blob: 375a8466e83751297794242ef413fdde4307302a [file] [log] [blame]
/*
* Copyright (C) 2008-2009 Advanced Micro Devices, Inc. All Rights Reserved.
*
* This file is part of libacml_mv.
*
* libacml_mv is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* libacml_mv is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with libacml_mv. If not, see
* <http://www.gnu.org/licenses/>.
*
*/
#include "../inc/libm_amd.h"
#include "../inc/libm_util_amd.h"
#define USE_NANF_WITH_FLAGS
#define USE_VALF_WITH_FLAGS
#define USE_INFINITYF_WITH_FLAGS
#define USE_HANDLE_ERRORF
#include "../inc/libm_inlines_amd.h"
#undef USE_NANF_WITH_FLAGS
#undef USE_VALF_WITH_FLAGS
#undef USE_INFINITYF_WITH_FLAGS
#undef USE_HANDLE_ERRORF
#include "../inc/libm_errno_amd.h"
#ifndef WINDOWS
/* Deal with errno for out-of-range result */
static inline float retval_errno_erange_overflow(float x)
{
struct exception exc;
exc.arg1 = (double)x;
exc.arg2 = (double)x;
exc.type = SING;
exc.name = (char *)"log1pf";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = -infinityf_with_flags(AMD_F_DIVBYZERO);
if (_LIB_VERSION == _POSIX_)
__set_errno(ERANGE);
else if (!matherr(&exc))
__set_errno(ERANGE);
return exc.retval;
}
/* Deal with errno for out-of-range argument */
static inline float retval_errno_edom(float x)
{
struct exception exc;
exc.arg1 = (double)x;
exc.arg2 = (double)x;
exc.type = DOMAIN;
exc.name = (char *)"log1pf";
if (_LIB_VERSION == _SVID_)
exc.retval = -HUGE;
else
exc.retval = nanf_with_flags(AMD_F_INVALID);
if (_LIB_VERSION == _POSIX_)
__set_errno(EDOM);
else if (!matherr(&exc))
{
if(_LIB_VERSION == _SVID_)
(void)fputs("log1pf: DOMAIN error\n", stderr);
__set_errno(EDOM);
}
return exc.retval;
}
#endif
#undef _FUNCNAME
#define _FUNCNAME "log1pf"
float FN_PROTOTYPE(log1pf)(float x)
{
int xexp;
double dx, r, f, f1, f2, q, u, v, z1, z2, poly, m2;
int index;
unsigned int ux, ax;
unsigned long long lux;
/*
Computes natural log(1+x) for float arguments. Algorithm is
basically a promotion of the arguments to double followed
by an inlined version of the double algorithm, simplified
for efficiency (see log1p_amd.c). Simplifications include:
* Special algorithm for arguments near 0.0 not required
* Scaling of denormalised arguments not required
* Shorter core series approximations used
Note that we use a lookup table of size 64 rather than 128,
and compensate by having extra terms in the minimax polynomial
for the kernel approximation.
*/
/* Arrays ln_lead_table and ln_tail_table contain
leading and trailing parts respectively of precomputed
values of natural log(1+i/64), for i = 0, 1, ..., 64.
