Add inputs that generate larger error bounds

(Using values from https://members.loria.fr/PZimmermann/papers/accuracy.pdf)

1 files changed, 174 insertions, 0 deletions

diff --git a/math/auto-libm-test-out-acos b/math/auto-libm-test-out-acos
index 04bd77bf43..c98ca8728a 100644
--- a/math/auto-libm-test-out-acos
+++ b/math/auto-libm-test-out-acos
@@ -2649,6 +2649,180 @@ acos -0x1.da00d8p-4
 = acos tonearest ibm128 -0x1.da00d8p-4 : 0x1.afd0ca8858c9ea46ebc1be7c98p+0 : inexact-ok
 = acos towardzero ibm128 -0x1.da00d8p-4 : 0x1.afd0ca8858c9ea46ebc1be7c978p+0 : inexact-ok
 = acos upward ibm128 -0x1.da00d8p-4 : 0x1.afd0ca8858c9ea46ebc1be7c98p+0 : inexact-ok
+acos 0x1.fffff3634acd6p-1
+= acos downward binary32 0xf.ffffap-4 : 0x3.76cf5cp-12 : inexact-ok
+= acos tonearest binary32 0xf.ffffap-4 : 0x3.76cf6p-12 : inexact-ok
+= acos towardzero binary32 0xf.ffffap-4 : 0x3.76cf5cp-12 : inexact-ok
+= acos upward binary32 0xf.ffffap-4 : 0x3.76cf6p-12 : inexact-ok
+= acos downward binary64 0xf.ffffap-4 : 0x3.76cf5ec671462p-12 : inexact-ok
+= acos tonearest binary64 0xf.ffffap-4 : 0x3.76cf5ec671462p-12 : inexact-ok
+= acos towardzero binary64 0xf.ffffap-4 : 0x3.76cf5ec671462p-12 : inexact-ok
+= acos upward binary64 0xf.ffffap-4 : 0x3.76cf5ec671464p-12 : inexact-ok
+= acos downward intel96 0xf.ffffap-4 : 0x3.76cf5ec671462a9p-12 : inexact-ok
+= acos tonearest intel96 0xf.ffffap-4 : 0x3.76cf5ec671462a94p-12 : inexact-ok
+= acos towardzero intel96 0xf.ffffap-4 : 0x3.76cf5ec671462a9p-12 : inexact-ok
+= acos upward intel96 0xf.ffffap-4 : 0x3.76cf5ec671462a94p-12 : inexact-ok
+= acos downward m68k96 0xf.ffffap-4 : 0x3.76cf5ec671462a9p-12 : inexact-ok
+= acos tonearest m68k96 0xf.ffffap-4 : 0x3.76cf5ec671462a94p-12 : inexact-ok
+= acos towardzero m68k96 0xf.ffffap-4 : 0x3.76cf5ec671462a9p-12 : inexact-ok
+= acos upward m68k96 0xf.ffffap-4 : 0x3.76cf5ec671462a94p-12 : inexact-ok
+= acos downward binary128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c151ep-12 : inexact-ok
+= acos tonearest binary128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c152p-12 : inexact-ok
+= acos towardzero binary128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c151ep-12 : inexact-ok
+= acos upward binary128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c152p-12 : inexact-ok
+= acos downward ibm128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c15p-12 : inexact-ok
+= acos tonearest ibm128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c15p-12 : inexact-ok
+= acos towardzero ibm128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c15p-12 : inexact-ok
+= acos upward ibm128 0xf.ffffap-4 : 0x3.76cf5ec671462a93def0c25c16p-12 : inexact-ok
+= acos downward binary32 0xf.ffff9p-4 : 0x3.bddd44p-12 : inexact-ok
+= acos tonearest binary32 0xf.ffff9p-4 : 0x3.bddd44p-12 : inexact-ok
+= acos towardzero binary32 0xf.ffff9p-4 : 0x3.bddd44p-12 : inexact-ok
+= acos upward binary32 0xf.ffff9p-4 : 0x3.bddd48p-12 : inexact-ok
+= acos downward binary64 0xf.ffff9p-4 : 0x3.bddd445bc8fdcp-12 : inexact-ok
+= acos tonearest binary64 0xf.ffff9p-4 : 0x3.bddd445bc8fdep-12 : inexact-ok
+= acos towardzero binary64 0xf.ffff9p-4 : 0x3.bddd445bc8fdcp-12 : inexact-ok
+= acos upward binary64 0xf.ffff9p-4 : 0x3.bddd445bc8fdep-12 : inexact-ok
+= acos downward intel96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd9p-12 : inexact-ok
+= acos tonearest intel96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd904p-12 : inexact-ok
+= acos towardzero intel96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd9p-12 : inexact-ok
+= acos upward intel96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd904p-12 : inexact-ok
+= acos downward m68k96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd9p-12 : inexact-ok
+= acos tonearest m68k96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd904p-12 : inexact-ok
+= acos towardzero m68k96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd9p-12 : inexact-ok
+= acos upward m68k96 0xf.ffff9p-4 : 0x3.bddd445bc8fdd904p-12 : inexact-ok
+= acos downward binary128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263ea4p-12 : inexact-ok
