From a8a40ee5750cb8a4280379a38c1ed490262481c4 Mon Sep 17 00:00:00 2001 From: Fabian Schriever Date: Fri, 6 Mar 2020 15:46:33 +0100 Subject: [PATCH] Fix error in exp in magnitude [2e-32,2e-28] 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 */ }