Go for Decimals (Josh Carpeggiani 2019)

Transcript

1. Go for Decimals Go for Decimals Joshua Carpeggiani Joshua Carpeggiani Software Engineer, ANZ Software Engineer, ANZ
2. Full Slides Full Slides Full slides available at Full slides available at gophercon.joshcarp.com/gophercon.slide gophercon.joshcarp.com/gophercon.slide (http://gophercon.joshcarp.com/gophercon.slide) (http://gophercon.joshcarp.com/gophercon.slide) 2 2
3. 3 3
4. Floating point numbers Floating point numbers 4 4
5. Floating point numbers Floating point numbers 5 5
6. Floating point numbers Floating point numbers 6 6
7. Floating point numbers Floating point numbers 7 7
8. Not all numbering systems are created equal Not all numbering systems are created equal 8 8
9. Binary Binary Bin -> Dec Bin -> Dec 0 = 0 0 = 0 1 = 1 1 = 1 10 = 2 10 = 2 100 = 4 100 = 4 12 12
10. Binary Binary Bin -> Dec Bin -> Dec 1 = 1 1 = 1 0.1 = 0.5 0.1 = 0.5 0.01 = 0.25 0.01 = 0.25 0.001 = 0.125 0.001 = 0.125 16 16
11. Binary floating point numbers Binary floating point numbers 0 0 2 2 . . 1 1 2 2 ×2 ×2 = 0.5 = 0.5 0 0 −1 −1 1.0 1.0 significand significand -1 -1 exponent exponent 17 17
12. Binary Binary Bin -> Dec Bin -> Dec 0.0001 = 0.0625 0.0001 = 0.0625 18 18
13. Binary Binary Bin -> Dec Bin -> Dec 0.00011 = 0.09375 0.00011 = 0.09375 19 19
14. Binary Binary Bin -> Dec Bin -> Dec 0.000110011 = 0.099609375 0.000110011 = 0.099609375 20 20
15. Binary Binary Bin -> Dec Bin -> Dec 0.00011001101 = 0.10009765625 0.00011001101 = 0.10009765625 21 21
16. Why? Why? 22 22
17. Another Decimal library Another Decimal library www.github.com/anz-bank/decimal www.github.com/anz-bank/decimal (http://www.github.com/anz-bank/decimal) (http://www.github.com/anz-bank/decimal) Project Goal: Implement a 64 & 128 bit decimal floating point library Project Goal: Implement a 64 & 128 bit decimal floating point library Conform as closely to IEEE 754-2008 standard as practical Conform as closely to IEEE 754-2008 standard as practical 23 23
18. Scientific notation Scientific notation 0 0 10 10 . . 1 1 10 10 1 1 -1 -1 24 24
19. Scientific notation Scientific notation 0 0 10 10 . . 1 1 10 10 1 1 -1 -1 1.0 1.0 25 25
20. Scientific notation Scientific notation 0 0 10 10 . . 1 1 10 10 ×10 ×10 1 1 -1 -1 1.0 1.0 -1 -1 26 26
21. Scientific notation Scientific notation ×10 ×10 1.0 1.0 -1 -1 27 27
22. Scientific notation Scientific notation ×10 ×10 + + ×10 ×10 1.0 1.0 -1 -1 2.0 2.0 -1 -1 28 28
23. Scientific notation Scientific notation ×10 ×10 + + ×10 ×10 = = ×10 ×10 1.0 1.0 -1 -1 2.0 2.0 -1 -1 3.0 3.0 -1 -1 29 29
24. Another Decimal library Another Decimal library 30 30
25. Another Decimal library Another Decimal library 31 31
26. Another Decimal library Another Decimal library 32 32
27. Another Decimal library Another Decimal library 33 33
28. Applause Applause 34 34
29. 37 37
30. The End? The End? Use decimals for everything? Use decimals for everything? 39 39
31. The End? The End? Use decimals for everything? Use decimals for everything? Why doesn't everything use this? Why doesn't everything use this? 40 40
32. The End? The End? Use decimals for everything? Use decimals for everything? Why doesn't everything use this? Why doesn't everything use this? Are decimals even that efficient? Are decimals even that efficient? 41 41
33. Decimal decoding Decimal decoding 9,999 + 1 9,999 + 1 = 10,000 = 10,000 43 43
34. Decimal decoding Decimal decoding 9,999 + 1 9,999 + 1 = 10,000 = 10,000 = = x x 10,000 10,000 1,000 1,000 10 10 ? ? 44 44
35. Decimal decoding Decimal decoding 9,999 + 1 9,999 + 1 = 10,000 = 10,000 = = x x x x 10,000 10,000 1,000 1,000 10 10 ? ? 1,000 1,000 10 10 1 1 45 45
36. Decimal decoding Decimal decoding ÷ ÷ 10,000 dec 10,000 dec 10 dec 10 dec 46 46
37. Decimal decoding Decimal decoding ÷ ÷ ÷ ÷ 10,000 dec 10,000 dec 10 dec 10 dec 10011100010000 10011100010000 1010 1010 47 47
38. Decimal decoding Decimal decoding ÷ ÷ ÷ ÷ some really long integer division here some really long integer division here 10,000 dec 10,000 dec 10 dec 10 dec 10011100010000 10011100010000 1010 1010 48 48
39. Decimal decoding Decimal decoding ÷ ÷ ÷ ÷ some really long integer division here some really long integer division here = = = 1,000 (dec) = 1,000 (dec) 10,000 dec 10,000 dec 10 dec 10 dec 10011100010000 10011100010000 1010 1010 1111101000 1111101000 49 49
40. Binary decoding Binary decoding 10011100010000 10011100010000 50 50
41. Binary Binary decoding decoding >> 4 >> 4 10011100010000 10011100010000 51 51
42. Binary decoding Binary decoding >> 4 >> 4 x x 10011100010000 10011100010000 1001110001 1001110001 2 2 4 4 52 52
43. Decimal vs Floating point Decimal vs Floating point 53 53
44. Software vs Hardware Software vs Hardware 54 54
45. 55 55
46. Binary floating point Add Binary floating point Add 56 56
47. Binary floating point Assembler Binary floating point Assembler 57 57
48. Binary floating point Assembler Binary floating point Assembler 58 58
49. Decimal Arithmetic in Go Decimal Arithmetic in Go
50. Decimal Arithmetic in Go Decimal Arithmetic in Go 60 60
51. Decimal Arithmetic in Go Decimal Arithmetic in Go 61 61
52. Decimal Arithmetic in Go Decimal Arithmetic in Go 62 62
53. Decimal Arithmetic in Go Decimal Arithmetic in Go 63 63
54. Is there a better way? Is there a better way? 64 64
55. A better solution A better solution 65 65
56. A better solution A better solution 66 66
57. Conclusion Conclusion Use floats if you really need performance and not precision Use floats if you really need performance and not precision Use ints as your smallest unit if you need precision and performance Use ints as your smallest unit if you need precision and performance Use decimals for everything else Use decimals for everything else Come contribute Come contribute github.com/anz-bank/decimal github.com/anz-bank/decimal 67 67
58. Looking forward Looking forward More optimisation More optimisation Implement 128 bit Implement 128 bit Assembler optimisations Assembler optimisations 68 68
59. Core Core 69 69
60. Thank you Thank you Joshua Carpeggiani Joshua Carpeggiani Software Engineer, ANZ Software Engineer, ANZ joshua.carpeggiani@anz.com joshua.carpeggiani@anz.com (mailto:joshua.carpeggiani@anz.com) (mailto:joshua.carpeggiani@anz.com)