src/math/expf.c

   1 /*
   2  * Single-precision e^x function.
   3  *
   4  * Copyright (c) 2017-2018, Arm Limited.
   5  * SPDX-License-Identifier: MIT
   6  */
   7
   8 #include <math.h>
   9 #include <stdint.h>
  10 #include "libm.h"
  11 #include "exp2f_data.h"
  12
  13 /*
  14 EXP2F_TABLE_BITS = 5
  15 EXP2F_POLY_ORDER = 3
  16
  17 ULP error: 0.502 (nearest rounding.)
  18 Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
  19 Wrong count: 170635 (all nearest rounding wrong results with fma.)
  20 Non-nearest ULP error: 1 (rounded ULP error)
  21 */
  22
  23 #define N (1 << EXP2F_TABLE_BITS)
  24 #define InvLn2N __exp2f_data.invln2_scaled
  25 #define T __exp2f_data.tab
  26 #define C __exp2f_data.poly_scaled
  27
  28 static inline uint32_t top12(float x)
  29 {
  30         return asuint(x) >> 20;
  31 }
  32
  33 float expf(float x)
  34 {
  35         uint32_t abstop;
  36         uint64_t ki, t;
  37         double_t kd, xd, z, r, r2, y, s;
  38
  39         xd = (double_t)x;
  40         abstop = top12(x) & 0x7ff;
  41         if (predict_false(abstop >= top12(88.0f))) {
  42                 /* |x| >= 88 or x is nan.  */
  43                 if (asuint(x) == asuint(-INFINITY))
  44                         return 0.0f;
  45                 if (abstop >= top12(INFINITY))
  46                         return x + x;
  47                 if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
  48                         return __math_oflowf(0);
  49                 if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
  50                         return __math_uflowf(0);
  51         }
  52
  53         /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
  54         z = InvLn2N * xd;
  55
  56         /* Round and convert z to int, the result is in [-150*N, 128*N] and
  57            ideally ties-to-even rule is used, otherwise the magnitude of r
  58            can be bigger which gives larger approximation error.  */
  59 #if TOINT_INTRINSICS
  60         kd = roundtoint(z);
  61         ki = converttoint(z);
  62 #else
  63 # define SHIFT __exp2f_data.shift
  64         kd = eval_as_double(z + SHIFT);
  65         ki = asuint64(kd);
  66         kd -= SHIFT;
  67 #endif
  68         r = z - kd;
  69
  70         /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  71         t = T[ki % N];
  72         t += ki << (52 - EXP2F_TABLE_BITS);
  73         s = asdouble(t);
  74         z = C[0] * r + C[1];
  75         r2 = r * r;
  76         y = C[2] * r + 1;
  77         y = z * r2 + y;
  78         y = y * s;
  79         return eval_as_float(y);
  80 }