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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 atan = __atan
  31 
  32 /* INDENT OFF */
  33 /*
  34  * atan(x)
  35  * Accurate Table look-up algorithm with polynomial approximation in
  36  * partially product form.
  37  *
  38  * -- K.C. Ng, October 17, 2004
  39  *
  40  * Algorithm
  41  *
  42  * (1). Purge off Inf and NaN and 0
  43  * (2). Reduce x to positive by atan(x) = -atan(-x).
  44  * (3). For x <= 1/8 and let z = x*x, return
  45  *      (2.1) if x < 2^(-prec/2), atan(x) = x  with inexact flag raised
  46  *      (2.2) if x < 2^(-prec/4-1), atan(x) = x+(x/3)(x*x)
  47  *      (2.3) if x < 2^(-prec/6-2), atan(x) = x+(z-5/3)(z*x/5)
  48  *      (2.4) Otherwise
  49  *              atan(x) = poly1(x) = x + A * B,
  50  *      where


  65  *              |atan(x)-poly2(x)|<= 2^-59.45
  66  *
  67  * (5). Now x is in (0.125, 8).
  68  *      Recall identity
  69  *              atan(x) = atan(y) + atan((x-y)/(1+x*y)).
  70  *      Let j = (ix - 0x3fc00000) >> 16, 0 <= j < 96, where ix is the high
  71  *      part of x in IEEE double format. Then
  72  *              atan(x) = atan(y[j]) + poly2((x-y[j])/(1+x*y[j]))
  73  *      where y[j] are carefully chosen so that it matches x to around 4.5
  74  *      bits and at the same time atan(y[j]) is very close to an IEEE double
  75  *      floating point number. Calculation indicates that
  76  *              max|(x-y[j])/(1+x*y[j])| < 0.0154
  77  *              j,x
  78  *
  79  * Accuracy: Maximum error observed is bounded by 0.6 ulp after testing
  80  * more than 10 million random arguments
  81  */
  82 /* INDENT ON */
  83 
  84 #include "libm.h"
  85 #include "libm_synonyms.h"
  86 #include "libm_protos.h"
  87 
  88 extern const double _TBL_atan[];
  89 static const double g[] = {
  90 /* one  = */  1.0,
  91 /* p1   = */  8.02176624254765935351230154992663301527500152588e-0002,
  92 /* p2   = */  1.27223421700559402580665846471674740314483642578e+0000,
  93 /* p3   = */ -1.20606901800503640842521235754247754812240600586e+0000,
  94 /* p4   = */ -2.36088967922325565496066701598465442657470703125e+0000,
  95 /* p5   = */  1.38345799501389166152875986881554126739501953125e+0000,
  96 /* p6   = */  1.06742368078953453469637224770849570631980895996e+0000,
  97 /* q1   = */ -1.42796626333911796935538518482644576579332351685e-0001,
  98 /* q2   = */  3.51427110447873227059810477159863497078605962912e+0000,
  99 /* q3   = */  5.92129112708164262457444237952586263418197631836e-0001,
 100 /* q4   = */ -1.99272234785683144409063061175402253866195678711e+0000,
 101 /* pio2hi */  1.570796326794896558e+00,
 102 /* pio2lo */  6.123233995736765886e-17,
 103 /* t1   = */ -0.333333333333333333333333333333333,
 104 /* t2   = */  0.2,
 105 /* t3   = */ -1.666666666666666666666666666666666,




  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 __atan = atan
  31 
  32 /* INDENT OFF */
  33 /*
  34  * atan(x)
  35  * Accurate Table look-up algorithm with polynomial approximation in
  36  * partially product form.
  37  *
  38  * -- K.C. Ng, October 17, 2004
  39  *
  40  * Algorithm
  41  *
  42  * (1). Purge off Inf and NaN and 0
  43  * (2). Reduce x to positive by atan(x) = -atan(-x).
  44  * (3). For x <= 1/8 and let z = x*x, return
  45  *      (2.1) if x < 2^(-prec/2), atan(x) = x  with inexact flag raised
  46  *      (2.2) if x < 2^(-prec/4-1), atan(x) = x+(x/3)(x*x)
  47  *      (2.3) if x < 2^(-prec/6-2), atan(x) = x+(z-5/3)(z*x/5)
  48  *      (2.4) Otherwise
  49  *              atan(x) = poly1(x) = x + A * B,
  50  *      where


  65  *              |atan(x)-poly2(x)|<= 2^-59.45
  66  *
  67  * (5). Now x is in (0.125, 8).
  68  *      Recall identity
  69  *              atan(x) = atan(y) + atan((x-y)/(1+x*y)).
  70  *      Let j = (ix - 0x3fc00000) >> 16, 0 <= j < 96, where ix is the high
  71  *      part of x in IEEE double format. Then
  72  *              atan(x) = atan(y[j]) + poly2((x-y[j])/(1+x*y[j]))
  73  *      where y[j] are carefully chosen so that it matches x to around 4.5
  74  *      bits and at the same time atan(y[j]) is very close to an IEEE double
  75  *      floating point number. Calculation indicates that
  76  *              max|(x-y[j])/(1+x*y[j])| < 0.0154
  77  *              j,x
  78  *
  79  * Accuracy: Maximum error observed is bounded by 0.6 ulp after testing
  80  * more than 10 million random arguments
  81  */
  82 /* INDENT ON */
  83 
  84 #include "libm.h"

  85 #include "libm_protos.h"
  86 
  87 extern const double _TBL_atan[];
  88 static const double g[] = {
  89 /* one  = */  1.0,
  90 /* p1   = */  8.02176624254765935351230154992663301527500152588e-0002,
  91 /* p2   = */  1.27223421700559402580665846471674740314483642578e+0000,
  92 /* p3   = */ -1.20606901800503640842521235754247754812240600586e+0000,
  93 /* p4   = */ -2.36088967922325565496066701598465442657470703125e+0000,
  94 /* p5   = */  1.38345799501389166152875986881554126739501953125e+0000,
  95 /* p6   = */  1.06742368078953453469637224770849570631980895996e+0000,
  96 /* q1   = */ -1.42796626333911796935538518482644576579332351685e-0001,
  97 /* q2   = */  3.51427110447873227059810477159863497078605962912e+0000,
  98 /* q3   = */  5.92129112708164262457444237952586263418197631836e-0001,
  99 /* q4   = */ -1.99272234785683144409063061175402253866195678711e+0000,
 100 /* pio2hi */  1.570796326794896558e+00,
 101 /* pio2lo */  6.123233995736765886e-17,
 102 /* t1   = */ -0.333333333333333333333333333333333,
 103 /* t2   = */  0.2,
 104 /* t3   = */ -1.666666666666666666666666666666666,