| /* |
| * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved. |
| * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| * |
| * This code is free software; you can redistribute it and/or modify it |
| * under the terms of the GNU General Public License version 2 only, as |
| * published by the Free Software Foundation. Oracle designates this |
| * particular file as subject to the "Classpath" exception as provided |
| * by Oracle in the LICENSE file that accompanied this code. |
| * |
| * This code 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 General Public License |
| * version 2 for more details (a copy is included in the LICENSE file that |
| * accompanied this code). |
| * |
| * You should have received a copy of the GNU General Public License version |
| * 2 along with this work; if not, write to the Free Software Foundation, |
| * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| * |
| * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA |
| * or visit www.oracle.com if you need additional information or have any |
| * questions. |
| */ |
| |
| /* __ieee754_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) |
| * where |
| * R(x^2) is a rational approximation of (asin(x)-x)/x^3 |
| * and its remez error is bounded by |
| * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) |
| * |
| * For x in [0.5,1] |
| * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) |
| * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; |
| * then for x>0.98 |
| * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
| * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) |
| * For x<=0.98, let pio4_hi = pio2_hi/2, then |
| * f = hi part of s; |
| * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) |
| * and |
| * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
| * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) |
| * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) |
| * |
| * Special cases: |
| * if x is NaN, return x itself; |
| * if |x|>1, return NaN with invalid signal. |
| * |
| */ |
| |
| |
| #include "fdlibm.h" |
| |
| #ifdef __STDC__ |
| static const double |
| #else |
| static double |
| #endif |
| one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
| huge = 1.000e+300, |
| pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ |
| pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ |
| pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ |
| /* coefficient for R(x^2) */ |
| pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
| pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
| pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
| pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
| pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
| pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
| qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
| qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
| qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
| qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
| |
| #ifdef __STDC__ |
| double __ieee754_asin(double x) |
| #else |
| double __ieee754_asin(x) |
| double x; |
| #endif |
| { |
| double t=0,w,p,q,c,r,s; |
| int hx,ix; |
| hx = __HI(x); |
| ix = hx&0x7fffffff; |
| if(ix>= 0x3ff00000) { /* |x|>= 1 */ |
| if(((ix-0x3ff00000)|__LO(x))==0) |
| /* 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 (ix<0x3fe00000) { /* |x|<0.5 */ |
| if(ix<0x3e400000) { /* if |x| < 2**-27 */ |
| if(huge+x>one) return x;/* return x with inexact if x!=0*/ |
| } else |
| t = x*x; |
| p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); |
| q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); |
| w = p/q; |
| return x+x*w; |
| } |
| /* 1> |x|>= 0.5 */ |
| w = one-fabs(x); |
| t = w*0.5; |
| p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); |
| q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); |
| s = sqrt(t); |
| if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ |
| w = p/q; |
| t = pio2_hi-(2.0*(s+s*w)-pio2_lo); |
| } else { |
| w = s; |
| __LO(w) = 0; |
| c = (t-w*w)/(s+w); |
| r = p/q; |
| p = 2.0*s*r-(pio2_lo-2.0*c); |
| q = pio4_hi-2.0*w; |
| t = pio4_hi-(p-q); |
| } |
| if(hx>0) return t; else return -t; |
| } |