5 ms·

I still remember when I encountered this and nobody else in the office knew about it either. We speculated about broken CPUs and compilers until somebody found

I still remember when I encountered this and nobody else in the office knew about it either. We speculated about broken CPUs and compilers until somebody found a newsgroup post that explained everything. Makes me wonder why we haven't switched to a better floating point model in the last decades. It will probably be slower but a lot of problems could be avoided.

dragontamer 7y ago
> Makes me wonder why we haven't switched to a better floating point model in the last decades. The opposite. Decimal floating points have been available in COBOL from the 1960s, but seem to have fallen out of favor in recent days. This might be a reason why bankers / financial data remains on ancient COBOL systems. Fun fact: PowerPC systems still support decimal-floats natively (even the most recent POWER9). I presume IBM is selling many systems that natively need that decimal-float functionality.
- goosehonk 7y ago
  Decimal floats are a lot older than COBOL. Many early relay computers (to the extent there were many such machines) used floating-point numbers with bi-quinary digits in the mantissa. https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal
- deleted 7y ago
  [deleted]
anchpop 7y ago
Many languages have types for infinite-precision rational numbers, for example Rational in Haskell.
throwaway2048 7y ago
Floating point is fundamentally a trade off between enumerable numbers (precision) and range between minimum/maximum numbers, it exists because fast operations on numbers are not possible with arbitrary precision constructs (you can easily have CPU/GPU operations where floating point numbers fit in registers, arbitrary precision by its very nature is arbitrarily large). With many operations this trade off makes sense, however its critical to understand the limitations of the model.
w-j-w 7y ago
At this time understanding floating point numbers falls under "programmer responsibility", and not languages follow the example set by C. Most languages are designed by people who find the idea of not understanding floating point numbers kind of absurd.
maxdamantus 7y ago
Unless you have a floating point model that supports arbitrary bases, you're always going to have the issue. Binary floats are unable to represent 1/10 just as decimal floats are unable to represent 1/3. And in case anyone's wondering about handling it by representing the repeating digits instead, here's the decimal representation of 1/12345 using repeating digits: 0.0[0008100445524503847711624139327663021466180639935196435803969218307006885378 69582827055488051842851356824625354394491697043337383556095585257189145402997164 84406642365330093155123531794248683677602268124746861077359254759011745646010530 57918185500202511138112596192790603483191575536654515998379910895099230457675172 13446739570676387201296071283920615633859862292426083434588902389631429728635074 92912110166059133252328878088294856217091940056703118671526933981368975293641150 26326447954637505062778452814904819765087079789388416362899959497772377480761441 87930336168489266909680032401782098015390846496557310652085864722559740785743215 87687322802754151478331308221952207371405427298501417577966788173349534224382341 02875658161198865937626569461320372620494127176994734710409072498987444309437019 03604698258404212231672742]
- amelius 7y ago
  > Unless you have a floating point model that supports arbitrary bases See also binary coded decimals. https://en.wikipedia.org/wiki/Binary-coded_decimal https://en.wikipedia.org/wiki/Binary-coded_decimal
  - snickerbockers 7y ago
    That's not a floating point.
    - amelius 7y ago
      From the article: > Programmable calculators manufactured by Texas Instruments, Hewlett-Packard, and others typically employ a floating-point BCD format, typically with two or three digits for the (decimal) exponent.
      - snickerbockers 7y ago
acqq 7y ago
Decimal floating point is standardized since 2008: https://en.wikipedia.org/wiki/Decimal_floating_point#IEEE_754-2008_encoding https://en.wikipedia.org/wiki/Decimal_floating_point#IEEE_75... But it's still not much used. E.g. for C++ it was proposed in 2012 for the first time http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n340... then revised in 2014: http://open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3871.html http://open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3871.ht... ...and... silence? https://www.reddit.com/r/cpp/comments/8d59mr/any_update_on_the_decimal_proposal/ https://www.reddit.com/r/cpp/comments/8d59mr/any_update_on_t...
- gowld 7y ago
  It's not important to most people, because decimal floating point only helps if your UI precision is exactly the same as your internal precision, which almost never happens. Seeing the occasional 0.300000000000004 is a good reminder that your 0.3858372895939229 isn't accurate either.
  - acqq 7y ago
    > It's not important to most people One can argue that nothing is important to most people. The correct calculations involving money, up to the last cent, are in fact important for people who do them or who are supposed to use them. I've implemented them in the software I've made to preform some financial stuff even in eighties, in spite of all the software which used binary floating point routines. And, of course, from the computer manufacturers, at least IBM cares too: https://www.ibm.com/support/pages/decimal-floating-point-users-guide-technology-preview-advance-toolchain-ibm-xl-cc-linux-131 https://www.ibm.com/support/pages/decimal-floating-point-use... Apparently, there are even processors which supports these formats in hardware. It's just still not mainstream.
gowld 7y ago
Being a lot slower is a worse problem than being off by an error of 2^60. And if it isn't, then you simply choose a different numeric type.
masklinn 7y ago
> Makes me wonder why we haven't switched to a better floating point model in the last decades. It will probably be slower but a lot of problems could be avoided. Pretty much all languages have some sort of decimal number. Few or none have made it the default because they're ignominiously slower than binary floating-point. To the extent that even languages which have made arbitrary precision integers their default firmly keep to binary floating-point.
- amyjess 7y ago
  > Few or none have made it the default because they're ignominiously slower than binary floating-point. You can strike the "none". Perl 6 uses rationals (Rat) by default, someone once told me Haskell does the same, and Groovy uses BigDecimal.
snickerbockers 7y ago
There is no "better floating point model" because floating point will always be floating point. Fixed point always has been and always will be an option if you don't like the exponential notation.
- crazygringo 7y ago
  > Fixed point always has been and always will be an option Not really. It would be really cool if fixed point number storage were an option... but I'm not aware of any popular language that provides it as a built-in primitive along with int and float, just as easy to use and choose as floats themselves. Yes probably every language has libraries somewhere that let you do it where you have to learn a lot of function call names. But it would be pretty cool to have a language with it built-in, e.g. for base-10 seven digits followed by two decimals: fixed(7,2) i; i = 395.25; i += 0.01; And obviously supporting any desired base between 2 and 16. Someone please let me know if there is such primitive-level support in any mainstream language!
  - snickerbockers 7y ago
    You don't need special support from the language, fixed-point arithmetic is effectively the same as integer. DOOM's implementation of fixed-point is a good example which should work on any platform as long as sizeof(int) >= 4. https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.10/m_fixed.h https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.... https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.10/m_fixed.c https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.... Addition and subtraction will work normally. Multiplication also works normally except you need to right-shift by FRAC_BITS afterwards (and probably also cast to a larger integer type beforehand to protect against overflow). Division is somewhat difficult since integer division is not what you want to do. DOOM's solution was to cast to double, perform the division, and then convert that back to fixed-point by multiplying by 1.0 before casting back to integer. This seems like cheating since it's using floating-point as an intermediate type, but it is safe to do because 64-bit floating point can represent all 32-bit integers. As long as you're on a platform with an FPU it's probably also faster than trying to roll your own division implementation.
ryandrake 7y ago
Wait, an entire office (presumably full of programmers) didn’t understand floating point representation? What office was this? Isn’t this topic covered first in every programming book or course where floating point math is covered?
- Ididntdothis 7y ago
  This was in the 90s. We were all self taught and I had never met anyone who had formal CS education.

