diff options
| author | Rich Felker <dalias@aerifal.cx> | 2012-03-13 01:17:53 -0400 |
|---|---|---|
| committer | Rich Felker <dalias@aerifal.cx> | 2012-03-13 01:17:53 -0400 |
| commit | b69f695acedd4ce2798ef9ea28d834ceccc789bd (patch) | |
| tree | eafd98b9b75160210f3295ac074d699f863d958e /src/complex | |
| parent | d46cf2e14cc4df7cc75e77d7009fcb6df1f48a33 (diff) | |
| download | musl-b69f695acedd4ce2798ef9ea28d834ceccc789bd.tar.gz | |
first commit of the new libm!
thanks to the hard work of Szabolcs Nagy (nsz), identifying the best
(from correctness and license standpoint) implementations from freebsd
and openbsd and cleaning them up! musl should now fully support c99
float and long double math functions, and has near-complete complex
math support. tgmath should also work (fully on gcc-compatible
compilers, and mostly on any c99 compiler).
based largely on commit 0376d44a890fea261506f1fc63833e7a686dca19 from
nsz's libm git repo, with some additions (dummy versions of a few
missing long double complex functions, etc.) by me.
various cleanups still need to be made, including re-adding (if
they're correct) some asm functions that were dropped.
Diffstat (limited to 'src/complex')
68 files changed, 2024 insertions, 0 deletions
diff --git a/src/complex/__cexp.c b/src/complex/__cexp.c new file mode 100644 index 00000000..f603e2be --- /dev/null +++ b/src/complex/__cexp.c @@ -0,0 +1,87 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/k_exp.c */ +/*- + * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "libm.h" + +static const uint32_t k = 1799; /* constant for reduction */ +static const double kln2 = 1246.97177782734161156; /* k * ln2 */ + +/* + * Compute exp(x), scaled to avoid spurious overflow. An exponent is + * returned separately in 'expt'. + * + * Input: ln(DBL_MAX) <= x < ln(2 * DBL_MAX / DBL_MIN_DENORM) ~= 1454.91 + * Output: 2**1023 <= y < 2**1024 + */ +static double __frexp_exp(double x, int *expt) +{ + double exp_x; + uint32_t hx; + + /* + * We use exp(x) = exp(x - kln2) * 2**k, carefully chosen to + * minimize |exp(kln2) - 2**k|. We also scale the exponent of + * exp_x to MAX_EXP so that the result can be multiplied by + * a tiny number without losing accuracy due to denormalization. + */ + exp_x = exp(x - kln2); + GET_HIGH_WORD(hx, exp_x); + *expt = (hx >> 20) - (0x3ff + 1023) + k; + SET_HIGH_WORD(exp_x, (hx & 0xfffff) | ((0x3ff + 1023) << 20)); + return exp_x; +} + +/* + * __ldexp_cexp(x, expt) compute exp(x) * 2**expt. + * It is intended for large arguments (real part >= ln(DBL_MAX)) + * where care is needed to avoid overflow. + * + * The present implementation is narrowly tailored for our hyperbolic and + * exponential functions. We assume expt is small (0 or -1), and the caller + * has filtered out very large x, for which overflow would be inevitable. + */ +double complex __ldexp_cexp(double complex z, int expt) +{ + double x, y, exp_x, scale1, scale2; + int ex_expt, half_expt; + + x = creal(z); + y = cimag(z); + exp_x = __frexp_exp(x, &ex_expt); + expt += ex_expt; + + /* + * Arrange so that scale1 * scale2 == 2**expt. We use this to + * compensate for scalbn being horrendously slow. + */ + half_expt = expt / 2; + INSERT_WORDS(scale1, (0x3ff + half_expt) << 20, 0); + half_expt = expt - half_expt; + INSERT_WORDS(scale2, (0x3ff + half_expt) << 20, 0); + + return cpack(cos(y) * exp_x * scale1 * scale2, sin(y) * exp_x * scale1 * scale2); +} diff --git a/src/complex/__cexpf.c b/src/complex/__cexpf.c new file mode 100644 index 00000000..47168e8f --- /dev/null +++ b/src/complex/__cexpf.c @@ -0,0 +1,68 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/k_expf.c */ +/*- + * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "libm.h" + +static const uint32_t k = 235; /* constant for reduction */ +static const float kln2 = 162.88958740F; /* k * ln2 */ + +/* + * See __cexp.c for details. + * + * Input: ln(FLT_MAX) <= x < ln(2 * FLT_MAX / FLT_MIN_DENORM) ~= 192.7 + * Output: 2**127 <= y < 2**128 + */ +static float __frexp_expf(float x, int *expt) +{ + float exp_x; + uint32_t hx; + + exp_x = expf(x - kln2); + GET_FLOAT_WORD(hx, exp_x); + *expt = (hx >> 23) - (0x7f + 127) + k; + SET_FLOAT_WORD(exp_x, (hx & 0x7fffff) | ((0x7f + 127) << 23)); + return exp_x; +} + +float complex __ldexp_cexpf(float complex z, int expt) +{ + float x, y, exp_x, scale1, scale2; + int ex_expt, half_expt; + + x = crealf(z); + y = cimagf(z); + exp_x = __frexp_expf(x, &ex_expt); + expt += ex_expt; + + half_expt = expt / 2; + SET_FLOAT_WORD(scale1, (0x7f + half_expt) << 23); + half_expt = expt - half_expt; + SET_FLOAT_WORD(scale2, (0x7f + half_expt) << 23); + + return cpackf(cosf(y) * exp_x * scale1 * scale2, + sinf(y) * exp_x * scale1 * scale2); +} diff --git a/src/complex/cabs.c b/src/complex/cabs.c new file mode 100644 index 00000000..f61d364e --- /dev/null +++ b/src/complex/cabs.c @@ -0,0 +1,6 @@ +#include "libm.h" + +double cabs(double complex z) +{ + return hypot(creal(z), cimag(z)); +} diff --git a/src/complex/cabsf.c b/src/complex/cabsf.c new file mode 100644 index 00000000..30b25c70 --- /dev/null +++ b/src/complex/cabsf.c @@ -0,0 +1,6 @@ +#include "libm.h" + +float cabsf(float complex z) +{ + return hypotf(crealf(z), cimagf(z)); +} diff --git a/src/complex/cabsl.c b/src/complex/cabsl.c new file mode 100644 index 00000000..40a067c1 --- /dev/null +++ b/src/complex/cabsl.c @@ -0,0 +1,13 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double cabsl(long double complex z) +{ + return cabs(z); +} +#else +long double cabsl(long double complex z) +{ + return hypotl(creall(z), cimagl(z)); +} +#endif diff --git a/src/complex/cacos.c b/src/complex/cacos.c new file mode 100644 index 00000000..3aca0519 --- /dev/null +++ b/src/complex/cacos.c @@ -0,0 +1,11 @@ +#include "libm.h" + +// FIXME: Hull et al. "Implementing the complex arcsine and arccosine functions using exception handling" 1997 + +/* acos(z) = pi/2 - asin(z) */ + +double complex cacos(double complex z) +{ + z = casin(z); + return cpack(M_PI_2 - creal(z), -cimag(z)); +} diff --git a/src/complex/cacosf.c b/src/complex/cacosf.c new file mode 100644 index 00000000..563766e7 --- /dev/null +++ b/src/complex/cacosf.c @@ -0,0 +1,9 @@ +#include "libm.h" + +// FIXME + +float complex cacosf(float complex z) +{ + z = casinf(z); + return cpackf((float)M_PI_2 - crealf(z), -cimagf(z)); +} diff --git a/src/complex/cacosh.c b/src/complex/cacosh.c new file mode 100644 index 00000000..c2dfc1ba --- /dev/null +++ b/src/complex/cacosh.c @@ -0,0 +1,9 @@ +#include "libm.h" + +/* acosh(z) = i acos(z) */ + +double complex cacosh(double complex z) +{ + z = cacos(z); + return cpack(-cimag(z), creal(z)); +} diff --git a/src/complex/cacoshf.c b/src/complex/cacoshf.c new file mode 100644 index 00000000..37ff8800 --- /dev/null +++ b/src/complex/cacoshf.c @@ -0,0 +1,7 @@ +#include "libm.h" + +float complex cacoshf(float complex z) +{ + z = cacosf(z); + return cpackf(-cimagf(z), crealf(z)); +} diff --git a/src/complex/cacoshl.c b/src/complex/cacoshl.c new file mode 100644 index 00000000..2a04e27b --- /dev/null +++ b/src/complex/cacoshl.c @@ -0,0 +1,14 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex cacoshl(long double complex z) +{ + return cacosh(z); +} +#else +long double complex cacoshl(long double complex z) +{ + z = cacosl(z); + return cpackl(-cimagl(z), creall(z)); +} +#endif diff --git a/src/complex/cacosl.c b/src/complex/cacosl.c new file mode 100644 index 00000000..5992e056 --- /dev/null +++ b/src/complex/cacosl.c @@ -0,0 +1,16 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex cacosl(long double complex z) +{ + return cacos(z); +} +#else +// FIXME +#define PI_2 1.57079632679489661923132169163975144L +long double complex cacosl(long double complex z) +{ + z = casinl(z); + return cpackl(PI_2 - creall(z), -cimagl(z)); +} +#endif diff --git a/src/complex/carg.c b/src/complex/carg.c new file mode 100644 index 00000000..d2d1b462 --- /dev/null +++ b/src/complex/carg.c @@ -0,0 +1,6 @@ +#include "libm.h" + +double carg(double complex z) +{ + return atan2(cimag(z), creal(z)); +} diff --git a/src/complex/cargf.c b/src/complex/cargf.c new file mode 100644 index 00000000..ce183c4b --- /dev/null +++ b/src/complex/cargf.c @@ -0,0 +1,6 @@ +#include "libm.h" + +float cargf(float complex z) +{ + return atan2f(cimagf(z), crealf(z)); +} diff --git a/src/complex/cargl.c b/src/complex/cargl.c new file mode 100644 index 00000000..e0d50478 --- /dev/null +++ b/src/complex/cargl.c @@ -0,0 +1,13 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double cargl(long double complex z) +{ + return carg(z); +} +#else +long double cargl(long double complex z) +{ + return atan2l(cimagl(z), creall(z)); +} +#endif diff --git a/src/complex/casin.c b/src/complex/casin.c new file mode 100644 index 00000000..79aff278 --- /dev/null +++ b/src/complex/casin.c @@ -0,0 +1,16 @@ +#include "libm.h" + +// FIXME + +/* asin(z) = -i log(i z + sqrt(1 - z*z)) */ + +double complex casin(double complex z) +{ + double complex w; + double x, y; + + x = creal(z); + y = cimag(z); + w = cpack(1.0 - (x - y)*(x + y), -2.0*x*y); + return clog(cpack(-y, x) + csqrt(w)); +} diff --git a/src/complex/casinf.c b/src/complex/casinf.c new file mode 100644 index 00000000..cb9863f6 --- /dev/null +++ b/src/complex/casinf.c @@ -0,0 +1,14 @@ +#include "libm.h" + +// FIXME + +float complex casinf(float complex z) +{ + float complex w; + float x, y; + + x = crealf(z); + y = cimagf(z); + w = cpackf(1.0 - (x - y)*(x + y), -2.0*x*y); + return clogf(cpackf(-y, x) + csqrtf(w)); +} diff --git a/src/complex/casinh.c b/src/complex/casinh.c new file mode 100644 index 00000000..f2b3fef8 --- /dev/null +++ b/src/complex/casinh.c @@ -0,0 +1,9 @@ +#include "libm.h" + +/* asinh(z) = -i asin(i z) */ + +double complex casinh(double complex z) +{ + z = casin(cpack(-cimag(z), creal(z))); + return cpack(cimag(z), -creal(z)); +} diff --git a/src/complex/casinhf.c b/src/complex/casinhf.c new file mode 100644 index 00000000..ed4af643 --- /dev/null +++ b/src/complex/casinhf.c @@ -0,0 +1,7 @@ +#include "libm.h" + +float complex casinhf(float complex z) +{ + z = casinf(cpackf(-cimagf(z), crealf(z))); + return cpackf(cimagf(z), -crealf(z)); +} diff --git a/src/complex/casinhl.c b/src/complex/casinhl.c new file mode 100644 index 00000000..e5d80cef --- /dev/null +++ b/src/complex/casinhl.c @@ -0,0 +1,14 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex casinhl(long double complex z) +{ + return casinh(z); +} +#else +long double complex casinhl(long double complex z) +{ + z = casinl(cpackl(-cimagl(z), creall(z))); + return cpackl(cimagl(z), -creall(z)); +} +#endif diff --git a/src/complex/casinl.c b/src/complex/casinl.c new file mode 100644 index 00000000..f9aa8ded --- /dev/null +++ b/src/complex/casinl.c @@ -0,0 +1,20 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex casinl(long double complex z) +{ + return casin(z); +} +#else +// FIXME +long double complex casinl(long double complex z) +{ + long double complex w; + long double x, y; + + x = creall(z); + y = cimagl(z); + w = cpackl(1.0 - (x - y)*(x + y), -2.0*x*y); + return clogl(cpackl(-y, x) + csqrtl(w)); +} +#endif diff --git a/src/complex/catan.c b/src/complex/catan.c new file mode 100644 index 00000000..39ce6cf2 --- /dev/null +++ b/src/complex/catan.c @@ -0,0 +1,119 @@ +/* origin: OpenBSD /usr/src/lib/libm/src/s_catan.c */ +/* + * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ +/* + * Complex circular arc tangent + * + * + * SYNOPSIS: + * + * double complex catan(); + * double complex z, w; + * + * w = catan (z); + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * catan(z) = -i catanh(iz). + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5900 1.3e-16 7.8e-18 + * IEEE -10,+10 30000 2.3e-15 8.5e-17 + * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, + * had peak relative error 1.5e-16, rms relative error + * 2.9e-17. See also clog(). + */ + +#include "libm.h" + +#define MAXNUM 1.0e308 + +static const double DP1 = 3.14159265160560607910E0; +static const double DP2 = 1.98418714791870343106E-9; +static const double DP3 = 1.14423774522196636802E-17; + +static double _redupi(double x) +{ + double t; + long i; + + t = x/M_PI; + if (t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +double complex catan(double complex z) +{ + double complex w; + double a, t, x, x2, y; + + x = creal(z); + y = cimag(z); + + if (x == 0.0 && y > 1.0) + goto