234 lines
6.8 KiB
C
234 lines
6.8 KiB
C
/* Single-precision pow function.
|
|
Copyright (c) 2017-2018 Arm Ltd. All rights reserved.
|
|
|
|
SPDX-License-Identifier: BSD-3-Clause
|
|
|
|
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"
|
|
|
|
/*
|
|
POWF_LOG2_POLY_ORDER = 5
|
|
EXP2F_TABLE_BITS = 5
|
|
|
|
ULP error: 0.82 (~ 0.5 + relerr*2^24)
|
|
relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
|
|
relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
|
|
relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
|
|
*/
|
|
|
|
#define N (1 << POWF_LOG2_TABLE_BITS)
|
|
#define T __powf_log2_data.tab
|
|
#define A __powf_log2_data.poly
|
|
#define OFF 0x3f330000
|
|
|
|
/* Subnormal input is normalized so ix has negative biased exponent.
|
|
Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set. */
|
|
static inline double_t
|
|
log2_inline (uint32_t ix)
|
|
{
|
|
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
|
double_t z, r, r2, r4, p, q, y, y0, invc, logc;
|
|
uint32_t iz, top, tmp;
|
|
int k, i;
|
|
|
|
/* x = 2^k z; where z is in range [OFF,2*OFF] and exact.
|
|
The range is split into N subintervals.
|
|
The ith subinterval contains z and c is near its center. */
|
|
tmp = ix - OFF;
|
|
i = (tmp >> (23 - POWF_LOG2_TABLE_BITS)) % N;
|
|
top = tmp & 0xff800000;
|
|
iz = ix - top;
|
|
k = (int32_t) top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
|
|
invc = T[i].invc;
|
|
logc = T[i].logc;
|
|
z = (double_t) asfloat (iz);
|
|
|
|
/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
|
|
r = z * invc - 1;
|
|
y0 = logc + (double_t) k;
|
|
|
|
/* Pipelined polynomial evaluation to approximate log1p(r)/ln2. */
|
|
r2 = r * r;
|
|
y = A[0] * r + A[1];
|
|
p = A[2] * r + A[3];
|
|
r4 = r2 * r2;
|
|
q = A[4] * r + y0;
|
|
q = p * r2 + q;
|
|
y = y * r4 + q;
|
|
return y;
|
|
}
|
|
|
|
#undef N
|
|
#undef T
|
|
#define N (1 << EXP2F_TABLE_BITS)
|
|
#define T __exp2f_data.tab
|
|
#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
|
|
|
|
/* The output of log2 and thus the input of exp2 is either scaled by N
|
|
(in case of fast toint intrinsics) or not. The unscaled xd must be
|
|
in [-1021,1023], sign_bias sets the sign of the result. */
|
|
static inline double_t
|
|
exp2_inline (double_t xd, uint32_t sign_bias)
|
|
{
|
|
uint64_t ki, ski, t;
|
|
/* double_t for better performance on targets with FLT_EVAL_METHOD==2. */
|
|
double_t kd, z, r, r2, y, s;
|
|
|
|
#if TOINT_INTRINSICS
|
|
# define C __exp2f_data.poly_scaled
|
|
/* N*x = k + r with r in [-1/2, 1/2] */
|
|
kd = roundtoint (xd); /* k */
|
|
ki = converttoint (xd);
|
|
#else
|
|
# define C __exp2f_data.poly
|
|
# define SHIFT __exp2f_data.shift_scaled
|
|
/* x = k/N + r with r in [-1/(2N), 1/(2N)] */
|
|
kd = (double) (xd + SHIFT); /* Rounding to double precision is required. */
|
|
ki = asuint64 (kd);
|
|
kd -= SHIFT; /* k/N */
|
|
#endif
|
|
r = xd - kd;
|
|
|
|