dragontamer 7y ago

> Makes me wonder why we haven't switched to a better floating point model in the last decades. The opposite. Decimal floating points have been available in COBOL from the 1960s, but seem to have fallen out of favor in recent days. This might be a reason why bankers / financial data remains on ancient COBOL systems. Fun fact: PowerPC systems still support decimal-floats natively (even the most recent POWER9). I presume IBM is selling many systems that natively need that decimal-float functionality.

goosehonk 7y ago
Decimal floats are a lot older than COBOL. Many early relay computers (to the extent there were many such machines) used floating-point numbers with bi-quinary digits in the mantissa. https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal https://en.wikipedia.org/wiki/Bi-quinary_coded_decimal
deleted 7y ago
[deleted]

anchpop 7y ago

Many languages have types for infinite-precision rational numbers, for example Rational in Haskell.

throwaway2048 7y ago

Floating point is fundamentally a trade off between enumerable numbers (precision) and range between minimum/maximum numbers, it exists because fast operations on numbers are not possible with arbitrary precision constructs (you can easily have CPU/GPU operations where floating point numbers fit in registers, arbitrary precision by its very nature is arbitrarily large). With many operations this trade off makes sense, however its critical to understand the limitations of the model.

w-j-w 7y ago

At this time understanding floating point numbers falls under "programmer responsibility", and not languages follow the example set by C. Most languages are designed by people who find the idea of not understanding floating point numbers kind of absurd.

maxdamantus 7y ago

Unless you have a floating point model that supports arbitrary bases, you're always going to have the issue. Binary floats are unable to represent 1/10 just as decimal floats are unable to represent 1/3. And in case anyone's wondering about handling it by representing the repeating digits instead, here's the decimal representation of 1/12345 using repeating digits: 0.0[0008100445524503847711624139327663021466180639935196435803969218307006885378 69582827055488051842851356824625354394491697043337383556095585257189145402997164 84406642365330093155123531794248683677602268124746861077359254759011745646010530 57918185500202511138112596192790603483191575536654515998379910895099230457675172 13446739570676387201296071283920615633859862292426083434588902389631429728635074 92912110166059133252328878088294856217091940056703118671526933981368975293641150 26326447954637505062778452814904819765087079789388416362899959497772377480761441 87930336168489266909680032401782098015390846496557310652085864722559740785743215 87687322802754151478331308221952207371405427298501417577966788173349534224382341 02875658161198865937626569461320372620494127176994734710409072498987444309437019 03604698258404212231672742]

