mirror of
https://github.com/ClickHouse/ClickHouse.git
synced 2024-12-12 17:32:32 +00:00
186 lines
4.9 KiB
C
186 lines
4.9 KiB
C
|
/*
|
||
|
* Copyright (c) 2017-2018, Arm Limited.
|
||
|
* SPDX-License-Identifier: MIT
|
||
|
*/
|
||
|
|
||
|
#include <math.h>
|
||
|
#include <stdint.h>
|
||
|
#include "libm.h"
|
||
|
#include "exp2f_data.h"
|
||
|
#include "powf_data.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 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 float exp2_inline(double_t xd, uint32_t sign_bias)
|
||
|
{
|
||
|
uint64_t ki, ski, t;
|
||
|
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 = eval_as_double(xd + SHIFT);
|
||
|
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 eval_as_float(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 (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000 ||
|
||
|
zeroinfnan(iy))) {
|
||
|
/* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan). */
|
||
|
if (predict_false(zeroinfnan(iy))) {
|
||
|
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 (predict_false(zeroinfnan(ix))) {
|
||
|
float_t x2 = x * x;
|
||
|
if (ix & 0x80000000 && checkint(iy) == 1)
|
||
|
x2 = -x2;
|
||
|
/* Without the barrier some versions of clang hoist the 1/x2 and
|
||
|
thus division by zero exception can be signaled spuriously. */
|
||
|
return iy & 0x80000000 ? fp_barrierf(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; /* cannot overflow, y is single prec. */
|
||
|
if (predict_false((asuint64(ylogx) >> 47 & 0xffff) >=
|
||
|
asuint64(126.0 * POWF_SCALE) >> 47)) {
|
||
|
/* |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);
|
||
|
}
|
||
|
return exp2_inline(ylogx, sign_bias);
|
||
|
}
|