/* * Single-precision e^x function. * * Copyright (c) 2017-2018, Arm Limited. * SPDX-License-Identifier: MIT */ #include "libc/math/math.h" #include "libc/math/libm.h" #include "libc/math/exp2f_data.h" /* EXP2F_TABLE_BITS = 5 EXP2F_POLY_ORDER = 3 ULP error: 0.502 (nearest rounding.) Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.) Wrong count: 170635 (all nearest rounding wrong results with fma.) Non-nearest ULP error: 1 (rounded ULP error) */ #define N (1 << EXP2F_TABLE_BITS) #define InvLn2N __exp2f_data.invln2_scaled #define T __exp2f_data.tab #define C __exp2f_data.poly_scaled static inline uint32_t top12(float x) { return asuint(x) >> 20; } float expf(float x) { uint32_t abstop; uint64_t ki, t; double_t kd, xd, z, r, r2, y, s; xd = (double_t)x; abstop = top12(x) & 0x7ff; if (predict_false(abstop >= top12(88.0f))) { /* |x| >= 88 or x is nan. */ if (asuint(x) == asuint(-INFINITY)) return 0.0f; if (abstop >= top12(INFINITY)) return x + x; if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */ return __math_oflowf(0); if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */ return __math_uflowf(0); } /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k. */ z = InvLn2N * xd; /* Round and convert z to int, the result is in [-150*N, 128*N] and ideally ties-to-even rule is used, otherwise the magnitude of r can be bigger which gives larger approximation error. */ #if TOINT_INTRINSICS kd = roundtoint(z); ki = converttoint(z); #else # define SHIFT __exp2f_data.shift kd = eval_as_double(z + SHIFT); ki = asuint64(kd); kd -= SHIFT; #endif r = z - kd; /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */ t = T[ki % N]; t += ki << (52 - EXP2F_TABLE_BITS); s = asdouble(t); z = C[0] * r + C[1]; r2 = r * r; y = C[2] * r + 1; y = z * r2 + y; y = y * s; return eval_as_float(y); }