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148 lines
4.5 KiB
C
148 lines
4.5 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_VALF_WITH_FLAGS
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#define USE_NANF_WITH_FLAGS
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#define USE_HANDLE_ERRORF
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#include "libm_inlines.h"
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#undef USE_NANF_WITH_FLAGS
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#undef USE_VALF_WITH_FLAGS
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#undef USE_HANDLE_ERRORF
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#include "libm_errno.h"
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#ifdef _MSC_VER
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// Disable "C4163: not available as intrinsic function" warning that older
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// compilers may issue here.
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#pragma warning(disable:4163)
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#pragma function(acosf)
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#endif
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float FN_PROTOTYPE(acosf)(float x)
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{
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/* Computes arccos(x).
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The argument is first reduced by noting that arccos(x)
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is invalid for abs(x) > 1. For denormal and small
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arguments arccos(x) = pi/2 to machine accuracy.
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Remaining argument ranges are handled as follows.
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For abs(x) <= 0.5 use
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arccos(x) = pi/2 - arcsin(x)
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= pi/2 - (x + x^3*R(x^2))
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where R(x^2) is a rational minimax approximation to
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(arcsin(x) - x)/x^3.
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For abs(x) > 0.5 exploit the identity:
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arccos(x) = pi - 2*arcsin(sqrt(1-x)/2)
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together with the above rational approximation, and
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reconstruct the terms carefully.
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*/
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/* Some constants and split constants. */
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static const float
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piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */
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static const double
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pi = 3.1415926535897933e+00, /* 0x400921fb54442d18 */
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piby2_head = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */
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piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */
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float u, y, s = 0.0F, r;
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int xexp, xnan, transform = 0;
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unsigned int ux, aux, xneg;
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GET_BITS_SP32(x, ux);
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aux = ux & ~SIGNBIT_SP32;
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xneg = (ux & SIGNBIT_SP32);
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xnan = (aux > PINFBITPATT_SP32);
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xexp = (int)((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
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/* Special cases */
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if (xnan)
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{
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return _handle_errorf("acosf", OP_ACOS, ux|0x00400000, _DOMAIN, 0,
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EDOM, x, 0.0F, 1);
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}
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else if (xexp < -26)
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/* y small enough that arccos(x) = pi/2 */
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return valf_with_flags(piby2, AMD_F_INEXACT);
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else if (xexp >= 0)
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{ /* abs(x) >= 1.0 */
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if (x == 1.0F)
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return 0.0F;
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else if (x == -1.0F)
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return valf_with_flags((float)pi, AMD_F_INEXACT);
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else
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return _handle_errorf("acosf", OP_ACOS, INDEFBITPATT_SP32, _DOMAIN,
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AMD_F_INVALID, EDOM, x, 0.0F, 1);
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}
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if (xneg) y = -x;
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else y = x;
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transform = (xexp >= -1); /* abs(x) >= 0.5 */
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if (transform)
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{ /* Transform y into the range [0,0.5) */
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r = 0.5F*(1.0F - y);
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/* VC++ intrinsic call */
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_mm_store_ss(&s, _mm_sqrt_ss(_mm_load_ss(&r)));
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y = s;
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}
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else
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r = y*y;
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/* Use a rational approximation for [0.0, 0.5] */
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u=r*(0.184161606965100694821398249421F +
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(-0.0565298683201845211985026327361F +
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(-0.0133819288943925804214011424456F -
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0.00396137437848476485201154797087F*r)*r)*r)/
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(1.10496961524520294485512696706F -
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0.836411276854206731913362287293F*r);
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if (transform)
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{
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/* Reconstruct acos carefully in transformed region */
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if (xneg)
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return (float)(pi - 2.0*(s+(y*u - piby2_tail)));
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else
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{
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float c, s1;
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unsigned int us;
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GET_BITS_SP32(s, us);
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PUT_BITS_SP32(0xffff0000 & us, s1);
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c = (r-s1*s1)/(s+s1);
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return 2.0F*s1 + (2.0F*c+2.0F*y*u);
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}
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}
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else
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return (float)(piby2_head - (x - (piby2_tail - x*u)));
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}
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