1. bigdecimal Ruby
The future of the bigdecimal
library and the number system
of Ruby
mrkn, Kenta Murata (Genetic Lab Co., Ltd)

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15. bigdecimal
Ruby
The future of the bigdecimal
library and the number system
of Ruby
mrkn, Kenta Murata (Genetic Lab Co., Ltd)

16. The bigdecimal library
✓ BigDecimal class
✓ BigMath module

17. BigDecimal class
✓ require ‘bigdecimal’
✓
Multiprecision oating point numbers
✓ 10n
10n-adic representation (modi ed BCD)

18. BigMath module
✓ BigDecimal Math
The Math module for BigDecimals
✓ For examples:
✓ Math::PI → BigMath.PI(n)
✓ Math.cos(x) → BigMath.cos(x, n)

19. Problems
✓
Behavior modes maintained by global variable
✓
Precision handlings
✓
Instance generation
✓
Calculation speed

20. Modes of BigDecimal
✓ BigDecimal
Controlling the behaviors of the system of
BigDecimal class
✓
Exception handling mode
✓ ( )
Rounding mode

21. Exception handling mode
✓
✓ In nity
✓ NaN
✓ Under ow
✓ Over ow
✓ Division by zero

22. Rounding modes
✓ Round up
✓ Round down (toward zero) ←IEEE754
✓ Round half up
✓ Round half down
✓ Banker’s rounding ←IEEE754
✓ Floor (toward +∞) ←IEEE754
✓ Ceiling (toward –∞) ←IEEE754

23. BigDecimal.mode
✓ /
The class method for getting or setting modes
✓
Maintained per-process
✓
That is a global variable

24. Global modes
✓
Thread unsafe
✓ 2
Cannot simultaneously start two threads which use
different modes
✓
Fiber unsafe

25. Which BD.mode(BD::EXCEPTION_NAN) is?
BD = BigDecimal
th = Thread.start {
BD.mode(BD::EXCEPTION_NAN, true)
...(A)...
}
BD.mode(BD::EXCEPTION_NAN, false)
...(B)...
th.join

26. Which BD.mode(BD::EXCEPTION_NAN) is?
BD = BigDecimal
th = Thread.start {
BD.mode(BD::EXCEPTION_NAN, true)
...(A)...
}
BD.mode(BD::EXCEPTION_NAN, false)
...(B)...
th.join
It is inde nite X(

27. Fiber unsafe
BD = BigDecimal
fa = Fiber.new {
BD.mode(BD::ROUND_MODE, BD::ROUND_UP)
}
Fiber.new {
BD.mode(BD::ROUND_MODE, BD::ROUND_DOWN)
fa.resume
BD.mode(BD::ROUND_MODE) #=> BD::ROUND_UP
}.resume

28. Modes in thread-local storages
✓ Introduced at r29099 (3 days ago)
✓
Modes are maintained per-thread
✓
Threads are initialized with default modes
✓
Fiber safe

29. Mode conserving block
✓
It makes temporary-mode-change easy
✓ BigDecimal.save_exception_mode { ... }
✓ BigDecimal.save_rounding_mode { ... }
✓ Introduced at r29127 (yesterday)
✓

30. Effective digits
✓
The number of effective digits
✓ : 3 (three digits are effective)
3.141592653589792...×100
↓
0.314 1592653589792...×101
✓

31. BigDecimal#precs
✓ prec[1]
The allocated length of the digit array
✓ prec[2]
The used length of the digit array
✓
Not the number of effective digits
✓
Do you use them?

32. BigDecimals don’t know their own effective digits
✓ ( )
We must maintain (multiple) the number of effective digits
✓ Float
As well as Floats
✓
It is too much convenient.
Should be maintained automatically.

33. Collaborate with Floats
✓ Float
Force converted into Floats
✓ Float::DIG
The number of digits is forced to Float::DIG
✓
It is dangerous, don’t mix them!

34. Code examples
### (1) ###
BigDecimal("3602879701896397.1") / 36028797018963968
#=> #<BigDecimal:10086d8e0,'0.1000000000 0000000555
1115123125 782702E0',36(54)> Float::DIG
### (2) ###
BigDecimal("3602879701896397.1") / 36028797018963968.0
#=> 1.0 ↑

35. Instance generation
✓
Generate from Strings
✓
Cannot generate from others X(

36. That is...
a = BigDecimal(“3.141592653589”) # OK
b = BigDecimal(42) # NG
c = BigDecimal(Rational(355, 113)) # NG
d = BigDecimal(3.141592653589) # NG

37. That is...
a = BigDecimal(“3.141592653589”) # OK
b = BigDecimal(42) # NG
c = BigDecimal(Rational(355, 113)) # NG
d = BigDecimal(3.141592653589) # NG
e = BigDecimal(a) # NG!!

38. Float is difficult
✓ Float::RADIX != 10
✓
Cannot convert exactly due to different radix
✓
Explicitly specifying the number of effective digits

39. Calculation speeds
✓
Implemented only schoolbook multiplication
✓
Implemented only schoolbook division
✓
Can get more high speed

40. e.g.) Karatsuba method
a = a0 × 10n + a1
b = b0 × 10n + b1
c = ab
= (a0 × 10n + a1)(b0 × 10n + b1)
= a0b0 × 102n + (a0b1 + a1b0) × 10n + a1b1
= a0b0 × 102n + [a0b0 + (a0 – a1)(b1 – b0) + a1b1] × 10n + a1b1

41. Other algorithms
✓ Toom-Cook method
✓ Schönhage-Strassen method
✓ Fürer method
✓ Neuton method (for reciprocal)

43. Number System of Ruby
(Float)
(BigDecimal)
Integer
Rational
N/A
Complex

44. Number System of Ruby
(Float)
(BigDecimal)
Integer
Rational
N/A
Complex

45. Computable Real
✓
Represents irrational numbers as algorithms
which generates them
✓
Decimal representations should be generated
only if needed

46. e.g.) e–iπ == –1
✓ Present:
CMath.exp(–Math::PI.i)
#=> (–1.0–1.2246467991473532e–16i)
✓ Ideal:
Math.exp(–Math::PI.i)
#=> –1

47. Summary
✓ BigDecimal
BigDecimal has some problems
✓
Some of these has been xed recently
✓
We need a class for computable real

48. Sapporo Kaigi 03
03
MIX
1 3 1 5

51. e rst edition
still in Junkudo.