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_VAL_WITH_FLAGS 31 #define USE_NAN_WITH_FLAGS 32 #define USE_HANDLE_ERROR 33 #include "libm_inlines.h" 34 #undef USE_VAL_WITH_FLAGS 35 #undef USE_NAN_WITH_FLAGS 36 #undef USE_HANDLE_ERROR 37 38 #include "libm_errno.h" 39 40 #ifdef _MSC_VER 41 #pragma function(atan) 42 #endif 43 44 double FN_PROTOTYPE(atan)(double x) 45 { 46 47 /* Some constants and split constants. */ 48 49 static double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */ 50 double chi, clo, v, s, q, z; 51 52 /* Find properties of argument x. */ 53 54 unsigned long long ux, aux, xneg; 55 GET_BITS_DP64(x, ux); 56 aux = ux & ~SIGNBIT_DP64; 57 xneg = (ux != aux); 58 59 if (xneg) v = -x; 60 else v = x; 61 62 /* Argument reduction to range [-7/16,7/16] */ 63 64 if (aux > 0x4003800000000000) /* v > 39./16. */ 65 { 66 67 if (aux > PINFBITPATT_DP64) 68 { 69 /* x is NaN */ 70 return _handle_error("atan", OP_ATAN, ux|0x0008000000000000, _DOMAIN, 0, 71 EDOM, x, 0.0, 1); 72 } 73 else if (v > 0x4370000000000000) 74 { /* abs(x) > 2^56 => arctan(1/x) is 75 insignificant compared to piby2 */ 76 if (xneg) 77 return val_with_flags(-piby2, AMD_F_INEXACT); 78 else 79 return val_with_flags(piby2, AMD_F_INEXACT); 80 } 81 82 x = -1.0/v; 83 /* (chi + clo) = arctan(infinity) */ 84 chi = 1.57079632679489655800e+00; /* 0x3ff921fb54442d18 */ 85 clo = 6.12323399573676480327e-17; /* 0x3c91a62633145c06 */ 86 } 87 else if (aux > 0x3ff3000000000000) /* 39./16. > v > 19./16. */ 88 { 89 x = (v-1.5)/(1.0+1.5*v); 90 /* (chi + clo) = arctan(1.5) */ 91 chi = 9.82793723247329054082e-01; /* 0x3fef730bd281f69b */ 92 clo = 1.39033110312309953701e-17; /* 0x3c7007887af0cbbc */ 93 } 94 else if (aux > 0x3fe6000000000000) /* 19./16. > v > 11./16. */ 95 { 96 x = (v-1.0)/(1.0+v); 97 /* (chi + clo) = arctan(1.) */ 98 chi = 7.85398163397448278999e-01; /* 0x3fe921fb54442d18 */ 99 clo = 3.06161699786838240164e-17; /* 0x3c81a62633145c06 */ 100 } 101 else if (aux > 0x3fdc000000000000) /* 11./16. > v > 7./16. */ 102 { 103 x = (2.0*v-1.0)/(2.0+v); 104 /* (chi + clo) = arctan(0.5) */ 105 chi = 4.63647609000806093515e-01; /* 0x3fddac670561bb4f */ 106 clo = 2.26987774529616809294e-17; /* 0x3c7a2b7f222f65e0 */ 107 } 108 else /* v < 7./16. */ 109 { 110 x = v; 111 chi = 0.0; 112 clo = 0.0; 113 } 114 115 /* Core approximation: Remez(4,4) on [-7/16,7/16] */ 116 117 s = x*x; 118 q = x*s* 119 (0.268297920532545909e0 + 120 (0.447677206805497472e0 + 121 (0.220638780716667420e0 + 122 (0.304455919504853031e-1 + 123 0.142316903342317766e-3*s)*s)*s)*s)/ 124 (0.804893761597637733e0 + 125 (0.182596787737507063e1 + 126 (0.141254259931958921e1 + 127 (0.424602594203847109e0 + 128 0.389525873944742195e-1*s)*s)*s)*s); 129 130 z = chi - ((q - clo) - x); 131 132 if (xneg) z = -z; 133 return z; 134 } 135