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/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*- |
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* |
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* ***** BEGIN LICENSE BLOCK ***** |
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* Version: MPL 1.1/GPL 2.0/LGPL 2.1 |
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* |
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* The contents of this file are subject to the Mozilla Public License Version |
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* 1.1 (the "License"); you may not use this file except in compliance with |
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* the License. You may obtain a copy of the License at |
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* http://www.mozilla.org/MPL/ |
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* |
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* Software distributed under the License is distributed on an "AS IS" basis, |
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* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License |
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* for the specific language governing rights and limitations under the |
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* License. |
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* |
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* The Original Code is Mozilla Communicator client code, released |
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* March 31, 1998. |
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* |
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* The Initial Developer of the Original Code is |
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* Sun Microsystems, Inc. |
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* Portions created by the Initial Developer are Copyright (C) 1998 |
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* the Initial Developer. All Rights Reserved. |
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* |
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* Contributor(s): |
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* |
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* Alternatively, the contents of this file may be used under the terms of |
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* either of the GNU General Public License Version 2 or later (the "GPL"), |
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* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"), |
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* in which case the provisions of the GPL or the LGPL are applicable instead |
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* of those above. If you wish to allow use of your version of this file only |
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* under the terms of either the GPL or the LGPL, and not to allow others to |
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* use your version of this file under the terms of the MPL, indicate your |
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* decision by deleting the provisions above and replace them with the notice |
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* and other provisions required by the GPL or the LGPL. If you do not delete |
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* the provisions above, a recipient may use your version of this file under |
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* the terms of any one of the MPL, the GPL or the LGPL. |
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* |
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* ***** END LICENSE BLOCK ***** */ |
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|
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/* @(#)e_acos.c 1.3 95/01/18 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
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* ==================================================== |
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*/ |
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|
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/* __ieee754_acos(x) |
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* Method : |
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* acos(x) = pi/2 - asin(x) |
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* acos(-x) = pi/2 + asin(x) |
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* For |x|<=0.5 |
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* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
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* For x>0.5 |
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* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
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* = 2asin(sqrt((1-x)/2)) |
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* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
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* = 2f + (2c + 2s*z*R(z)) |
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* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
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* for f so that f+c ~ sqrt(z). |
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* For x<-0.5 |
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* acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
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* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
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* |
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* Special cases: |
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* if x is NaN, return x itself; |
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* if |x|>1, return NaN with invalid signal. |
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* |
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* Function needed: sqrt |
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*/ |
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|
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#include "fdlibm.h" |
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|
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#ifdef __STDC__ |
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static const double |
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#else |
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static double |
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#endif |
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one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
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pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ |
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pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ |
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pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ |
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pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
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pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
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pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
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pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
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pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
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pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
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qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
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qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
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qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
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qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
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|
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#ifdef __STDC__ |
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double __ieee754_acos(double x) |
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#else |
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double __ieee754_acos(x) |
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double x; |
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#endif |
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{ |
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fd_twoints u; |
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double df; |
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double z,p,q,r,w,s,c; |
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int hx,ix; |
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u.d = x; |
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hx = __HI(u); |
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ix = hx&0x7fffffff; |
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if(ix>=0x3ff00000) { /* |x| >= 1 */ |
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if(((ix-0x3ff00000)|__LO(u))==0) { /* |x|==1 */ |
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if(hx>0) return 0.0; /* acos(1) = 0 */ |
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else return pi+2.0*pio2_lo; /* acos(-1)= pi */ |
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} |
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return (x-x)/(x-x); /* acos(|x|>1) is NaN */ |
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} |
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if(ix<0x3fe00000) { /* |x| < 0.5 */ |
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if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ |
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z = x*x; |
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
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r = p/q; |
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return pio2_hi - (x - (pio2_lo-x*r)); |
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} else if (hx<0) { /* x < -0.5 */ |
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z = (one+x)*0.5; |
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
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s = fd_sqrt(z); |
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r = p/q; |
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w = r*s-pio2_lo; |
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return pi - 2.0*(s+w); |
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} else { /* x > 0.5 */ |
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z = (one-x)*0.5; |
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s = fd_sqrt(z); |
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u.d = s; |
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__LO(u) = 0; |
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df = u.d; |
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c = (z-df*df)/(s+df); |
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p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
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q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
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r = p/q; |
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w = r*s+c; |
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return 2.0*(df+w); |
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} |
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} |
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