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135 lines
4 KiB
C
135 lines
4 KiB
C
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/*******************************************************************************
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MIT License
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-----------
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Copyright (c) 2002-2019 Advanced Micro Devices, Inc.
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this Software and associated documentaon files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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THE SOFTWARE.
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*******************************************************************************/
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#include "libm.h"
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#include "libm_util.h"
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#define USE_VAL_WITH_FLAGS
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#define USE_NAN_WITH_FLAGS
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#define USE_HANDLE_ERROR
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#include "libm_inlines.h"
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#undef USE_VAL_WITH_FLAGS
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#undef USE_NAN_WITH_FLAGS
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#undef USE_HANDLE_ERROR
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#include "libm_errno.h"
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#ifdef _MSC_VER
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#pragma function(atan)
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#endif
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double FN_PROTOTYPE(atan)(double x)
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{
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/* Some constants and split constants. */
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static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */
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double chi, clo, v, s, q, z;
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/* Find properties of argument x. */
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unsigned long long ux, aux, xneg;
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GET_BITS_DP64(x, ux);
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aux = ux & ~SIGNBIT_DP64;
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xneg = (ux != aux);
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if (xneg) v = -x;
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else v = x;
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/* Argument reduction to range [-7/16,7/16] */
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if (aux > 0x4003800000000000) /* v > 39./16. */
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{
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if (aux > PINFBITPATT_DP64)
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{
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/* x is NaN */
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return _handle_error("atan", OP_ATAN, ux|0x0008000000000000, _DOMAIN, 0,
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EDOM, x, 0.0, 1);
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}
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else if (v > 0x4370000000000000)
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{ /* abs(x) > 2^56 => arctan(1/x) is
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insignificant compared to piby2 */
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if (xneg)
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return val_with_flags(-piby2, AMD_F_INEXACT);
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else
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return val_with_flags(piby2, AMD_F_INEXACT);
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}
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x = -1.0/v;
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/* (chi + clo) = arctan(infinity) */
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chi = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */
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clo = 6.12323399573676480327e-17; /* 0x3c91a62633145c06 */
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}
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else if (aux > 0x3ff3000000000000) /* 39./16. > v > 19./16. */
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{
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x = (v-1.5)/(1.0+1.5*v);
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/* (chi + clo) = arctan(1.5) */
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chi = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */
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clo = 1.39033110312309953701e-17; /* 0x3c7007887af0cbbc */
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}
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else if (aux > 0x3fe6000000000000) /* 19./16. > v > 11./16. */
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{
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x = (v-1.0)/(1.0+v);
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/* (chi + clo) = arctan(1.) */
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chi = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */
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clo = 3.06161699786838240164e-17; /* 0x3c81a62633145c06 */
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}
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else if (aux > 0x3fdc000000000000) /* 11./16. > v > 7./16. */
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{
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x = (2.0*v-1.0)/(2.0+v);
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/* (chi + clo) = arctan(0.5) */
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chi = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */
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clo = 2.26987774529616809294e-17; /* 0x3c7a2b7f222f65e0 */
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}
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else /* v < 7./16. */
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{
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x = v;
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chi = 0.0;
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clo = 0.0;
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}
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/* Core approximation: Remez(4,4) on [-7/16,7/16] */
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s = x*x;
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q = x*s*
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(0.268297920532545909e0 +
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(0.447677206805497472e0 +
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(0.220638780716667420e0 +
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(0.304455919504853031e-1 +
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0.142316903342317766e-3*s)*s)*s)*s)/
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(0.804893761597637733e0 +
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(0.182596787737507063e1 +
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(0.141254259931958921e1 +
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(0.424602594203847109e0 +
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0.389525873944742195e-1*s)*s)*s)*s);
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z = chi - ((q - clo) - x);
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if (xneg) z = -z;
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return z;
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}
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