Fix casinh spurious underflows away from [-i,i] (bug 15062).

1 files changed, 186 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 63c6aed..b828774 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -244,6 +244,24 @@ ifloat: 1
 Test "Imaginary part of: cacos (-0 - 1.5 i) == pi/2 + 1.194763217287109304111930828519090523536 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (-0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Real part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442100 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Real part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+float: 1
+ifloat: 1
+Test "Imaginary part of: cacos (-0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442100 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Real part of: cacos (-1.0 + 0x1p50 i) == 1.570796326794897507409741391764983781004 - 3.535050620855721078027883819436759661753e1 i":
 float: 1
 ifloat: 1
@@ -257,9 +275,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 + 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: cacos (-1.5 - 0 i) == pi + 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-1025 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-129 i) == 3.141592653589793238462643383279502884195 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (-1.5 - 0x1.fp-16385 i) == 3.141592653589793238462643383279502884197 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: cacos (-2 - 3 i) == 2.1414491111159960199416055713254211 + 1.9833870299165354323470769028940395 i":
 float: 1
 ifloat: 1
@@ -281,6 +317,18 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: cacos (0x1.fp-1025 + 1.5 i) == 1.570796326794896619231321691639751442099 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-1025 - 1.5 i) == 1.570796326794896619231321691639751442099 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 + 1.5 i) == 1.570796326794896619231321691639751442097 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: cacos (0x1.fp-129 - 1.5 i) == 1.570796326794896619231321691639751442097 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: cacos (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 - 7.107906849659093345062145442726115449315e2 i":
 double: 1
 idouble: 1
@@ -294,9 +342,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 + 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: cacos (1.5 - 0 i) == +0 + 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-1025 i) == 4.819934639999230680322935210539402497827e-309 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-129 i) == 2.546345110742945032959687790021055102355e-39 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: cacos (1.5 - 0x1.fp-16385 i) == 7.282957076134209141226696333885150260319e-4933 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 
 # cacosh
 Test "Real part of: cacosh (+0 + 0.5 i) == 0.4812118250596034474977589134243684231352 + pi/2 i":
@@ -460,6 +526,18 @@ ifloat: 1
 Test "Imaginary part of: casin (-0 - 1.5 i) == -0 - 1.194763217287109304111930828519090523536 i":
 double: 1
 idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 + 1.5 i) == -2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-1025 - 1.5 i) == -2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 + 1.5 i) == -1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (-0x1.fp-129 - 1.5 i) == -1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (-1.5 + +0 i) == -pi/2 + 0.9624236501192068949955178268487368462704 i":
 double: 1
 float: 1
@@ -467,9 +545,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 + 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: casin (-1.5 - 0 i) == -pi/2 - 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-1025 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-129 i) == -1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (-1.5 - 0x1.fp-16385 i) == -1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casin (0.75 + 1.25 i) == 0.453276177638793913448921196101971749 + 1.13239363160530819522266333696834467 i":
 double: 1
 float: 1
@@ -482,6 +578,18 @@ float: 1
 ifloat: 1
 ildouble: 2
 ldouble: 2
+Test "Imaginary part of: casin (0x1.fp-1025 + 1.5 i) == 2.989196569048182929051881765490354365918e-309 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-1025 - 1.5 i) == 2.989196569048182929051881765490354365918e-309 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 + 1.5 i) == 1.579176199917649005841160751101628985741e-39 + 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
+Test "Imaginary part of: casin (0x1.fp-129 - 1.5 i) == 1.579176199917649005841160751101628985741e-39 - 1.194763217287109304111930828519090523536 i":
+double: 1
+idouble: 1
 Test "Imaginary part of: casin (0x1.fp1023 + 0x1.fp1023 i) == 7.853981633974483096156608458198757210493e-1 + 7.107906849659093345062145442726115449315e2 i":
 double: 1
 idouble: 1
@@ -495,9 +603,27 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 + 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 + 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 Test "Imaginary part of: casin (1.5 - 0 i) == pi/2 - 0.9624236501192068949955178268487368462704 i":
 ildouble: 1
 ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-1025 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-129 i) == 1.570796326794896619231321691639751442096 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
+Test "Imaginary part of: casin (1.5 - 0x1.fp-16385 i) == 1.570796326794896619231321691639751442099 - 9.624236501192068949955178268487368462704e-1 i":
+ildouble: 1
+ldouble: 1
 
 # casinh
 Test "Real part of: casinh (+0 + 1.5 i) == 0.9624236501192068949955178268487368462704 + pi/2 i":
@@ -534,6 +660,24 @@ idouble: 2
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-1025 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-129 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 + 1.5 i) == -9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (-0x1.fp-16385 - 1.5 i) == -9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casinh (-1.0 + +0 i) == -0.8813735870195430252326093249797923090282 + +0 i":
 double: 2
 float: 1
@@ -553,11 +697,23 @@ double: 2
 float: 1
 idouble: 2
 ifloat: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 + 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (-1.5 - 0 i) == -1.194763217287109304111930828519090523536 - 0 i":
 double: 2
 float: 1
 idouble: 2
 ifloat: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-1025 i) == -1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (-1.5 - 0x1.fp-129 i) == -1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (-2 - 3 i) == -1.9686379257930962917886650952454982 - 0.96465850440760279204541105949953237 i":
 double: 5
 float: 1
@@ -592,6 +748,24 @@ idouble: 1
 ifloat: 1
 ildouble: 1
 ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-1025 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-129 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442096 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 + 1.5 i) == 9.624236501192068949955178268487368462704e-1 + 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
+Test "Real part of: casinh (0x1.fp-16385 - 1.5 i) == 9.624236501192068949955178268487368462704e-1 - 1.570796326794896619231321691639751442099 i":
+ildouble: 1
+ldouble: 1
 Test "Real part of: casinh (0x1.fp1023 + 0x1.fp1023 i) == 7.107906849659093345062145442726115449315e2 + 7.853981633974483096156608458198757210493e-1 i":
 double: 1
 idouble: 1
@@ -611,9 +785,21 @@ ifloat: 1
 Test "Real part of: casinh (1.5 + +0 i) == 1.194763217287109304111930828519090523536 + +0 i":
 double: 1
 idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 + 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 + 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 + 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 Test "Real part of: casinh (1.5 - 0 i) == 1.194763217287109304111930828519090523536 - 0 i":
 double: 1
 idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-1025 i) == 1.194763217287109304111930828519090523536 - 2.989196569048182929051881765490354365918e-309 i":
+double: 1
+idouble: 1
+Test "Real part of: casinh (1.5 - 0x1.fp-129 i) == 1.194763217287109304111930828519090523536 - 1.579176199917649005841160751101628985741e-39 i":
+double: 1
+idouble: 1
 
 # catan
 Test "Real part of: catan (-2 - 3 i) == -1.4099210495965755225306193844604208 - 0.22907268296853876629588180294200276 i":