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+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+/*
+ __float128 expansions are
+ Copyright (C) 2001 Stephen L. Moshier <moshier@na-net.ornl.gov>
+ and are incorporated herein by permission of the author. The author
+ reserves the right to distribute this material elsewhere under different
+ copying permissions. These modifications are distributed here under
+ the following terms:
+
+ This 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.
+
+ This 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 this library; if not, write to the Free Software
+ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
+
+/* __ieee754_acosl(x)
+ * Method :
+ * acos(x) = pi/2 - asin(x)
+ * acos(-x) = pi/2 + asin(x)
+ * For |x| <= 0.375
+ * acos(x) = pi/2 - asin(x)
+ * Between .375 and .5 the approximation is
+ * acos(0.4375 + x) = acos(0.4375) + x P(x) / Q(x)
+ * Between .5 and .625 the approximation is
+ * acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
+ * For x > 0.625,
+ * acos(x) = 2 asin(sqrt((1-x)/2))
+ * computed with an extended precision square root in the leading term.
+ * For x < -0.625
+ * acos(x) = pi - 2 asin(sqrt((1-|x|)/2))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ * Functions needed: __ieee754_sqrtl.
+ */
+
+#include "quadmath-imp.h"
+
+static const __float128
+ one = 1.0Q,
+ pio2_hi = 1.5707963267948966192313216916397514420986Q,
+ pio2_lo = 4.3359050650618905123985220130216759843812E-35Q,
+
+ /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x)
+ -0.0625 <= x <= 0.0625
+ peak relative error 3.3e-35 */
+
+ rS0 = 5.619049346208901520945464704848780243887E0Q,
+ rS1 = -4.460504162777731472539175700169871920352E1Q,
+ rS2 = 1.317669505315409261479577040530751477488E2Q,
+ rS3 = -1.626532582423661989632442410808596009227E2Q,
+ rS4 = 3.144806644195158614904369445440583873264E1Q,
+ rS5 = 9.806674443470740708765165604769099559553E1Q,
+ rS6 = -5.708468492052010816555762842394927806920E1Q,
+ rS7 = -1.396540499232262112248553357962639431922E1Q,
+ rS8 = 1.126243289311910363001762058295832610344E1Q,
+ rS9 = 4.956179821329901954211277873774472383512E-1Q,
+ rS10 = -3.313227657082367169241333738391762525780E-1Q,
+
+ sS0 = -4.645814742084009935700221277307007679325E0Q,
+ sS1 = 3.879074822457694323970438316317961918430E1Q,
+ sS2 = -1.221986588013474694623973554726201001066E2Q,
+ sS3 = 1.658821150347718105012079876756201905822E2Q,
+ sS4 = -4.804379630977558197953176474426239748977E1Q,
+ sS5 = -1.004296417397316948114344573811562952793E2Q,
+ sS6 = 7.530281592861320234941101403870010111138E1Q,
+ sS7 = 1.270735595411673647119592092304357226607E1Q,
+ sS8 = -1.815144839646376500705105967064792930282E1Q,
+ sS9 = -7.821597334910963922204235247786840828217E-2Q,
+ /* 1.000000000000000000000000000000000000000E0 */
+
+ acosr5625 = 9.7338991014954640492751132535550279812151E-1Q,
