diff options
Diffstat (limited to 'math')
| -rw-r--r-- | math/k_casinh_template.c | 210 | ||||
| -rw-r--r-- | math/s_casin_template.c | 66 | ||||
| -rw-r--r-- | math/s_casinh_template.c | 73 | ||||
| -rw-r--r-- | math/s_csin_template.c | 171 | ||||
| -rw-r--r-- | math/s_csinh_template.c | 166 |
5 files changed, 686 insertions, 0 deletions
diff --git a/math/k_casinh_template.c b/math/k_casinh_template.c new file mode 100644 index 0000000000..354dde1f3e --- /dev/null +++ b/math/k_casinh_template.c @@ -0,0 +1,210 @@ +/* Return arc hyperbole sine for double value, with the imaginary part + of the result possibly adjusted for use in computing other + functions. + Copyright (C) 1997-2016 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <complex.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Return the complex inverse hyperbolic sine of finite nonzero Z, + with the imaginary part of the result subtracted from pi/2 if ADJ + is nonzero. */ + +__complex__ double +__kernel_casinh (__complex__ double x, int adj) +{ + __complex__ double res; + double rx, ix; + __complex__ double y; + + /* Avoid cancellation by reducing to the first quadrant. */ + rx = fabs (__real__ x); + ix = fabs (__imag__ x); + + if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON) + { + /* For large x in the first quadrant, x + csqrt (1 + x * x) + is sufficiently close to 2 * x to make no significant + difference to the result; avoid possible overflow from + the squaring and addition. */ + __real__ y = rx; + __imag__ y = ix; + + if (adj) + { + double t = __real__ y; + __real__ y = __copysign (__imag__ y, __imag__ x); + __imag__ y = t; + } + + res = __clog (y); + __real__ res += M_LN2; + } + else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0) + { + double s = __ieee754_hypot (1.0, rx); + + __real__ res = __ieee754_log (rx + s); + if (adj) + __imag__ res = __ieee754_atan2 (s, __imag__ x); + else + __imag__ res = __ieee754_atan2 (ix, s); + } + else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5) + { + double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0)); + + __real__ res = __ieee754_log (ix + s); + if (adj) + __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x)); + else + __imag__ res = __ieee754_atan2 (s, rx); + } + else if (ix > 1.0 && ix < 1.5 && rx < 0.5) + { + if (rx < DBL_EPSILON * DBL_EPSILON) + { + double ix2m1 = (ix + 1.0) * (ix - 1.0); + double s = __ieee754_sqrt (ix2m1); + + __real__ res = __log1p (2.0 * (ix2m1 + ix * s)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x)); + else + __imag__ res = __ieee754_atan2 (s, rx); + } + else + { + double ix2m1 = (ix + 1.0) * (ix - 1.0); + double rx2 = rx * rx; + double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix); + double d = __ieee754_sqrt (ix2m1 * ix2m1 + f); + double dp = d + ix2m1; + double dm = f / dp; + double r1 = __ieee754_sqrt ((dm + rx2) / 2.0); + double r2 = rx * ix / r1; + + __real__ res = __log1p (rx2 + dp + 2.0 * (rx * r1 + ix * r2)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx + r1, __copysign (ix + r2, + __imag__ x)); + else + __imag__ res = __ieee754_atan2 (ix + r2, rx + r1); + } + } + else if (ix == 1.0 && rx < 0.5) + { + if (rx < DBL_EPSILON / 8.0) + { + __real__ res = __log1p (2.0 * (rx + __ieee754_sqrt (rx))) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (__ieee754_sqrt (rx), + __copysign (1.0, __imag__ x)); + else + __imag__ res = __ieee754_atan2 (1.0, __ieee754_sqrt (rx)); + } + else + { + double d = rx * __ieee754_sqrt (4.0 + rx * rx); + double s1 = __ieee754_sqrt ((d + rx * rx) / 2.0); + double s2 = __ieee754_sqrt ((d - rx * rx) / 2.0); + + __real__ res = __log1p (rx * rx + d + 2.0 * (rx * s1 + s2)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx + s1, __copysign (1.0 + s2, + __imag__ x)); + else + __imag__ res = __ieee754_atan2 (1.0 + s2, rx + s1); + } + } + else if (ix < 1.0 && rx < 0.5) + { + if (ix >= DBL_EPSILON) + { + if (rx < DBL_EPSILON * DBL_EPSILON) + { + double onemix2 = (1.0 + ix) * (1.0 - ix); + double s = __ieee754_sqrt (onemix2); + + __real__ res = __log1p (2.0 * rx / s) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (s, __imag__ x); + else + __imag__ res = __ieee754_atan2 (ix, s); + } + else + { + double onemix2 = (1.0 + ix) * (1.0 - ix); + double rx2 = rx * rx; + double f = rx2 * (2.0 + rx2 + 2.0 * ix * ix); + double d = __ieee754_sqrt (onemix2 * onemix2 + f); + double dp = d + onemix2; + double dm = f / dp; + double r1 = __ieee754_sqrt ((dp + rx2) / 2.0); + double r2 = rx * ix / r1; + + __real__ res + = __log1p (rx2 + dm + 2.0 * (rx * r1 + ix * r2)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (rx + r1, + __copysign (ix + r2, + __imag__ x)); + else + __imag__ res = __ieee754_atan2 (ix + r2, rx + r1); + } + } + else + { + double s = __ieee754_hypot (1.0, rx); + + __real__ res = __log1p (2.0 * rx * (rx + s)) / 2.0; + if (adj) + __imag__ res = __ieee754_atan2 (s, __imag__ x); + else + __imag__ res = __ieee754_atan2 (ix, s); + } + math_check_force_underflow_nonneg (__real__ res); + } + else + { + __real__ y = (rx - ix) * (rx + ix) + 1.0; + __imag__ y = 2.0 * rx * ix; + + y = __csqrt (y); + + __real__ y += rx; + __imag__ y += ix; + + if (adj) + { + double t = __real__ y; + __real__ y = __copysign (__imag__ y, __imag__ x); + __imag__ y = t; + } + + res = __clog (y); + } + + /* Give results the correct sign for the original argument. */ + __real__ res = __copysign (__real__ res, __real__ x); + __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x)); + + return res; +} diff --git a/math/s_casin_template.c b/math/s_casin_template.c new file mode 100644 index 0000000000..a37933b597 --- /dev/null +++ b/math/s_casin_template.c @@ -0,0 +1,66 @@ +/* Return arc sine of complex double value. + Copyright (C) 1997-2016 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <complex.h> +#include <math.h> +#include <math_private.h> + + +__complex__ double +__casin (__complex__ double x) +{ + __complex__ double res; + + if (isnan (__real__ x) || isnan (__imag__ x)) + { + if (__real__ x == 0.0) + { + res = x; + } + else if (isinf (__real__ x) || isinf (__imag__ x)) + { + __real__ res = __nan (""); + __imag__ res = __copysign (HUGE_VAL, __imag__ x); + } + else + { + __real__ res = __nan (""); + __imag__ res = __nan (""); + } + } + else + { + __complex__ double y; + + __real__ y = -__imag__ x; + __imag__ y = __real__ x; + + y = __casinh (y); + + __real__ res = __imag__ y; + __imag__ res = -__real__ y; + } + + return res; +} +weak_alias (__casin, casin) +#ifdef NO_LONG_DOUBLE +strong_alias (__casin, __casinl) +weak_alias (__casin, casinl) +#endif diff --git a/math/s_casinh_template.c b/math/s_casinh_template.c new file mode 100644 index 0000000000..32cbc13991 --- /dev/null +++ b/math/s_casinh_template.c @@ -0,0 +1,73 @@ +/* Return arc hyperbole sine for double value. + Copyright (C) 1997-2016 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <complex.h> +#include <math.h> +#include <math_private.h> + +__complex__ double +__casinh (__complex__ double x) +{ + __complex__ double res; + int rcls = fpclassify (__real__ x); + int icls = fpclassify (__imag__ x); + + if (rcls <= FP_INFINITE || icls <= FP_INFINITE) + { + if (icls == FP_INFINITE) + { + __real__ res = __copysign (HUGE_VAL, __real__ x); + + if (rcls == FP_NAN) + __imag__ res = __nan (""); + else + __imag__ res = __copysign (rcls >= FP_ZERO ? M_PI_2 : M_PI_4, + __imag__ x); + } + else if (rcls <= FP_INFINITE) + { + __real__ res = __real__ x; + if ((rcls == FP_INFINITE && icls >= FP_ZERO) + || (rcls == FP_NAN && icls == FP_ZERO)) + __imag__ res = __copysign (0.0, __imag__ x); + else + __imag__ res = __nan (""); + } + else + { + __real__ res = __nan (""); + __imag__ res = __nan (""); + } + } + else if (rcls == FP_ZERO && icls == FP_ZERO) + { + res = x; + } + else + { + res = __kernel_casinh (x, 0); + } + + return res; +} +weak_alias (__casinh, casinh) +#ifdef NO_LONG_DOUBLE +strong_alias (__casinh, __casinhl) +weak_alias (__casinh, casinhl) +#endif diff --git a/math/s_csin_template.c b/math/s_csin_template.c new file mode 100644 index 0000000000..e071aa650e --- /dev/null +++ b/math/s_csin_template.c @@ -0,0 +1,171 @@ +/* Complex sine function for double. + Copyright (C) 1997-2016 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <complex.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +__complex__ double +__csin (__complex__ double x) +{ + __complex__ double retval; + int negate = signbit (__real__ x); + int rcls = fpclassify (__real__ x); + int icls = fpclassify (__imag__ x); + + __real__ x = fabs (__real__ x); + + if (__glibc_likely (icls >= FP_ZERO)) + { + /* Imaginary part is finite. */ + if (__glibc_likely (rcls >= FP_ZERO)) + { + /* Real part is finite. */ + const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2); + double sinix, cosix; + + if (__glibc_likely (__real__ x > DBL_MIN)) + { + __sincos (__real__ x, &sinix, &cosix); + } + else + { + sinix = __real__ x; + cosix = 1.0; + } + + if (negate) + sinix = -sinix; + + if (fabs (__imag__ x) > t) + { + double exp_t = __ieee754_exp (t); + double ix = fabs (__imag__ x); + if (signbit (__imag__ x)) + cosix = -cosix; + ix -= t; + sinix *= exp_t / 2.0; + cosix *= exp_t / 2.0; + if (ix > t) + { + ix -= t; + sinix *= exp_t; + cosix *= exp_t; + } + if (ix > t) + { + /* Overflow (original imaginary part of x > 3t). */ + __real__ retval = DBL_MAX * sinix; + __imag__ retval = DBL_MAX * cosix; + } + else + { + double exp_val = __ieee754_exp (ix); + __real__ retval = exp_val * sinix; + __imag__ retval = exp_val * cosix; + } + } + else + { + __real__ retval = __ieee754_cosh (__imag__ x) * sinix; + __imag__ retval = __ieee754_sinh (__imag__ x) * cosix; + } + + math_check_force_underflow_complex (retval); + } + else + { + if (icls == FP_ZERO) + { + /* Imaginary part is 0.0. */ + __real__ retval = __nan (""); + __imag__ retval = __imag__ x; + + if (rcls == FP_INFINITE) + feraiseexcept (FE_INVALID); + } + else + { + __real__ retval = __nan (""); + __imag__ retval = __nan (""); + + feraiseexcept (FE_INVALID); + } + } + } + else if (icls == FP_INFINITE) + { + /* Imaginary part is infinite. */ + if (rcls == FP_ZERO) + { + /* Real part is 0.0. */ + __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0); + __imag__ retval = __imag__ x; + } + else if (rcls > FP_ZERO) + { + /* Real part is finite. */ + double sinix, cosix; + + if (__glibc_likely (__real__ x > DBL_MIN)) + { + __sincos (__real__ x, &sinix, &cosix); + } + else + { + sinix = __real__ x; + cosix = 1.0; + } + + __real__ retval = __copysign (HUGE_VAL, sinix); + __imag__ retval = __copysign (HUGE_VAL, cosix); + + if (negate) + __real__ retval = -__real__ retval; + if (signbit (__imag__ x)) + __imag__ retval = -__imag__ retval; + } + else + { + /* The addition raises the invalid exception. */ + __real__ retval = __nan (""); + __imag__ retval = HUGE_VAL; + + if (rcls == FP_INFINITE) + feraiseexcept (FE_INVALID); + } + } + else + { + if (rcls == FP_ZERO) + __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0); + else + __real__ retval = __nan (""); + __imag__ retval = __nan (""); + } + + return retval; +} +weak_alias (__csin, csin) +#ifdef NO_LONG_DOUBLE +strong_alias (__csin, __csinl) +weak_alias (__csin, csinl) +#endif diff --git a/math/s_csinh_template.c b/math/s_csinh_template.c new file mode 100644 index 0000000000..5fb60ed0cb --- /dev/null +++ b/math/s_csinh_template.c @@ -0,0 +1,166 @@ +/* Complex sine hyperbole function for double. + Copyright (C) 1997-2016 Free Software Foundation, Inc. + This file is part of the GNU C Library. + Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <complex.h> +#include <fenv.h> +#include <math.h> +#include <math_private.h> +#include <float.h> + +__complex__ double +__csinh (__complex__ double x) +{ + __complex__ double retval; + int negate = signbit (__real__ x); + int rcls = fpclassify (__real__ x); + int icls = fpclassify (__imag__ x); + + __real__ x = fabs (__real__ x); + + if (__glibc_likely (rcls >= FP_ZERO)) + { + /* Real part is finite. */ + if (__glibc_likely (icls >= FP_ZERO)) + { + /* Imaginary part is finite. */ + const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2); + double sinix, cosix; + + if (__glibc_likely (fabs (__imag__ x) > DBL_MIN)) + { + __sincos (__imag__ x, &sinix, &cosix); + } + else + { + sinix = __imag__ x; + cosix = 1.0; + } + + if (negate) + cosix = -cosix; + + if (fabs (__real__ x) > t) + { + double exp_t = __ieee754_exp (t); + double rx = fabs (__real__ x); + if (signbit (__real__ x)) + cosix = -cosix; + rx -= t; + sinix *= exp_t / 2.0; + cosix *= exp_t / 2.0; + if (rx > t) + { + rx -= t; + sinix *= exp_t; + cosix *= exp_t; + } + if (rx > t) + { + /* Overflow (original real part of x > 3t). */ + __real__ retval = DBL_MAX * cosix; + __imag__ retval = DBL_MAX * sinix; + } + else + { + double exp_val = __ieee754_exp (rx); + __real__ retval = exp_val * cosix; + __imag__ retval = exp_val * sinix; + } + } + else + { + __real__ retval = __ieee754_sinh (__real__ x) * cosix; + __imag__ retval = __ieee754_cosh (__real__ x) * sinix; + } + + math_check_force_underflow_complex (retval); + } + else + { + if (rcls == FP_ZERO) + { + /* Real part is 0.0. */ + __real__ retval = __copysign (0.0, negate ? -1.0 : 1.0); + __imag__ retval = __nan ("") + __nan (""); + + if (icls == FP_INFINITE) + feraiseexcept (FE_INVALID); + } + else + { + __real__ retval = __nan (""); + __imag__ retval = __nan (""); + + feraiseexcept (FE_INVALID); + } + } + } + else if (rcls == FP_INFINITE) + { + /* Real part is infinite. */ + if (__glibc_likely (icls > FP_ZERO)) + { + /* Imaginary part is finite. */ + double sinix, cosix; + + if (__glibc_likely (fabs (__imag__ x) > DBL_MIN)) + { + __sincos (__imag__ x, &sinix, &cosix); + } + else + { + sinix = __imag__ x; + cosix = 1.0; + } + + __real__ retval = __copysign (HUGE_VAL, cosix); + __imag__ retval = __copysign (HUGE_VAL, sinix); + + if (negate) + __real__ retval = -__real__ retval; + } + else if (icls == FP_ZERO) + { + /* Imaginary part is 0.0. */ + __real__ retval = negate ? -HUGE_VAL : HUGE_VAL; + __imag__ retval = __imag__ x; + } + else + { + /* The addition raises the invalid exception. */ + __real__ retval = HUGE_VAL; + __imag__ retval = __nan ("") + __nan (""); + + if (icls == FP_INFINITE) + feraiseexcept (FE_INVALID); + } + } + else + { + __real__ retval = __nan (""); + __imag__ retval = __imag__ x == 0.0 ? __imag__ x : __nan (""); + } + + return retval; +} +weak_alias (__csinh, csinh) +#ifdef NO_LONG_DOUBLE +strong_alias (__csinh, __csinhl) +weak_alias (__csinh, csinhl) +#endif |