ln_lead_table contains the first 24 bits of precision,
and ln_tail_table contains a further 53 bits precision. */
static const double ln_lead_table[65] = {
0.00000000000000000000e+00, /* 0x0000000000000000 */
1.55041813850402832031e-02, /* 0x3f8fc0a800000000 */
3.07716131210327148438e-02, /* 0x3f9f829800000000 */
4.58095073699951171875e-02, /* 0x3fa7745800000000 */
6.06245994567871093750e-02, /* 0x3faf0a3000000000 */
7.52233862876892089844e-02, /* 0x3fb341d700000000 */
8.96121263504028320312e-02, /* 0x3fb6f0d200000000 */
1.03796780109405517578e-01, /* 0x3fba926d00000000 */
1.17783010005950927734e-01, /* 0x3fbe270700000000 */
1.31576299667358398438e-01, /* 0x3fc0d77e00000000 */
1.45181953907012939453e-01, /* 0x3fc2955280000000 */
1.58604979515075683594e-01, /* 0x3fc44d2b00000000 */
1.71850204467773437500e-01, /* 0x3fc5ff3000000000 */
1.84922337532043457031e-01, /* 0x3fc7ab8900000000 */
1.97825729846954345703e-01, /* 0x3fc9525a80000000 */
2.10564732551574707031e-01, /* 0x3fcaf3c900000000 */
2.23143517971038818359e-01, /* 0x3fcc8ff780000000 */
2.35566020011901855469e-01, /* 0x3fce270700000000 */
2.47836112976074218750e-01, /* 0x3fcfb91800000000 */
2.59957492351531982422e-01, /* 0x3fd0a324c0000000 */
2.71933674812316894531e-01, /* 0x3fd1675c80000000 */
2.83768117427825927734e-01, /* 0x3fd22941c0000000 */
2.95464158058166503906e-01, /* 0x3fd2e8e280000000 */
3.07025015354156494141e-01, /* 0x3fd3a64c40000000 */
3.18453729152679443359e-01, /* 0x3fd4618bc0000000 */
3.29753279685974121094e-01, /* 0x3fd51aad80000000 */
3.40926527976989746094e-01, /* 0x3fd5d1bd80000000 */
3.51976394653320312500e-01, /* 0x3fd686c800000000 */
3.62905442714691162109e-01, /* 0x3fd739d7c0000000 */
3.73716354370117187500e-01, /* 0x3fd7eaf800000000 */
3.84411692619323730469e-01, /* 0x3fd89a3380000000 */
3.94993782043457031250e-01, /* 0x3fd9479400000000 */
4.05465066432952880859e-01, /* 0x3fd9f323c0000000 */
4.15827870368957519531e-01, /* 0x3fda9cec80000000 */
4.26084339618682861328e-01, /* 0x3fdb44f740000000 */
4.36236739158630371094e-01, /* 0x3fdbeb4d80000000 */
4.46287095546722412109e-01, /* 0x3fdc8ff7c0000000 */
4.56237375736236572266e-01, /* 0x3fdd32fe40000000 */
4.66089725494384765625e-01, /* 0x3fddd46a00000000 */
4.75845873355865478516e-01, /* 0x3fde744240000000 */
4.85507786273956298828e-01, /* 0x3fdf128f40000000 */
4.95077252388000488281e-01, /* 0x3fdfaf5880000000 */
5.04556000232696533203e-01, /* 0x3fe02552a0000000 */
5.13945698738098144531e-01, /* 0x3fe0723e40000000 */
5.23248136043548583984e-01, /* 0x3fe0be72e0000000 */
5.32464742660522460938e-01, /* 0x3fe109f380000000 */
5.41597247123718261719e-01, /* 0x3fe154c3c0000000 */
5.50647079944610595703e-01, /* 0x3fe19ee6a0000000 */
5.59615731239318847656e-01, /* 0x3fe1e85f40000000 */
5.68504691123962402344e-01, /* 0x3fe23130c0000000 */
5.77315330505371093750e-01, /* 0x3fe2795e00000000 */
5.86049020290374755859e-01, /* 0x3fe2c0e9e0000000 */
5.94707071781158447266e-01, /* 0x3fe307d720000000 */
