* [PATCH] Fix error in exp in magnitude [2e-32,2e-28]
@ 2020-03-06 14:49 Fabian Schriever
2020-03-09 9:12 ` Corinna Vinschen
0 siblings, 1 reply; 2+ messages in thread
From: Fabian Schriever @ 2020-03-06 14:49 UTC (permalink / raw)
To: newlib; +Cc: Fabian Schriever
While testing the exp function we noticed some errors at the specified
magnitude. Within this range the exp function returns the input value +1
as an output. We chose to run a test of 1m exponentially spaced values
in the ranges [-2^-27,-2^-32] and [2^-32,2^-27] which showed 7603 and
3912 results with an error of >=0.5 ULP (compared with MPFR in 128 bit)
with the highest being 0.56 ULP and 0.53 ULP.
It's easy to fix by changing the magnitude at which the input value +1
is returned from <2^-28 to <2^-32 and using the polynomial instead. This
reduces the number of results with an error of >=0.5 ULP to 485 and 479
in above tests, all of which are exactly 0.5 ULP.
As we were already checking on exp we also took a look at expf. For expf
the magnitude where the input value +1 is returned can be increased from
<2^-28 to <2^-23 without accuracy loss for a slight performance
improvement. To ensure this was the correct value we tested all values
in the ranges [-2^-17,-2^-28] and [2^-28,2^-17] (~92.3m values each).
---
newlib/libm/math/e_exp.c | 2 +-
newlib/libm/math/ef_exp.c | 2 +-
2 files changed, 2 insertions(+), 2 deletions(-)
diff --git a/newlib/libm/math/e_exp.c b/newlib/libm/math/e_exp.c
index 81ea64dfb..d23b1162b 100644
--- a/newlib/libm/math/e_exp.c
+++ b/newlib/libm/math/e_exp.c
@@ -142,7 +142,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
}
x = hi - lo;
}
- else if(hx < 0x3e300000) { /* when |x|<2**-28 */
+ else if(hx < 0x3df00000) { /* when |x|<2**-32 */
if(huge+x>one) return one+x;/* trigger inexact */
}
diff --git a/newlib/libm/math/ef_exp.c b/newlib/libm/math/ef_exp.c
index e817370ac..fb3e2ffe6 100644
--- a/newlib/libm/math/ef_exp.c
+++ b/newlib/libm/math/ef_exp.c
@@ -77,7 +77,7 @@ P5 = 4.1381369442e-08; /* 0x3331bb4c */
}
x = hi - lo;
}
- else if(hx < 0x31800000) { /* when |x|<2**-28 */
+ else if(hx < 0x34000000) { /* when |x|<2**-23 */
if(huge+x>one) return one+x;/* trigger inexact */
}
--
2.24.1.windows.2
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: [PATCH] Fix error in exp in magnitude [2e-32,2e-28]
2020-03-06 14:49 [PATCH] Fix error in exp in magnitude [2e-32,2e-28] Fabian Schriever
@ 2020-03-09 9:12 ` Corinna Vinschen
0 siblings, 0 replies; 2+ messages in thread
From: Corinna Vinschen @ 2020-03-09 9:12 UTC (permalink / raw)
To: newlib
[-- Attachment #1: Type: text/plain, Size: 2318 bytes --]
On Mar 6 15:46, Fabian Schriever wrote:
> While testing the exp function we noticed some errors at the specified
> magnitude. Within this range the exp function returns the input value +1
> as an output. We chose to run a test of 1m exponentially spaced values
> in the ranges [-2^-27,-2^-32] and [2^-32,2^-27] which showed 7603 and
> 3912 results with an error of >=0.5 ULP (compared with MPFR in 128 bit)
> with the highest being 0.56 ULP and 0.53 ULP.
>
> It's easy to fix by changing the magnitude at which the input value +1
> is returned from <2^-28 to <2^-32 and using the polynomial instead. This
> reduces the number of results with an error of >=0.5 ULP to 485 and 479
> in above tests, all of which are exactly 0.5 ULP.
>
> As we were already checking on exp we also took a look at expf. For expf
> the magnitude where the input value +1 is returned can be increased from
> <2^-28 to <2^-23 without accuracy loss for a slight performance
> improvement. To ensure this was the correct value we tested all values
> in the ranges [-2^-17,-2^-28] and [2^-28,2^-17] (~92.3m values each).
> ---
> newlib/libm/math/e_exp.c | 2 +-
> newlib/libm/math/ef_exp.c | 2 +-
> 2 files changed, 2 insertions(+), 2 deletions(-)
>
> diff --git a/newlib/libm/math/e_exp.c b/newlib/libm/math/e_exp.c
> index 81ea64dfb..d23b1162b 100644
> --- a/newlib/libm/math/e_exp.c
> +++ b/newlib/libm/math/e_exp.c
> @@ -142,7 +142,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */
> }
> x = hi - lo;
> }
> - else if(hx < 0x3e300000) { /* when |x|<2**-28 */
> + else if(hx < 0x3df00000) { /* when |x|<2**-32 */
> if(huge+x>one) return one+x;/* trigger inexact */
> }
>
> diff --git a/newlib/libm/math/ef_exp.c b/newlib/libm/math/ef_exp.c
> index e817370ac..fb3e2ffe6 100644
> --- a/newlib/libm/math/ef_exp.c
> +++ b/newlib/libm/math/ef_exp.c
> @@ -77,7 +77,7 @@ P5 = 4.1381369442e-08; /* 0x3331bb4c */
> }
> x = hi - lo;
> }
> - else if(hx < 0x31800000) { /* when |x|<2**-28 */
> + else if(hx < 0x34000000) { /* when |x|<2**-23 */
> if(huge+x>one) return one+x;/* trigger inexact */
> }
>
> --
> 2.24.1.windows.2
>
Pushed.
Thanks,
Corinna
--
Corinna Vinschen
Cygwin Maintainer
Red Hat
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