131 lines
2.9 KiB
C
131 lines
2.9 KiB
C
/* $OpenBSD: s_casinl.c,v 1.3 2011/07/20 21:02:51 martynas Exp $ */
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/*
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* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
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*
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* Permission to use, copy, modify, and distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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*/
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/* casinl()
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*
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* Complex circular arc sine
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*
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*
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*
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* SYNOPSIS:
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*
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* long double complex casinl();
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* long double complex z, w;
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*
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* w = casinl( z );
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*
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*
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*
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* DESCRIPTION:
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*
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* Inverse complex sine:
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*
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* 2
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* w = -i clog( iz + csqrt( 1 - z ) ).
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*
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*
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* ACCURACY:
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*
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* Relative error:
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* arithmetic domain # trials peak rms
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* DEC -10,+10 10100 2.1e-15 3.4e-16
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* IEEE -10,+10 30000 2.2e-14 2.7e-15
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* Larger relative error can be observed for z near zero.
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* Also tested by csin(casin(z)) = z.
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*/
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#include <float.h>
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#include <openlibm_complex.h>
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#include <openlibm_math.h>
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#if LDBL_MANT_DIG == 64
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static const long double MACHEPL= 5.42101086242752217003726400434970855712890625E-20L;
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#elif LDBL_MANT_DIG == 113
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static const long double MACHEPL = 9.629649721936179265279889712924636592690508e-35L;
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#endif
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static const long double PIO2L = 1.570796326794896619231321691639751442098585L;
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long double complex
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casinl(long double complex z)
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{
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long double complex w;
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long double x, y, b;
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static long double complex ca, ct, zz, z2;
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x = creall(z);
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y = cimagl(z);
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if (y == 0.0L) {
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if (fabsl(x) > 1.0L) {
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w = PIO2L + 0.0L * I;
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/*mtherr( "casinl", DOMAIN );*/
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}
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else {
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w = asinl(x) + 0.0L * I;
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}
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return (w);
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}
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/* Power series expansion */
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b = cabsl(z);
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if (b < 0.125L) {
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long double complex sum;
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long double n, cn;
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z2 = (x - y) * (x + y) + (2.0L * x * y) * I;
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cn = 1.0L;
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n = 1.0L;
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ca = x + y * I;
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sum = x + y * I;
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do {
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ct = z2 * ca;
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ca = ct;
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cn *= n;
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n += 1.0L;
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cn /= n;
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n += 1.0L;
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b = cn/n;
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ct *= b;
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sum += ct;
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b = cabsl(ct);
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}
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while (b > MACHEPL);
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w = sum;
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return w;
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}
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ca = x + y * I;
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ct = ca * I; /* iz */
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/* sqrt(1 - z*z) */
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/* cmul(&ca, &ca, &zz) */
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/* x * x - y * y */
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zz = (x - y) * (x + y) + (2.0L * x * y) * I;
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zz = 1.0L - creall(zz) - cimagl(zz) * I;
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z2 = csqrtl(zz);
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zz = ct + z2;
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zz = clogl(zz);
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/* multiply by 1/i = -i */
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w = zz * (-1.0L * I);
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return (w);
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}
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