10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25 /*
26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #pragma weak asin = __asin
31
32 /* INDENT OFF */
33 /*
34 * asin(x)
35 * Method :
36 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
37 * we approximate asin(x) on [0,0.5] by
38 * asin(x) = x + x*x^2*R(x^2)
39 * where
40 * R(x^2) is a rational approximation of (asin(x)-x)/x^3
41 * and its remez error is bounded by
42 * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
43 *
44 * For x in [0.5,1]
45 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
46 * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
47 * then for x>0.98
48 * asin(x) = pi/2 - 2*(s+s*z*R(z))
49 * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
50 * For x<=0.98, let pio4_hi = pio2_hi/2, then
51 * f = hi part of s;
52 * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
53 * and
54 * asin(x) = pi/2 - 2*(s+s*z*R(z))
55 * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
56 * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
57 *
58 * Special cases:
59 * if x is NaN, return x itself;
60 * if |x|>1, return NaN with invalid signal.
61 *
62 */
63 /* INDENT ON */
64
65 #include "libm_synonyms.h" /* __asin, __sqrt, __isnan */
66 #include "libm_protos.h" /* _SVID_libm_error */
67 #include "libm_macros.h"
68 #include <math.h>
69
70 /* INDENT OFF */
71 static const double xxx[] = {
72 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
73 /* huge */ 1.000e+300,
74 /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */
75 /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */
76 /* pio4_hi */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
77 /* coefficient for R(x^2) */
78 /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */
79 /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */
80 /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */
81 /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */
82 /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */
83 /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */
84 /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */
85 /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */
|
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22 /*
23 * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
24 */
25 /*
26 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
27 * Use is subject to license terms.
28 */
29
30 #pragma weak __asin = asin
31
32 /* INDENT OFF */
33 /*
34 * asin(x)
35 * Method :
36 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
37 * we approximate asin(x) on [0,0.5] by
38 * asin(x) = x + x*x^2*R(x^2)
39 * where
40 * R(x^2) is a rational approximation of (asin(x)-x)/x^3
41 * and its remez error is bounded by
42 * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
43 *
44 * For x in [0.5,1]
45 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
46 * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
47 * then for x>0.98
48 * asin(x) = pi/2 - 2*(s+s*z*R(z))
49 * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
50 * For x<=0.98, let pio4_hi = pio2_hi/2, then
51 * f = hi part of s;
52 * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
53 * and
54 * asin(x) = pi/2 - 2*(s+s*z*R(z))
55 * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
56 * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
57 *
58 * Special cases:
59 * if x is NaN, return x itself;
60 * if |x|>1, return NaN with invalid signal.
61 *
62 */
63 /* INDENT ON */
64
65 #include "libm_protos.h" /* _SVID_libm_error */
66 #include "libm_macros.h"
67 #include <math.h>
68
69 /* INDENT OFF */
70 static const double xxx[] = {
71 /* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
72 /* huge */ 1.000e+300,
73 /* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */
74 /* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */
75 /* pio4_hi */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
76 /* coefficient for R(x^2) */
77 /* pS0 */ 1.66666666666666657415e-01, /* 3FC55555, 55555555 */
78 /* pS1 */ -3.25565818622400915405e-01, /* BFD4D612, 03EB6F7D */
79 /* pS2 */ 2.01212532134862925881e-01, /* 3FC9C155, 0E884455 */
80 /* pS3 */ -4.00555345006794114027e-02, /* BFA48228, B5688F3B */
81 /* pS4 */ 7.91534994289814532176e-04, /* 3F49EFE0, 7501B288 */
82 /* pS5 */ 3.47933107596021167570e-05, /* 3F023DE1, 0DFDF709 */
83 /* qS1 */ -2.40339491173441421878e+00, /* C0033A27, 1C8A2D4B */
84 /* qS2 */ 2.02094576023350569471e+00, /* 40002AE5, 9C598AC8 */
|