+ pimacosr5625 = 2.1682027434402468335351320579240000860757E0Q,
+
+ /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x)
+ -0.0625 <= x <= 0.0625
+ peak relative error 2.1e-35 */
+
+ P0 = 2.177690192235413635229046633751390484892E0Q,
+ P1 = -2.848698225706605746657192566166142909573E1Q,
+ P2 = 1.040076477655245590871244795403659880304E2Q,
+ P3 = -1.400087608918906358323551402881238180553E2Q,
+ P4 = 2.221047917671449176051896400503615543757E1Q,
+ P5 = 9.643714856395587663736110523917499638702E1Q,
+ P6 = -5.158406639829833829027457284942389079196E1Q,
+ P7 = -1.578651828337585944715290382181219741813E1Q,
+ P8 = 1.093632715903802870546857764647931045906E1Q,
+ P9 = 5.448925479898460003048760932274085300103E-1Q,
+ P10 = -3.315886001095605268470690485170092986337E-1Q,
+ Q0 = -1.958219113487162405143608843774587557016E0Q,
+ Q1 = 2.614577866876185080678907676023269360520E1Q,
+ Q2 = -9.990858606464150981009763389881793660938E1Q,
+ Q3 = 1.443958741356995763628660823395334281596E2Q,
+ Q4 = -3.206441012484232867657763518369723873129E1Q,
+ Q5 = -1.048560885341833443564920145642588991492E2Q,
+ Q6 = 6.745883931909770880159915641984874746358E1Q,
+ Q7 = 1.806809656342804436118449982647641392951E1Q,
+ Q8 = -1.770150690652438294290020775359580915464E1Q,
+ Q9 = -5.659156469628629327045433069052560211164E-1Q,
+ /* 1.000000000000000000000000000000000000000E0 */
+
+ acosr4375 = 1.1179797320499710475919903296900511518755E0Q,
+ pimacosr4375 = 2.0236129215398221908706530535894517323217E0Q,
+
+ /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
+ 0 <= x <= 0.5
+ peak relative error 1.9e-35 */
+ pS0 = -8.358099012470680544198472400254596543711E2Q,
+ pS1 = 3.674973957689619490312782828051860366493E3Q,
+ pS2 = -6.730729094812979665807581609853656623219E3Q,
+ pS3 = 6.643843795209060298375552684423454077633E3Q,
+ pS4 = -3.817341990928606692235481812252049415993E3Q,
+ pS5 = 1.284635388402653715636722822195716476156E3Q,
+ pS6 = -2.410736125231549204856567737329112037867E2Q,
+ pS7 = 2.219191969382402856557594215833622156220E1Q,
+ pS8 = -7.249056260830627156600112195061001036533E-1Q,
+ pS9 = 1.055923570937755300061509030361395604448E-3Q,
+
+ qS0 = -5.014859407482408326519083440151745519205E3Q,
+ qS1 = 2.430653047950480068881028451580393430537E4Q,
+ qS2 = -4.997904737193653607449250593976069726962E4Q,
+ qS3 = 5.675712336110456923807959930107347511086E4Q,
+ qS4 = -3.881523118339661268482937768522572588022E4Q,
+ qS5 = 1.634202194895541569749717032234510811216E4Q,
+ qS6 = -4.151452662440709301601820849901296953752E3Q,
+ qS7 = 5.956050864057192019085175976175695342168E2Q,
+ qS8 = -4.175375777334867025769346564600396877176E1Q;
+ /* 1.000000000000000000000000000000000000000E0 */
+
+__float128
+acosq (__float128 x)
+{
+ __float128 z, r, w, p, q, s, t, f2;
+ int32_t ix, sign;
+ ieee854_float128 u;
+
+ u.value = x;
+ sign = u.words32.w0;
