * x2 + eta * sigma * Sqr(T)) + (H / S) ^ (2 * mu) * Application.NormSDist(eta * y2 - eta * sigma * Sqr(T)))
If CallPutFlag = "Cdi" Then
If X > H Then
UOBarrierOption = CC + EE
ElseIf X < H Then
UOBarrierOption = AA - BB + DD + EE
End Function
ElseIf CallPutFlag = "Cui" Then
If X > H Then
UOBarrierOption = AA + EE
ElseIf X < H Then
UOBarrierOption = BB - CC + DD + EE
End Function
ElseIf CallPutFlag = "Pdi" Then
If X > H Then
UOBarrierOption = BB - CC + DD + EE
ElseIf X < H Then
UOBarrierOption = AA + EE
End Function
ElseIf CallPutFlag = "Pui" Then
If X > H Then
UOBarrierOption = AA - BB + DD + EE
ElseIf X < H Then
UOBarrierOption = CC + EE
End Function
ElseIf CallPutFlag = "Cdo" Then
If X > H Then
UOBarrierOption = AA - CC + FF
ElseIf X < H Then
UOBarrierOption = BB - DD + FF
End Function
ElseIf CallPutFlag = "Cuo" Then
If X > H Then
UOBarrierOption = F
ElseIf X < H Then
UOBarrierOption = AA - BB + CC - DD + FF
End Function
ElseIf CallPutFlag = "Pdo" Then
If X > H Then
UOBarrierOption = AA - BB + CC - DD + FF
ElseIf X < H Then
UOBarrierOption = F
End Function
ElseIf CallPutFlag = "Puo" Then
If X > H Then
UOBarrierOption = BB - DD + FF
ElseIf X < H Then
UOBarrierOption = AA - CC + FF
End Function
End If
End Function
P.S. I have different "phi"s and "eta"s for different types of option barriers (cdi, pdi and etc.). Right now I am trying different combinations, but it also gives "end if function missing" type of error
If your function returns something you must declare the type returned in the function, and assign the returned value to the function, for exmaple:
Function CalculateSquareRoot(NumberArg As Double) As Double
If NumberArg < 0 Then ' Evaluate argument.
Exit Function ' Exit to calling procedure.
Else
CalculateSquareRoot = Sqr(NumberArg) ' Return square root.
End If
End Function
See the As Double and the CalculateSquareRoot = Sqr(NumberArg). That is what the function returns.
If it does not return anything, and its just a method, you should declare it with Sub().
Sub()
'your method
End Sub
I am a beginner in VB. I wrote a little program to simulate dosing regimens of antibiotics using some exponential equations and pharmacokinetic data.
The problem I have is that I want to display on a graph the following mathematical function:
That simulates the concentration variation at different intervals of time:
Where:
b(t) is the concentration at time t that will be plotted as Y axis, t is time (plotted on the x-axis).
b(0) is the concentration at time 0 and it is a known variable.
u(t-a1) is a function that has the value u(t-a1)=b(o) if t=a1 or 0 if t<>a1
a1 is the time at which a next dose is given.
alpha is the elimination rate constant, a variable that is known.
What I have so far:
Dim y, x As Double
For x = 0 To 24 Step 1
For n As Double = 1 To 24 / tau
y = (1 - test_condition(n * tau, x)) * css * Math.Exp(-ke * x) + test_condition(n * tau, x) * css * Math.Exp(-ke * (x - n * tau))
Chart1.Series("Concentratie1").Points.AddXY(x, y)
Next
Next
The test_condition:
if x=tau then test_condition= 1 else 0
It is close but I don't get an exponential decay after a dose ... don't know how to make that happen.