ovrf; + + x2 = x * x; + a = 1.0 - x2 - (y * y); + if (a == 0.0) + goto ovrf; + + t = 0.5 * atan2(2.0 * x, a); + w = _redupi(t); + + t = y - 1.0; + a = x2 + (t * t); + if (a == 0.0) + goto ovrf; + + t = y + 1.0; + a = (x2 + t * t)/a; + w = w + (0.25 * log(a)) * I; + return w; + +ovrf: + // FIXME + w = MAXNUM + MAXNUM * I; + return w; +} diff --git a/src/complex/catanf.c b/src/complex/catanf.c new file mode 100644 index 00000000..8533bde3 --- /dev/null +++ b/src/complex/catanf.c @@ -0,0 +1,115 @@ +/* origin: OpenBSD /usr/src/lib/libm/src/s_catanf.c */ +/* + * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ +/* + * Complex circular arc tangent + * + * + * SYNOPSIS: + * + * float complex catanf(); + * float complex z, w; + * + * w = catanf( z ); + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -10,+10 30000 2.3e-6 5.2e-8 + */ + +#include "libm.h" + +#define MAXNUMF 1.0e38F + +static const double DP1 = 3.140625; +static const double DP2 = 9.67502593994140625E-4; +static const double DP3 = 1.509957990978376432E-7; + +static float _redupif(float xx) +{ + float x, t; + long i; + + x = xx; + t = x/(float)M_PI; + if (t >= 0.0f) + t += 0.5f; + else + t -= 0.5f; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +float complex catanf(float complex z) +{ + float complex w; + float a, t, x, x2, y; + + x = crealf(z); + y = cimagf(z); + + if ((x == 0.0f) && (y > 1.0f)) + goto ovrf; + + x2 = x * x; + a = 1.0f - x2 - (y * y); + if (a == 0.0f) + goto ovrf; + + t = 0.5f * atan2f(2.0f * x, a); + w = _redupif(t); + + t = y - 1.0f; + a = x2 + (t * t); + if (a == 0.0f) + goto ovrf; + + t = y + 1.0f; + a = (x2 + (t * t))/a; + w = w + (0.25f * logf (a)) * I; + return w; + +ovrf: + // FIXME + w = MAXNUMF + MAXNUMF * I; + return w; +} diff --git a/src/complex/catanh.c b/src/complex/catanh.c new file mode 100644 index 00000000..b1628022 --- /dev/null +++ b/src/complex/catanh.c @@ -0,0 +1,9 @@ +#include "libm.h" + +/* atanh = -i atan(i z) */ + +double complex catanh(double complex z) +{ + z = catan(cpack(-cimag(z), creal(z))); + return cpack(cimag(z), -creal(z)); +} diff --git a/src/complex/catanhf.c b/src/complex/catanhf.c new file mode 100644 index 00000000..e1d1e648 --- /dev/null +++ b/src/complex/catanhf.c @@ -0,0 +1,7 @@ +#include "libm.h" + +float complex catanhf(float complex z) +{ + z = catanf(cpackf(-cimagf(z), crealf(z))); + return cpackf(cimagf(z), -crealf(z)); +} diff --git a/src/complex/catanhl.c b/src/complex/catanhl.c new file mode 100644 index 00000000..0a9374a3 --- /dev/null +++ b/src/complex/catanhl.c @@ -0,0 +1,14 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex catanhl(long double complex z) +{ + return catanh(z); +} +#else +long double complex catanhl(long double complex z) +{ + z = catanl(cpackl(-cimagl(z), creall(z))); + return cpackl(cimagl(z), -creall(z)); +} +#endif diff --git a/src/complex/catanl.c b/src/complex/catanl.c new file mode 100644 index 00000000..5ace7704 --- /dev/null +++ b/src/complex/catanl.c @@ -0,0 +1,126 @@ +/* origin: OpenBSD /usr/src/lib/libm/src/s_catanl.c */ +/* + * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> + * + * Permission to use, copy, modify, and distribute this software for any + * purpose with or without fee is hereby granted, provided that the above + * copyright notice and this permission notice appear in all copies. + * + * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + */ +/* + * Complex circular arc tangent + * + * + * SYNOPSIS: + * + * long double complex catanl(); + * long double complex z, w; + * + * w = catanl( z ); + * + * + * DESCRIPTION: + * + * If + * z = x + iy, + * + * then + * 1 ( 2x ) + * Re w = - arctan(-----------) + k PI + * 2 ( 2 2) + * (1 - x - y ) + * + * ( 2 2) + * 1 (x + (y+1) ) + * Im w = - log(------------) + * 4 ( 2 2) + * (x + (y-1) ) + * + * Where k is an arbitrary integer. + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * DEC -10,+10 5900 1.3e-16 7.8e-18 + * IEEE -10,+10 30000 2.3e-15 8.5e-17 + * The check catan( ctan(z) ) = z, with |x| and |y| < PI/2, + * had peak relative error 1.5e-16, rms relative error + * 2.9e-17. See also clog(). + */ + +#include <complex.h> +#include <float.h> +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex catanl(long double complex z) +{ + return catan(z); +} +#else +static const long double PIL = 3.141592653589793238462643383279502884197169L; +static const long double DP1 = 3.14159265358979323829596852490908531763125L; +static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; +static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; + +static long double redupil(long double x) +{ + long double t; + long i; + + t = x / PIL; + if (t >= 0.0L) + t += 0.5L; + else + t -= 0.5L; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +long double complex catanl(long double complex z) +{ + long double complex w; + long double a, t, x, x2, y; + + x = creall(z); + y = cimagl(z); + + if ((x == 0.0L) && (y > 1.0L)) + goto ovrf; + + x2 = x * x; + a = 1.0L - x2 - (y * y); + if (a == 0.0L) + goto ovrf; + + t = atan2l(2.0L * x, a) * 0.5L; + w = redupil(t); + + t = y - 1.0L; + a = x2 + (t * t); + if (a == 0.0L) + goto ovrf; + + t = y + 1.0L; + a = (x2 + (t * t)) / a; + w = w + (0.25L * logl(a)) * I; + return w; + +ovrf: + // FIXME + w = LDBL_MAX + LDBL_MAX * I; + return w; +} +#endif diff --git a/src/complex/ccos.c b/src/complex/ccos.c new file mode 100644 index 00000000..5754c238 --- /dev/null +++ b/src/complex/ccos.c @@ -0,0 +1,8 @@ +#include "libm.h" + +/* cos(z) = cosh(i z) */ + +double complex ccos(double complex z) +{ + return ccosh(cpack(-cimag(z), creal(z))); +} diff --git a/src/complex/ccosf.c b/src/complex/ccosf.c new file mode 100644 index 00000000..9b72c4f4 --- /dev/null +++ b/src/complex/ccosf.c @@ -0,0 +1,6 @@ +#include "libm.h" + +float complex ccosf(float complex z) +{ + return ccoshf(cpackf(-cimagf(z), crealf(z))); +} diff --git a/src/complex/ccosh.c b/src/complex/ccosh.c new file mode 100644 index 00000000..81f29432 --- /dev/null +++ b/src/complex/ccosh.c @@ -0,0 +1,140 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_ccosh.c */ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +/* + * Hyperbolic cosine of a complex argument z = x + i y. + * + * cosh(z) = cosh(x+iy) + * = cosh(x) cos(y) + i sinh(x) sin(y). + * + * Exceptional values are noted in the comments within the source code. + * These values and the return value were taken from n1124.pdf. + */ + +#include "libm.h" + +static const double huge = 0x1p1023; + +double complex ccosh(double complex z) +{ + double x, y, h; + int32_t hx, hy, ix, iy, lx, ly; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hx, lx, x); + EXTRACT_WORDS(hy, ly, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + /* Handle the nearly-non-exceptional cases where x and y are finite. */ + if (ix < 0x7ff00000 && iy < 0x7ff00000) { + if ((iy | ly) == 0) + return cpack(cosh(x), x * y); + if (ix < 0x40360000) /* small x: normal case */ + return cpack(cosh(x) * cos(y), sinh(x) * sin(y)); + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (ix < 0x40862e42) { + /* x < 710: exp(|x|) won't overflow */ + h = exp(fabs(x)) * 0.5; + return cpack(h * cos(y), copysign(h, x) * sin(y)); + } else if (ix < 0x4096bbaa) { + /* x < 1455: scale to avoid overflow */ + z = __ldexp_cexp(cpack(fabs(x), y), -1); + return cpack(creal(z), cimag(z) * copysign(1, x)); + } else { + /* x >= 1455: the result always overflows */ + h = huge * x; + return cpack(h * h * cos(y), h * sin(y)); + } + } + + /* + * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as dNaN. Raise the invalid floating-point exception. + * + * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as d(NaN). + */ + if ((ix | lx) == 0 && iy >= 0x7ff00000) + return cpack(y - y, copysign(0, x * (y - y))); + + /* + * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0. + * + * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0. + * The sign of 0 in the result is unspecified. + */ + if ((iy | ly) == 0 && ix >= 0x7ff00000) { + if (((hx & 0xfffff) | lx) == 0) + return cpack(x * x, copysign(0, x) * y); + return cpack(x * x, copysign(0, (x + x) * y)); + } + + /* + * cosh(x +- I Inf) = dNaN + I dNaN. + * Raise the invalid floating-point exception for finite nonzero x. + * + * cosh(x + I NaN) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero x. Choice = don't raise (except for signaling NaNs). + */ + if (ix < 0x7ff00000 && iy >= 0x7ff00000) + return cpack(y - y, x * (y - y)); + + /* + * cosh(+-Inf + I NaN) = +Inf + I d(NaN). + * + * cosh(+-Inf +- I Inf) = +Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = always +. + * Raise the invalid floating-point exception. + * + * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y) + */ + if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (iy >= 0x7ff00000) + return cpack(x * x, x * (y - y)); + return cpack((x * x) * cos(y), x * sin(y)); + } + + /* + * cosh(NaN + I NaN) = d(NaN) + I d(NaN). + * + * cosh(NaN +- I Inf) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception. + * Choice = raise. + * + * cosh(NaN + I y) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero y. Choice = don't raise (except for signaling NaNs). + */ + return cpack((x * x) * (y - y), (x + x) * (y - y)); +} diff --git a/src/complex/ccoshf.c b/src/complex/ccoshf.c new file mode 100644 index 00000000..683e77fa --- /dev/null +++ b/src/complex/ccoshf.c @@ -0,0 +1,90 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_ccoshf.c */ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +/* + * Hyperbolic cosine of a complex argument. See s_ccosh.c for details. + */ + +#include "libm.h" + +static const float huge = 0x1p127; + +float complex ccoshf(float complex z) +{ + float x, y, h; + int32_t hx, hy, ix, iy; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hx, x); + GET_FLOAT_WORD(hy, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + if (ix < 0x7f800000 && iy < 0x7f800000) { + if (iy == 0) + return cpackf(coshf(x), x * y); + if (ix < 0x41100000) /* small x: normal case */ + return cpackf(coshf(x) * cosf(y), sinhf(x) * sinf(y)); + + /* |x| >= 9, so cosh(x) ~= exp(|x|) */ + if (ix < 0x42b17218) { + /* x < 88.7: expf(|x|) won't overflow */ + h = expf(fabsf(x)) * 0.5f; + return cpackf(h * cosf(y), copysignf(h, x) * sinf(y)); + } else if (ix < 0x4340b1e7) { + /* x < 192.7: scale to avoid overflow */ + z = __ldexp_cexpf(cpackf(fabsf(x), y), -1); + return cpackf(crealf(z), cimagf(z) * copysignf(1, x)); + } else { + /* x >= 192.7: the result always overflows */ + h = huge * x; + return cpackf(h * h * cosf(y), h * sinf(y)); + } + } + + if (ix == 0 && iy >= 0x7f800000) + return cpackf(y - y, copysignf(0, x * (y - y))); + + if (iy == 0 && ix >= 0x7f800000) { + if ((hx & 0x7fffff) == 0) + return cpackf(x * x, copysignf(0, x) * y); + return cpackf(x * x, copysignf(0, (x + x) * y)); + } + + if (ix < 0x7f800000 && iy >= 0x7f800000) + return cpackf(y - y, x * (y - y)); + + if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (iy >= 0x7f800000) + return cpackf(x * x, x * (y - y)); + return cpackf((x * x) * cosf(y), x * sinf(y)); + } + + return cpackf((x * x) * (y - y), (x + x) * (y - y)); +} diff --git a/src/complex/ccoshl.c b/src/complex/ccoshl.c new file mode 100644 index 00000000..9b2aed9e --- /dev/null +++ b/src/complex/ccoshl.c @@ -0,0 +1,7 @@ +#include "libm.h" + +//FIXME +long double complex ccoshl(long double complex z) +{ + return ccosh(z); +} diff --git a/src/complex/ccosl.c b/src/complex/ccosl.c new file mode 100644 index 00000000..e37825a9 --- /dev/null +++ b/src/complex/ccosl.c @@ -0,0 +1,13 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex ccosl(long double complex z) +{ + return ccos(z); +} +#else +long double complex ccosl(long double complex z) +{ + return ccoshl(cpackl(-cimagl(z), creall(z))); +} +#endif diff --git a/src/complex/cexp.c b/src/complex/cexp.c new file mode 100644 index 00000000..3b8bb752 --- /dev/null +++ b/src/complex/cexp.c @@ -0,0 +1,83 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_cexp.c */ +/*- + * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "libm.h" + +static const uint32_t +exp_ovfl = 0x40862e42, /* high bits of MAX_EXP * ln2 ~= 710 */ +cexp_ovfl = 0x4096b8e4; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ + +double complex cexp(double complex z) +{ + double x, y, exp_x; + uint32_t hx, hy, lx, ly; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hy, ly, y); + hy &= 0x7fffffff; + + /* cexp(x + I 0) = exp(x) + I 0 */ + if ((hy | ly) == 0) + return cpack(exp(x), y); + EXTRACT_WORDS(hx, lx, x); + /* cexp(0 + I y) = cos(y) + I sin(y) */ + if (((hx & 0x7fffffff) | lx) == 0) + return cpack(cos(y), sin(y)); + + if (hy >= 0x7ff00000) { + if (lx != 0 || (hx & 0x7fffffff) != 0x7ff00000) { + /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ + return cpack(y - y, y - y); + } else if (hx & 0x80000000) { + /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ + return cpack(0.0, 0.0); + } else { + /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ + return cpack(x, y - y); + } + } + + if (hx >= exp_ovfl && hx <= cexp_ovfl) { + /* + * x is between 709.7 and 1454.3, so we must scale to avoid + * overflow in exp(x). + */ + return __ldexp_cexp(z, 0); + } else { + /* + * Cases covered here: + * - x < exp_ovfl and exp(x) won't overflow (common case) + * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 + * - x = +-Inf (generated by exp()) + * - x = NaN (spurious inexact exception from y) + */ + exp_x = exp(x); + return cpack(exp_x * cos(y), exp_x * sin(y)); + } +} diff --git a/src/complex/cexpf.c b/src/complex/cexpf.c new file mode 100644 index 00000000..0cf13a3d --- /dev/null +++ b/src/complex/cexpf.c @@ -0,0 +1,83 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_cexpf.c */ +/*- + * Copyright (c) 2011 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "libm.h" + +static const uint32_t +exp_ovfl = 0x42b17218, /* MAX_EXP * ln2 ~= 88.722839355 */ +cexp_ovfl = 0x43400074; /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */ + +float complex cexpf(float complex z) +{ + float x, y, exp_x; + uint32_t hx, hy; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hy, y); + hy &= 0x7fffffff; + + /* cexp(x + I 0) = exp(x) + I 0 */ + if (hy == 0) + return cpackf(expf(x), y); + GET_FLOAT_WORD(hx, x); + /* cexp(0 + I y) = cos(y) + I sin(y) */ + if ((hx & 0x7fffffff) == 0) + return cpackf(cosf(y), sinf(y)); + + if (hy >= 0x7f800000) { + if ((hx & 0x7fffffff) != 0x7f800000) { + /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */ + return cpackf(y - y, y - y); + } else if (hx & 0x80000000) { + /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */ + return cpackf(0.0, 0.0); + } else { + /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */ + return cpackf(x, y - y); + } + } + + if (hx >= exp_ovfl && hx <= cexp_ovfl) { + /* + * x is between 88.7 and 192, so we must scale to avoid + * overflow in expf(x). + */ + return __ldexp_cexpf(z, 0); + } else { + /* + * Cases covered here: + * - x < exp_ovfl and exp(x) won't overflow (common case) + * - x > cexp_ovfl, so exp(x) * s overflows for all s > 0 + * - x = +-Inf (generated by exp()) + * - x = NaN (spurious inexact exception from y) + */ + exp_x = expf(x); + return cpackf(exp_x * cosf(y), exp_x * sinf(y)); + } +} diff --git a/src/complex/cexpl.c b/src/complex/cexpl.c new file mode 100644 index 00000000..a27f85c0 --- /dev/null +++ b/src/complex/cexpl.c @@ -0,0 +1,7 @@ +#include "libm.h" + +//FIXME +long double complex cexpl(long double complex z) +{ + return cexp(z); +} diff --git a/src/complex/cimag.c b/src/complex/cimag.c new file mode 100644 index 00000000..5e1ad46b --- /dev/null +++ b/src/complex/cimag.c @@ -0,0 +1,7 @@ +#include "libm.h" + +double (cimag)(double complex z) +{ + union dcomplex u = {z}; + return u.a[1]; +} diff --git a/src/complex/cimagf.c b/src/complex/cimagf.c new file mode 100644 index 00000000..99fffc58 --- /dev/null +++ b/src/complex/cimagf.c @@ -0,0 +1,7 @@ +#include "libm.h" + +float (cimagf)(float complex z) +{ + union fcomplex u = {z}; + return u.a[1]; +} diff --git a/src/complex/cimagl.c b/src/complex/cimagl.c new file mode 100644 index 00000000..d9a0780c --- /dev/null +++ b/src/complex/cimagl.c @@ -0,0 +1,7 @@ +#include "libm.h" + +long double (cimagl)(long double complex z) +{ + union lcomplex u = {z}; + return u.a[1]; +} diff --git a/src/complex/clog.c b/src/complex/clog.c new file mode 100644 index 00000000..6f10a115 --- /dev/null +++ b/src/complex/clog.c @@ -0,0 +1,14 @@ +#include "libm.h" + +// FIXME + +/* log(z) = log(|z|) + i arg(z) */ + +double complex clog(double complex z) +{ + double r, phi; + + r = cabs(z); + phi = carg(z); + return cpack(log(r), phi); +} diff --git a/src/complex/clogf.c b/src/complex/clogf.c new file mode 100644 index 00000000..f3aec54d --- /dev/null +++ b/src/complex/clogf.c @@ -0,0 +1,12 @@ +#include "libm.h" + +// FIXME + +float complex clogf(float complex z) +{ + float r, phi; + + r = cabsf(z); + phi = cargf(z); + return cpackf(logf(r), phi); +} diff --git a/src/complex/clogl.c b/src/complex/clogl.c new file mode 100644 index 00000000..5b84ba59 --- /dev/null +++ b/src/complex/clogl.c @@ -0,0 +1,18 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex clogl(long double complex z) +{ + return clog(z); +} +#else +// FIXME +long double complex clogl(long double complex z) +{ + long double r, phi; + + r = cabsl(z); + phi = cargl(z); + return cpackl(logl(r), phi); +} +#endif diff --git a/src/complex/conj.c b/src/complex/conj.c new file mode 100644 index 00000000..4aceea7b --- /dev/null +++ b/src/complex/conj.c @@ -0,0 +1,6 @@ +#include "libm.h" + +double complex conj(double complex z) +{ + return cpack(creal(z), -cimag(z)); +} diff --git a/src/complex/conjf.c b/src/complex/conjf.c new file mode 100644 index 00000000..31556800 --- /dev/null +++ b/src/complex/conjf.c @@ -0,0 +1,6 @@ +#include "libm.h" + +float complex conjf(float complex z) +{ + return cpackf(crealf(z), -cimagf(z)); +} diff --git a/src/complex/conjl.c b/src/complex/conjl.c new file mode 100644 index 00000000..01332262 --- /dev/null +++ b/src/complex/conjl.c @@ -0,0 +1,6 @@ +#include "libm.h" + +long double complex conjl(long double complex z) +{ + return cpackl(creall(z), -cimagl(z)); +} diff --git a/src/complex/cpow.c b/src/complex/cpow.c new file mode 100644 index 00000000..f863588f --- /dev/null +++ b/src/complex/cpow.c @@ -0,0 +1,8 @@ +#include "libm.h" + +/* pow(z, c) = exp(c log(z)), See C99 G.6.4.1 */ + +double complex cpow(double complex z, double complex c) +{ + return cexp(c * clog(z)); +} diff --git a/src/complex/cpowf.c b/src/complex/cpowf.c new