diff options
Diffstat (limited to 'lib/libm/common_source/asincos.c')
| -rw-r--r-- | lib/libm/common_source/asincos.c | 38 |
1 files changed, 19 insertions, 19 deletions
diff --git a/lib/libm/common_source/asincos.c b/lib/libm/common_source/asincos.c index c746b16..12d0e14 100644 --- a/lib/libm/common_source/asincos.c +++ b/lib/libm/common_source/asincos.c @@ -45,12 +45,12 @@ static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93"; * sqrt(x) * * Required kernel function: - * atan2(y,x) + * atan2(y,x) * - * Method : - * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is + * 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, + * 1-x*x if x < 0.5, * 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5. * * Special cases: @@ -59,22 +59,22 @@ static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93"; * * 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 ..... + * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , - * 56 bits PI = 3.141592653589793 227020265 ..... , + * 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 + * + * 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))); * @@ -82,7 +82,7 @@ static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93"; * * 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 + * 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. */ @@ -97,7 +97,7 @@ double x; s=copysign(x,one); if(s <= 0.5) return(atan2(x,sqrt(one-x*x))); - else + else { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); } } @@ -112,9 +112,9 @@ double x; * sqrt(x) * * Required kernel function: - * atan2(y,x) + * atan2(y,x) * - * Method : + * Method : * ________ * / 1 - x * acos(x) = 2*atan2( / -------- , 1 ) . @@ -126,22 +126,22 @@ double x; * * 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 ..... + * pi = 3.141592653589793 23846264338327 ..... * 53 bits PI = 3.141592653589793 115997963 ..... , - * 56 bits PI = 3.141592653589793 227020265 ..... , + * 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 + * + * 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))); * @@ -149,7 +149,7 @@ double x; * * 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 + * 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. */ |