6.03290796279907226562e-01, /* 0x3fe34e2880000000 */
6.11801505088806152344e-01, /* 0x3fe393e0c0000000 */
6.20240390300750732422e-01, /* 0x3fe3d90260000000 */
6.28608644008636474609e-01, /* 0x3fe41d8fe0000000 */
6.36907458305358886719e-01, /* 0x3fe4618bc0000000 */
6.45137906074523925781e-01, /* 0x3fe4a4f840000000 */
6.53301239013671875000e-01, /* 0x3fe4e7d800000000 */
6.61398470401763916016e-01, /* 0x3fe52a2d20000000 */
6.69430613517761230469e-01, /* 0x3fe56bf9c0000000 */
6.77398800849914550781e-01, /* 0x3fe5ad4040000000 */
6.85303986072540283203e-01, /* 0x3fe5ee02a0000000 */
6.93147122859954833984e-01}; /* 0x3fe62e42e0000000 */
static const double ln_tail_table[65] = {
0.00000000000000000000e+00, /* 0x0000000000000000 */
5.15092497094772879206e-09, /* 0x3e361f807c79f3db */
4.55457209735272790188e-08, /* 0x3e6873c1980267c8 */
2.86612990859791781788e-08, /* 0x3e5ec65b9f88c69e */
2.23596477332056055352e-08, /* 0x3e58022c54cc2f99 */
3.49498983167142274770e-08, /* 0x3e62c37a3a125330 */
3.23392843005887000414e-08, /* 0x3e615cad69737c93 */
1.35722380472479366661e-08, /* 0x3e4d256ab1b285e9 */
2.56504325268044191098e-08, /* 0x3e5b8abcb97a7aa2 */
5.81213608741512136843e-08, /* 0x3e6f34239659a5dc */
5.59374849578288093334e-08, /* 0x3e6e07fd48d30177 */
5.06615629004996189970e-08, /* 0x3e6b32df4799f4f6 */
5.24588857848400955725e-08, /* 0x3e6c29e4f4f21cf8 */
9.61968535632653505972e-10, /* 0x3e1086c848df1b59 */
1.34829655346594463137e-08, /* 0x3e4cf456b4764130 */
3.65557749306383026498e-08, /* 0x3e63a02ffcb63398 */
3.33431709374069198903e-08, /* 0x3e61e6a6886b0976 */
5.13008650536088382197e-08, /* 0x3e6b8abcb97a7aa2 */
5.09285070380306053751e-08, /* 0x3e6b578f8aa35552 */
3.20853940845502057341e-08, /* 0x3e6139c871afb9fc */
4.06713248643004200446e-08, /* 0x3e65d5d30701ce64 */
5.57028186706125221168e-08, /* 0x3e6de7bcb2d12142 */
5.48356693724804282546e-08, /* 0x3e6d708e984e1664 */
1.99407553679345001938e-08, /* 0x3e556945e9c72f36 */
1.96585517245087232086e-09, /* 0x3e20e2f613e85bda */
6.68649386072067321503e-09, /* 0x3e3cb7e0b42724f6 */
5.89936034642113390002e-08, /* 0x3e6fac04e52846c7 */
2.85038578721554472484e-08, /* 0x3e5e9b14aec442be */
5.09746772910284482606e-08, /* 0x3e6b5de8034e7126 */
5.54234668933210171467e-08, /* 0x3e6dc157e1b259d3 */
6.29100830926604004874e-09, /* 0x3e3b05096ad69c62 */
2.61974119468563937716e-08, /* 0x3e5c2116faba4cdd */
4.16752115011186398935e-08, /* 0x3e665fcc25f95b47 */
2.47747534460820790327e-08, /* 0x3e5a9a08498d4850 */
5.56922172017964209793e-08, /* 0x3e6de647b1465f77 */
2.76162876992552906035e-08, /* 0x3e5da71b7bf7861d */
7.08169709942321478061e-09, /* 0x3e3e6a6886b09760 */
5.77453510221151779025e-08, /* 0x3e6f0075eab0ef64 */
4.43021445893361960146e-09, /* 0x3e33071282fb989b */
3.15140984357495864573e-08, /* 0x3e60eb43c3f1bed2 */
2.95077445089736670973e-08, /* 0x3e5faf06ecb35c84 */
1.44098510263167149349e-08, /* 0x3e4ef1e63db35f68 */
