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GeneralRe: Humor or silly mistake Pin
phil.o2-Jun-20 8:10
professionalphil.o2-Jun-20 8:10 
GeneralRe: Humor or silly mistake Pin
CodeWraith2-Jun-20 8:19
CodeWraith2-Jun-20 8:19 
GeneralRe: Humor or silly mistake Pin
kalberts2-Jun-20 9:45
kalberts2-Jun-20 9:45 
GeneralRe: Humor or silly mistake Pin
kalberts2-Jun-20 8:50
kalberts2-Jun-20 8:50 
GeneralRe: Humor or silly mistake Pin
W Balboos, GHB2-Jun-20 9:35
W Balboos, GHB2-Jun-20 9:35 
GeneralRe: Humor or silly mistake Pin
jeron12-Jun-20 8:23
jeron12-Jun-20 8:23 
GeneralRe: Humor or silly mistake Pin
CodeWraith2-Jun-20 7:27
CodeWraith2-Jun-20 7:27 
GeneralRe: Humor or silly mistake Pin
kalberts2-Jun-20 9:27
kalberts2-Jun-20 9:27 
True story, from a while ago when universities (e.g. in Bergen, Norway) still had classical IBM 308x mainframes (i.e. in the mid 1980s):

One professor at the Bergen University was teaching a course in numerical methods for calculating e.g. trigonometric functions, including error propagation and error estimation. When the students ran tests on the errors in arctan (which may be a little nasty, for extreme values), the errors turned out to be larger than would be expected for the given word length.

The professor was not one to just shrug at this with a a "so what?" - he made a request to IBM to investigate the cause of this greater-than-expected error. This is where my coworker came in, working at IBM at the time; he was set to analyze it.

That IBM 3083 library function, written in assembly, was a simple adaptation of the IBM 380 and 370 functions. Which were adaptations of the IBM 360 series function. (Now we are back to the early 1960s.) But even though the 360 instruction set was new, the library function was rewritten directly based on the IBM 7090 assembly code library function. Which was an adaptation of the IBM 709 library function...

The 709 was introduced in 1957. At that time, constants such as pi was calculated by hand, and entered in hexadecimal format in the source code. Being a constand, the job was done; no need to recalculate it.

But 709/7090 were 36 bit machines. The 360, 370, 380 and 3083 were 32 bit machines. In the move to a different word length, the least significant bits of the 36 bit hex value had simply been chopped off; noone had cared to look for rounding. The error estimates made by the professor had assumed a rounding of the least significant bit of pi.

Once IBM replaced the hexadecimal (and later chopped off) pi value from the 709, and replaced it with a properly rounded value, the arctan errors matched perfectly with the professor's estimates for the given word length.
GeneralRe: Humor or silly mistake Pin
OriginalGriff2-Jun-20 8:12
mveOriginalGriff2-Jun-20 8:12 
GeneralRe: Humor or silly mistake Pin
TheGreatAndPowerfulOz2-Jun-20 15:14
TheGreatAndPowerfulOz2-Jun-20 15:14 
GeneralThought of the Day Pin
OriginalGriff2-Jun-20 4:27
mveOriginalGriff2-Jun-20 4:27 
GeneralRe: Thought of the Day Pin
Daniel Pfeffer2-Jun-20 4:59
professionalDaniel Pfeffer2-Jun-20 4:59 
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Peter_in_27802-Jun-20 5:04
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DRHuff2-Jun-20 5:09
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fd97502-Jun-20 5:09
professionalfd97502-Jun-20 5:09 
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W Balboos, GHB2-Jun-20 5:14
W Balboos, GHB2-Jun-20 5:14 
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jeron12-Jun-20 5:41
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Mike Hankey2-Jun-20 5:43
mveMike Hankey2-Jun-20 5:43 
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davecasdf3-Jun-20 3:43
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Mike Hankey3-Jun-20 3:47
mveMike Hankey3-Jun-20 3:47 
GeneralRe: Thought of the Day Pin
Richard MacCutchan2-Jun-20 6:20
mveRichard MacCutchan2-Jun-20 6:20 
GeneralReading a quotation... Pin
Sander Rossel2-Jun-20 3:37
professionalSander Rossel2-Jun-20 3:37 
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  Forogar  2-Jun-20 3:40
professional  Forogar  2-Jun-20 3:40 
JokeRe: Reading a quotation... Pin
PIEBALDconsult2-Jun-20 3:41
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Sander Rossel2-Jun-20 3:44
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