This works!! for tau (dosing interval) every 4 hours. Can it be rearranged somehow because the tau (dosing interval) will vary (sometimes 4 hours, sometimes every 6 hours)?:
Dim y, x, y2, x2, y3, x3, y4, x4, x5, x6, y5, y6 As Double
For x = 0 To tau Step 1
y = exponential_decay(css, ke, x) + test_condition(tau, x) * (css - Val(mic))
Chart1.Series("Bolus 1").Points.AddXY(x, y)
Next
For x2 = tau To 2 * tau Step 1
y2 = exponential_decay(css, ke, x2 - tau) + test_condition(2 * tau, x2) * (css - Val(mic))
Chart1.Series("Bolus 2").Points.AddXY(x2, y2)
Next
For x3 = 2 * tau To 3 * tau Step 1
y3 = exponential_decay(css, ke, x3 - 2 * tau) + test_condition(3 * tau, x3) * (css - Val(mic))
Chart1.Series("Bolus 3").Points.AddXY(x3, y3)
Next
For x4 = 3 * tau To 4 * tau Step 1
y4 = exponential_decay(css, ke, x4 - 3 * tau) + test_condition(4 * tau, x4) * (css - Val(mic))
Chart1.Series("Bolus 4").Points.AddXY(x4, y4)
Next
For x5 = 4 * tau To 5 * tau Step 1
y5 = exponential_decay(css, ke, x5 - 4 * tau) + test_condition(5 * tau, x5) * (css - Val(mic))
Chart1.Series("Bolus 4").Points.AddXY(x5, y5)
Next
For x6 = 5 * tau To 32 Step 1
y6 = exponential_decay(css, ke, x6 - 5 * tau)
Chart1.Series("Bolus 4").Points.AddXY(x6, y6)
Next
End Sub
I managed to solve the problem:
this function f relates time (t) to dosing interval (tau)
Private Function f(ByVal t As Double, ByVal tau As Double)
Dim n As Integer
For n = 0 To 24 / tau
If t = n * tau Then
f = n * tau
ElseIf t < tau Then
f = 0
ElseIf t > n * tau And t < (n + 1) * tau Then
f = n * tau
ElseIf t >= (n + 1) * tau Then
f = n * tau
End If
Next
End Function
And this is what I draw on the chart:
For x = 0 To 36 Step 0.5
y = exponential_decay(css, ke, x - f(x, tau))
Chart1.Series("Intermitent Dosage").Points.AddXY(x, y)
Next
With a series with a START, INCREMENT, and MAX:
START = 100
INCREMENT = 30
MAX = 315
e.g. 100, 130, 160, 190, 220, 250, 280, 310
Given an arbitrary number X return:
the values remaining in the series where the first value is >= X
the offset Y (catch up amount needed to get from X to first value of the series).
Example
In:
START = 100
INCREMENT = 30
MAX = 315
X = 210
Out:
Y = 10
S = 220, 250, 280, 310
UPDATE -- From MBo answer:
float max = 315.0;
float inc = 30.0;
float start = 100.0;
float x = 210.0;
float k0 = ceil( (x-start) / inc) ;
float k1 = floor( (max - start) / inc) ;
for (int i=k0; i<=k1; i++)
{
NSLog(#" output: %d: %f", i, start + i * inc);
}
output: 4: 220.000000
output: 5: 250.000000
output: 6: 280.000000
output: 7: 310.000000
MBo integer approach will be nicer.
School math:
Start + k0 * Inc >= X
k0 * Inc >= X - Start
k0 >= (X - Start) / Inc
Programming math:
k0 = Ceil(1.0 * (X - Start) / Inc)
k1 = Floor(1.0 * (Max - Start) / Inc)
for i = k0 to k1 (including both ends)
output Start + i * Inc
Integer math:
k0 = (X - Start + Inc - 1) / Inc //such integer division makes ceiling
k1 = (Max - Start) / Inc //integer division makes flooring
for i = k0 to k1 (including both ends)
output Start + i * Inc
Example:
START = 100
INCREMENT = 30
MAX = 315
X = 210
k0 = Ceil((210 - 100) / 30) = Ceil(3.7) = 4
k1 = Floor((315 - 100) / 30) = Floor(7.2) = 7
first 100 + 4 * 30 = 220
last 100 + 7 * 30 = 310
Solve the inequation
X <= S + K.I <= M
This is equivalent to
K0 = Ceil((X - S) / I) <= K <= Floor((M - S) / I) = K1
and
Y = X - (S + K0.I).