file mode 100644 index 00000000..53c65dcb --- /dev/null +++ b/src/complex/cpowf.c @@ -0,0 +1,6 @@ +#include "libm.h" + +float complex cpowf(float complex z, float complex c) +{ + return cexpf(c * clogf(z)); +} diff --git a/src/complex/cpowl.c b/src/complex/cpowl.c new file mode 100644 index 00000000..c1a80a7b --- /dev/null +++ b/src/complex/cpowl.c @@ -0,0 +1,13 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex cpowl(long double complex z, long double complex c) +{ + return cpow(z, c); +} +#else +long double complex cpowl(long double complex z, long double complex c) +{ + return cexpl(c * clogl(z)); +} +#endif diff --git a/src/complex/cproj.c b/src/complex/cproj.c new file mode 100644 index 00000000..1cf9bb94 --- /dev/null +++ b/src/complex/cproj.c @@ -0,0 +1,8 @@ +#include "libm.h" + +double complex cproj(double complex z) +{ + if (isinf(creal(z)) || isinf(cimag(z))) + return cpack(INFINITY, copysign(0.0, creal(z))); + return z; +} diff --git a/src/complex/cprojf.c b/src/complex/cprojf.c new file mode 100644 index 00000000..71129743 --- /dev/null +++ b/src/complex/cprojf.c @@ -0,0 +1,8 @@ +#include "libm.h" + +float complex cprojf(float complex z) +{ + if (isinf(crealf(z)) || isinf(cimagf(z))) + return cpackf(INFINITY, copysignf(0.0, crealf(z))); + return z; +} diff --git a/src/complex/cprojl.c b/src/complex/cprojl.c new file mode 100644 index 00000000..72e50cf5 --- /dev/null +++ b/src/complex/cprojl.c @@ -0,0 +1,15 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex cprojl(long double complex z) +{ + return cproj(z); +} +#else +long double complex cprojl(long double complex z) +{ + if (isinf(creall(z)) || isinf(cimagl(z))) + return cpackl(INFINITY, copysignl(0.0, creall(z))); + return z; +} +#endif diff --git a/src/complex/creal.c b/src/complex/creal.c new file mode 100644 index 00000000..2bb91812 --- /dev/null +++ b/src/complex/creal.c @@ -0,0 +1,6 @@ +#include <complex.h> + +double creal(double complex z) +{ + return z; +} diff --git a/src/complex/crealf.c b/src/complex/crealf.c new file mode 100644 index 00000000..078232f0 --- /dev/null +++ b/src/complex/crealf.c @@ -0,0 +1,6 @@ +#include <complex.h> + +float crealf(float complex z) +{ + return z; +} diff --git a/src/complex/creall.c b/src/complex/creall.c new file mode 100644 index 00000000..56e64097 --- /dev/null +++ b/src/complex/creall.c @@ -0,0 +1,6 @@ +#include <complex.h> + +long double creall(long double complex z) +{ + return z; +} diff --git a/src/complex/csin.c b/src/complex/csin.c new file mode 100644 index 00000000..246a4595 --- /dev/null +++ b/src/complex/csin.c @@ -0,0 +1,9 @@ +#include "libm.h" + +/* sin(z) = -i sinh(i z) */ + +double complex csin(double complex z) +{ + z = csinh(cpack(-cimag(z), creal(z))); + return cpack(cimag(z), -creal(z)); +} diff --git a/src/complex/csinf.c b/src/complex/csinf.c new file mode 100644 index 00000000..3aabe8f8 --- /dev/null +++ b/src/complex/csinf.c @@ -0,0 +1,7 @@ +#include "libm.h" + +float complex csinf(float complex z) +{ + z = csinhf(cpackf(-cimagf(z), crealf(z))); + return cpackf(cimagf(z), -crealf(z)); +} diff --git a/src/complex/csinh.c b/src/complex/csinh.c new file mode 100644 index 00000000..fe16f06b --- /dev/null +++ b/src/complex/csinh.c @@ -0,0 +1,141 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +/* + * Hyperbolic sine of a complex argument z = x + i y. + * + * sinh(z) = sinh(x+iy) + * = sinh(x) cos(y) + i cosh(x) sin(y). + * + * Exceptional values are noted in the comments within the source code. + * These values and the return value were taken from n1124.pdf. + */ + +#include "libm.h" + +static const double huge = 0x1p1023; + +double complex csinh(double complex z) +{ + double x, y, h; + int32_t hx, hy, ix, iy, lx, ly; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hx, lx, x); + EXTRACT_WORDS(hy, ly, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + /* Handle the nearly-non-exceptional cases where x and y are finite. */ + if (ix < 0x7ff00000 && iy < 0x7ff00000) { + if ((iy | ly) == 0) + return cpack(sinh(x), y); + if (ix < 0x40360000) /* small x: normal case */ + return cpack(sinh(x) * cos(y), cosh(x) * sin(y)); + + /* |x| >= 22, so cosh(x) ~= exp(|x|) */ + if (ix < 0x40862e42) { + /* x < 710: exp(|x|) won't overflow */ + h = exp(fabs(x)) * 0.5; + return cpack(copysign(h, x) * cos(y), h * sin(y)); + } else if (ix < 0x4096bbaa) { + /* x < 1455: scale to avoid overflow */ + z = __ldexp_cexp(cpack(fabs(x), y), -1); + return cpack(creal(z) * copysign(1, x), cimag(z)); + } else { + /* x >= 1455: the result always overflows */ + h = huge * x; + return cpack(h * cos(y), h * h * sin(y)); + } + } + + /* + * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. + * The sign of 0 in the result is unspecified. Choice = normally + * the same as dNaN. Raise the invalid floating-point exception. + * + * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). + * The sign of 0 in the result is unspecified. Choice = normally + * the same as d(NaN). + */ + if ((ix | lx) == 0 && iy >= 0x7ff00000) + return cpack(copysign(0, x * (y - y)), y - y); + + /* + * sinh(+-Inf +- I 0) = +-Inf + I +-0. + * + * sinh(NaN +- I 0) = d(NaN) + I +-0. + */ + if ((iy | ly) == 0 && ix >= 0x7ff00000) { + if (((hx & 0xfffff) | lx) == 0) + return cpack(x, y); + return cpack(x, copysign(0, y)); + } + + /* + * sinh(x +- I Inf) = dNaN + I dNaN. + * Raise the invalid floating-point exception for finite nonzero x. + * + * sinh(x + I NaN) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero x. Choice = don't raise (except for signaling NaNs). + */ + if (ix < 0x7ff00000 && iy >= 0x7ff00000) + return cpack(y - y, x * (y - y)); + + /* + * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). + * The sign of Inf in the result is unspecified. Choice = normally + * the same as d(NaN). + * + * sinh(+-Inf +- I Inf) = +Inf + I dNaN. + * The sign of Inf in the result is unspecified. Choice = always +. + * Raise the invalid floating-point exception. + * + * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) + */ + if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { + if (iy >= 0x7ff00000) + return cpack(x * x, x * (y - y)); + return cpack(x * cos(y), INFINITY * sin(y)); + } + + /* + * sinh(NaN + I NaN) = d(NaN) + I d(NaN). + * + * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception. + * Choice = raise. + * + * sinh(NaN + I y) = d(NaN) + I d(NaN). + * Optionally raises the invalid floating-point exception for finite + * nonzero y. Choice = don't raise (except for signaling NaNs). + */ + return cpack((x * x) * (y - y), (x + x) * (y - y)); +} diff --git a/src/complex/csinhf.c b/src/complex/csinhf.c new file mode 100644 index 00000000..bbb116c2 --- /dev/null +++ b/src/complex/csinhf.c @@ -0,0 +1,90 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_csinhf.c */ +/*- + * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +/* + * Hyperbolic sine of a complex argument z. See s_csinh.c for details. + */ + +#include "libm.h" + +static const float huge = 0x1p127; + +float complex csinhf(float complex z) +{ + float x, y, h; + int32_t hx, hy, ix, iy; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hx, x); + GET_FLOAT_WORD(hy, y); + + ix = 0x7fffffff & hx; + iy = 0x7fffffff & hy; + + if (ix < 0x7f800000 && iy < 0x7f800000) { + if (iy == 0) + return cpackf(sinhf(x), y); + if (ix < 0x41100000) /* small x: normal case */ + return cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)); + + /* |x| >= 9, so cosh(x) ~= exp(|x|) */ + if (ix < 0x42b17218) { + /* x < 88.7: expf(|x|) won't overflow */ + h = expf(fabsf(x)) * 0.5f; + return cpackf(copysignf(h, x) * cosf(y), h * sinf(y)); + } else if (ix < 0x4340b1e7) { + /* x < 192.7: scale to avoid overflow */ + z = __ldexp_cexpf(cpackf(fabsf(x), y), -1); + return cpackf(crealf(z) * copysignf(1, x), cimagf(z)); + } else { + /* x >= 192.7: the result always overflows */ + h = huge * x; + return cpackf(h * cosf(y), h * h * sinf(y)); + } + } + + if (ix == 0 && iy >= 0x7f800000) + return cpackf(copysignf(0, x * (y - y)), y - y); + + if (iy == 0 && ix >= 0x7f800000) { + if ((hx & 0x7fffff) == 0) + return cpackf(x, y); + return cpackf(x, copysignf(0, y)); + } + + if (ix < 0x7f800000 && iy >= 0x7f800000) + return cpackf(y - y, x * (y - y)); + + if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) { + if (iy >= 0x7f800000) + return cpackf(x * x, x * (y - y)); + return cpackf(x * cosf(y), INFINITY * sinf(y)); + } + + return cpackf((x * x) * (y - y), (x + x) * (y - y)); +} diff --git a/src/complex/csinhl.c b/src/complex/csinhl.c new file mode 100644 index 00000000..c566653b --- /dev/null +++ b/src/complex/csinhl.c @@ -0,0 +1,7 @@ +#include "libm.h" + +//FIXME +long double complex csinhl(long double complex z) +{ + return csinh(z); +} diff --git a/src/complex/csinl.c b/src/complex/csinl.c new file mode 100644 index 00000000..4ad86745 --- /dev/null +++ b/src/complex/csinl.c @@ -0,0 +1,14 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex csinl(long double complex z) +{ + return csin(z); +} +#else +long double complex csinl(long double complex z) +{ + z = csinhl(cpackl(-cimagl(z), creall(z))); + return cpackl(cimagl(z), -creall(z)); +} +#endif diff --git a/src/complex/csqrt.c b/src/complex/csqrt.c new file mode 100644 index 00000000..21fb879d --- /dev/null +++ b/src/complex/csqrt.c @@ -0,0 +1,100 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */ +/*- + * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "libm.h" + +/* + * gcc doesn't implement complex multiplication or division correctly, + * so we need to handle infinities specially. We turn on this pragma to + * notify conforming c99 compilers that the fast-but-incorrect code that + * gcc generates is acceptable, since the special cases have already been + * handled. + */ +#pragma STDC CX_LIMITED_RANGE ON + +/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */ +#define THRESH 0x1.a827999fcef32p+1022 + +double complex csqrt(double complex z) +{ + double complex result; + double a, b; + double t; + int scale; + + a = creal(z); + b = cimag(z); + + /* Handle special cases. */ + if (z == 0) + return cpack(0, b); + if (isinf(b)) + return cpack(INFINITY, b); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return cpack(a, t); /* return NaN + NaN i */ + } + if (isinf(a)) { + /* + * csqrt(inf + NaN i) = inf + NaN i + * csqrt(inf + y i) = inf + 0 i + * csqrt(-inf + NaN i) = NaN +- inf i + * csqrt(-inf + y i) = 0 + inf i + */ + if (signbit(a)) + return cpack(fabs(b - b), copysign(a, b)); + else + return cpack(a, copysign(b - b, b)); + } + /* + * The remaining special case (b is NaN) is handled just fine by + * the normal code path below. + */ + + /* Scale to avoid overflow. */ + if (fabs(a) >= THRESH || fabs(b) >= THRESH) { + a *= 0.25; + b *= 0.25; + scale = 1; + } else { + scale = 0; + } + + /* Algorithm 312, CACM vol 10, Oct 1967. */ + if (a >= 0) { + t = sqrt((a + hypot(a, b)) * 0.5); + result = cpack(t, b / (2 * t)); + } else { + t = sqrt((-a + hypot(a, b)) * 0.5); + result = cpack(fabs(b) / (2 * t), copysign(t, b)); + } + + /* Rescale. */ + if (scale) + result *= 2; + return result; +} diff --git a/src/complex/csqrtf.c b/src/complex/csqrtf.c new file mode 100644 index 00000000..16487c23 --- /dev/null +++ b/src/complex/csqrtf.c @@ -0,0 +1,82 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrtf.c */ +/*- + * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG> + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include "libm.h" + +/* + * gcc doesn't implement complex multiplication or division correctly, + * so we need to handle infinities specially. We turn on this pragma to + * notify conforming c99 compilers that the fast-but-incorrect code that + * gcc generates is acceptable, since the special cases have already been + * handled. + */ +#pragma STDC CX_LIMITED_RANGE ON + +float complex csqrtf(float complex z) +{ + float a = crealf(z), b = cimagf(z); + double t; + + /* Handle special cases. */ + if (z == 0) + return cpackf(0, b); + if (isinf(b)) + return cpackf(INFINITY, b); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return cpackf(a, t); /* return NaN + NaN i */ + } + if (isinf(a)) { + /* + * csqrtf(inf + NaN i) = inf + NaN i + * csqrtf(inf + y i) = inf + 0 i + * csqrtf(-inf + NaN i) = NaN +- inf i + * csqrtf(-inf + y i) = 0 + inf i + */ + if (signbit(a)) + return cpackf(fabsf(b - b), copysignf(a, b)); + else + return