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Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/e_acosl.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/e_acosl.c | 328 |
1 files changed, 0 insertions, 328 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/e_acosl.c b/sysdeps/ieee754/ldbl-128ibm/e_acosl.c deleted file mode 100644 index 8823fd6..0000000 --- a/sysdeps/ieee754/ldbl-128ibm/e_acosl.c +++ /dev/null @@ -1,328 +0,0 @@ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* - Long double 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 "math.h" -#include "math_private.h" - -#ifdef __STDC__ -static const long double -#else -static long double -#endif - one = 1.0L, - pio2_hi = 1.5707963267948966192313216916397514420986L, - pio2_lo = 4.3359050650618905123985220130216759843812E-35L, - - /* acos(0.5625 + x) = acos(0.5625) + x rS(x) / sS(x) - -0.0625 <= x <= 0.0625 - peak relative error 3.3e-35 */ - - rS0 = 5.619049346208901520945464704848780243887E0L, - 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 */ - - acosr5625 = 9.7338991014954640492751132535550279812151E-1L, - pimacosr5625 = 2.1682027434402468335351320579240000860757E0L, - - /* acos(0.4375 + x) = acos(0.4375) + x rS(x) / sS(x) - -0.0625 <= x <= 0.0625 - peak relative error 2.1e-35 */ - - P0 = 2.177690192235413635229046633751390484892E0L, - P1 = -2.848698225706605746657192566166142909573E1L, - P2 = 1.040076477655245590871244795403659880304E2L, - P3 = -1.400087608918906358323551402881238180553E2L, - P4 = 2.221047917671449176051896400503615543757E1L, - P5 = 9.643714856395587663736110523917499638702E1L, - P6 = -5.158406639829833829027457284942389079196E1L, - P7 = -1.578651828337585944715290382181219741813E1L, - P8 = 1.093632715903802870546857764647931045906E1L, - P9 = 5.448925479898460003048760932274085300103E-1L, - P10 = -3.315886001095605268470690485170092986337E-1L, - Q0 = -1.958219113487162405143608843774587557016E0L, - Q1 = 2.614577866876185080678907676023269360520E1L, - Q2 = -9.990858606464150981009763389881793660938E1L, - Q3 = 1.443958741356995763628660823395334281596E2L, - Q4 = -3.206441012484232867657763518369723873129E1L, - Q5 = -1.048560885341833443564920145642588991492E2L, - Q6 = 6.745883931909770880159915641984874746358E1L, - Q7 = 1.806809656342804436118449982647641392951E1L, - Q8 = -1.770150690652438294290020775359580915464E1L, - Q9 = -5.659156469628629327045433069052560211164E-1L, - /* 1.000000000000000000000000000000000000000E0 */ - - acosr4375 = 1.1179797320499710475919903296900511518755E0L, - pimacosr4375 = 2.0236129215398221908706530535894517323217E0L, - - /* 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 */ - -#ifdef __STDC__ -long double -__ieee754_acosl (long double x) -#else -long double -__ieee754_acosl (x) - long double x; -#endif -{ - long double z, r, w, p, q, s, t, f2; - int32_t ix, sign; - ieee854_long_double_shape_type u; - - u.value = x; - sign = u.parts32.w0; - ix = sign & 0x7fffffff; - u.parts32.w0 = ix; /* |x| */ - if (ix >= 0x3ff00000) /* |x| >= 1 */ - { - if (ix == 0x3ff00000 - && (u.parts32.w1 | (u.parts32.w2&0x7fffffff) | u.parts32.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 < 0x3fe00000) /* |x| < 0.5 */ - { - if (ix < 0x3c600000) /* |x| < 2**-57 */ - return pio2_hi + pio2_lo; - if (ix < 0x3fde0000) /* |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 - 0.4375L; - 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 < 0x3fe40000) /* |x| < 0.625 */ - { - t = u.value - 0.5625L; - 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 = __ieee754_sqrtl (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.parts32.w2 = 0; - u.parts32.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; - } -} |