mirror of
https://github.com/autc04/Retro68.git
synced 2024-11-29 12:50:35 +00:00
114 lines
3.6 KiB
C
114 lines
3.6 KiB
C
/* Single-precision e^x function.
|
|
Copyright (c) 2017 ARM Ltd. All rights reserved.
|
|
|
|
Redistribution and use in source and binary forms, with or without
|
|
modification, are permitted provided that the following conditions
|
|
are met:
|
|
1. Redistributions of source code must retain the above copyright
|
|
notice, this list of conditions and the following disclaimer.
|
|
2. Redistributions in binary form must reproduce the above copyright
|
|
notice, this list of conditions and the following disclaimer in the
|
|
documentation and/or other materials provided with the distribution.
|
|
3. The name of the company may not be used to endorse or promote
|
|
products derived from this software without specific prior written
|
|
permission.
|
|
|
|
THIS SOFTWARE IS PROVIDED BY ARM LTD ``AS IS AND ANY EXPRESS OR IMPLIED
|
|
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
|
|
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
|
|
IN NO EVENT SHALL ARM LTD BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
|
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
|
|
TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
|
|
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
|
|
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
|
|
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */
|
|
|
|
#include "fdlibm.h"
|
|
#if !__OBSOLETE_MATH
|
|
|
|
#include <math.h>
|
|
#include <stdint.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 (__builtin_expect (abstop >= top12 (88.0f), 0))
|
|
{
|
|
/* |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 = (double) (z + SHIFT); /* Rounding to double precision is required. */
|
|
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;
|
|
}
|
|
#endif /* !__OBSOLETE_MATH */
|