| /* |
| * Copyright (c) 2014 Advanced Micro Devices, Inc. |
| * |
| * Permission is hereby granted, free of charge, to any person obtaining a copy |
| * of this software and associated documentation files (the "Software"), to deal |
| * in the Software without restriction, including without limitation the rights |
| * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
| * copies of the Software, and to permit persons to whom the Software is |
| * furnished to do so, subject to the following conditions: |
| * |
| * The above copyright notice and this permission notice shall be included in |
| * all copies or substantial portions of the Software. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
| * THE SOFTWARE. |
| */ |
| |
| #include "math64.h" |
| |
| __attribute__((overloadable)) double |
| acos(double x) |
| { |
| // Computes arccos(x). |
| // The argument is first reduced by noting that arccos(x) |
| // is invalid for abs(x) > 1. For denormal and small |
| // arguments arccos(x) = pi/2 to machine accuracy. |
| // Remaining argument ranges are handled as follows. |
| // For abs(x) <= 0.5 use |
| // arccos(x) = pi/2 - arcsin(x) |
| // = pi/2 - (x + x^3*R(x^2)) |
| // where R(x^2) is a rational minimax approximation to |
| // (arcsin(x) - x)/x^3. |
| // For abs(x) > 0.5 exploit the identity: |
| // arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) |
| // together with the above rational approximation, and |
| // reconstruct the terms carefully. |
| |
| const double pi = 3.1415926535897933e+00; /* 0x400921fb54442d18 */ |
| const double piby2 = 1.5707963267948965580e+00; /* 0x3ff921fb54442d18 */ |
| const double piby2_head = 1.5707963267948965580e+00; /* 0x3ff921fb54442d18 */ |
| const double piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */ |
| |
| double y = fabs(x); |
| int xneg = as_int2(x).hi < 0; |
| int xexp = (as_int2(y).hi >> 20) - EXPBIAS_DP64; |
| |
| // abs(x) >= 0.5 |
| int transform = xexp >= -1; |
| |
| double rt = 0.5 * (1.0 - y); |
| double y2 = y * y; |
| double r = transform ? rt : y2; |
| |
| // Use a rational approximation for [0.0, 0.5] |
| double un = fma(r, |
| fma(r, |
| fma(r, |
| fma(r, |
| fma(r, 0.0000482901920344786991880522822991, |
| 0.00109242697235074662306043804220), |
| -0.0549989809235685841612020091328), |
| 0.275558175256937652532686256258), |
| -0.445017216867635649900123110649), |
| 0.227485835556935010735943483075); |
| |
| double ud = fma(r, |
| fma(r, |
| fma(r, |
| fma(r, 0.105869422087204370341222318533, |
| -0.943639137032492685763471240072), |
| 2.76568859157270989520376345954), |
| -3.28431505720958658909889444194), |
| 1.36491501334161032038194214209); |
| |
| double u = r * MATH_DIVIDE(un, ud); |
| |
| // Reconstruct acos carefully in transformed region |
| double s = sqrt(r); |
| double ztn = fma(-2.0, (s + fma(s, u, -piby2_tail)), pi); |
| |
| double s1 = as_double(as_ulong(s) & 0xffffffff00000000UL); |
| double c = MATH_DIVIDE(fma(-s1, s1, r), s + s1); |
| double ztp = 2.0 * (s1 + fma(s, u, c)); |
| double zt = xneg ? ztn : ztp; |
| double z = piby2_head - (x - fma(-x, u, piby2_tail)); |
| |
| z = transform ? zt : z; |
| |
| z = xexp < -56 ? piby2 : z; |
| /* z = xexp >= 0 ? as_double(QNANBITPATT_DP64) : z; This check for nan is not working */ |
| z = isnan(x) ? as_double((as_ulong(x) | QNANBITPATT_DP64)) : z; |
| z = x == 1.0 ? 0.0 : z; |
| z = x == -1.0 ? pi : z; |
| |
| return z; |
| } |
| |