From bcc8d6617ba029c288fff9680a02b9a3b1caa9c0 Mon Sep 17 00:00:00 2001 From: Joseph Myers Date: Mon, 9 Apr 2012 22:31:35 +0000 Subject: Fix ctan, ctanh overflow (bug 11521). --- math/libm-test.inc | 60 ++++++++++++++++++++++++++++++++++++++++++++++++++++++ math/s_ctan.c | 44 ++++++++++++++++++++++++++++----------- math/s_ctanf.c | 44 ++++++++++++++++++++++++++++----------- math/s_ctanh.c | 43 ++++++++++++++++++++++++++++---------- math/s_ctanhf.c | 43 ++++++++++++++++++++++++++++---------- math/s_ctanhl.c | 43 ++++++++++++++++++++++++++++---------- math/s_ctanl.c | 45 ++++++++++++++++++++++++++++------------ 7 files changed, 252 insertions(+), 70 deletions(-) (limited to 'math') diff --git a/math/libm-test.inc b/math/libm-test.inc index 0533483..a551b9f 100644 --- a/math/libm-test.inc +++ b/math/libm-test.inc @@ -2840,6 +2840,36 @@ ctan_test (void) TEST_c_c (ctan, 0.75L, 1.25L, 0.160807785916206426725166058173438663L, 0.975363285031235646193581759755216379L); TEST_c_c (ctan, -2, -3, 0.376402564150424829275122113032269084e-2L, -1.00323862735360980144635859782192726L); + TEST_c_c (ctan, 1, 45, 1.490158918874345552942703234806348520895e-39L, 1.000000000000000000000000000000000000001L); + TEST_c_c (ctan, 1, 47, 2.729321264492904590777293425576722354636e-41L, 1.0); + +#ifndef TEST_FLOAT + TEST_c_c (ctan, 1, 355, 8.140551093483276762350406321792653551513e-309L, 1.0); + TEST_c_c (ctan, 1, 365, 1.677892637497921890115075995898773550884e-317L, 1.0); +#endif + +#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384 + TEST_c_c (ctan, 1, 5680, 4.725214596136812019616700920476949798307e-4934L, 1.0); + TEST_c_c (ctan, 1, 5690, 9.739393181626937151720816611272607059057e-4943L, 1.0); +#endif + + TEST_c_c (ctan, 0x3.243f6cp-1, 0, -2.287733242885645987394874673945769518150e7L, 0.0); + + TEST_c_c (ctan, 0x1p127, 1, 0.2446359391192790896381501310437708987204L, 0.9101334047676183761532873794426475906201L); + +#ifndef TEST_FLOAT + TEST_c_c (ctan, 0x1p1023, 1, -0.2254627924997545057926782581695274244229L, 0.8786063118883068695462540226219865087189L); +#endif + +#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384 + TEST_c_c (ctan, 0x1p16383L, 1, 0.1608598776370396607204448234354670036772L, 0.8133818522051542536316746743877629761488L); +#endif + + TEST_c_c (ctan, 50000, 50000, plus_zero, 1.0); + TEST_c_c (ctan, 50000, -50000, plus_zero, -1.0); + TEST_c_c (ctan, -50000, 50000, minus_zero, 1.0); + TEST_c_c (ctan, -50000, -50000, minus_zero, -1.0); + END (ctan, complex); } @@ -2899,6 +2929,36 @@ ctanh_test (void) TEST_c_c (ctanh, 0.75L, 1.25L, 1.37260757053378320258048606571226857L, 0.385795952609750664177596760720790220L); TEST_c_c (ctanh, -2, -3, -0.965385879022133124278480269394560686L, 0.988437503832249372031403430350121098e-2L); + TEST_c_c (ctanh, 45, 1, 1.000000000000000000000000000000000000001L, 1.490158918874345552942703234806348520895e-39L); + TEST_c_c (ctanh, 47, 1, 1.0, 2.729321264492904590777293425576722354636e-41L); + +#ifndef TEST_FLOAT + TEST_c_c (ctanh, 355, 1, 1.0, 8.140551093483276762350406321792653551513e-309L); + TEST_c_c (ctanh, 365, 1, 1.0, 1.677892637497921890115075995898773550884e-317L); +#endif + +#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384 + TEST_c_c (ctanh, 5680, 1, 1.0, 4.725214596136812019616700920476949798307e-4934L); + TEST_c_c (ctanh, 5690, 1, 1.0, 9.739393181626937151720816611272607059057e-4943L); +#endif + + TEST_c_c (ctanh, 0, 0x3.243f6cp-1, 0.0, -2.287733242885645987394874673945769518150e7L); + + TEST_c_c (ctanh, 1, 0x1p127, 0.9101334047676183761532873794426475906201L, 0.2446359391192790896381501310437708987204L); + +#ifndef TEST_FLOAT + TEST_c_c (ctanh, 1, 0x1p1023, 0.8786063118883068695462540226219865087189L, -0.2254627924997545057926782581695274244229L); +#endif + +#if defined TEST_LDOUBLE && LDBL_MAX_EXP >= 16384 + TEST_c_c (ctanh, 1, 