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 acos = __acos
  31 
  32 /* INDENT OFF */
  33 /*
  34  * acos(x)
  35  * Method :
  36  *      acos(x)  = pi/2 - asin(x)
  37  *      acos(-x) = pi/2 + asin(x)
  38  * For |x|<=0.5
  39  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
  40  * For x>0.5
  41  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  42  *              = 2asin(sqrt((1-x)/2))
  43  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
  44  *              = 2f + (2c + 2s*z*R(z))
  45  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  46  *     for f so that f+c ~ sqrt(z).
  47  * For x<-0.5
  48  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  49  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  50  *
  51  * Special cases:
  52  *      if x is NaN, return x itself;
  53  *      if |x|>1, return NaN with invalid signal.
  54  *
  55  * Function needed: sqrt
  56  */
  57 /* INDENT ON */
  58 
  59 #include "libm_synonyms.h"      /* __acos, __sqrt, __isnan */
  60 #include "libm_protos.h"        /* _SVID_libm_error */
  61 #include "libm_macros.h"
  62 #include <math.h>
  63 
  64 /* INDENT OFF */
  65 static const double xxx[] = {
  66 /* one */        1.00000000000000000000e+00,    /* 3FF00000, 00000000 */
  67 /* pi */         3.14159265358979311600e+00,    /* 400921FB, 54442D18 */
  68 /* pio2_hi */    1.57079632679489655800e+00,    /* 3FF921FB, 54442D18 */
  69 /* pio2_lo */    6.12323399573676603587e-17,    /* 3C91A626, 33145C07 */
  70 /* pS0 */        1.66666666666666657415e-01,    /* 3FC55555, 55555555 */
  71 /* pS1 */       -3.25565818622400915405e-01,    /* BFD4D612, 03EB6F7D */
  72 /* pS2 */        2.01212532134862925881e-01,    /* 3FC9C155, 0E884455 */
  73 /* pS3 */       -4.00555345006794114027e-02,    /* BFA48228, B5688F3B */
  74 /* pS4 */        7.91534994289814532176e-04,    /* 3F49EFE0, 7501B288 */
  75 /* pS5 */        3.47933107596021167570e-05,    /* 3F023DE1, 0DFDF709 */
  76 /* qS1 */       -2.40339491173441421878e+00,    /* C0033A27, 1C8A2D4B */
  77 /* qS2 */        2.02094576023350569471e+00,    /* 40002AE5, 9C598AC8 */
  78 /* qS3 */       -6.88283971605453293030e-01,    /* BFE6066C, 1B8D0159 */
  79 /* qS4 */        7.70381505559019352791e-02     /* 3FB3B8C5, B12E9282 */

  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 __acos = acos
  31 
  32 /* INDENT OFF */
  33 /*
  34  * acos(x)
  35  * Method :
  36  *      acos(x)  = pi/2 - asin(x)
  37  *      acos(-x) = pi/2 + asin(x)
  38  * For |x|<=0.5
  39  *      acos(x) = pi/2 - (x + x*x^2*R(x^2))     (see asin.c)
  40  * For x>0.5
  41  *      acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
  42  *              = 2asin(sqrt((1-x)/2))
  43  *              = 2s + 2s*z*R(z)        ...z=(1-x)/2, s=sqrt(z)
  44  *              = 2f + (2c + 2s*z*R(z))
  45  *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
  46  *     for f so that f+c ~ sqrt(z).
  47  * For x<-0.5
  48  *      acos(x) = pi - 2asin(sqrt((1-|x|)/2))
  49  *              = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
  50  *
  51  * Special cases:
  52  *      if x is NaN, return x itself;
  53  *      if |x|>1, return NaN with invalid signal.
  54  *
  55  * Function needed: sqrt
  56  */
  57 /* INDENT ON */
  58 

  59 #include "libm_protos.h"        /* _SVID_libm_error */
  60 #include "libm_macros.h"
  61 #include <math.h>
  62 
  63 /* INDENT OFF */
  64 static const double xxx[] = {
  65 /* one */        1.00000000000000000000e+00,    /* 3FF00000, 00000000 */
  66 /* pi */         3.14159265358979311600e+00,    /* 400921FB, 54442D18 */
  67 /* pio2_hi */    1.57079632679489655800e+00,    /* 3FF921FB, 54442D18 */
  68 /* pio2_lo */    6.12323399573676603587e-17,    /* 3C91A626, 33145C07 */
  69 /* pS0 */        1.66666666666666657415e-01,    /* 3FC55555, 55555555 */
  70 /* pS1 */       -3.25565818622400915405e-01,    /* BFD4D612, 03EB6F7D */
  71 /* pS2 */        2.01212532134862925881e-01,    /* 3FC9C155, 0E884455 */
  72 /* pS3 */       -4.00555345006794114027e-02,    /* BFA48228, B5688F3B */
  73 /* pS4 */        7.91534994289814532176e-04,    /* 3F49EFE0, 7501B288 */
  74 /* pS5 */        3.47933107596021167570e-05,    /* 3F023DE1, 0DFDF709 */
  75 /* qS1 */       -2.40339491173441421878e+00,    /* C0033A27, 1C8A2D4B */
  76 /* qS2 */        2.02094576023350569471e+00,    /* 40002AE5, 9C598AC8 */
  77 /* qS3 */       -6.88283971605453293030e-01,    /* BFE6066C, 1B8D0159 */
  78 /* qS4 */        7.70381505559019352791e-02     /* 3FB3B8C5, B12E9282 */