474 lines
14 KiB
C
Executable File
474 lines
14 KiB
C
Executable File
#include "math_private.h"
|
|
#include "wcclibm.h"
|
|
|
|
|
|
|
|
/* e_rem_pio2f.c -- float version of e_rem_pio2.c
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[ ] =
|
|
"$NetBSD: e_rem_pio2f.c,v 1.5 1995/05/10 20:46:03 jtc Exp $";
|
|
#endif
|
|
|
|
/* __ieee754_rem_pio2f(x,y)
|
|
|
|
return the remainder of x rem pi/2 in y[ 0 ]+y[ 1 ]
|
|
use __kernel_rem_pio2f()
|
|
*/
|
|
|
|
/* This array is like the one in e_rem_pio2.c, but the numbers are
|
|
single precision and the last 8 bits are forced to 0. */
|
|
static const int32_t susan_npio2_hw[ ] = {
|
|
0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
|
|
0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
|
|
0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
|
|
0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
|
|
0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
|
|
0x4242c700, 0x42490f00
|
|
};
|
|
|
|
/*
|
|
invpio2: 24 bits of 2/pi
|
|
pio2_1: first 17 bit of pi/2
|
|
pio2_1t: pi/2 - pio2_1
|
|
pio2_2: second 17 bit of pi/2
|
|
pio2_2t: pi/2 - (pio2_1+pio2_2)
|
|
pio2_3: third 17 bit of pi/2
|
|
pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
|
|
*/
|
|
|
|
static const float
|
|
/* zero = 0.0000000000e+00f, /\* 0x00000000 *\/ */
|
|
/* half = 5.0000000000e-01f, /\* 0x3f000000 *\/ */
|
|
/* two8 = 2.5600000000e+02f, /\* 0x43800000 *\/ */
|
|
susan_invpio2 = 6.3661980629e-01f, /* 0x3f22f984 */
|
|
susan_pio2_1 = 1.5707855225e+00f, /* 0x3fc90f80 */
|
|
susan_pio2_1t = 1.0804334124e-05f, /* 0x37354443 */
|
|
susan_pio2_2 = 1.0804273188e-05f, /* 0x37354400 */
|
|
susan_pio2_2t = 6.0770999344e-11f, /* 0x2e85a308 */
|
|
susan_pio2_3 = 6.0770943833e-11f, /* 0x2e85a300 */
|
|
susan_pio2_3t = 6.1232342629e-17f; /* 0x248d3132 */
|
|
|
|
int32_t susan___ieee754_rem_pio2f( float x, float *y )
|
|
{
|
|
float z, w, t, r, fn;
|
|
int32_t i, j, n, ix, hx;
|
|
|
|
GET_FLOAT_WORD( hx, x );
|
|
ix = hx & 0x7fffffff;
|
|
if ( ix <= 0x3f490fd8 ) { /* |x| ~<= pi/4 , no need for reduction */
|
|
y[ 0 ] = x;
|
|
y[ 1 ] = 0;
|
|
return 0;
|
|
}
|
|
if ( ix < 0x4016cbe4 ) { /* |x| < 3pi/4, special case with n=+-1 */
|
|
if ( hx > 0 ) {
|
|
z = x - susan_pio2_1;
|
|
if ( ( ix & 0xfffffff0 ) != 0x3fc90fd0 ) { /* 24+24 bit pi OK */
|
|
y[ 0 ] = z - susan_pio2_1t;
|
|
y[ 1 ] = ( z - y[ 0 ] ) - susan_pio2_1t;
|
|
} else { /* near pi/2, use 24+24+24 bit pi */
|
|
z -= susan_pio2_2;
|
|
y[ 0 ] = z - susan_pio2_2t;
|
|
