# lm/gnu-smalltalk forked from bonzini/smalltalk

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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. * ==================================================== */ #include "mathl.h" /* Long double expansions contributed by Stephen L. Moshier */ /* 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 static const long double one = 1.0L, huge = 1.0e+4932L, 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 asinl (long double x) { long double y, t, p, q; int sign; sign = 1; y = x; if (x < 0.0L) { sign = -1; y = -x; } if (y >= 1.0L) /* |x|>= 1 */ { if (y == 1.0L) /* asin(1)=+-pi/2 with inexact */ return x * pio2_hi + x * pio2_lo; return (x - x) / (x - x); /* asin(|x|>1) is NaN */ } else if (y < 0.5L) /* |x| < 0.5 */ { if (y < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */ if (huge + y > one) return y; /* return x with inexact if x!=0 */ 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 x + x * (p / q); } else if (y < 0.625) /* 0.625 */ { t = y - 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; t = asinr5625 + p / q; } else t = pio2_hi + pio2_lo - 2 * asinl(sqrtl((1-y)/2)); return t * sign; } #if 0 main() { printf ("%.18Lg %.18Lg\n", asinl(1.0L), 1.5707963267948966192313216916397514420984L); printf ("%.18Lg %.18Lg\n", asinl(0.7071067811865475244008443621048490392848L), 0.7853981633974483096156608458198757210492L); printf ("%.18Lg %.18Lg\n", asinl(0.5L), 0.5235987755982988730771072305465838140328L); printf ("%.18Lg %.18Lg\n", asinl(0.3090169943749474241022934171828190588600L), 0.3141592653589793238462643383279502884196L); printf ("%.18Lg %.18Lg\n", asinl(-1.0L), -1.5707963267948966192313216916397514420984L); printf ("%.18Lg %.18Lg\n", asinl(-0.7071067811865475244008443621048490392848L), -0.7853981633974483096156608458198757210492L); printf ("%.18Lg %.18Lg\n", asinl(-0.5L), -0.5235987755982988730771072305465838140328L); printf ("%.18Lg %.18Lg\n", asinl(-0.3090169943749474241022934171828190588600L), -0.3141592653589793238462643383279502884196L); } #endif