/* 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)
+ * 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)
* Between .5 and .625 the approximation is
* asin(0.5625 + x) = asin(0.5625) + x rS(x) / sS(x)
- * For x in [0.625,1]
- * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
+ * For x in [0.625,1]
+ * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
*
* Special cases:
- * if x is NaN, return x itself;
- * if |x|>1, return NaN with invalid signal.
+ * if x is NaN, return x itself;
+ * if |x|>1, return NaN with invalid signal.
*
*/
pio2_lo = 4.3359050650618905123985220130216759843812E-35L,
pio4_hi = 7.8539816339744830961566084581987569936977E-1L,
- /* coefficient for R(x^2) */
+ /* coefficient for R(x^2) */
/* asin(x) = x + x^3 pS(x^2) / qS(x^2)
0 <= x <= 0.5
return t;
}
- if (x >= 1.0L) /* |x|>= 1 */
+ if (x >= 1.0L) /* |x|>= 1 */
{
if (x == 1.0L)
- return 0.0L; /* return zero */
+ return 0.0L; /* return zero */
- return (x - x) / (x - x); /* asin(|x|>1) is NaN */
+ return (x - x) / (x - x); /* asin(|x|>1) is NaN */
}
else if (x < 0.5L) /* |x| < 0.5 */
{
if (x < 0.000000000000000006938893903907228377647697925567626953125L) /* |x| < 2**-57 */
- /* acos(0)=+-pi/2 with inexact */
- return x * pio2_hi + x * pio2_lo;
+ /* acos(0)=+-pi/2 with inexact */
+ return x * pio2_hi + x * pio2_lo;
t = x * x;
p = (((((((((pS9 * t
{
t = x - 0.5625;
p = ((((((((((rS10 * t
- + rS9) * t
- + rS8) * t
- + rS7) * t
- + rS6) * t
- + rS5) * t
- + rS4) * t
- + rS3) * t
- + rS2) * t
- + rS1) * t
- + rS0) * 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;
+ + sS9) * t
+ + sS8) * t
+ + sS7) * t
+ + sS6) * t
+ + sS5) * t
+ + sS4) * t
+ + sS3) * t
+ + sS2) * t
+ + sS1) * t
+ + sS0;
return (pio2_hi - asinr5625) - (p / q - pio2_lo);
}