1.05196987538551827693e-08, /* 0x3e469743fb1a71a5 */
5.23641361722697546261e-08, /* 0x3e6c1cdf404e5796 */
7.72099925253243069458e-09, /* 0x3e4094aa0ada625e */
5.62089493829364197156e-08, /* 0x3e6e2d4c96fde3ec */
3.53090261098577946927e-08, /* 0x3e62f4d5e9a98f34 */
3.80080516835568242269e-08, /* 0x3e6467c96ecc5cbe */
5.66961038386146408282e-08, /* 0x3e6e7040d03dec5a */
4.42287063097349852717e-08, /* 0x3e67bebf4282de36 */
3.45294525105681104660e-08, /* 0x3e6289b11aeb783f */
2.47132034530447431509e-08, /* 0x3e5a891d1772f538 */
3.59655343422487209774e-08, /* 0x3e634f10be1fb591 */
5.51581770357780862071e-08, /* 0x3e6d9ce1d316eb93 */
3.60171867511861372793e-08, /* 0x3e63562a19a9c442 */
1.94511067964296180547e-08, /* 0x3e54e2adf548084c */
1.54137376631349347838e-08, /* 0x3e508ce55cc8c97a */
3.93171034490174464173e-09, /* 0x3e30e2f613e85bda */
5.52990607758839766440e-08, /* 0x3e6db03ebb0227bf */
3.29990737637586136511e-08, /* 0x3e61b75bb09cb098 */
1.18436010922446096216e-08, /* 0x3e496f16abb9df22 */
4.04248680368301346709e-08, /* 0x3e65b3f399411c62 */
2.27418915900284316293e-08, /* 0x3e586b3e59f65355 */
1.70263791333409206020e-08, /* 0x3e52482ceae1ac12 */
5.76999904754328540596e-08}; /* 0x3e6efa39ef35793c */
static const double
log2 = 6.931471805599453e-01, /* 0x3fe62e42fefa39ef */
/* Approximating polynomial coefficients */
cb_1 = 8.33333333333333593622e-02, /* 0x3fb5555555555557 */
cb_2 = 1.24999999978138668903e-02; /* 0x3f89999999865ede */
GET_BITS_SP32(x, ux);
ax = ux & ~SIGNBIT_SP32;
if ((ux & EXPBITS_SP32) == EXPBITS_SP32)
{
/* x is either NaN or infinity */
if (ux & MANTBITS_SP32)
{
/* x is NaN */
#ifdef WINDOWS
return handle_errorf(_FUNCNAME, ux|0x00400000, _DOMAIN,
0, EDOM, x, 0.0F);
#else
return x + x; /* Raise invalid if it is a signalling NaN */
#endif
}
else
{
/* x is infinity */
if (ux & SIGNBIT_SP32)
{
/* x is negative infinity. Return a NaN. */
#ifdef WINDOWS
return handle_errorf(_FUNCNAME, INDEFBITPATT_SP32, _DOMAIN,
AMD_F_INVALID, EDOM, x, 0.0F);
#else
return retval_errno_edom(x);
#endif
}
else
return x;
}
}
else if (ux >= 0xbf800000)
{
/* x <= -1.0 */
if (ux > 0xbf800000)
{
/* x is less than -1.0. Return a NaN. */
#ifdef WINDOWS
return handle_errorf(_FUNCNAME, INDEFBITPATT_SP32, _DOMAIN,
AMD_F_INVALID, EDOM, x, 0.0F);
#else
return retval_errno_edom(x);
#endif
}
else
{
/* x is exactly -1.0. Return -infinity with div-by-zero flag. */
#ifdef WINDOWS
return handle_errorf(_FUNCNAME, NINFBITPATT_SP32, _SING,
AMD_F_DIVBYZERO, ERANGE, x, 0.0F);
#else
return retval_errno_erange_overflow(x);
#endif
}
}
else if (ax < 0x33800000)
{
if (ax == 0x00000000)
{
/* x is +/-zero. Return the same zero. */
return x;
}
else
/* abs(x) is less than float epsilon. Return x with inexact. */
return valf_with_flags(x, AMD_F_INEXACT);
}
dx = x;
/*
First, we decompose the argument dx to the form
1 + dx = 2**M * (F1 + F2),
where 1 <= F1+F2 < 2, M has the value of an integer,
F1 = 1 + j/64, j ranges from 0 to 64, and |F2| <= 1/128.