0x1p16383L, 0.8133818522051542536316746743877629761488L, 0.1608598776370396607204448234354670036772L); +#endif + + TEST_c_c (ctanh, 50000, 50000, 1.0, plus_zero); + TEST_c_c (ctanh, 50000, -50000, 1.0, minus_zero); + TEST_c_c (ctanh, -50000, 50000, -1.0, plus_zero); + TEST_c_c (ctanh, -50000, -50000, -1.0, minus_zero); + END (ctanh, complex); } diff --git a/math/s_ctan.c b/math/s_ctan.c index c838fad..78117b3 100644 --- a/math/s_ctan.c +++ b/math/s_ctan.c @@ -1,5 +1,5 @@ /* Complex tangent function for double. - Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. @@ -20,9 +20,8 @@ #include #include #include - #include - +#include __complex__ double __ctan (__complex__ double x) @@ -51,24 +50,45 @@ __ctan (__complex__ double x) } else { - double sin2rx, cos2rx; + double sinrx, cosrx; double den; + const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); - __sincos (2.0 * __real__ x, &sin2rx, &cos2rx); + /* 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). */ - den = cos2rx + __ieee754_cosh (2.0 * __imag__ x); + __sincos (__real__ x, &sinrx, &cosrx); - if (den == 0.0) + if (fabs (__imag__ x) > t) { - __complex__ double ez = __cexp (1.0i * x); - __complex__ double emz = __cexp (-1.0i * x); + /* Avoid intermediate overflow when the real part of the + result may be subnormal. Ignoring negligible terms, the + imaginary part is +/- 1, the real part is + sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ + double exp_2t = __ieee754_exp (2 * t); - res = (ez - emz) / (ez + emz) * -1.0i; + __imag__ res = __copysign (1.0, __imag__ x); + __real__ res = 4 * sinrx * cosrx; + __imag__ x = fabs (__imag__ x); + __imag__ x -= t; + __real__ res /= exp_2t; + if (__imag__ x > t) + { + /* Underflow (original imaginary part of x has absolute + value > 2t). */ + __real__ res /= exp_2t; + } + else + __real__ res /= __ieee754_exp (2 * __imag__ x); } else { - __real__ res = sin2rx / den; - __imag__ res = __ieee754_sinh (2.0 * __imag__ x) / den; + double sinhix = __ieee754_sinh (__imag__ x); + double coshix = __ieee754_cosh (__imag__ x); + + den = cosrx * cosrx + sinhix * sinhix; + __real__ res = sinrx * cosrx / den; + __imag__ res = sinhix * coshix / den; } } diff --git a/math/s_ctanf.c b/math/s_ctanf.c index 5f7f28a..4cba559 100644 --- a/math/s_ctanf.c +++ b/math/s_ctanf.c @@ -1,5 +1,5 @@ /* Complex tangent function for float. - Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. @@ -21,7 +21,7 @@ #include #include #include - +#include __complex__ float __ctanf (__complex__ float x) @@ -50,25 +50,45 @@ __ctanf (__complex__ float x) } else { - float sin2rx, cos2rx; + float sinrx, cosrx; float den; + const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2); - __sincosf (2.0 * __real__ x, &sin2rx, &cos2rx); - - den = cos2rx + __ieee754_coshf (2.0 * __imag__ x); + /* 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). */ + __sincosf (__real__ x, &sinrx, &cosrx); - if (den == 0.0) + if (fabsf (__imag__ x) > t) { - __complex__ float ez = __cexpf (1.0i * x); - __complex__ float emz = __cexpf (-1.0i * x); + /* Avoid intermediate overflow when the real part of the + result may be subnormal. Ignoring negligible terms, the + imaginary part is +/- 1, the real part is + sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ + float exp_2t = __ieee754_expf (2 * t); - res = (ez - emz) / (ez + emz) * -1.0i; + __imag__ res = __copysignf (1.0, __imag__ x); + __real__ res = 4 * sinrx * cosrx; + __imag__ x = fabsf (__imag__ x); + __imag__ x -= t; + __real__ res /= exp_2t; + if (__imag__ x > t) + { + /* Underflow (original imaginary part of x has absolute + value > 2t). */ + __real__ res /= exp_2t; + } + else + __real__ res /= __ieee754_expf (2 * __imag__ x); } else { - __real__ res = sin2rx / den; - __imag__ res = __ieee754_sinhf (2.0 * __imag__ x) / den; + float sinhix = __ieee754_sinhf (__imag__ x); + float coshix = __ieee754_coshf (__imag__ x); + + den = cosrx * cosrx + sinhix * sinhix; + __real__ res = sinrx * cosrx / den; + __imag__ res = sinhix * coshix / den; } } diff --git a/math/s_ctanh.c b/math/s_ctanh.c index 9cecb8b..201871e 100644 --- a/math/s_ctanh.c +++ b/math/s_ctanh.c @@ -1,5 +1,5 @@ /* Complex hyperbole tangent for double. - Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. @@ -21,7 +21,7 @@ #include #include #include - +#include __complex__ double __ctanh (__complex__ double x) @@ -50,24 +50,45 @@ __ctanh (__complex__ double x) } else { - double sin2ix, cos2ix; + double sinix, cosix; double den; + const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); - __sincos (2.0 * __imag__ x, &sin2ix, &cos2ix); + /* 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). */ - den = (__ieee754_cosh (2.0 * __real__ x) + cos2ix); + __sincos (__imag__ x, &sinix, &cosix); - if (den == 0.0) + if (fabs (__real__ x) > t) { - __complex__ double ez = __cexp (x); - __complex__ double emz = __cexp (-x); + /* Avoid intermediate overflow when the imaginary part of + the result may be subnormal. Ignoring negligible terms, + the real part is +/- 1, the imaginary part is + sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ + double exp_2t = __ieee754_exp (2 * t); - res = (ez - emz) / (ez + emz); + __real__ res = __copysign (1.0, __real__ x); + __imag__ res = 4 * sinix * cosix; + __real__ x = fabs (__real__ x); + __real__ x -= t; + __imag__ res /= exp_2t; + if (__real__ x > t) + { + /* Underflow (original real part of x has absolute value + > 2t). */ + __imag__ res /= exp_2t; + } + else + __imag__ res /= __ieee754_exp (2 * __real__ x); } else { - __real__ res = __ieee754_sinh (2.0 * __real__ x) / den; - __imag__ res = sin2ix / den; + double sinhrx = __ieee754_sinh (__real__ x); + double coshrx = __ieee754_cosh (__real__ x); + + den = sinhrx * sinhrx + cosix * cosix; + __real__ res = sinhrx * coshrx / den; + __imag__ res = sinix * cosix / den; } } diff --git a/math/s_ctanhf.c b/math/s_ctanhf.c index fce5aaf..e505155 100644 --- a/math/s_ctanhf.c +++ b/math/s_ctanhf.c @@ -1,5 +1,5 @@ /* Complex hyperbole tangent for float. - Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. @@ -21,7 +21,7 @@ #include #include #include - +#include __complex__ float __ctanhf (__complex__ float x) @@ -50,24 +50,45 @@ __ctanhf (__complex__ float x) } else { - float sin2ix, cos2ix; + float sinix, cosix; float den; + const int t = (int) ((FLT_MAX_EXP - 1) * M_LN2 / 2); - __sincosf (2.0 * __imag__ x, &sin2ix, &cos2ix); + /* 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). */ - den = (__ieee754_coshf (2.0 * __real__ x) + cos2ix); + __sincosf (__imag__ x, &sinix, &cosix); - if (den == 0.0f) + if (fabsf (__real__ x) > t) { - __complex__ float ez = __cexpf (x); - __complex__ float emz = __cexpf (-x); + /* Avoid intermediate overflow when the imaginary part of + the result may be subnormal. Ignoring negligible terms, + the real part is +/- 1, the imaginary part is + sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ + float exp_2t = __ieee754_expf (2 * t); - res = (ez - emz) / (ez + emz); + __real__ res = __copysignf (1.0, __real__ x); + __imag__ res = 4 * sinix * cosix; + __real__ x = fabsf (__real__ x); + __real__ x -= t; + __imag__ res /= exp_2t; + if (__real__ x > t) + { + /* Underflow (original real part of x has absolute value + > 2t). */ + __imag__ res /= exp_2t; + } + else + __imag__ res /= __ieee754_expf (2 * __real__ x); } else { - __real__ res = __ieee754_sinhf (2.0 * __real__ x) / den; - __imag__ res = sin2ix / den; + float sinhrx = __ieee754_sinhf (__real__ x); + float coshrx = __ieee754_coshf (__real__ x); + + den = sinhrx * sinhrx + cosix * cosix; + __real__ res = sinhrx * coshrx / den; + __imag__ res = sinix * cosix / den; } } diff --git a/math/s_ctanhl.c