libc/AOR_v20.02/math/expf.c

   1 /*
   2  * Single-precision e^x function.
   3  *
   4  * Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
   5  * See https://llvm.org/LICENSE.txt for license information.
   6  * SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
   7  */
   8
   9 #include <math.h>
  10 #include <stdint.h>
  11 #include "math_config.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
  29 top12 (float x)
  30 {
  31   return asuint (x) >> 20;
  32 }
  33
  34 float
  35 expf (float x)
  36 {
  37   uint32_t abstop;
  38   uint64_t ki, t;
  39   /* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
  40   double_t kd, xd, z, r, r2, y, s;
  41
  42   xd = (double_t) x;
  43   abstop = top12 (x) & 0x7ff;
  44   if (unlikely (abstop >= top12 (88.0f)))
  45     {
  46       /* |x| >= 88 or x is nan.  */
  47       if (asuint (x) == asuint (-INFINITY))
  48         return 0.0f;
  49       if (abstop >= top12 (INFINITY))
  50         return x + x;
  51       if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
  52         return __math_oflowf (0);
  53       if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
  54         return __math_uflowf (0);
  55 #if WANT_ERRNO_UFLOW
  56       if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */
  57         return __math_may_uflowf (0);
  58 #endif
  59     }
  60
  61   /* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
  62   z = InvLn2N * xd;
  63
  64   /* Round and convert z to int, the result is in [-150*N, 128*N] and
  65      ideally nearest int is used, otherwise the magnitude of r can be
  66      bigger which gives larger approximation error.  */
  67 #if TOINT_INTRINSICS
  68   kd = roundtoint (z);
  69   ki = converttoint (z);
  70 #else
  71 # define SHIFT __exp2f_data.shift
  72   kd = eval_as_double (z + SHIFT);
  73   ki = asuint64 (kd);
  74   kd -= SHIFT;
  75 #endif
  76   r = z - kd;
  77
  78   /* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
  79   t = T[ki % N];
  80   t += ki << (52 - EXP2F_TABLE_BITS);
  81   s = asdouble (t);
  82   z = C[0] * r + C[1];
  83   r2 = r * r;
  84   y = C[2] * r + 1;
  85   y = z * r2 + y;
  86   y = y * s;
  87   return eval_as_float (y);
  88 }
  89 #if USE_GLIBC_ABI
  90 strong_alias (expf, __expf_finite)
  91 hidden_alias (expf, __ieee754_expf)
  92 #endif