amelius 7y ago
> Unless you have a floating point model that supports arbitrary bases See also binary coded decimals. https://en.wikipedia.org/wiki/Binary-coded_decimal https://en.wikipedia.org/wiki/Binary-coded_decimal
- snickerbockers 7y ago
  That's not a floating point.
  - amelius 7y ago
    From the article: > Programmable calculators manufactured by Texas Instruments, Hewlett-Packard, and others typically employ a floating-point BCD format, typically with two or three digits for the (decimal) exponent.
    - snickerbockers 7y ago

acqq 7y ago

Decimal floating point is standardized since 2008: https://en.wikipedia.org/wiki/Decimal_floating_point#IEEE_754-2008_encoding https://en.wikipedia.org/wiki/Decimal_floating_point#IEEE_75... But it's still not much used. E.g. for C++ it was proposed in 2012 for the first time http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n3407.html http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2012/n340... then revised in 2014: http://open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3871.html http://open-std.org/jtc1/sc22/wg21/docs/papers/2014/n3871.ht... ...and... silence? https://www.reddit.com/r/cpp/comments/8d59mr/any_update_on_the_decimal_proposal/ https://www.reddit.com/r/cpp/comments/8d59mr/any_update_on_t...

gowld 7y ago
It's not important to most people, because decimal floating point only helps if your UI precision is exactly the same as your internal precision, which almost never happens. Seeing the occasional 0.300000000000004 is a good reminder that your 0.3858372895939229 isn't accurate either.
- acqq 7y ago
  > It's not important to most people One can argue that nothing is important to most people. The correct calculations involving money, up to the last cent, are in fact important for people who do them or who are supposed to use them. I've implemented them in the software I've made to preform some financial stuff even in eighties, in spite of all the software which used binary floating point routines. And, of course, from the computer manufacturers, at least IBM cares too: https://www.ibm.com/support/pages/decimal-floating-point-users-guide-technology-preview-advance-toolchain-ibm-xl-cc-linux-131 https://www.ibm.com/support/pages/decimal-floating-point-use... Apparently, there are even processors which supports these formats in hardware. It's just still not mainstream.

gowld 7y ago

Being a lot slower is a worse problem than being off by an error of 2^60. And if it isn't, then you simply choose a different numeric type.

masklinn 7y ago

> Makes me wonder why we haven't switched to a better floating point model in the last decades. It will probably be slower but a lot of problems could be avoided. Pretty much all languages have some sort of decimal number. Few or none have made it the default because they're ignominiously slower than binary floating-point. To the extent that even languages which have made arbitrary precision integers their default firmly keep to binary floating-point.

amyjess 7y ago
> Few or none have made it the default because they're ignominiously slower than binary floating-point. You can strike the "none". Perl 6 uses rationals (Rat) by default, someone once told me Haskell does the same, and Groovy uses BigDecimal.

snickerbockers 7y ago

There is no "better floating point model" because floating point will always be floating point. Fixed point always has been and always will be an option if you don't like the exponential notation.

crazygringo 7y ago
> Fixed point always has been and always will be an option Not really. It would be really cool if fixed point number storage were an option... but I'm not aware of any popular language that provides it as a built-in primitive along with int and float, just as easy to use and choose as floats themselves. Yes probably every language has libraries somewhere that let you do it where you have to learn a lot of function call names. But it would be pretty cool to have a language with it built-in, e.g. for base-10 seven digits followed by two decimals: fixed(7,2) i; i = 395.25; i += 0.01; And obviously supporting any desired base between 2 and 16. Someone please let me know if there is such primitive-level support in any mainstream language!
- snickerbockers 7y ago
  You don't need special support from the language, fixed-point arithmetic is effectively the same as integer. DOOM's implementation of fixed-point is a good example which should work on any platform as long as sizeof(int) >= 4. https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.10/m_fixed.h https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.... https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.10/m_fixed.c https://github.com/id-Software/DOOM/blob/master/linuxdoom-1.... Addition and subtraction will work normally. Multiplication also works normally except you need to right-shift by FRAC_BITS afterwards (and probably also cast to a larger integer type beforehand to protect against overflow). Division is somewhat difficult since integer division is not what you want to do. DOOM's solution was to cast to double, perform the division, and then convert that back to fixed-point by multiplying by 1.0 before casting back to integer. This seems like cheating since it's using floating-point as an intermediate type, but it is safe to do because 64-bit floating point can represent all 32-bit integers. As long as you're on a platform with an FPU it's probably also faster than trying to roll your own division implementation.

ryandrake 7y ago

Wait, an entire office (presumably full of programmers) didn’t understand floating point representation? What office was this? Isn’t this topic covered first in every programming book or course where floating point math is covered?

Ididntdothis 7y ago
This was in the 90s. We were all self taught and I had never met anyone who had formal CS education.