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5261 libm should stop using synonyms.h


  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 */