+= acos tonearest binary128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263ea4p-12 : inexact-ok
+= acos towardzero binary128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263ea4p-12 : inexact-ok
+= acos upward binary128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263ea6p-12 : inexact-ok
+= acos downward ibm128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263ep-12 : inexact-ok
+= acos tonearest ibm128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263fp-12 : inexact-ok
+= acos towardzero ibm128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263ep-12 : inexact-ok
+= acos upward ibm128 0xf.ffff9p-4 : 0x3.bddd445bc8fdd903a92245263fp-12 : inexact-ok
+= acos downward binary64 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd922p-12 : inexact-ok
+= acos tonearest binary64 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd924p-12 : inexact-ok
+= acos towardzero binary64 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd922p-12 : inexact-ok
+= acos upward binary64 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd924p-12 : inexact-ok
+= acos downward intel96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923p-12 : inexact-ok
+= acos tonearest intel96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923p-12 : inexact-ok
+= acos towardzero intel96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923p-12 : inexact-ok
+= acos upward intel96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923004p-12 : inexact-ok
+= acos downward m68k96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923p-12 : inexact-ok
+= acos tonearest m68k96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923p-12 : inexact-ok
+= acos towardzero m68k96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923p-12 : inexact-ok
+= acos upward m68k96 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd923004p-12 : inexact-ok
+= acos downward binary128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cf6p-12 : inexact-ok
+= acos tonearest binary128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cf62p-12 : inexact-ok
+= acos towardzero binary128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cf6p-12 : inexact-ok
+= acos upward binary128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cf62p-12 : inexact-ok
+= acos downward ibm128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cfp-12 : inexact-ok
+= acos tonearest ibm128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cfp-12 : inexact-ok
+= acos towardzero ibm128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414cfp-12 : inexact-ok
+= acos upward ibm128 0xf.ffff9b1a566bp-4 : 0x3.8d25c52edd92300000026414dp-12 : inexact-ok
+acos 0xf.fe00271d507ee5dp-4
+= acos downward binary32 0xf.fe003p-4 : 0x7.ffb55p-8 : inexact-ok
+= acos tonearest binary32 0xf.fe003p-4 : 0x7.ffb55p-8 : inexact-ok
+= acos towardzero binary32 0xf.fe003p-4 : 0x7.ffb55p-8 : inexact-ok
+= acos upward binary32 0xf.fe003p-4 : 0x7.ffb558p-8 : inexact-ok
+= acos downward binary64 0xf.fe003p-4 : 0x7.ffb550aec7a54p-8 : inexact-ok
+= acos tonearest binary64 0xf.fe003p-4 : 0x7.ffb550aec7a58p-8 : inexact-ok
+= acos towardzero binary64 0xf.fe003p-4 : 0x7.ffb550aec7a54p-8 : inexact-ok
+= acos upward binary64 0xf.fe003p-4 : 0x7.ffb550aec7a58p-8 : inexact-ok
+= acos downward intel96 0xf.fe003p-4 : 0x7.ffb550aec7a5639p-8 : inexact-ok
+= acos tonearest intel96 0xf.fe003p-4 : 0x7.ffb550aec7a56398p-8 : inexact-ok
+= acos towardzero intel96 0xf.fe003p-4 : 0x7.ffb550aec7a5639p-8 : inexact-ok
+= acos upward intel96 0xf.fe003p-4 : 0x7.ffb550aec7a56398p-8 : inexact-ok
+= acos downward m68k96 0xf.fe003p-4 : 0x7.ffb550aec7a5639p-8 : inexact-ok
+= acos tonearest m68k96 0xf.fe003p-4 : 0x7.ffb550aec7a56398p-8 : inexact-ok
+= acos towardzero m68k96 0xf.fe003p-4 : 0x7.ffb550aec7a5639p-8 : inexact-ok
+= acos upward m68k96 0xf.fe003p-4 : 0x7.ffb550aec7a56398p-8 : inexact-ok
+= acos downward binary128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648655f7p-8 : inexact-ok
+= acos tonearest binary128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648655f7p-8 : inexact-ok
