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Diffstat (limited to 'sysdeps/generic/asincos.c')
| -rw-r--r-- | sysdeps/generic/asincos.c | 169 |
1 files changed, 169 insertions, 0 deletions
diff --git a/sysdeps/generic/asincos.c b/sysdeps/generic/asincos.c new file mode 100644 index 0000000000..c746b1652a --- /dev/null +++ b/sysdeps/generic/asincos.c @@ -0,0 +1,169 @@ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* ASIN(X) + * RETURNS ARC SINE OF X + * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) + * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. + * + * Required system supported functions: + * copysign(x,y) + * sqrt(x) + * + * Required kernel function: + * atan2(y,x) + * + * Method : + * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is + * computed as follows + * 1-x*x if x < 0.5, + * 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5. + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN. + * + * Accuracy: + * 1) If atan2() uses machine PI, then + * + * asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded; + * and PI is the exact pi rounded to machine precision (see atan2 for + * details): + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with more than 200,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 2.06 ulps. (comparing against (PI/pi)*(exact asin(x))); + * + * 2) If atan2() uses true pi, then + * + * asin(x) returns the exact asin(x) with error below about 2 ulps. + * + * In a test run with more than 1,024,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 1.99 ulps. + */ + +double asin(x) +double x; +{ + double s,t,copysign(),atan2(),sqrt(),one=1.0; +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(vax)&&!defined(tahoe) */ + s=copysign(x,one); + if(s <= 0.5) + return(atan2(x,sqrt(one-x*x))); + else + { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); } + +} + +/* ACOS(X) + * RETURNS ARC COS OF X + * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) + * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. + * + * Required system supported functions: + * copysign(x,y) + * sqrt(x) + * + * Required kernel function: + * atan2(y,x) + * + * Method : + * ________ + * / 1 - x + * acos(x) = 2*atan2( / -------- , 1 ) . + * \/ 1 + x + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN. + * + * Accuracy: + * 1) If atan2() uses machine PI, then + * + * acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded; + * and PI is the exact pi rounded to machine precision (see atan2 for + * details): + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with more than 200,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 2.07 ulps. (comparing against (PI/pi)*(exact acos(x))); + * + * 2) If atan2() uses true pi, then + * + * acos(x) returns the exact acos(x) with error below about 2 ulps. + * + * In a test run with more than 1,024,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 2.15 ulps. + */ + +double acos(x) +double x; +{ + double t,copysign(),atan2(),sqrt(),one=1.0; +#if !defined(vax)&&!defined(tahoe) + if(x!=x) return(x); +#endif /* !defined(vax)&&!defined(tahoe) */ + if( x != -1.0) + t=atan2(sqrt((one-x)/(one+x)),one); + else + t=atan2(one,0.0); /* t = PI/2 */ + return(t+t); +} |