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Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 1: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 2: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 3: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 4: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 5: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 6: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 7: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 8: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 9: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

( + )

!!

Page 10: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 11: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 12: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1)

Page 13: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1)

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Page 14: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1)

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Page 15: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1)

! ( )

! ( )

Page 16: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 17: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1) ( )

Page 18: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1) ( )

! (1)( )

Page 19: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1) ( )

! (1)( )

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Page 20: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! (1) ( )

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Page 21: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 22: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 23: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! ( + )

Page 24: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! ( + )

!

Page 25: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! ( + )

!

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Page 26: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 27: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 28: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 29: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

(1)

Page 30: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 31: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

( ) ( )

Page 32: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 33: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 34: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 35: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 36: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 37: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 38: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 39: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 40: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 41: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 42: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 43: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 44: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 45: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 46: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 47: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 48: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 49: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 50: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 51: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 52: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 53: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 54: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 55: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 56: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 57: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 58: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 59: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 60: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 61: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 62: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 63: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 64: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! ( )! ( 1 − 2)! ( )! (1)

Page 65: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

! ( )! ( 1 − 2)! ( )! (1)

( 1 − 2) 1 2

Page 66: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 67: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 68: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 69: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 70: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 71: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 72: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 73: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 74: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 75: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 76: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 77: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 78: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 79: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 80: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
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Page 82: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 83: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
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Page 85: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?

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Page 86: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 87: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 88: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
Page 89: Implementing Combiners - Parallel Programming in Scalaweek4-all.pdf · AKTH2K2MiBM;+QK#BM2`b >Qr+ Mr2BKTH2K2Mi+QK#BM2`b\ RXhrQ@T? b2+QMbi`m+iBQM i?2+QK#BM2`mb2b MBMi2`K2/B i2/ i bi`m+im`2rBi?
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