Note that it is possible to have K0 > K1, and there is no solution.
I am getting a compile error in Excel VBA which says Expected Sub, Function or Property. The function I am using is given below which is trying to copy the rate function in Excel.
Thanks for your help.
Function rate_m(nper As Double, pmt As Double, pv As Double, fv As Double, types As Double, guess As Double) As Variant
Dim y, y0, y1, x0, x1, f, i As Double
Dim FINANCIAL_MAX_ITERATIONS As Double
Dim FINANCIAL_PRECISION As Double
If IsNull(guess) Then guess = 0.01
If IsNull(fv) Then fv = 0
If IsNull(types) Then types = 0
FINANCIAL_MAX_ITERATIONS = 128 'Bet accuracy with 128
FINANCIAL_PRECISION = 0.0000001 '1.0e-8
y , y0, y1, x0, x1, f, i = 0
rate_m = guess
If Abs(rate_m) < FINANCIAL_PRECISION Then
y = pv * (1 + nper * rate_m) + pmt * (1 + rate_m * types) * nper + fv
Else
f = Exp(nper * Log(1 + rate_m))
y = pv * f + pmt * (1 / rate_m + types) * (f - 1) + fv
y0 = pv + pmt * nper + fv
y1 = pv * f + pmt * (1 / rate_m + types) * (f - 1) + fv
End If
'find root by Newton secant method
i , x0 = 0
x1 = rate_m
While Abs(y0 - y1) > FINANCIAL_PRECISION & i < FINANCIAL_MAX_ITERATIONS
rate_m = (y1 * x0 - y0 * x1) / (y1 - y0)
x0 = x1
x1 = rate_m
If Abs(rate_m) < FINANCIAL_PRECISION Then
y = pv * (1 + nper * rate_m) + pmt * (1 + rate_m * types) * nper + fv
Else
f = Exp(nper * Log(1 + rate_m))
y = pv * f + pmt * (1 / rate_m + types) * (f - 1) + fv
End If
y0 = y1
y1 = y
i = i + 1
Wend
End Function
A couple things...
First, you have to assign each variable individually...like this:
y = 0
y0 = 0
y1 = 0
x0 = 0
x1 = 0
f = 0
i = 0
Second, you probably want to DIM your variables all as Double. Unfortunately, this line:
Dim y, y0, y1, x0, x1, f, i As Double
Only declares i as a Double, all the others will be a Variant. You need to declare each one individually, like this:
Dim y As Double
Dim y0 As Double
Dim y1 As Double
Dim x0 As Double
Dim x1 As Double
Dim f As Double
Dim i As Double
Every IF ends with a End If (unless in a single line) and While...loop. You might want to take a look at VBA's syntax:
http://msdn.microsoft.com/en-us/library/office/ee814737(v=office.14).aspx
EDIT: You have to declare variable individually, instead of:
y , y0, y1, x0, x1, f, i = 0
you could do:
y = 0
y0 = 0
y1 = 0
x0 = 0
x1 = 0
f = 0
i = 0
So I wrote a quick function in VBA for Excel, but every time I call it, it gives me a #value error. I don't know what I am doing wrong. Can anyone help?
Function h(UA, k, A, Af_At, Delta, l)
h1 = 0
m = (2 * h1 / k / Delta) ^ 0.5
ml = m * l
Nf = WorksheetFunction.Tanh(ml)
No = 1 - Af_At * (1 - Nf / ml)
UA1 = h1 * A * No / 2
While UA > UA1
UA_old = UA1
h_old = h1
h1 = h1 + 0.5
m = (2 * h1 / k / Delta) ^ 0.5
ml = m * l
Nf = WorksheetFunction.Tanh(ml)
No = 1 - Af_At * (1 - Nf / ml)
UA1 = h1 * A * No / 2
Wend
h = h_old + (UA - UA_old) * (h1 - h_old) / (UA1 - UA_old)
End Function
I call it using: =h(10,1,1,1,1,1) in the insert function bar.
Division by zero at
No = 1 - Af_At * (1 - Nf / ml)
m1 is zero because h1 is zero.
You should change:
h1 = 0