1 2 /******************************************************************************* 3 MIT License 4 ----------- 5 6 Copyright (c) 2002-2019 Advanced Micro Devices, Inc. 7 8 Permission is hereby granted, free of charge, to any person obtaining a copy 9 of this Software and associated documentaon files (the "Software"), to deal 10 in the Software without restriction, including without limitation the rights 11 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 12 copies of the Software, and to permit persons to whom the Software is 13 furnished to do so, subject to the following conditions: 14 15 The above copyright notice and this permission notice shall be included in 16 all copies or substantial portions of the Software. 17 18 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 19 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 20 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 21 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 22 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 23 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 24 THE SOFTWARE. 25 *******************************************************************************/ 26 27 #include "libm.h" 28 #include "libm_util.h" 29 30 #define USE_VALF_WITH_FLAGS 31 #define USE_NANF_WITH_FLAGS 32 #define USE_HANDLE_ERRORF 33 #include "libm_inlines.h" 34 #undef USE_NANF_WITH_FLAGS 35 #undef USE_VALF_WITH_FLAGS 36 #undef USE_HANDLE_ERRORF 37 38 #include "libm_errno.h" 39 40 #ifdef _MSC_VER 41 // Disable "C4163: not available as intrinsic function" warning that older 42 // compilers may issue here. 43 #pragma warning(disable:4163) 44 #pragma function(acosf) 45 #endif 46 47 float FN_PROTOTYPE(acosf)(float x) 48 { 49 /* Computes arccos(x). 50 The argument is first reduced by noting that arccos(x) 51 is invalid for abs(x) > 1. For denormal and small 52 arguments arccos(x) = pi/2 to machine accuracy. 53 Remaining argument ranges are handled as follows. 54 For abs(x) <= 0.5 use 55 arccos(x) = pi/2 - arcsin(x) 56 = pi/2 - (x + x^3*R(x^2)) 57 where R(x^2) is a rational minimax approximation to 58 (arcsin(x) - x)/x^3. 59 For abs(x) > 0.5 exploit the identity: 60 arccos(x) = pi - 2*arcsin(sqrt(1-x)/2) 61 together with the above rational approximation, and 62 reconstruct the terms carefully. 63 */ 64 65 /* Some constants and split constants. */ 66 67 static const float 68 piby2 = 1.5707963705e+00F; /* 0x3fc90fdb */ 69 static const double 70 pi = 3.1415926535897933e+00, /* 0x400921fb54442d18 */ 71 piby2_head = 1.5707963267948965580e+00, /* 0x3ff921fb54442d18 */ 72 piby2_tail = 6.12323399573676603587e-17; /* 0x3c91a62633145c07 */ 73 74 float u, y, s = 0.0F, r; 75 int xexp, xnan, transform = 0; 76 77 unsigned int ux, aux, xneg; 78 79 GET_BITS_SP32(x, ux); 80 aux = ux & ~SIGNBIT_SP32; 81 xneg = (ux & SIGNBIT_SP32); 82 xnan = (aux > PINFBITPATT_SP32); 83 xexp = (int)((ux & EXPBITS_SP32) >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; 84 85 /* Special cases */ 86 87 if (xnan) 88 { 89 return _handle_errorf("acosf", OP_ACOS, ux|0x00400000, _DOMAIN, 0, 90 EDOM, x, 0.0F, 1); 91 } 92 else if (xexp < -26) 93 /* y small enough that arccos(x) = pi/2 */ 94 return valf_with_flags(piby2, AMD_F_INEXACT); 95 else if (xexp >= 0) 96 { /* abs(x) >= 1.0 */ 97 if (x == 1.0F) 98 return 0.0F; 99 else if (x == -1.0F) 100 return valf_with_flags((float)pi, AMD_F_INEXACT); 101 else 102 return _handle_errorf("acosf", OP_ACOS, INDEFBITPATT_SP32, _DOMAIN, 103 AMD_F_INVALID, EDOM, x, 0.0F, 1); 104 } 105 106 if (xneg) y = -x; 107 else y = x; 108 109 transform = (xexp >= -1); /* abs(x) >= 0.5 */ 110 111 if (transform) 112 { /* Transform y into the range [0,0.5) */ 113 r = 0.5F*(1.0F - y); 114 /* VC++ intrinsic call */ 115 _mm_store_ss(&s, _mm_sqrt_ss(_mm_load_ss(&r))); 116 y = s; 117 } 118 else 119 r = y*y; 120 121 /* Use a rational approximation for [0.0, 0.5] */ 122 123 u=r*(0.184161606965100694821398249421F + 124 (-0.0565298683201845211985026327361F + 125 (-0.0133819288943925804214011424456F - 126 0.00396137437848476485201154797087F*r)*r)*r)/ 127 (1.10496961524520294485512696706F - 128 0.836411276854206731913362287293F*r); 129 130 if (transform) 131 { 132 /* Reconstruct acos carefully in transformed region */ 133 if (xneg) 134 return (float)(pi - 2.0*(s+(y*u - piby2_tail))); 135 else 136 { 137 float c, s1; 138 unsigned int us; 139 GET_BITS_SP32(s, us); 140 PUT_BITS_SP32(0xffff0000 & us, s1); 141 c = (r-s1*s1)/(s+s1); 142 return 2.0F*s1 + (2.0F*c+2.0F*y*u); 143 } 144 } 145 else 146 return (float)(piby2_head - (x - (piby2_tail - x*u))); 147 } 148