/* Single-precision e^x function.

   Copyright (C) 2017-2018 Free Software Foundation, Inc.

   This file is part of the GNU C Library.

   The GNU C Library is free software; you can redistribute it and/or

   modify it under the terms of the GNU Lesser General Public

   License as published by the Free Software Foundation; either

   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public

   License along with the GNU C Library; if not, see

   <http://www.gnu.org/licenses/>.  */

#ifdef __expf

# undef libm_hidden_proto

# define libm_hidden_proto(ignored)

#endif

#include <math.h>

#include <math-narrow-eval.h>

#include <stdint.h>

#include <shlib-compat.h>

#include <libm-alias-float.h>

#include "math_config.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 for better performance on targets with FLT_EVAL_METHOD==2.  */

  double_t kd, xd, z, r, r2, y, s;

  xd = (double_t) x;

  abstop = top12 (x) & 0x7ff;

  if (__glibc_unlikely (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);

#if WANT_ERRNO_UFLOW

      if (x < -0x1.9d1d9ep6f) /* x < log(0x1p-149) ~= -103.28 */

	return __math_may_uflowf (0);

#endif

    }

  /* 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);

#elif TOINT_RINT

  kd = rint (z);

  ki = (long) kd;

#elif TOINT_SHIFT

# define SHIFT __exp2f_data.shift

  kd = math_narrow_eval ((double) (z + SHIFT)); /* Needs to be double.  */

  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 (float) y;

}

#ifndef __expf

hidden_def (__expf)

strong_alias (__expf, __ieee754_expf)

strong_alias (__expf, __expf_finite)

versioned_symbol (libm, __expf, expf, GLIBC_2_27);

libm_alias_float_other (__exp, exp)

#endif