+= acos towardzero binary128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648655f7p-8 : inexact-ok
+= acos upward binary128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648655f74p-8 : inexact-ok
+= acos downward ibm128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648655ep-8 : inexact-ok
+= acos tonearest ibm128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648656p-8 : inexact-ok
+= acos towardzero ibm128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648655ep-8 : inexact-ok
+= acos upward ibm128 0xf.fe003p-4 : 0x7.ffb550aec7a5639438e648656p-8 : inexact-ok
+= acos downward binary32 0xf.fe002p-4 : 0x7.ffd55p-8 : inexact-ok
+= acos tonearest binary32 0xf.fe002p-4 : 0x7.ffd55p-8 : inexact-ok
+= acos towardzero binary32 0xf.fe002p-4 : 0x7.ffd55p-8 : inexact-ok
+= acos upward binary32 0xf.fe002p-4 : 0x7.ffd558p-8 : inexact-ok
+= acos downward binary64 0xf.fe002p-4 : 0x7.ffd552eedca58p-8 : inexact-ok
+= acos tonearest binary64 0xf.fe002p-4 : 0x7.ffd552eedca5cp-8 : inexact-ok
+= acos towardzero binary64 0xf.fe002p-4 : 0x7.ffd552eedca58p-8 : inexact-ok
+= acos upward binary64 0xf.fe002p-4 : 0x7.ffd552eedca5cp-8 : inexact-ok
+= acos downward intel96 0xf.fe002p-4 : 0x7.ffd552eedca5ade8p-8 : inexact-ok
+= acos tonearest intel96 0xf.fe002p-4 : 0x7.ffd552eedca5adfp-8 : inexact-ok
+= acos towardzero intel96 0xf.fe002p-4 : 0x7.ffd552eedca5ade8p-8 : inexact-ok
+= acos upward intel96 0xf.fe002p-4 : 0x7.ffd552eedca5adfp-8 : inexact-ok
+= acos downward m68k96 0xf.fe002p-4 : 0x7.ffd552eedca5ade8p-8 : inexact-ok
+= acos tonearest m68k96 0xf.fe002p-4 : 0x7.ffd552eedca5adfp-8 : inexact-ok
+= acos towardzero m68k96 0xf.fe002p-4 : 0x7.ffd552eedca5ade8p-8 : inexact-ok
+= acos upward m68k96 0xf.fe002p-4 : 0x7.ffd552eedca5adfp-8 : inexact-ok
+= acos downward binary128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b755351p-8 : inexact-ok
+= acos tonearest binary128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b7553514p-8 : inexact-ok
+= acos towardzero binary128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b755351p-8 : inexact-ok
+= acos upward binary128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b7553514p-8 : inexact-ok
+= acos downward ibm128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b75534p-8 : inexact-ok
+= acos tonearest ibm128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b75536p-8 : inexact-ok
+= acos towardzero ibm128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b75534p-8 : inexact-ok
+= acos upward ibm128 0xf.fe002p-4 : 0x7.ffd552eedca5adef3be2b75536p-8 : inexact-ok
+= acos downward binary64 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526cp-8 : inexact-ok
+= acos tonearest binary64 0xf.fe00271d507fp-4 : 0x7.ffc7175d8527p-8 : inexact-ok
+= acos towardzero binary64 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526cp-8 : inexact-ok
+= acos upward binary64 0xf.fe00271d507fp-4 : 0x7.ffc7175d8527p-8 : inexact-ok
+= acos downward intel96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8dp-8 : inexact-ok
+= acos tonearest intel96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8dp-8 : inexact-ok
+= acos towardzero intel96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8dp-8 : inexact-ok
+= acos upward intel96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d8p-8 : inexact-ok
+= acos downward m68k96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8dp-8 : inexact-ok
+= acos tonearest m68k96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8dp-8 : inexact-ok
+= acos towardzero m68k96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8dp-8 : inexact-ok
+= acos upward m68k96 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d8p-8 : inexact-ok
+= acos downward binary128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757ae8p-8 : inexact-ok
+= acos tonearest binary128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757ae8p-8 : inexact-ok
+= acos towardzero binary128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757ae8p-8 : inexact-ok
+= acos upward binary128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757aecp-8 : inexact-ok
