From 28cfe84316f92dbb3e48831d6f7eb4511e3ddf60 Mon Sep 17 00:00:00 2001 From: Adhemerval Zanella Date: Wed, 11 Jul 2012 09:19:27 -0300 Subject: [PATCH] Fix ctan, ctanh of subnormals in round-upwards mode (bug 14328). IBM long double fixes and POWER ulps update. --- ChangeLog | 7 + sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c | 38 ++-- sysdeps/ieee754/ldbl-128ibm/s_ctanl.c | 34 ++- sysdeps/powerpc/fpu/libm-test-ulps | 275 ++++++++++++++++++++++++- 4 files changed, 331 insertions(+), 23 deletions(-) diff --git a/ChangeLog b/ChangeLog index f1a8d2c254..8011f8b043 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,10 @@ +2012-07-11 Adhemerval Zanella + + * sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c: Do not call sinh and cosh + for subnormals or multiply small sinh result by itself. + * sysdeps/ieee754/ldbl-128ibm/s_ctanl.c: Likewise. + * sysdeps/powerpc/fpu/libm-test-ulps: Update. + 2012-07-11 David S. Miller * sysdeps/sparc/fpu/libm-test-ulps: Update. diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c b/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c index 2ab80a2246..e11ce56781 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_ctanhl.c @@ -25,6 +25,8 @@ #include +/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */ +static const long double ldbl_eps = 0x1p-106L; __complex__ long double __ctanhl (__complex__ long double x) @@ -35,8 +37,8 @@ __ctanhl (__complex__ long double x) { if (__isinfl (__real__ x)) { - __real__ res = __copysignl (1.0, __real__ x); - __imag__ res = __copysignl (0.0, __imag__ x); + __real__ res = __copysignl (1.0L, __real__ x); + __imag__ res = __copysignl (0.0L, __imag__ x); } else if (__imag__ x == 0.0) { @@ -57,7 +59,7 @@ __ctanhl (__complex__ long double x) { long double sinix, cosix; long double den; - const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); + const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L); /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ @@ -71,7 +73,7 @@ __ctanhl (__complex__ long double x) the real part is +/- 1, the imaginary part is sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ long double exp_2t = __ieee754_expl (2 * t); - __real__ res = __copysignl (1.0, __real__ x); + __real__ res = __copysignl (1.0L, __real__ x); __imag__ res = 4 * sinix * cosix; __real__ x = fabsl (__real__ x); __real__ x -= t; @@ -83,22 +85,34 @@ __ctanhl (__complex__ long double x) __imag__ res /= exp_2t; } else - __imag__ res /= __ieee754_expl (2 * __real__ x); + __imag__ res /= __ieee754_expl (2.0L * __real__ x); } else { - long double sinhrx = __ieee754_sinhl (__real__ x); - long double coshrx = __ieee754_coshl (__real__ x); + long double sinhrx, coshrx; + if (fabs (__real__ x) > LDBL_MIN) + { + sinhrx = __ieee754_sinhl (__real__ x); + coshrx = __ieee754_coshl (__real__ x); + } + else + { + sinhrx = __real__ x; + coshrx = 1.0L; + } - den = sinhrx * sinhrx + cosix * cosix; - __real__ res = sinhrx * coshrx / den; - __imag__ res = sinix * cosix / den; + if (fabsl (sinhrx) > fabsl (cosix) * ldbl_eps) + den = sinhrx * sinhrx + cosix * cosix; + else + den = cosix * cosix; + __real__ res = sinhrx * (coshrx / den); + __imag__ res = sinix * (cosix / den); } /* __gcc_qmul does not respect -0.0 so we need the following fixup. */ - if ((__real__ res == 0.0) && (__real__ x == 0.0)) + if ((__real__ res == 0.0L) && (__real__ x == 0.0L)) __real__ res = __real__ x; - if ((__real__ res == 0.0) && (__imag__ x == 0.0)) + if ((__real__ res == 0.0L) && (__imag__ x == 0.0L)) __imag__ res = __imag__ x; } diff --git a/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c b/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c index 9d89bbe311..34a370a308 100644 --- a/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c +++ b/sysdeps/ieee754/ldbl-128ibm/s_ctanl.c @@ -25,6 +25,8 @@ #include +/* IBM long double GCC builtin sets LDBL_EPSILON == LDBL_DENORM_MIN */ +static const long double ldbl_eps = 0x1p-106L; __complex__ long double __ctanl (__complex__ long double x) @@ -55,7 +57,7 @@ __ctanl (__complex__ long double x) { long double sinrx, cosrx; long double den; - const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); + const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2.0L); /* tan(x+iy) = (sin(2x) + i*sinh(2y))/(cos(2x) + cosh(2y)) = (sin(x)*cos(x) + i*sinh(y)*cosh(y)/(cos(x)^2 + sinh(y)^2). */ @@ -70,7 +72,7 @@ __ctanl (__complex__ long double x) sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ long double exp_2t = __ieee754_expl (2 * t); - __imag__ res = __copysignl (1.0, __imag__ x); + __imag__ res = __copysignl (1.0L, __imag__ x); __real__ res = 