y[ 1 ] = ( z - y[ 0 ] ) - susan_pio2_2t;
|
|
}
|
|
return 1;
|
|
} else { /* negative x */
|
|
z = x + susan_pio2_1;
|
|
if ( ( ix & 0xfffffff0 ) != 0x3fc90fd0 ) { /* 24+24 bit pi OK */
|
|
y[ 0 ] = z + susan_pio2_1t;
|
|
y[ 1 ] = ( z - y[ 0 ] ) + susan_pio2_1t;
|
|
} else { /* near pi/2, use 24+24+24 bit pi */
|
|
z += susan_pio2_2;
|
|
y[ 0 ] = z + susan_pio2_2t;
|
|
y[ 1 ] = ( z - y[ 0 ] ) + susan_pio2_2t;
|
|
}
|
|
return -1;
|
|
}
|
|
}
|
|
if ( ix <= 0x43490f80 ) { /* |x| ~<= 2^7*(pi/2), medium size */
|
|
t = fabsf( x );
|
|
n = ( int32_t ) ( t * susan_invpio2 + susan_half );
|
|
fn = ( float )n;
|
|
r = t - fn * susan_pio2_1;
|
|
w = fn * susan_pio2_1t; /* 1st round good to 40 bit */
|
|
if ( n < 32 && ( int32_t )( ix & 0xffffff00 ) != susan_npio2_hw[ n - 1 ] ) {
|
|
y[ 0 ] = r - w; /* quick check no cancellation */
|
|
} else {
|
|
u_int32_t high;
|
|
j = ix >> 23;
|
|
y[ 0 ] = r - w;
|
|
GET_FLOAT_WORD( high, y[ 0 ] );
|
|
i = j - ( ( high >> 23 ) & 0xff );
|
|
if ( i > 8 ) { /* 2nd iteration needed, good to 57 */
|
|
t = r;
|
|
w = fn * susan_pio2_2;
|
|
r = t - w;
|
|
w = fn * susan_pio2_2t - ( ( t - r ) - w );
|
|
y[ 0 ] = r - w;
|
|
GET_FLOAT_WORD( high, y[ 0 ] );
|
|
i = j - ( ( high >> 23 ) & 0xff );
|
|
if ( i > 25 ) { /* 3rd iteration need, 74 bits acc */
|
|
t = r; /* will cover all possible cases */
|
|
w = fn * susan_pio2_3;
|
|
r = t - w;
|
|
w = fn * susan_pio2_3t - ( ( t - r ) - w );
|
|
y[ 0 ] = r - w;
|
|
}
|
|
}
|
|
}
|
|
y[ 1 ] = ( r - y[ 0 ] ) - w;
|
|
if ( hx < 0 ) {
|
|
y[ 0 ] = -y[ 0 ];
|
|
y[ 1 ] = -y[ 1 ];
|
|
return -n;
|
|
} else return n;
|
|
}
|
|
/*
|
|
all other (large) arguments
|
|
*/
|
|
if ( ix >= 0x7f800000 ) { /* x is inf or NaN */
|
|
y[ 0 ] = y[ 1 ] = x - x;
|
|
return 0;
|
|
}
|
|
|
|
y[ 0 ] = y[ 1 ] = x - x;
|
|
return 0; /* dummy initialisation */
|
|
return 0; /* doesn't happen for our input */
|
|
}
|
|
|
|
/* k_cosf.c -- float version of k_cos.c
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[ ] = "$NetBSD: k_cosf.c,v 1.4 1995/05/10 20:46:23 jtc Exp $";
|
|
#endif
|
|
|
|
|
|
static const float
|
|
/* one = 1.0000000000e+00, /\* 0x3f800000 *\/ */
|
|
susan_C1 = 4.1666667908e-02f, /* 0x3d2aaaab */
|
|
susan_C2 = -1.3888889225e-03f, /* 0xbab60b61 */
|
|
susan_C3 = 2.4801587642e-05f, /* 0x37d00d01 */
|
|
susan_C4 = -2.7557314297e-07f, /* 0xb493f27c */
|
|
susan_C5 = 2.0875723372e-09f, /* 0x310f74f6 */
|
|
susan_C6 = -1.1359647598e-11f; /* 0xad47d74e */
|
|
|
|
float susan___kernel_cosf( float x, float y )
|
|
{
|
|
