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| author | Eric Kunze <eric.kunze@arm.com> | 2024-04-10 15:26:55 -0700 |
|---|---|---|
| committer | Eric Kunze <eric.kunze@arm.com> | 2024-04-18 08:15:08 -0700 |
| commit | 0e121c064e051716bdfca892b210fa52c792ac29 (patch) | |
| tree | fe9b31770921ebadd735b7443d9537ca90ce7379 /chapters | |
| parent | 9d14082fe5176ec91d006d89ccdb2d62f6ca839f (diff) | |
| download | specification-0e121c064e051716bdfca892b210fa52c792ac29.tar.gz | |
Clarify error bound for non-normal values
Signed-off-by: Eric Kunze <eric.kunze@arm.com>
Change-Id: I9678952cc78cdf90272ccd5179b6220c293d62f7
Diffstat (limited to 'chapters')
| -rw-r--r-- | chapters/introduction.adoc | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/chapters/introduction.adoc b/chapters/introduction.adoc index 0030757..5406129 100644 --- a/chapters/introduction.adoc +++ b/chapters/introduction.adoc @@ -280,7 +280,7 @@ Otherwise the result must be within 5 ulp of the mathematical result. | <<EXP>> | Let `x` be an input element and `out_imp` the implementation output of `exp(x)`. + Let `out_ref` be the result of the fp64_t reference implementation of `exp(x)`. + -Let `err_bnd = abs(out_ref) * exp2(-normal_frac<in_out_t>) * (1+abs(x))` + +Let `err_bnd = calcAbsErrorBound<in_out_t>(out_ref, (1+abs(x)), 0, 1)` + Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be true | <<POW>> @@ -288,19 +288,19 @@ Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be Let `out_imp` be the implementation output of `pow(x,y)`. + If `x` is less than zero and `y` is non-integral then the result must be a NaN. + Let `out_ref` be the result of the fp64_t reference implementation of `pow(x,y)`. + -Let `err_bnd = abs(out_ref) * exp2(-normal_frac<in_out_t>) * (2 * (1+abs(log(abs(x))*y)))` + +Let `err_bnd = calcAbsErrorBound<in_out_t>(out_ref, 2 * (1+abs(log(abs(x))*y)), 0, 1)` + Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be true | <<SIGMOID>> | Let `x` be an input element and `out_imp` the implementation output. + Let `out_ref` be the result of the fp64_t reference implementation. + -Let `err_bnd = abs(out_ref) * exp2(-normal_frac<in_out_t>) * (2 * (1+abs(x)))` + +Let `err_bnd = calcAbsErrorBound<in_out_t>(out_ref, 2 * (1+abs(x)), 0, 1)` + Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be true | <<TANH>> | Let `x` be an input element and `out_imp` the implementation output. + Let `out_ref` be the result of the fp64_t reference implementation. + -Let `err_bnd = exp2(-normal_frac<in_out_t>) * max(0.5, abs(out_ref) * (4 * (1+abs(x))))` + +Let `err_bnd = calcAbsErrorBound<in_out_t>(out_ref, 4 * (1+abs(x)), 0.5, 1)` + Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be true | <<REDUCE_SUM>> @@ -321,13 +321,13 @@ Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be | <<COS>> | Let `x` be an input element and `out_imp` the implementation output of `cos(x)`. + Let `out_ref` be the result of the fp64_t reference implementation of `cos(x)`. + -Let `err_bnd = abs(x) * exp2(-normal_frac<in_out_t>/2)` + +Let `err_bnd = calcAbsErrorBound<in_out_t>(x, 1+abs(x), 0, 2)` + Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be true | <<SIN>> | Let `x` be an input element and `out_imp` the implementation output of `sin(x)`. + Let `out_ref` be the result of the fp64_t reference implementation of `sin(x)`. + -Let `err_bnd = abs(x) * exp2(-normal_frac<in_out_t>/2)` + +Let `err_bnd = calcAbsErrorBound<in_out_t>(x, abs(x), 0, 2)` + Then `tosa_reference_check_fp_bnd<in_out_t>(out_imp, out_ref, err_bnd)` must be true | <<RESIZE>> |