Re: Scheduled review of Decimal library

From: Kostas Savvidis (kotika98_at_[hidden])
Date: 2024-10-08 15:35:50

> On 8 Oct 2024, at 15:01, Matt Borland <matt_at_[hidden]> wrote:
> 
> Do you have specific suggestions? I reworded and expanded the since you raised concerns last time.

You might simply want to start by saying that the intended user of this library is someone who NEEDS to store and operate with decimal fractions like 0.1. Other than that, decimal arithmetic is not superior in any way. For example on a trinary computer 1.0/3.0 + 2.0/3.0 == 1.0, but on binary or decimal it is not.

1) "Decimal floating point numbers avoid this issue by storing the significand in base-10 (decimal)."

Not true. My understanding from your explanations was that your library internally uses BID - binary encoded decimal. State that.

2) "The other major difference between binary and decimal floating point types is that the latter allows for multiple representations of the same number. For example 1e5 could also be stored as 0.1e6, 0.01e7, so on and so forth."

Does your library really store 0.01e7 as such? In excel, when I type 535e-6 it immediately changes it into 5.35e-4 -- correct behavior it seems to me. 

Related: Wikipedia article on engineering notation states: "Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten is always selected to be divisible by three to match the common metric prefixes"  
--- I do not know if this is widely used but choosing this option for printing must be within scope for your library. Excel has it
with custom formatting ###.0E+00 , this will make the exponent a multiple of three: 535.0E-06, unbelievable but true.

3) "These are referred to as cohorts which binary does not have as there is only one way to represent each number in binary floating point."

I try 0x11p-5 versus 0x1.1p-1 in my C++17 compiler, it is accepted and printed as the same number.
It could be that I misunderstand what you are trying to say here and you mean that the library does not necessarily impose normalized numbers, but a detailed explanation of this must be in the documentation.

To be honest, I would like to require any Boost author to be required to document in detail the algorithms implemented by the library.
Maybe you would like to set the good example? What exactly does your library do when it does the four arithmetic operations?

> It was added a bit back after your request. See: https://cppalliance.org/decimal/decimal.html#cmath_trunc_to. 

trunc is good but round is also essential and highly nontrivial. 

See Cowlishaw paper:
"4.1.1. Commercial rounding. The extra rounding mode
is called round-half-up, which is a requirement for many
financial calculations (especially for tax purposes and in
Europe). In this mode, if the digits discarded during
rounding represent greater than or equal to half (0.5) of
the value of a one in the next left position then the re-
sult should be rounded up. Otherwise the discarded dig-
its are ignored. This is in contrast to round-half-even,
the default IEEE 854 rounding mode, where if the dis-
carded digits are exactly half of the next digit then the
least significant digit of the result will be even.
It is also recommended that implementations offer two
further rounding modes: round-half-down (where a 0.5
case is rounded down) and round-up (round away from
zero). "

"4.2.6. ... An important operator, rescale, sets the exponent of a
number and adjusts its coefficient (with rounding, if
necessary) to maintain its value. For example, rescaling
the number {0, 1234567, −4} so its exponent is −2 gives
{0, 12346, −2}. This example is the familiar, and very
heavily used, ‘round to cents’ operation, although rescale
has many other uses (round-to-integer is a special case
of rescale, for example)."

The point he makes in 4.2.5 should also be taken into account somehow. 

Best Regards,
Kostas