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_SPLITEXP 31 #define USE_SCALEDOUBLE_1 32 #define USE_SCALEDOUBLE_2 33 #define USE_ZERO_WITH_FLAGS 34 #define USE_INFINITY_WITH_FLAGS 35 #define USE_HANDLE_ERROR 36 37 #include "libm_inlines.h" 38 #undef USE_ZERO_WITH_FLAGS 39 #undef USE_SPLITEXP 40 #undef USE_SCALEDOUBLE_1 41 #undef USE_SCALEDOUBLE_2 42 #undef USE_INFINITY_WITH_FLAGS 43 #undef USE_HANDLE_ERROR 44 45 #include "libm_errno.h" 46 47 /* exp2 is only provided for use by powf under Windows, so give 48 it a leading underscore. */ 49 double FN_PROTOTYPE(_exp2)(double x) 50 { 51 static const double 52 max_exp2_arg = 1024.0, /* 0x4090000000000000 */ 53 min_exp2_arg = -1074.0, /* 0xc090c80000000000 */ 54 log2 = 6.931471805599453094178e-01, /* 0x3fe62e42fefa39ef */ 55 log2_lead = 6.93147167563438415527E-01, /* 0x3fe62e42f8000000 */ 56 log2_tail = 1.29965068938898869640E-08, /* 0x3e4be8e7bcd5e4f1 */ 57 one_by_32_lead = 0.03125; 58 59 double y, z1, z2, z, hx, tx, y1, y2; 60 int m; 61 unsigned long long ux, ax; 62 63 /* 64 Computation of exp2(x). 65 66 We compute the values m, z1, and z2 such that 67 exp2(x) = 2**m * (z1 + z2), where exp2(x) is 2**x. 68 69 Computations needed in order to obtain m, z1, and z2 70 involve three steps. 71 72 First, we reduce the argument x to the form 73 x = n/32 + remainder, 74 where n has the value of an integer and |remainder| <= 1/64. 75 The value of n = x * 32 rounded to the nearest integer and 76 the remainder = x - n/32. 77 78 Second, we approximate exp2(r1 + r2) - 1 where r1 is the leading 79 part of the remainder and r2 is the trailing part of the remainder. 80 81 Third, we reconstruct exp2(x) so that 82 exp2(x) = 2**m * (z1 + z2). 83 */ 84 85 86 GET_BITS_DP64(x, ux); 87 ax = ux & (~SIGNBIT_DP64); 88 89 if (ax >= 0x4090000000000000) /* abs(x) >= 1024.0 */ 90 { 91 if(ax >= 0x7ff0000000000000) 92 { 93 /* x is either NaN or infinity */ 94 if (ux & MANTBITS_DP64) 95 /* x is NaN */ 96 return _handle_error("exp2", OP_EXP, ux|0x0008000000000000, _DOMAIN, 97 0, EDOM, x, 0.0, 1); 98 else if (ux & SIGNBIT_DP64) 99 /* x is negative infinity; return 0.0 with no flags. */ 100 return 0.0; 101 else 102 /* x is positive infinity */ 103 return x; 104 } 105 if (x > max_exp2_arg) 106 /* Return +infinity with overflow flag */ 107 return _handle_error("exp2", OP_EXP, PINFBITPATT_DP64, _OVERFLOW, 108 AMD_F_OVERFLOW | AMD_F_INEXACT, ERANGE, x, 0.0, 1); 109 else if (x < min_exp2_arg) 110 /* x is negative. Return +zero with underflow and inexact flags */ 111 return _handle_error("exp2", OP_EXP, 0, _UNDERFLOW, 112 AMD_F_UNDERFLOW | AMD_F_INEXACT, ERANGE, x, 0.0, 1); 113 } 114 115 116 /* Handle small arguments separately */ 117 if (ax < 0x3fb7154764ee6c2f) /* abs(x) < 1/(16*log2) */ 118 { 119 if (ax < 0x3c00000000000000) /* abs(x) < 2^(-63) */ 120 return 1.0 + x; /* Raises inexact if x is non-zero */ 121 else 122 { 123 /* Split x into hx (head) and tx (tail). */ 124 unsigned long long u; 125 hx = x; 126 GET_BITS_DP64(hx, u); 127 u &= 0xfffffffff8000000; 128 PUT_BITS_DP64(u, hx); 129 tx = x - hx; 130 /* Carefully multiply x by log2. y1 is the most significant 131 part of the result, and y2 the least significant part */ 132 y1 = x * log2_lead; 133 y2 = (((hx * log2_lead - y1) + hx * log2_tail) + 134 tx * log2_lead) + tx * log2_tail; 135 136 y = y1 + y2; 137 z = (9.99564649780173690e-1 + 138 (1.61251249355268050e-5 + 139 (2.37986978239838493e-2 + 140 2.68724774856111190e-7*y)*y)*y)/ 141 (9.99564649780173692e-1 + 142 (-4.99766199765151309e-1 + 143 (1.070876894098586184e-1 + 144 (-1.189773642681502232e-2 + 145 5.9480622371960190616e-4*y)*y)*y)*y); 146 z = ((z * y1) + (z * y2)) + 1.0; 147 } 148 } 149 else 150 { 151 /* Find m, z1 and z2 such that exp2(x) = 2**m * (z1 + z2) */ 152 153 splitexp(x, log2, 32.0, one_by_32_lead, 0.0, &m, &z1, &z2); 154 155 /* Scale (z1 + z2) by 2.0**m */ 156 if (m > EMIN_DP64 && m < EMAX_DP64) 157 z = scaleDouble_1((z1+z2),m); 158 else 159 z = scaleDouble_2((z1+z2),m); 160 } 161 return z; 162 } 163