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-rw-r--r--math/k_casinh_template.c210
-rw-r--r--math/s_casin_template.c66
-rw-r--r--math/s_casinh_template.c73
-rw-r--r--math/s_csin_template.c171
-rw-r--r--math/s_csinh_template.c166
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
generated by cgit v1.2.3 (git 2.25.1) at 2024-11-18 11:53:29 +0000