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GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
PIEBALDconsult8-Jun-22 9:21
mvePIEBALDconsult8-Jun-22 9:21 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
Patrice T8-Jun-22 16:38
mvePatrice T8-Jun-22 16:38 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
Daniel Pfeffer8-Jun-22 22:57
professionalDaniel Pfeffer8-Jun-22 22:57 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
Amarnath S8-Jun-22 18:04
professionalAmarnath S8-Jun-22 18:04 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
GuyThiebaut8-Jun-22 23:20
professionalGuyThiebaut8-Jun-22 23:20 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
Tony Hill8-Jun-22 23:59
mveTony Hill8-Jun-22 23:59 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
enhzflep9-Jun-22 17:07
enhzflep9-Jun-22 17:07 
GeneralRe: A bigger piece of the pi: Finding the 100-trillionth digit Pin
trønderen10-Jun-22 3:05
trønderen10-Jun-22 3:05 
Years ago (I believe it was in the late 1970s), University of Bergen, Norway, ran a huge IBM mainframe. The IT department had a professor teaching a course in error propagation, and in preparing the course material, he saw that the error in calculating the arctan(), which may be a little nasty for extreme values, was higher than one should expect, given 32 bits of precision. As a good researcher should do, he set out to find the explanation.

To make a long story short: In the old days, you didn't repeat calculations unless needed. For the old IBM 709, the binary representation of pi had been calculated, and the hex bit pattern was copied whenever needed. For the IBM 7090 Fortran library, the hex was copied without any change. 709/7090 were 36 bit machines. The 360 series were 32 bits. So when the Fortran library was ported, the least significant, last four bits, i.e. the last hex digit, of the pi constant, was chopped off.

No one considered rounding. The chopped-off bits were significantly above '.5' (or 1000 as a bit pattern), so the last retained bit should have been rounded up to 1. It remained at 0. No updates to the Fortran library was required (or, at least the pi constant was unchanged), and later to 303x.

Once the least significant pi bit was correctly rounded up to 1, the error in the arctan() function dropped to the level predicted by the theoretical analysis.
NewsRust is hard, or: the misery of mainstream programming Pin
Kent Sharkey8-Jun-22 7:46
staffKent Sharkey8-Jun-22 7:46 
GeneralRe: Rust is hard, or: the misery of mainstream programming Pin
Greg Utas9-Jun-22 0:51
professionalGreg Utas9-Jun-22 0:51 
NewsMicrosoft trying to kill HDD boot drives by 2023: report Pin
Kent Sharkey8-Jun-22 7:46
staffKent Sharkey8-Jun-22 7:46 
GeneralRe: Microsoft trying to kill HDD boot drives by 2023: report Pin
Nelek8-Jun-22 8:20
protectorNelek8-Jun-22 8:20 
GeneralRe: Microsoft trying to kill HDD boot drives by 2023: report Pin
Dan Neely9-Jun-22 3:44
Dan Neely9-Jun-22 3:44 
GeneralRe: Microsoft trying to kill HDD boot drives by 2023: report Pin
obermd9-Jun-22 3:33
obermd9-Jun-22 3:33 
NewsMicrosoft HoloLens boss Alex Kipman is out after misconduct allegations Pin
abmv7-Jun-22 18:31
professionalabmv7-Jun-22 18:31 
GeneralRe: Microsoft HoloLens boss Alex Kipman is out after misconduct allegations Pin
Marc Clifton8-Jun-22 2:15
mvaMarc Clifton8-Jun-22 2:15 
GeneralRe: Microsoft HoloLens boss Alex Kipman is out after misconduct allegations Pin
Kent Sharkey8-Jun-22 7:40
staffKent Sharkey8-Jun-22 7:40 
GeneralRe: Microsoft HoloLens boss Alex Kipman is out after misconduct allegations Pin
maze38-Jun-22 22:50
professionalmaze38-Jun-22 22:50 
GeneralRe: Microsoft HoloLens boss Alex Kipman is out after misconduct allegations Pin
Dan Neely9-Jun-22 3:52
Dan Neely9-Jun-22 3:52 
NewsNarcissistic bosses stymie knowledge flow, cooperation inside organizations Pin
Kent Sharkey7-Jun-22 10:01
staffKent Sharkey7-Jun-22 10:01 
GeneralRe: Narcissistic bosses stymie knowledge flow, cooperation inside organizations Pin
David O'Neil7-Jun-22 17:35
professionalDavid O'Neil7-Jun-22 17:35 
GeneralRe: Narcissistic bosses stymie knowledge flow, cooperation inside organizations Pin
Greg Utas8-Jun-22 0:39
professionalGreg Utas8-Jun-22 0:39 
GeneralRe: Narcissistic bosses stymie knowledge flow, cooperation inside organizations Pin
Nelek8-Jun-22 1:59
protectorNelek8-Jun-22 1:59 
NewsIETF publishes HTTP/3 RFC to take the web from TCP to UDP Pin
Kent Sharkey7-Jun-22 9:46
staffKent Sharkey7-Jun-22 9:46 
GeneralRe: IETF publishes HTTP/3 RFC to take the web from TCP to UDP Pin
Greg Utas8-Jun-22 0:36
professionalGreg Utas8-Jun-22 0:36 

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