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freebsd
GitHub Repository: freebsd/freebsd-src
 Path: blob/main/contrib/arm-optimized-routines/math/aarch64/experimental/expm1f_1u6.c
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/*

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 * Single-precision e^x - 1 function.

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 *

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 * Copyright (c) 2022-2024, Arm Limited.

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 * SPDX-License-Identifier: MIT OR Apache-2.0 WITH LLVM-exception

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 */

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#include "poly_scalar_f32.h"

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#include "math_config.h"

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#include "test_sig.h"

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#include "test_defs.h"

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#define Shift (0x1.8p23f)

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#define InvLn2 (0x1.715476p+0f)

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#define Ln2hi (0x1.62e4p-1f)

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#define Ln2lo (0x1.7f7d1cp-20f)

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#define AbsMask (0x7fffffff)

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#define InfLimit                                                              \

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  (0x1.644716p6) /* Smallest value of x for which expm1(x) overflows.  */

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#define NegLimit                                                              \

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  (-0x1.9bbabcp+6) /* Largest value of x for which expm1(x) rounds to 1.  */

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/* Approximation for exp(x) - 1 using polynomial on a reduced interval.

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   The maximum error is 1.51 ULP:

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   expm1f(0x1.8baa96p-2) got 0x1.e2fb9p-2

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			want 0x1.e2fb94p-2.  */

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float

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expm1f (float x)

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{

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  uint32_t ix = asuint (x);

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  uint32_t ax = ix & AbsMask;

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  /* Tiny: |x| < 0x1p-23. expm1(x) is closely approximated by x.

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     Inf:  x == +Inf => expm1(x) = x.  */

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  if (ax <= 0x34000000 || (ix == 0x7f800000))

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    return x;

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  /* +/-NaN.  */

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  if (ax > 0x7f800000)

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    return __math_invalidf (x);

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  if (x >= InfLimit)

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    return __math_oflowf (0);

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  if (x <= NegLimit || ix == 0xff800000)

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    return -1;

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  /* Reduce argument to smaller range:

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     Let i = round(x / ln2)

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     and f = x - i * ln2, then f is in [-ln2/2, ln2/2].

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     exp(x) - 1 = 2^i * (expm1(f) + 1) - 1

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     where 2^i is exact because i is an integer.  */

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  float j = fmaf (InvLn2, x, Shift) - Shift;

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  int32_t i = j;

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  float f = fmaf (j, -Ln2hi, x);

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  f = fmaf (j, -Ln2lo, f);

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  /* Approximate expm1(f) using polynomial.

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     Taylor expansion for expm1(x) has the form:

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	 x + ax^2 + bx^3 + cx^4 ....

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     So we calculate the polynomial P(f) = a + bf + cf^2 + ...

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     and assemble the approximation expm1(f) ~= f + f^2 * P(f).  */

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  float p = fmaf (f * f, horner_4_f32 (f, __expm1f_poly), f);

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  /* Assemble the result, using a slight rearrangement to achieve acceptable

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     accuracy.

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     expm1(x) ~= 2^i * (p + 1) - 1

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     Let t = 2^(i - 1).  */

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  float t = ldexpf (0.5f, i);

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  /* expm1(x) ~= 2 * (p * t + (t - 1/2)).  */

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  return 2 * fmaf (p, t, t - 0.5f);

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}

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TEST_SIG (S, F, 1, expm1, -9.9, 9.9)

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TEST_ULP (expm1f, 1.02)

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TEST_SYM_INTERVAL (expm1f, 0, 0x1p-23, 1000)

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TEST_INTERVAL (expm1f, 0x1p-23, 0x1.644716p6, 100000)

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TEST_INTERVAL (expm1f, 0x1.644716p6, inf, 1000)

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TEST_INTERVAL (expm1f, -0x1p-23, -0x1.9bbabcp+6, 100000)

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TEST_INTERVAL (expm1f, -0x1.9bbabcp+6, -inf, 1000)

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