Using BigDecimal and double

(c) Higher Frequency Trading

Using BigDecimal and double

Using BigDecimal and double(Or why you can use double for money)

Higher Frequency Trading(c) Peter Lawrey


Nearest representable value

Floating point numbers are represented using a sum of powers of two e.g. 9.75 = 8 + 1 + 0.5 + 0.25

Values like 0.1 cannot be exactly represented using floating point but when you print it, it “knows” to print the simplest number which would be represented at this value.


Rounding a double

Why do we get errors with double

– Representation errors, • 0.1 is not exactly 0.1

• new BigDecimal(0.1)– Using BigDecimal.valueOf(0.1) instead.

– Rounding errors, • each calculation gives the closest match


Rounding a double

Rounding errors are not random errors. You can predict that the error will be less than 1 ulp.

If you display a number with such as error it will have a sane toString()

However, if you perform a calculation on a value which cannot be exactly represented, you will see the error.


Rounding a double

Ways to round to significant digits

public static double round2(double d) {

return Math.round(d * 1e2) / 1e2;

}


OpenHFT Java-Lang /**

* Performs a round which is accurate to within 1 ulp.

* i.e. for values very close to 0.5 it might be rounded up or down.

* This is a pragmatic choice for performance reasons as it is assumed you are not working on the edge of the precision of double.

*/

public static double round2(double d) {

final double factor = 1e2;

return d > WHOLE_NUMBER || d < -WHOLE_NUMBER ?

(long) (d < 0 ? d * factor - 0.5 : d * factor + 0.5) / factor : d;

}


Errors and doubleExercise 10 mins Use BigDecimal to print the actual value of 0.1 Print the values of x for

for(double d = 0.0; d != 1.0; d += 0.1)

Print the values of x for

for(int x = 0; x != 10; x++) {

double d = x * 0.1;

Print the values of x for

for(int x = 0; x != 10; x++) {

double d = x / 10.0;


BigDecimal or double

Exercise 20 mins. Write a loop to take the mid price of 1000 bid

and ask values as BigDecimal and double. Use randomly generated prices.

– What sort of distribution should your use? Test the mid values are the same. How long does each take? Why?


rounding double

Exercise 20 mins. Write a function for rounding a double

– Using Math.round

– Using / of whole numbers Compare the result with BigDecimal. Can this be written without Math.round? Is this any faster?


Caching BigDecimal

Exercise 30 mins. Write a function to cache BigDecimals created

from a double.

public BigDecimal intern(double d) Compare the performance with

BigDecimal.valueOf() for values 0.01 to 1.00 Is this any faster?

Using BigDecimal and double

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