b/math/s_ctanhl.c index d22e13a..e5d6779 100644 --- a/math/s_ctanhl.c +++ b/math/s_ctanhl.c @@ -1,5 +1,5 @@ /* Complex hyperbole tangent for long double. - Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. @@ -21,7 +21,7 @@ #include #include #include - +#include __complex__ long double __ctanhl (__complex__ long double x) @@ -50,24 +50,45 @@ __ctanhl (__complex__ long double x) } else { - long double sin2ix, cos2ix; + long double sinix, cosix; long double den; + const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); - __sincosl (2.0 * __imag__ x, &sin2ix, &cos2ix); + /* 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). */ - den = (__ieee754_coshl (2.0 * __real__ x) + cos2ix); + __sincosl (__imag__ x, &sinix, &cosix); - if (den == 0.0L) + if (fabsl (__real__ x) > t) { - __complex__ long double ez = __cexpl (x); - __complex__ long double emz = __cexpl (-x); + /* Avoid intermediate overflow when the imaginary part of + the result may be subnormal. Ignoring negligible terms, + 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); - res = (ez - emz) / (ez + emz); + __real__ res = __copysignl (1.0, __real__ x); + __imag__ res = 4 * sinix * cosix; + __real__ x = fabsl (__real__ x); + __real__ x -= t; + __imag__ res /= exp_2t; + if (__real__ x > t) + { + /* Underflow (original real part of x has absolute value + > 2t). */ + __imag__ res /= exp_2t; + } + else + __imag__ res /= __ieee754_expl (2 * __real__ x); } else { - __real__ res = __ieee754_sinhl (2.0 * __real__ x) / den; - __imag__ res = sin2ix / den; + long double sinhrx = __ieee754_sinhl (__real__ x); + long double coshrx = __ieee754_coshl (__real__ x); + + den = sinhrx * sinhrx + cosix * cosix; + __real__ res = sinhrx * coshrx / den; + __imag__ res = sinix * cosix / den; } } diff --git a/math/s_ctanl.c b/math/s_ctanl.c index 112dd72..12d700c 100644 --- a/math/s_ctanl.c +++ b/math/s_ctanl.c @@ -1,5 +1,5 @@ /* Complex tangent function for long double. - Copyright (C) 1997, 2005, 2011 Free Software Foundation, Inc. + Copyright (C) 1997-2012 Free Software Foundation, Inc. This file is part of the GNU C Library. Contributed by Ulrich Drepper , 1997. @@ -20,9 +20,8 @@ #include #include #include - #include - +#include __complex__ long double __ctanl (__complex__ long double x) @@ -51,25 +50,45 @@ __ctanl (__complex__ long double x) } else { - long double sin2rx, cos2rx; + long double sinrx, cosrx; long double den; + const int t = (int) ((LDBL_MAX_EXP - 1) * M_LN2l / 2); - __sincosl (2.0 * __real__ x, &sin2rx, &cos2rx); - - den = cos2rx + __ieee754_coshl (2.0 * __imag__ x); + /* 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). */ + __sincosl (__real__ x, &sinrx, &cosrx); - if (den == 0.0) + if (fabsl (__imag__ x) > t) { - __complex__ long double ez = __cexpl (1.0i * x); - __complex__ long double emz = __cexpl (-1.0i * x); + /* Avoid intermediate overflow when the real part of the + result may be subnormal. Ignoring negligible terms, the + imaginary part is +/- 1, the real part is + sin(x)*cos(x)/sinh(y)^2 = 4*sin(x)*cos(x)/exp(2y). */ + long double exp_2t = __ieee754_expl (2 * t); - res = (ez - emz) / (ez + emz) * -1.0i; + __imag__ res = __copysignl (1.0, __imag__ x); + __real__ res = 4 * sinrx * cosrx; + __imag__ x = fabsl (__imag__ x); + __imag__ x -= t; + __real__ res /= exp_2t; + if (__imag__ x > t) + { + /* Underflow (original imaginary part of x has absolute + value > 2t). */ + __real__ res /= exp_2t; + } + else + __real__ res /= __ieee754_expl (2 * __imag__ x); } else { - __real__ res = sin2rx / den; - __imag__ res = __ieee754_sinhl (2.0 * __imag__ x) / den; + long double sinhix = __ieee754_sinhl (__imag__ x); + long double coshix = __ieee754_coshl (__imag__ x); + + den = cosrx * cosrx + sinhix * sinhix; + __real__ res = sinrx * cosrx / den; + __imag__ res = sinhix * coshix / den; } } -- cgit v1.1