--- /dev/null
+/*
+ * ====================================================
+ * 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.
+ * ====================================================
+ */
+
+#include "mathl.h"
+
+/*
+ Long double expansions contributed by
+ Stephen L. Moshier <moshier@na-net.ornl.gov>
+*/
+
+/* asin(x)
+ * Method :
+ * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
+ * we approximate asin(x) on [0,0.5] by
+ * asin(x) = x + x*x^2*R(x^2)
+ * Between .5 and .625 the approximation is
+ * asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
+ * For x in [0.625,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ *
+ * Special cases:
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
+ *
+ */
+
+
+#include <math.h>
+
+static const long double
+ one = 1.0L,
+ huge = 1.0e+4932L,
+ pi = 3.1415926535897932384626433832795028841972L,
+ pio2_hi = 1.5707963267948966192313216916397514420986L,
+ pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
+ pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
+
+ /* coefficient for R(x^2) */
+
+ /* asin(x) = x + x^3 pS(x^2) / qS(x^2)
+ 0 <= x <= 0.5
+ peak relative error 1.9e-35 */
+ pS0 = -8.358099012470680544198472400254596543711E2L,
+ pS1 = 3.674973957689619490312782828051860366493E3L,
+ pS2 = -6.730729094812979665807581609853656623219E3L,
+ pS3 = 6.643843795209060298375552684423454077633E3L,
+ pS4 = -3.817341990928606692235481812252049415993E3L,
+ pS5 = 1.284635388402653715636722822195716476156E3L,
+ pS6 = -2.410736125231549204856567737329112037867E2L,
+ pS7 = 2.219191969382402856557594215833622156220E1L,
+ pS8 = -7.249056260830627156600112195061001036533E-1L,
+ pS9 = 1.055923570937755300061509030361395604448E-3L,
+
+ qS0 = -5.014859407482408326519083440151745519205E3L,
+ qS1 = 2.430653047950480068881028451580393430537E4L,
+ qS2 = -4.997904737193653607449250593976069726962E4L,
+ qS3 = 5.675712336110456923807959930107347511086E4L,
+ qS4 = -3.881523118339661268482937768522572588022E4L,
+ qS5 = 1.634202194895541569749717032234510811216E4L,
+ qS6 = -4.151452662440709301601820849901296953752E3L,
+ qS7 = 5.956050864057192019085175976175695342168E2L,
+ qS8 = -4.175375777334867025769346564600396877176E1L,
+ /* 1.000000000000000000000000000000000000000E0 */
+
+ /* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
+ -0.0625 <= x <= 0.0625
+ peak relative error 3.3e-35 */
+ rS0 = -5.619049346208901520945464704848780243887E0L,
+ rS1 = 4.460504162777731472539175700169871920352E1L,
+ rS2 = -1.317669505315409261479577040530751477488E2L,
+ rS3 = 1.626532582423661989632442410808596009227E2L,
+ rS4 = -3.144806644195158614904369445440583873264E1L,
+ rS5 = -9.806674443470740708765165604769099559553E1L,
+ rS6 = 5.708468492052010816555762842394927806920E1L,
+ rS7 = 1.396540499232262112248553357962639431922E1L,
+ rS8 = -1.126243289311910363001762058295832610344E1L,
+ rS9 = -4.956179821329901954211277873774472383512E-1L,
+ rS10 = 3.313227657082367169241333738391762525780E-1L,
+
+ sS0 = -4.645814742084009935700221277307007679325E0L,
+ sS1 = 3.879074822457694323970438316317961918430E1L,
+ sS2 = -1.221986588013474694623973554726201001066E2L,
+ sS3 = 1.658821150347718105012079876756201905822E2L,
+ sS4 = -4.804379630977558197953176474426239748977E1L,
+ sS5 = -1.004296417397316948114344573811562952793E2L,
+ sS6 = 7.530281592861320234941101403870010111138E1L,
+ sS7 = 1.270735595411673647119592092304357226607E1L,
+ sS8 = -1.815144839646376500705105967064792930282E1L,
+ sS9 = -7.821597334910963922204235247786840828217E-2L,
+ /* 1.000000000000000000000000000000000000000E0 */
+
+ asinr5625 = 5.9740641664535021430381036628424864397707E-1L;
+
+
+long double
+acosl (long double x)
+{
+ long double t, p, q;
+
+ if (x < 0.0L)
+ {
+ t = pi - acosl(-x);
+ if (huge + x > one) /* return with inexact */
+ return t;
+ }
+
+ if (x >= 1.0L) /* |x|>= 1 */
+ {
+ if (x == 1.0L)
+ return 0.0L; /* return zero */
+
+ return (x - x) / (x - x); /* asin(|x|>1) is NaN */
+ }
+
+ else if (x < 0.5L) /* |x| < 0.5 */
+ {
+ if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */
+ /* acos(0)=+-pi/2 with inexact */
+ return x * pio2_hi + x * pio2_lo;
+
+ t = x * x;
+ p = (((((((((pS9 * t
+ + pS8) * t
+ + pS7) * t
+ + pS6) * t
+ + pS5) * t
+ + pS4) * t
+ + pS3) * t
+ + pS2) * t
+ + pS1) * t
+ + pS0) * t;
+
+ q = (((((((( t
+ + qS8) * t
+ + qS7) * t
+ + qS6) * t
+ + qS5) * t
+ + qS4) * t
+ + qS3) * t
+ + qS2) * t
+ + qS1) * t
+ + qS0;
+
+ return pio2_hi - (x + x * (p / q) - pio2_lo);
+ }
+
+ else if (x < 0.625) /* 0.625 */
+ {
+ t = x - 0.5625;
+ 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;
+
+ return (pio2_hi - asinr5625) - (p / q - pio2_lo);
+ }
+ else
+ return 2 * asinl(sqrtl((1-x)/2));
+}
+
+#if 0
+main()
+{
+ printf ("%.18Lg %.18Lg\n",
+ acosl(1.0L),
+ 1.5707963267948966192313216916397514420984L -
+ 1.5707963267948966192313216916397514420984L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(0.7071067811865475244008443621048490392848L),
+ 1.5707963267948966192313216916397514420984L -
+ 0.7853981633974483096156608458198757210492L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(0.5L),
+ 1.5707963267948966192313216916397514420984L -
+ 0.5235987755982988730771072305465838140328L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(0.3090169943749474241022934171828190588600L),
+ 1.5707963267948966192313216916397514420984L -
+ 0.3141592653589793238462643383279502884196L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(-1.0L),
+ 1.5707963267948966192313216916397514420984L -
+ -1.5707963267948966192313216916397514420984L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(-0.7071067811865475244008443621048490392848L),
+ 1.5707963267948966192313216916397514420984L -
+ -0.7853981633974483096156608458198757210492L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(-0.5L),
+ 1.5707963267948966192313216916397514420984L -
+ -0.5235987755982988730771072305465838140328L);
+ printf ("%.18Lg %.18Lg\n",
+ acosl(-0.3090169943749474241022934171828190588600L),
+ 1.5707963267948966192313216916397514420984L -
+ -0.3141592653589793238462643383279502884196L);
+}
+#endif
projects / gnulib.git / blobdiff