Second, we approximate log( 1 + F2/F1 ) by an odd polynomial
in U, where U = 2 F2 / (2 F2 + F1).
Note that log( 1 + F2/F1 ) = log( 1 + U/2 ) - log( 1 - U/2 ).
The core approximation calculates
Poly = [log( 1 + U/2 ) - log( 1 - U/2 )]/U - 1.
Note that log(1 + U/2) - log(1 - U/2) = 2 arctanh ( U/2 ),
thus, Poly = 2 arctanh( U/2 ) / U - 1.
It is not hard to see that
log(dx) = M*log(2) + log(F1) + log( 1 + F2/F1 ).
Hence, we return Z1 = log(F1), and Z2 = log( 1 + F2/F1).
The values of log(F1) are calculated beforehand and stored
in the program.
*/
f = 1.0 + dx;
GET_BITS_DP64(f, lux);
/* Store the exponent of f = 1 + dx in xexp and put
f into the range [1.0,2.0) */
xexp = (int)((lux & EXPBITS_DP64) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64;
PUT_BITS_DP64((lux & MANTBITS_DP64) | ONEEXPBITS_DP64, f);
/* Now (1+dx) = 2**(xexp) * f, 1 <= f < 2. */
/* Set index to be the nearest integer to 64*f */
/* 64 <= index <= 128 */
/*
r = 64.0 * f;
index = (int)(r + 0.5);
*/
/* This code instead of the above can save several cycles.
It only works because 64 <= r < 128, so
the nearest integer is always contained in exactly
7 bits, and the right shift is always the same. */
index = (int)((((lux & 0x000fc00000000000) | 0x0010000000000000) >> 46)
+ ((lux & 0x0000200000000000) >> 45));
f1 = index * 0.015625; /* 0.015625 = 1/64 */
index -= 64;
/* Now take great care to compute f2 such that f1 + f2 = f */
if (xexp <= -2 || xexp >= MANTLENGTH_DP64 + 8)
{
f2 = f - f1;
}
else
{
/* Create the number m2 = 2.0^(-xexp) */
lux = (unsigned long long)(0x3ff - xexp) << EXPSHIFTBITS_DP64;
PUT_BITS_DP64(lux,m2);
if (xexp <= MANTLENGTH_DP64 - 1)
{
f2 = (m2 - f1) + m2*dx;
}
else
{
f2 = (m2*dx - f1) + m2;
}
}
/* At this point, dx = 2**xexp * ( f1 + f2 ) where
f1 = j/64, j = 1, 2, ..., 64 and |f2| <= 1/128. */
z1 = ln_lead_table[index];
q = ln_tail_table[index];
/* Calculate u = 2 f2 / ( 2 f1 + f2 ) = f2 / ( f1 + 0.5*f2 ) */
u = f2 / (f1 + 0.5 * f2);
/* Here, |u| <= 2(exp(1/16)-1) / (exp(1/16)+1).
The core approximation calculates
poly = [log(1 + u/2) - log(1 - u/2)]/u - 1 */
v = u * u;
poly = (v * (cb_1 + v * cb_2));
z2 = q + (u + u * poly);
/* Now z1,z2 is an extra-precise approximation of log(f). */
/* Add xexp * log(2) to z1,z2 to get the result log(1+x). */
r = xexp * log2 + z1 + z2;
/* Natural log(1+x) */
return (float)r;
}
weak_alias (__log1pf, log1pf)