fix compile errors with pow/powf #136
|
|
@ -82,6 +82,7 @@ double log2(double);
|
|||
float log2f(float);
|
||||
|
||||
double pow(double, double);
|
||||
float powf(float, float);
|
||||
|
||||
double scalbn(double, int);
|
||||
|
||||
|
|
|
|||
|
|
@ -0,0 +1,6 @@
|
|||
#include "libm.h"
|
||||
|
||||
float __math_oflowf(uint32_t sign)
|
||||
{
|
||||
return __math_xflowf(sign, 0x1p97f);
|
||||
}
|
||||
|
|
@ -0,0 +1,6 @@
|
|||
#include "libm.h"
|
||||
|
||||
float __math_uflowf(uint32_t sign)
|
||||
{
|
||||
return __math_xflowf(sign, 0x1p-95f);
|
||||
}
|
||||
|
|
@ -0,0 +1,35 @@
|
|||
/*
|
||||
* Shared data between expf, exp2f and powf.
|
||||
*
|
||||
* Copyright (c) 2017-2018, Arm Limited.
|
||||
* SPDX-License-Identifier: MIT
|
||||
*/
|
||||
|
||||
#include "exp2f_data.h"
|
||||
|
||||
#define N (1 << EXP2F_TABLE_BITS)
|
||||
|
||||
const struct exp2f_data __exp2f_data = {
|
||||
/* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
|
||||
used for computing 2^(k/N) for an int |k| < 150 N as
|
||||
double(tab[k%N] + (k << 52-BITS)) */
|
||||
.tab = {
|
||||
0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
|
||||
0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
|
||||
0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
|
||||
0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
|
||||
0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
|
||||
0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
|
||||
0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
|
||||
0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
|
||||
},
|
||||
.shift_scaled = 0x1.8p+52 / N,
|
||||
.poly = {
|
||||
0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1,
|
||||
},
|
||||
.shift = 0x1.8p+52,
|
||||
.invln2_scaled = 0x1.71547652b82fep+0 * N,
|
||||
.poly_scaled = {
|
||||
0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N,
|
||||
},
|
||||
};
|
||||
|
|
@ -0,0 +1,23 @@
|
|||
/*
|
||||
* Copyright (c) 2017-2018, Arm Limited.
|
||||
* SPDX-License-Identifier: MIT
|
||||
*/
|
||||
#ifndef _EXP2F_DATA_H
|
||||
#define _EXP2F_DATA_H
|
||||
|
||||
#include <features.h>
|
||||
#include <stdint.h>
|
||||
|
||||
/* Shared between expf, exp2f and powf. */
|
||||
#define EXP2F_TABLE_BITS 5
|
||||
#define EXP2F_POLY_ORDER 3
|
||||
extern const struct exp2f_data {
|
||||
uint64_t tab[1 << EXP2F_TABLE_BITS];
|
||||
double shift_scaled;
|
||||
double poly[EXP2F_POLY_ORDER];
|
||||
double shift;
|
||||
double invln2_scaled;
|
||||
double poly_scaled[EXP2F_POLY_ORDER];
|
||||
} __exp2f_data;
|
||||
|
||||
#endif
|
||||
|
|
@ -1,3 +1,6 @@
|
|||
#ifndef _LIBM_H
|
||||
#define _LIBM_H
|
||||
|
||||
#include <float.h>
|
||||
#include <math.h>
|
||||
#include <stdint.h>
|
||||
|
|
@ -144,8 +147,13 @@ int __rem_pio2f(float, double*);
|
|||
float __sindf(double);
|
||||
float __cosdf(double);
|
||||
|
||||
float __math_xflowf(uint32_t, float);
|
||||
float __math_uflowf(uint32_t);
|
||||
float __math_oflowf(uint32_t);
|
||||
float __math_invalidf(float);
|
||||
double __math_xflow(uint32_t, double);
|
||||
double __math_uflow(uint32_t);
|
||||
double __math_oflow(uint32_t);
|
||||
double __math_invalid(double);
|
||||
|
||||
#endif // _LIBM_H
|
||||
|
|
|
|||
|
|
@ -0,0 +1,187 @@
|
|||
/*
|
||||
* 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. */
|
||||
// NOTE(orca): no fp barriers
|
||||
//return iy & 0x80000000 ? fp_barrierf(1 / x2) : x2;
|
||||
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; /* 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);
|
||||
}
|
||||
|
|
@ -0,0 +1,34 @@
|
|||
/*
|
||||
* Data definition for powf.
|
||||
*
|
||||
* Copyright (c) 2017-2018, Arm Limited.
|
||||
* SPDX-License-Identifier: MIT
|
||||
*/
|
||||
|
||||
#include "powf_data.h"
|
||||
|
||||
const struct powf_log2_data __powf_log2_data = {
|
||||
.tab = {
|
||||
{ 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE },
|
||||
{ 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE },
|
||||
{ 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE },
|
||||
{ 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE },
|
||||
{ 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE },
|
||||
{ 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE },
|
||||
{ 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE },
|
||||
{ 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE },
|
||||
{ 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE },
|
||||
{ 0x1p+0, 0x0p+0 * POWF_SCALE },
|
||||
{ 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE },
|
||||
{ 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE },
|
||||
{ 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE },
|
||||
{ 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE },
|
||||
{ 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE },
|
||||
{ 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE },
|
||||
},
|
||||
.poly = {
|
||||
0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE,
|
||||
0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE,
|
||||
0x1.71547652ab82bp0 * POWF_SCALE,
|
||||
}
|
||||
};
|
||||
|
|
@ -0,0 +1,26 @@
|
|||
/*
|
||||
* Copyright (c) 2017-2018, Arm Limited.
|
||||
* SPDX-License-Identifier: MIT
|
||||
*/
|
||||
#ifndef _POWF_DATA_H
|
||||
#define _POWF_DATA_H
|
||||
|
||||
#include "libm.h"
|
||||
#include "exp2f_data.h"
|
||||
|
||||
#define POWF_LOG2_TABLE_BITS 4
|
||||
#define POWF_LOG2_POLY_ORDER 5
|
||||
#if TOINT_INTRINSICS
|
||||
#define POWF_SCALE_BITS EXP2F_TABLE_BITS
|
||||
#else
|
||||
#define POWF_SCALE_BITS 0
|
||||
#endif
|
||||
#define POWF_SCALE ((double)(1 << POWF_SCALE_BITS))
|
||||
extern const struct powf_log2_data {
|
||||
struct {
|
||||
double invc, logc;
|
||||
} tab[1 << POWF_LOG2_TABLE_BITS];
|
||||
double poly[POWF_LOG2_POLY_ORDER];
|
||||
} __powf_log2_data;
|
||||
|
||||
#endif
|
||||
Loading…
Reference in New Issue