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Old 2019-06-01, 20:33   #34
lavalamp
 
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I thought the world of finance used binary coded decimal to avoid such rounding errors.
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Old 2019-06-01, 20:43   #35
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Quote:
Originally Posted by retina View Post
I suspect it was finance. Before 64bit integer CPUs were introduced "everyone" used the FPU to compute their millions. Excel is a good example of this.

And yes, rounding problems were rife. But how else to handle fractional percentages with only integer arithmetic?

Quake and gaming and stuff ... ;-)


In all seriousness, every time you use a float or double in C++ you're using the fpu unit.
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Old 2019-06-01, 20:47   #36
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Quote:
Originally Posted by lavalamp View Post
I thought the world of finance used binary coded decimal to avoid such rounding errors.
The FPU also natively supports BCD formats. But "no one" ever used it, it was too cumbersome to deal with. And it doesn't help with a table mortgage payment computation for 30 years with monthly rests at 4.56% p/a.
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Old 2019-06-01, 21:24   #37
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.. And it doesn't help with a table mortgage payment computation for 30 years with monthly rests at 4.56% p/a.

I suggest to not get a mortgage in the first place.
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Old 2019-06-01, 21:27   #38
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I suggest to not get a mortgage in the first place.
And pay rental for ever? Or live in the forest/jungle? Sleep in the street?
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Old 2019-06-01, 23:31   #39
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Double precision frees you from having to do numerical analysis every time you implement an algorithm in floating point; William Kahan has a series of papers on how various computations will silently give wrong results when not given enough precision or shortcuts in how floating point is implemented (i.e. flush to zero instead of denormals which are expensive in hardware).

Likewise linear algebra on ill-conditioned systems only gets good answers if you throw more digits at it; applications such as Bailey's Inverse Symbolic Calculator need higher precision floating point IIRC. Linear algebra is a subroutine inside lots of other algorithms and you don't want it to silently give you garbage. Shewchuck's work in robust automatic triangulation is hugely important because it relies on increasing precision when problems get hard, including switching to double-double arithmetic if necessary. This is another subroutine deep inside other stuff (i.e. finite element analysis) that has to work or all the layers above it will break.

Of course around here the killer app for double precision floating point is FFTs :)
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Old 2019-06-02, 16:01   #40
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And pay rental for ever? Or live in the forest/jungle? Sleep in the street?

Save money for a house. At least in today's economic climate it's not wise to get a mortgage. You can buy a house after the next 'Great Depression 2.0' for a fifth of the price.
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Old 2019-06-02, 16:49   #41
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Quote:
Originally Posted by joblack View Post
Save money for a house. At least in today's economic climate it's not wise to get a mortgage. You can buy a house after the next 'Great Depression 2.0' for a fifth of the price.
That 2.0 might be 40 years from now, for one; this is terrible advice generally. There are locales where house prices are too high to justify purchase, but that observation is fully independent from using a mortgage to do the purchasing. Your advice is similar to saying "don't buy any stocks, because google and amazon are going to crash."

Mortgage rates in USA are around 4.0% for classic 30-year-fixed-rate notes. At those rates, there are many many places in the US where home prices are (1) not very high, and (2) low enough that a 20% down payment leaves a mortgage cheaper than rent.
There remain places where buying homes (with a mortgage) simply to rent out is profitable; while home prices may fall, rent is much less likely to do so and will fall less if it does. If homes as investment are profitable, surely one can find more value in living in such a home.

Last fiddled with by VBCurtis on 2019-06-02 at 19:36 Reason: spellcheck: primes -> prices, ii -> i
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Old 2019-06-02, 19:04   #42
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Quote:
Originally Posted by VBCurtis View Post
Mortgage rates in USA are around 4.0% for classic 30-year-fixed-rate notes. At those rates, there are many many places in the US where home prices are (1) not very high, and (2) low enough that a 20% down payment leaves a mortgage cheaper than rent.
There remain places where buying homes (with a mortgage) simply to rent out is profitable; while home primes may fall, rent is much less likely to do so and will fall less if it does. If homes as iinvestment are profitable, surely one can find more value in living in such a home.
To quote a legendarily loud English band, Hello, Cleveland! Hello, Cleveland!. Did they ever make it out of that Escher-esque boiler room, I wonder.
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Old 2019-06-03, 01:05   #43
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This sounds suspiciously like an argument for quadp in modern processors:

Quote:
Originally Posted by jasonp View Post
Likewise linear algebra on ill-conditioned systems only gets good answers if you throw more digits at it; applications such as Bailey's Inverse Symbolic Calculator need higher precision floating point IIRC. Linear algebra is a subroutine inside lots of other algorithms and you don't want it to silently give you garbage. Shewchuck's work in robust automatic triangulation is hugely important because it relies on increasing precision when problems get hard, including switching to double-double arithmetic if necessary. This is another subroutine deep inside other stuff (i.e. finite element analysis) that has to work or all the layers above it will break.
There was an additional question that someone posed earlier that I don't think was addressed. In GPUs the architecture seems to be such that some number of single precision floating point units (4?) are combined, perhaps power-ranger style, to compute with double precision. Could it not also be the case that mighty morphing x86 architecture could do something similar and combine areas of the FPU for doubles to also compute quads?

This seems like a fairly sensible way to include quad precision support without adding a ton of extra silicon devoted specifically to it. And hey, if they wanted to include all the same FMA and vectorisation support for quads too that'd be excellent. Even if quad FLOPS were 1/4 (or lower) than double FLOPS, that's still perfectly acceptable.

The registers could still be maintained at 64 bits wide if the 128 bit floats were simply given and returned as an upper and lower half. It would just mean that the CPU instruction would need to be given 6 arguments instead of 3 for a mul.
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Old 2019-06-03, 01:10   #44
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Quote:
Originally Posted by ewmayer View Post
To quote a legendarily loud English band, Hello, Cleveland! Hello, Cleveland!. Did they ever make it out of that Escher-esque boiler room, I wonder.


"Buy a house for the price of a VCR"
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