/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
|
|
t = T[ki % N];
|
|
ski = ki + sign_bias;
|
|
t += ski << (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 y;
|
|
}
|
|
|
|
/* Returns 0 if not int, 1 if odd int, 2 if even int. The argument is
|
|
the bit representation of a non-zero finite floating-point value. */
|
|
static inline int
|
|
checkint (uint32_t iy)
|
|
{
|
|
int e = iy >> 23 & 0xff;
|
|
if (e < 0x7f)
|
|
return 0;
|
|
if (e > 0x7f + 23)
|
|
return 2;
|
|
if (iy & ((1 << (0x7f + 23 - e)) - 1))
|
|
return 0;
|
|
if (iy & (1 << (0x7f + 23 - e)))
|
|
return 1;
|
|
return 2;
|
|
}
|
|
|
|
static inline int
|
|
zeroinfnan (uint32_t ix)
|
|
{
|
|
return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
|
|
}
|
|
|
|
float
|
|
powf (float x, float y)
|
|
{
|
|
uint32_t sign_bias = 0;
|
|
uint32_t ix, iy;
|
|
|
|
ix = asuint (x);
|
|
iy = asuint (y);
|
|
if (__builtin_expect (ix - 0x00800000 >= 0x7f800000 - 0x00800000
|
|
|| zeroinfnan (iy),
|
|
0))
|
|
{
|
|
/* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */
|
|
if (__builtin_expect (zeroinfnan (iy), 0))
|
|
{
|
|
if (2 * iy == 0)
|
|
return issignalingf_inline (x) ? x + y : 1.0f;
|
|
if (ix == 0x3f800000)
|
|
return issignalingf_inline (y) ? x + y : 1.0f;
|
|
if (2 * ix > 2u * 0x7f800000 || 2 * iy > 2u * 0x7f800000)
|
|
return x + y;
|
|
if (2 * ix == 2 * 0x3f800000)
|
|
return 1.0f;
|
|
if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
|
|
return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf. */
|
|
return y * y;
|
|
}
|
|
if (__builtin_expect (zeroinfnan (ix), 0))
|
|
{
|
|
float_t x2 = x * x;
|
|
if (ix & 0x80000000 && checkint (iy) == 1)
|
|
{
|
|
x2 = -x2;
|
|
sign_bias = 1;
|
|
}
|
|
#if WANT_ERRNO
|
|
if (2 * ix == 0 && iy & 0x80000000)
|
|
return __math_divzerof (sign_bias);
|
|
#endif
|
|
return iy & 0x80000000 ? 1 / x2 : x2;
|
|
}
|
|
/* x and y are non-zero finite. */
|
|
if (ix & 0x80000000)
|
|
{
|
|
/* Finite x < 0. */
|
|
int yint = checkint (iy);
|
|
if (yint == 0)
|
|
return __math_invalidf (x);
|
|
if (yint == 1)
|
|
sign_bias = SIGN_BIAS;
|
|
ix &= 0x7fffffff;
|
|
}
|
|
if (ix < 0x00800000)
|
|
{
|
|
/* Normalize subnormal x so exponent becomes negative. */
|
|
ix = asuint (x * 0x1p23f);
|
|
ix &= 0x7fffffff;
|
|
ix -= 23 << 23;
|
|
}
|
|
}
|
|
double_t logx = log2_inline (ix);
|
|
double_t ylogx = y * logx; /* Note: cannot overflow, y is single prec. */
|
|
if (__builtin_expect ((asuint64 (ylogx) >> 47 & 0xffff)
|
|
>= asuint64 (126.0 * POWF_SCALE) >> 47,
|
|
0))
|
|
{
|
|
/* |y*log(x)| >= 126. */
|
|
if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
|
|
return __math_oflowf (sign_bias);
|
|
if (ylogx <= -150.0 * POWF_SCALE)
|
|
return __math_uflowf (sign_bias);
|
|
#if WANT_ERRNO_UFLOW
|
|
if (ylogx < -149.0 * POWF_SCALE)
|
|
return __math_may_uflowf (sign_bias);
|
|
#endif
|
|
}
|
|
return (float) exp2_inline (ylogx, sign_bias);
|
|
}
|
|
#endif /* !__OBSOLETE_MATH */
|