4 * sinrx * cosrx; __imag__ x = fabsl (__imag__ x); __imag__ x -= t; @@ -82,23 +84,35 @@ __ctanl (__complex__ long double x) __real__ res /= exp_2t; } else - __real__ res /= __ieee754_expl (2 * __imag__ x); + __real__ res /= __ieee754_expl (2.0L * __imag__ x); } else { - long double sinhix = __ieee754_sinhl (__imag__ x); - long double coshix = __ieee754_coshl (__imag__ x); + long double sinhix, coshix; + if (fabsl (__imag__ x) > LDBL_MIN) + { + sinhix = __ieee754_sinhl (__imag__ x); + coshix = __ieee754_coshl (__imag__ x); + } + else + { + sinhix = __imag__ x; + coshix = 1.0L; + } - den = cosrx * cosrx + sinhix * sinhix; - __real__ res = sinrx * cosrx / den; - __imag__ res = sinhix * coshix / den; + if (fabsl (sinhix) > fabsl (cosrx) * ldbl_eps) + den = cosrx * cosrx + sinhix * sinhix; + else + den = cosrx * cosrx; + __real__ res = sinrx * (cosrx / den); + __imag__ res = sinhix * (coshix / den); } /* __gcc_qmul does not respect -0.0 so we need the following fixup. */ - if ((__real__ res == 0.0) && (__real__ x == 0.0)) + if ((__real__ res == 0.0L) && (__real__ x == 0.0L)) __real__ res = __real__ x; - if ((__real__ res == 0.0) && (__imag__ x == 0.0)) + if ((__real__ res == 0.0L) && (__imag__ x == 0.0L)) __imag__ res = __imag__ x; } diff --git a/sysdeps/powerpc/fpu/libm-test-ulps b/sysdeps/powerpc/fpu/libm-test-ulps index 66576a52a5..ffb8e3a952 100644 --- a/sysdeps/powerpc/fpu/libm-test-ulps +++ b/sysdeps/powerpc/fpu/libm-test-ulps @@ -1336,33 +1336,120 @@ ldouble: 1 Test "Real part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i": double: 1 idouble: 1 +Test "Imaginary part of: ctan (0x1p1023 + 1 i) == -0.2254627924997545057926782581695274244229 + 0.8786063118883068695462540226219865087189 i": +ildouble: 1 +ldouble: 1 Test "Real part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i": float: 1 ifloat: 1 +ildouble: 1 +ldouble: 1 Test "Imaginary part of: ctan (0x1p127 + 1 i) == 0.2446359391192790896381501310437708987204 + 0.9101334047676183761532873794426475906201 i": double: 1 float: 1 idouble: 1 ifloat: 1 +ildouble: 2 +ldouble: 2 Test "Real part of: ctan (0x3.243f6cp-1 + 0 i) == -2.287733242885645987394874673945769518150e7 + 0.0 i": float: 1 ifloat: 1 +ildouble: 2 +ldouble: 2 Test "Real part of: ctan (1 + 47 i) == 2.729321264492904590777293425576722354636e-41 + 1.0 i": ildouble: 2 ldouble: 2 +# ctan_downward +Test "Real part of: ctan_downward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i": +ildouble: 3 +ldouble: 3 +Test "Real part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 4 +ldouble: 4 +Test "Imaginary part of: ctan_downward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +float: 1 +ifloat: 1 +ildouble: 10 +ldouble: 10 + +# ctan_tonearest +Test "Real part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +float: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 +Test "Imaginary part of: ctan_tonearest (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 + +# ctan_towardzero +Test "Real part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i": +ldouble: 4 +ildouble: 4 +Test "Imaginary part of: ctan_towardzero (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i": +ildouble: 13 +ldouble: 13 +Test "Real part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +float: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 +Test "Imaginary part of: ctan_towardzero (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +float: 1 +ifloat: 1 +ildouble: 10 +ldouble: 10 + +# ctan_upward +Test "Real part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i": +double: 1 +idouble: 1 +ildouble: 6 +ldouble: 6 +Test "Imaginary part of: ctan_upward (0x1.921fb54442d18p+0 + 0x1p-1074 i) == 1.633123935319536975596773704152891653086e16 + 1.317719414943508315995636961402669067843e-291 i": +ildouble: 10 +ldouble: 10 +Test "Real part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 6 +ldouble: 6 +Test "Imaginary part of: ctan_upward (0x1.921fb6p+0 + 0x1p-149 i) == -2.287733242885645987394874673945769518150e7 + 7.334008549954377778731880988481078535821e-31 i": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +ildouble: 1 +ldouble: 1 + # ctanh Test "Real part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i": double: 1 float: 2 idouble: 1 ifloat: 2 +idouble: 2 +ildouble: 2 +ldouble: 2 Test "Imaginary part of: ctanh (-2 - 3 i) == -0.965385879022133124278480269394560686 + 0.988437503832249372031403430350121098e-2 i": double: 1 idouble: 1 +ildouble: 2 +ldouble: 2 Test "Imaginary part of: ctanh (0 + 0x3.243f6cp-1 i) == 0.0 - 2.287733242885645987394874673945769518150e7 i": float: 1 ifloat: 1 +ildouble: 2 +ldouble: 2 Test "Imaginary