| /* |
| * 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 "math32.h" |
| |
| __attribute__((overloadable)) float |
| acosh(float x) |
| { |
| uint ux = as_uint(x); |
| |
| // Arguments greater than 1/sqrt(epsilon) in magnitude are |
| // approximated by acosh(x) = ln(2) + ln(x) |
| // For 2.0 <= x <= 1/sqrt(epsilon) the approximation is |
| // acosh(x) = ln(x + sqrt(x*x-1)) */ |
| int high = ux > 0x46000000U; |
| int med = ux > 0x40000000U; |
| |
| float w = x - 1.0f; |
| float s = w*w + 2.0f*w; |
| float t = x*x - 1.0f; |
| float r = MATH_SQRT(med ? t : s) + (med ? x : w); |
| float v = (high ? x : r) - (med ? 1.0f : 0.0f); |
| float z = log1p(v) + (high ? 0x1.62e430p-1f : 0.0f); |
| |
| z = ux >= PINFBITPATT_SP32 ? x : z; |
| z = x < 1.0f ? as_float(QNANBITPATT_SP32) : z; |
| |
| return z; |
| } |
| |