1*31914882SAlex Richardson /* 2*31914882SAlex Richardson * Single-precision 2^x function. 3*31914882SAlex Richardson * 4*31914882SAlex Richardson * Copyright (c) 2017-2018, Arm Limited. 5*31914882SAlex Richardson * SPDX-License-Identifier: MIT 6*31914882SAlex Richardson */ 7*31914882SAlex Richardson 8*31914882SAlex Richardson #include <math.h> 9*31914882SAlex Richardson #include <stdint.h> 10*31914882SAlex Richardson #include "math_config.h" 11*31914882SAlex Richardson 12*31914882SAlex Richardson /* 13*31914882SAlex Richardson EXP2F_TABLE_BITS = 5 14*31914882SAlex Richardson EXP2F_POLY_ORDER = 3 15*31914882SAlex Richardson 16*31914882SAlex Richardson ULP error: 0.502 (nearest rounding.) 17*31914882SAlex Richardson Relative error: 1.69 * 2^-34 in [-1/64, 1/64] (before rounding.) 18*31914882SAlex Richardson Wrong count: 168353 (all nearest rounding wrong results with fma.) 19*31914882SAlex Richardson Non-nearest ULP error: 1 (rounded ULP error) 20*31914882SAlex Richardson */ 21*31914882SAlex Richardson 22*31914882SAlex Richardson #define N (1 << EXP2F_TABLE_BITS) 23*31914882SAlex Richardson #define T __exp2f_data.tab 24*31914882SAlex Richardson #define C __exp2f_data.poly 25*31914882SAlex Richardson #define SHIFT __exp2f_data.shift_scaled 26*31914882SAlex Richardson 27*31914882SAlex Richardson static inline uint32_t 28*31914882SAlex Richardson top12 (float x) 29*31914882SAlex Richardson { 30*31914882SAlex Richardson return asuint (x) >> 20; 31*31914882SAlex Richardson } 32*31914882SAlex Richardson 33*31914882SAlex Richardson float 34*31914882SAlex Richardson exp2f (float x) 35*31914882SAlex Richardson { 36*31914882SAlex Richardson uint32_t abstop; 37*31914882SAlex Richardson uint64_t ki, t; 38*31914882SAlex Richardson /* double_t for better performance on targets with FLT_EVAL_METHOD==2. */ 39*31914882SAlex Richardson double_t kd, xd, z, r, r2, y, s; 40*31914882SAlex Richardson 41*31914882SAlex Richardson xd = (double_t) x; 42*31914882SAlex Richardson abstop = top12 (x) & 0x7ff; 43*31914882SAlex Richardson if (unlikely (abstop >= top12 (128.0f))) 44*31914882SAlex Richardson { 45*31914882SAlex Richardson /* |x| >= 128 or x is nan. */ 46*31914882SAlex Richardson if (asuint (x) == asuint (-INFINITY)) 47*31914882SAlex Richardson return 0.0f; 48*31914882SAlex Richardson if (abstop >= top12 (INFINITY)) 49*31914882SAlex Richardson return x + x; 50*31914882SAlex Richardson if (x > 0.0f) 51*31914882SAlex Richardson return __math_oflowf (0); 52*31914882SAlex Richardson if (x <= -150.0f) 53*31914882SAlex Richardson return __math_uflowf (0); 54*31914882SAlex Richardson #if WANT_ERRNO_UFLOW 55*31914882SAlex Richardson if (x < -149.0f) 56*31914882SAlex Richardson return __math_may_uflowf (0); 57*31914882SAlex Richardson #endif 58*31914882SAlex Richardson } 59*31914882SAlex Richardson 60*31914882SAlex Richardson /* x = k/N + r with r in [-1/(2N), 1/(2N)] and int k. */ 61*31914882SAlex Richardson kd = eval_as_double (xd + SHIFT); 62*31914882SAlex Richardson ki = asuint64 (kd); 63*31914882SAlex Richardson kd -= SHIFT; /* k/N for int k. */ 64*31914882SAlex Richardson r = xd - kd; 65*31914882SAlex Richardson 66*31914882SAlex Richardson /* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ 67*31914882SAlex Richardson t = T[ki % N]; 68*31914882SAlex Richardson t += ki << (52 - EXP2F_TABLE_BITS); 69*31914882SAlex Richardson s = asdouble (t); 70*31914882SAlex Richardson z = C[0] * r + C[1]; 71*31914882SAlex Richardson r2 = r * r; 72*31914882SAlex Richardson y = C[2] * r + 1; 73*31914882SAlex Richardson y = z * r2 + y; 74*31914882SAlex Richardson y = y * s; 75*31914882SAlex Richardson return eval_as_float (y); 76*31914882SAlex Richardson } 77*31914882SAlex Richardson #if USE_GLIBC_ABI 78*31914882SAlex Richardson strong_alias (exp2f, __exp2f_finite) 79*31914882SAlex Richardson hidden_alias (exp2f, __ieee754_exp2f) 80*31914882SAlex Richardson #endif 81