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author | Richard Maw <richard.maw@codethink.co.uk> | 2012-01-17 14:43:55 +0000 |
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committer | Richard Maw <richard.maw@codethink.co.uk> | 2012-01-17 14:43:55 +0000 |
commit | 2de9abc5c9d40b3c716307d67d16146f823fd554 (patch) | |
tree | 6979db67934ddc8b564150b465846a383b428ff8 /gnulib/lib/acosl.c | |
parent | 33cc1c6fda6e72a7bae1401e9b2cec495a4d3ff1 (diff) | |
download | patch-baserock/bootstrap.tar.gz |
add the output of bootstrapbaserock/bootstrap-pass2baserock/bootstrap
Diffstat (limited to 'gnulib/lib/acosl.c')
m--------- | gnulib | 0 | ||||
-rw-r--r-- | gnulib/lib/acosl.c | 238 |
2 files changed, 238 insertions, 0 deletions
diff --git a/gnulib b/gnulib deleted file mode 160000 -Subproject 443bc5ffcf7429e557f4a371b0661abe98ddbc1 diff --git a/gnulib/lib/acosl.c b/gnulib/lib/acosl.c new file mode 100644 index 0000000..c864631 --- /dev/null +++ b/gnulib/lib/acosl.c @@ -0,0 +1,238 @@ +/* + * ==================================================== + * 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 <config.h> + +/* Specification. */ +#include <math.h> + +#if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE + +long double +acosl (long double x) +{ + return acos (x); +} + +#else + +/* + 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. + * + */ + + +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)); +} + +#endif + +#if 0 +int +main (void) +{ + 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 |