+ ix = sign & 0x7fffffff;
+ u.words32.w0 = ix; /* |x| */
+ if (ix >= 0x3fff0000) /* |x| >= 1 */
+ {
+ if (ix == 0x3fff0000
+ && (u.words32.w1 | u.words32.w2 | u.words32.w3) == 0)
+ { /* |x| == 1 */
+ if ((sign & 0x80000000) == 0)
+ return 0.0; /* acos(1) = 0 */
+ else
+ return (2.0 * pio2_hi) + (2.0 * pio2_lo); /* acos(-1)= pi */
+ }
+ return (x - x) / (x - x); /* acos(|x| > 1) is NaN */
+ }
+ else if (ix < 0x3ffe0000) /* |x| < 0.5 */
+ {
+ if (ix < 0x3fc60000) /* |x| < 2**-57 */
+ return pio2_hi + pio2_lo;
+ if (ix < 0x3ffde000) /* |x| < .4375 */
+ {
+ /* Arcsine of x. */
+ z = x * x;
+ p = (((((((((pS9 * z
+ + pS8) * z
+ + pS7) * z
+ + pS6) * z
+ + pS5) * z
+ + pS4) * z
+ + pS3) * z
+ + pS2) * z
+ + pS1) * z
+ + pS0) * z;
+ q = (((((((( z
+ + qS8) * z
+ + qS7) * z
+ + qS6) * z
+ + qS5) * z
+ + qS4) * z
+ + qS3) * z
+ + qS2) * z
+ + qS1) * z
+ + qS0;
+ r = x + x * p / q;
+ z = pio2_hi - (r - pio2_lo);
+ return z;
+ }
+ /* .4375 <= |x| < .5 */
+ t = u.value - 0.4375Q;
+ p = ((((((((((P10 * t
+ + P9) * t
+ + P8) * t
+ + P7) * t
+ + P6) * t
+ + P5) * t
+ + P4) * t
+ + P3) * t
+ + P2) * t
+ + P1) * t
+ + P0) * t;
+
+ q = (((((((((t
+ + Q9) * t
+ + Q8) * t
+ + Q7) * t
+ + Q6) * t
+ + Q5) * t
+ + Q4) * t
+ + Q3) * t
+ + Q2) * t
+ + Q1) * t
+ + Q0;
+ r = p / q;
+ if (sign & 0x80000000)
+ r = pimacosr4375 - r;
+ else
+ r = acosr4375 + r;
+ return r;
+ }
+ else if (ix < 0x3ffe4000) /* |x| < 0.625 */
+ {
+ t = u.value - 0.5625Q;
+ p = ((((((((((rS10 * t
+ + rS9) * t
+ + rS8) * t
+ + rS7) * t
+ + rS6) * t
+ + rS5) * t
+ + rS4) * t
+ + rS3) * t
+ + rS2) * t
+ + rS1) * t
+ + rS0) * t;
+
+ q = (((((((((t
+ + sS9) * t
+ + sS8) * t
+ + sS7) * t
+ + sS6) * t
+ + sS5) * t
+ + sS4) * t
+ + sS3) * t
+ + sS2) * t
+ + sS1) * t
+ + sS0;
+ if (sign & 0x80000000)
+ r = pimacosr5625 - p / q;
+ else
+ r = acosr5625 + p / q;
+ return r;
+ }
+ else
+ { /* |x| >= .625 */
+ z = (one - u.value) * 0.5;
+ s = sqrtq (z);
+ /* Compute an extended precision square root from
+ the Newton iteration s -> 0.5 * (s + z / s).
+ The change w from s to the improved value is
+ w = 0.5 * (s + z / s) - s = (s^2 + z)/2s - s = (z - s^2)/2s.
+ Express s = f1 + f2 where f1 * f1 is exactly representable.
+ w = (z - s^2)/2s = (z - f1^2 - 2 f1 f2 - f2^2)/2s .
+ s + w has extended precision. */
+ u.value = s;
+ u.words32.w2 = 0;
+ u.words32.w3 = 0;
+ f2 = s - u.value;
+ w = z - u.value * u.value;
+ w = w - 2.0 * u.value * f2;
+ w = w - f2 * f2;
+ w = w / (2.0 * s);
+ /* Arcsine of s. */
+ p = (((((((((pS9 * z
+ + pS8) * z
+ + pS7) * z
+ + pS6) * z
+ + pS5) * z
+ + pS4) * z
+ + pS3) * z
+ + pS2) * z
+ + pS1) * z
+ + pS0) * z;
+ q = (((((((( z
+ + qS8) * z
+ + qS7) * z
+ + qS6) * z
+ + qS5) * z
+ + qS4) * z
+ + qS3) * z
+ + qS2) * z
+ + qS1) * z
+ + qS0;
+ r = s + (w + s * p / q);
+
+ if (sign & 0x80000000)
+ w = pio2_hi + (pio2_lo - r);
+ else
+ w = r;
+ return 2.0 * w;
+ }
+}