+= acos downward ibm128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757ap-8 : inexact-ok
+= acos tonearest ibm128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757ap-8 : inexact-ok
+= acos towardzero ibm128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757ap-8 : inexact-ok
+= acos upward ibm128 0xf.fe00271d507fp-4 : 0x7.ffc7175d8526e8d2a5d9ca757cp-8 : inexact-ok
+= acos downward binary64 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626cp-8 : inexact-ok
+= acos tonearest binary64 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8627p-8 : inexact-ok
+= acos towardzero binary64 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626cp-8 : inexact-ok
+= acos upward binary64 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8627p-8 : inexact-ok
+= acos downward intel96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa98p-8 : inexact-ok
+= acos tonearest intel96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa98p-8 : inexact-ok
+= acos towardzero intel96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa98p-8 : inexact-ok
+= acos upward intel96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626faap-8 : inexact-ok
+= acos downward m68k96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa98p-8 : inexact-ok
+= acos tonearest m68k96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa98p-8 : inexact-ok
+= acos towardzero m68k96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa98p-8 : inexact-ok
+= acos upward m68k96 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626faap-8 : inexact-ok
+= acos downward binary128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3b1cp-8 : inexact-ok
+= acos tonearest binary128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3b2p-8 : inexact-ok
+= acos towardzero binary128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3b1cp-8 : inexact-ok
+= acos upward binary128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3b2p-8 : inexact-ok
+= acos downward ibm128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3ap-8 : inexact-ok
+= acos tonearest ibm128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3cp-8 : inexact-ok
+= acos towardzero ibm128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3ap-8 : inexact-ok
+= acos upward ibm128 0xf.fe00271d507e8p-4 : 0x7.ffc7175d8626fa9a9b2f299f3cp-8 : inexact-ok
+= acos downward intel96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c7p-8 : inexact-ok
+= acos tonearest intel96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c78p-8 : inexact-ok
+= acos towardzero intel96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c7p-8 : inexact-ok
+= acos upward intel96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c78p-8 : inexact-ok
+= acos downward m68k96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c7p-8 : inexact-ok
+= acos tonearest m68k96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c78p-8 : inexact-ok
+= acos towardzero m68k96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c7p-8 : inexact-ok
+= acos upward m68k96 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c78p-8 : inexact-ok
+= acos downward binary128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686aecp-8 : inexact-ok
+= acos tonearest binary128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686aecp-8 : inexact-ok
+= acos towardzero binary128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686aecp-8 : inexact-ok
+= acos upward binary128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686afp-8 : inexact-ok
+= acos downward ibm128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686ap-8 : inexact-ok
+= acos tonearest ibm128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686ap-8 : inexact-ok
+= acos towardzero ibm128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686ap-8 : inexact-ok
+= acos upward ibm128 0xf.fe00271d507ee5dp-4 : 0x7.ffc7175d855b4c75eeab24686cp-8 : inexact-ok
 acos min
 = acos downward binary32 0x4p-128 : 0x1.921fb4p+0 : inexact-ok
 = acos tonearest binary32 0x4p-128 : 0x1.921fb6p+0 : inexact-ok