cpackf(a, copysignf(b - b, b)); + } + /* + * The remaining special case (b is NaN) is handled just fine by + * the normal code path below. + */ + + /* + * We compute t in double precision to avoid overflow and to + * provide correct rounding in nearly all cases. + * This is Algorithm 312, CACM vol 10, Oct 1967. + */ + if (a >= 0) { + t = sqrt((a + hypot(a, b)) * 0.5); + return cpackf(t, b / (2.0 * t)); + } else { + t = sqrt((-a + hypot(a, b)) * 0.5); + return cpackf(fabsf(b) / (2.0 * t), copysignf(t, b)); + } +} diff --git a/src/complex/csqrtl.c b/src/complex/csqrtl.c new file mode 100644 index 00000000..0600ef3b --- /dev/null +++ b/src/complex/csqrtl.c @@ -0,0 +1,7 @@ +#include "libm.h" + +//FIXME +long double complex csqrtl(long double complex z) +{ + return csqrt(z); +} diff --git a/src/complex/ctan.c b/src/complex/ctan.c new file mode 100644 index 00000000..4741a4df --- /dev/null +++ b/src/complex/ctan.c @@ -0,0 +1,9 @@ +#include "libm.h" + +/* tan(z) = -i tanh(i z) */ + +double complex ctan(double complex z) +{ + z = ctanh(cpack(-cimag(z), creal(z))); + return cpack(cimag(z), -creal(z)); +} diff --git a/src/complex/ctanf.c b/src/complex/ctanf.c new file mode 100644 index 00000000..9bbeb051 --- /dev/null +++ b/src/complex/ctanf.c @@ -0,0 +1,7 @@ +#include "libm.h" + +float complex ctanf(float complex z) +{ + z = ctanhf(cpackf(-cimagf(z), crealf(z))); + return cpackf(cimagf(z), -crealf(z)); +} diff --git a/src/complex/ctanh.c b/src/complex/ctanh.c new file mode 100644 index 00000000..dd569fc3 --- /dev/null +++ b/src/complex/ctanh.c @@ -0,0 +1,127 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.c */ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +/* + * Hyperbolic tangent of a complex argument z = x + i y. + * + * The algorithm is from: + * + * W. Kahan. Branch Cuts for Complex Elementary Functions or Much + * Ado About Nothing's Sign Bit. In The State of the Art in + * Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987. + * + * Method: + * + * Let t = tan(x) + * beta = 1/cos^2(y) + * s = sinh(x) + * rho = cosh(x) + * + * We have: + * + * tanh(z) = sinh(z) / cosh(z) + * + * sinh(x) cos(y) + i cosh(x) sin(y) + * = --------------------------------- + * cosh(x) cos(y) + i sinh(x) sin(y) + * + * cosh(x) sinh(x) / cos^2(y) + i tan(y) + * = ------------------------------------- + * 1 + sinh^2(x) / cos^2(y) + * + * beta rho s + i t + * = ---------------- + * 1 + beta s^2 + * + * Modifications: + * + * I omitted the original algorithm's handling of overflow in tan(x) after + * verifying with nearpi.c that this can't happen in IEEE single or double + * precision. I also handle large x differently. + */ + +#include "libm.h" + +double complex ctanh(double complex z) +{ + double x, y; + double t, beta, s, rho, denom; + uint32_t hx, ix, lx; + + x = creal(z); + y = cimag(z); + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; + + /* + * ctanh(NaN + i 0) = NaN + i 0 + * + * ctanh(NaN + i y) = NaN + i NaN for y != 0 + * + * The imaginary part has the sign of x*sin(2*y), but there's no + * special effort to get this right. + * + * ctanh(+-Inf +- i Inf) = +-1 +- 0 + * + * ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite + * + * The imaginary part of the sign is unspecified. This special + * case is only needed to avoid a spurious invalid exception when + * y is infinite. + */ + if (ix >= 0x7ff00000) { + if ((ix & 0xfffff) | lx) /* x is NaN */ + return cpack(x, (y == 0 ? y : x * y)); + SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */ + return cpack(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))); + } + + /* + * ctanh(x + i NAN) = NaN + i NaN + * ctanh(x +- i Inf) = NaN + i NaN + */ + if (!isfinite(y)) + return cpack(y - y, y - y); + + /* + * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the + * approximation sinh^2(huge) ~= exp(2*huge) / 4. + * We use a modified formula to avoid spurious overflow. + */ + if (ix >= 0x40360000) { /* x >= 22 */ + double exp_mx = exp(-fabs(x)); + return cpack(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx); + } + + /* Kahan's algorithm */ + t = tan(y); + beta = 1.0 + t * t; /* = 1 / cos^2(y) */ + s = sinh(x); + rho = sqrt(1 + s * s); /* = cosh(x) */ + denom = 1 + beta * s * s; + return cpack((beta * rho * s) / denom, t / denom); +} diff --git a/src/complex/ctanhf.c b/src/complex/ctanhf.c new file mode 100644 index 00000000..7d746134 --- /dev/null +++ b/src/complex/ctanhf.c @@ -0,0 +1,66 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanhf.c */ +/*- + * Copyright (c) 2011 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ +/* + * Hyperbolic tangent of a complex argument z. See s_ctanh.c for details. + */ + +#include "libm.h" + +float complex ctanhf(float complex z) +{ + float x, y; + float t, beta, s, rho, denom; + uint32_t hx, ix; + + x = crealf(z); + y = cimagf(z); + + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; + + if (ix >= 0x7f800000) { + if (ix & 0x7fffff) + return cpackf(x, (y == 0 ? y : x * y)); + SET_FLOAT_WORD(x, hx - 0x40000000); + return cpackf(x, copysignf(0, isinf(y) ? y : sinf(y) * cosf(y))); + } + + if (!isfinite(y)) + return cpackf(y - y, y - y); + + if (ix >= 0x41300000) { /* x >= 11 */ + float exp_mx = expf(-fabsf(x)); + return cpackf(copysignf(1, x), 4 * sinf(y) * cosf(y) * exp_mx * exp_mx); + } + + t = tanf(y); + beta = 1.0 + t * t; + s = sinhf(x); + rho = sqrtf(1 + s * s); + denom = 1 + beta * s * s; + return cpackf((beta * rho * s) / denom, t / denom); +} diff --git a/src/complex/ctanhl.c b/src/complex/ctanhl.c new file mode 100644 index 00000000..89a75d13 --- /dev/null +++ b/src/complex/ctanhl.c @@ -0,0 +1,7 @@ +#include "libm.h" + +//FIXME +long double complex ctanhl(long double complex z) +{ + return ctanh(z); +} diff --git a/src/complex/ctanl.c b/src/complex/ctanl.c new file mode 100644 index 00000000..4b4c99b6 --- /dev/null +++ b/src/complex/ctanl.c @@ -0,0 +1,14 @@ +#include "libm.h" + +#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024 +long double complex ctanl(long double complex z) +{ + return ctan(z); +} +#else +long double complex ctanl(long double complex z) +{ + z = ctanhl(cpackl(-cimagl(z), creall(z))); + return cpackl(cimagl(z), -creall(z)); +} +#endif |