[Numpy-discussion] Re: representation of valid float type range

[Klaus Zimmermann]

Hello,

perhaps it would be best to have an issue about this on github?
It might be worth pointing out that the original problem triggers a 
floating point error that can be caught and handled via errstate. This 
might be used either in linspace itself, or, if you think this rare 
problem is likely to affect you, you might wrap your call to linspace, 
for example:

```
i = finfo(float64)
a = array([i.max, i.min, 0.], dtype=float64)
with errstate(over="raise"):
    a[2] = a[1] - a[0]
```
or
```
with errstate(over="raise"):
    linspace(i.min, i.max)
```

Cheers
Klaus


On 1/10/22 13:10, Hameer Abbasi wrote:
Hello all.

I believe that over the years there were multiple proposals to replace the linspace 
formula start + n *(stop - start) / (npoints - 1) with a * start + b * end with a, b 
linearly spaced between 0 and 1 with npoints. Concretely, a = n / (npoints - 1), b = 
1 - a. Here, 0 <= n < npoints.

I believe this would fix the issue here among many others. However, it was 
always rejected due to backward-incompatibility concerns. Perhaps it’s time to 
revisit this issue.

Best regards,
Hameer Abbasi

Am 10.01.2022 um 12:59 schrieb alejandro.giacome...@gmail.com:

I see what you mean, there is, however, some inconsistency on how this is 
handled, and it's not entirely intuitive

```
_type=np.int8
N=8
np.linspace(
    start=np.iinfo(_type).min,
    stop=np.iinfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([-128,  -92,  -56,  -19,   17,   54,   90,  127], dtype=int8)

_type=np.float16
np.linspace(
    start=np.finfo(_type).min,
    stop=np.finfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([-65504., -46784., -28080.,  -9360.,   9360.,  28080.,  46784.,
            65504.], dtype=float16)


_type=np.float32
np.linspace(
    start=np.finfo(_type).min,
    stop=np.finfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([-3.4028235e+38, -2.4305882e+38, -1.4583529e+38, -4.8611764e+37,
            4.8611764e+37,  1.4583529e+38,  2.4305882e+38,  3.4028235e+38],
          dtype=float32)

_type=np.float64
np.linspace(
    start=np.finfo(_type).min,
    stop=np.finfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([            nan,             inf,             inf,             inf,
                       inf,             inf,             inf, 1.79769313e+308])

_type=np.float64
np.linspace(
    start=0,
    stop=np.finfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([0.00000000e+000, 2.56813305e+307, 5.13626610e+307, 7.70439915e+307,
           1.02725322e+308, 1.28406652e+308, 1.54087983e+308, 1.79769313e+308])

_type=np.float64
np.linspace(
    start=-1e291,
    stop=np.finfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([-1.00000000e+291,  2.56813305e+307,  5.13626610e+307,
            7.70439915e+307,  1.02725322e+308,  1.28406652e+308,
            1.54087983e+308,  1.79769313e+308])

_type=np.float64
np.linspace(
    start=-1e292,
    stop=np.finfo(_type).max,
    num=N,
    dtype=_type,
)
=>    array([            nan,             inf,             inf,             inf,
                       inf,             inf,             inf, 1.79769313e+308])


_type=np.float16
np.logspace(
    start=np.finfo(_type).minexp,
    stop=np.finfo(_type).maxexp,
    num=N,
    dtype=_type,
    base=2,
)
=>    array([6.104e-05, 1.190e-03, 2.322e-02, 4.529e-01, 8.836e+00, 1.722e+02,
           3.360e+03,       inf], dtype=float16)

_type=np.float16
np.logspace(
    start=np.finfo(_type).minexp,
    stop=np.finfo(_type).maxexp,
    num=N,
    dtype=_type,
    base=2,
    endpoint=False,
)
=>    array([6.104e-05, 8.211e-04, 1.105e-02, 1.487e-01, 2.000e+00, 2.691e+01,
           3.620e+02, 4.872e+03], dtype=float16)

_type=np.float64
np.logspace(
    start=np.finfo(_type).minexp,
    stop=np.finfo(_type).maxexp,
    num=N,
    dtype=_type,
    base=2,
    endpoint=False,
)
=>    array([2.22507386e-308, 2.16653556e-231, 2.10953732e-154, 2.05403862e-077,
           2.00000000e+000, 1.94738306e+077, 1.89615038e+154, 1.84626556e+231])
```
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