part of: ctanh (0 + pi/4 i) == 0.0 + 1.0 i": double: 1 float: 1 @@ -1378,22 +1465,100 @@ float: 1 ifloat: 1 ildouble: 2 ldouble: 2 +Test "Real part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i": +ildouble: 1 +ldouble: 1 Test "Imaginary part of: ctanh (1 + 0x1p1023 i) == 0.8786063118883068695462540226219865087189 - 0.2254627924997545057926782581695274244229 i": -double: 1 idouble: 1 +double: 1 Test "Real part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i": double: 1 float: 1 idouble: 1 ifloat: 1 +ildouble: 2 +ldouble: 2 Test "Imaginary part of: ctanh (1 + 0x1p127 i) == 0.9101334047676183761532873794426475906201 + 0.2446359391192790896381501310437708987204 i": double: 1 float: 1 ifloat: 1 +ildouble: 1 +ldouble: 1 Test "Imaginary part of: ctanh (47 + 1 i) == 1.0 + 2.729321264492904590777293425576722354636e-41 i": ildouble: 2 ldouble: 2 +# ctanh_downward +Test "Imaginary part of: ctanh_downward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i": +ildouble: 3 +ldouble: 3 +Test "Real part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +float: 1 +ifloat: 1 +ildouble: 10 +ldouble: 10 +Test "Imaginary part of: ctanh_downward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 4 +ldouble: 4 + +# ctanh_tonearest +Test "Real part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: ctanh_tonearest (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +float: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 + +# ctanh_towardzero +Test "Real part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i": +ildouble: 13 +ldouble: 13 +Test "Imaginary part of: ctanh_towardzero (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i": +ildouble: 4 +ldouble: 4 +Test "Real part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +float: 1 +ifloat: 1 +ildouble: 10 +ldouble: 10 +Test "Imaginary part of: ctanh_towardzero (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +float: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 + +# ctanh_upward +Test "Real part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i": +ildouble: 10 +ldouble: 10 +Test "Imaginary part of: ctanh_upward (0x1p-1074 + 0x1.921fb54442d18p+0 i) == 1.317719414943508315995636961402669067843e-291 + 1.633123935319536975596773704152891653086e16 i": +double: 1 +idouble: 1 +ildouble: 6 +ldouble: 6 +Test "Real part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +ildouble: 1 +ldouble: 1 +Test "Imaginary part of: ctanh_upward (0x1p-149 + 0x1.921fb6p+0 i) == 7.334008549954377778731880988481078535821e-31 - 2.287733242885645987394874673945769518150e7 i": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 3 +ldouble: 3 + # erf Test "erf (1.25) == 0.922900128256458230136523481197281140": double: 1 @@ -2714,9 +2879,63 @@ double: 1 float: 1 idouble: 1 ifloat: 1 +ildouble: 2 +ldouble: 2 + +Function: Real part of "ctan_downward": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 4 +ldouble: 4 + +Function: Imaginary part of "ctan_downward": +float: 1 +ifloat: 1 +ildouble: 10 +ldouble: 10 + +Function: Real part of "ctan_tonearest": +float: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 + +Function: Imaginary part of "ctan_tonearest": +float: 1 +ifloat: 1 ildouble: 1 ldouble: 1 +Function: Real part of "ctan_towardzero": +float: 1 +ifloat: 1 +ildouble: 4 +ldouble: 4 + +Function: Imaginary part of "ctan_towardzero": +float: 1 +ifloat: 1 +ildouble: 13 +ldouble: 13 + +Function: Real part of "ctan_upward": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 6 +ldouble: 6 + +Function: Imaginary part of "ctan_upward": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +ildouble: 10 +ldouble: 10 + Function: Real part of "ctanh": double: 1 float: 2 @@ -2733,6 +2952,60 @@ ifloat: 1 ildouble: 2 ldouble: 2 +Function: Real part of "ctanh_downward": +float: 1 +ifloat: 1 +ildouble: 10 +ldouble: 10 + +Function: Imaginary part of "ctanh_downward": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 4 +ldouble: 4 + +Function: Real part of "ctanh_tonearest": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 + +Function: Imaginary part of "ctanh_tonearest": +float: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 + +Function: Real part of "ctanh_towardzero": +float: 1 +ifloat: 1 +ildouble: 13 +ldouble: 13 + +Function: Imaginary part of "ctanh_towardzero": +float: 1 +ifloat: 1 +ildouble: 4 +ldouble: 4 + +Function: Real part of "ctanh_upward": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +ildouble: 10 +ldouble: 10 + +Function: Imaginary part of "ctanh_upward": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 6 +ldouble: 6 + Function: "erf": double: 1 idouble: 1 -- 2.43.5