float a, hz, z, r, qx;
|
|
int32_t ix;
|
|
GET_FLOAT_WORD( ix, x );
|
|
ix &= 0x7fffffff; /* ix = |x|'s high word*/
|
|
if ( ix < 0x32000000 ) { /* if x < 2**27 */
|
|
if ( ( ( int )x ) == 0 ) return susan_one; /* generate inexact */
|
|
}
|
|
z = x * x;
|
|
r = z * ( susan_C1 + z * ( susan_C2 + z * ( susan_C3 + z * ( susan_C4 + z *
|
|
( susan_C5 + z * susan_C6 ) ) ) ) );
|
|
if ( ix < 0x3e99999a ) /* if |x| < 0.3 */
|
|
return susan_one - ( ( float )0.5f * z - ( z * r - x * y ) );
|
|
else {
|
|
if ( ix > 0x3f480000 ) /* x > 0.78125 */
|
|
qx = ( float )0.28125f;
|
|
|
|
else {
|
|
SET_FLOAT_WORD( qx, ix - 0x01000000 ); /* x/4 */
|
|
}
|
|
hz = ( float )0.5f * z - qx;
|
|
a = susan_one - qx;
|
|
return a - ( hz - ( z * r - x * y ) );
|
|
}
|
|
}
|
|
|
|
/* k_sinf.c -- float version of k_sin.c
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[ ] = "$NetBSD: k_sinf.c,v 1.4 1995/05/10 20:46:33 jtc Exp $";
|
|
#endif
|
|
|
|
|
|
static const float
|
|
/* half = 5.0000000000e-01f,/\* 0x3f000000 *\/ */
|
|
susan_S1 = -1.6666667163e-01f, /* 0xbe2aaaab */
|
|
susan_S2 = 8.3333337680e-03f, /* 0x3c088889 */
|
|
susan_S3 = -1.9841270114e-04f, /* 0xb9500d01 */
|
|
susan_S4 = 2.7557314297e-06f, /* 0x3638ef1b */
|
|
susan_S5 = -2.5050759689e-08f, /* 0xb2d72f34 */
|
|
susan_S6 = 1.5896910177e-10f; /* 0x2f2ec9d3 */
|
|
|
|
float susan___kernel_sinf( float x, float y, int iy )
|
|
{
|
|
float z, r, v;
|
|
int32_t ix;
|
|
GET_FLOAT_WORD( ix, x );
|
|
ix &= 0x7fffffff; /* high word of x */
|
|
if ( ix < 0x32000000 ) { /* |x| < 2**-27 */
|
|
if ( ( int )x == 0 ) return x; /* generate inexact */
|
|
}
|
|
z = x * x;
|
|
v = z * x;
|
|
r = susan_S2 + z * ( susan_S3 + z * ( susan_S4 + z * ( susan_S5 + z *
|
|
susan_S6 ) ) );
|
|
if ( iy == 0 ) return x + v * ( susan_S1 + z * r );
|
|
else return x - ( ( z * ( susan_half * y - v * r ) - y ) - v * susan_S1 );
|
|
}
|
|
/* s_atanf.c -- float version of s_atan.c.
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
#if defined(LIBM_SCCS) && !defined(lint)
|
|
static char rcsid[ ] = "$NetBSD: s_atanf.c,v 1.4 1995/05/10 20:46:47 jtc Exp $";
|
|
#endif
|
|
|
|
|
|
static const float susan_atanhi[ ] = {
|
|
4.6364760399e-01f, /* atan(0.5)hi 0x3eed6338 */
|
|
7.8539812565e-01f, /* atan(1.0)hi 0x3f490fda */
|
|
9.8279368877e-01f, /* atan(1.5)hi 0x3f7b985e */
|
|
1.5707962513e+00f, /* atan(inf)hi 0x3fc90fda */
|
|
};
|
|
|
|
static const float susan_atanlo[ ] = {
|
|
5.0121582440e-09f, /* atan(0.5)lo 0x31ac3769 */
|
|
3.7748947079e-08f, /* atan(1.0)lo 0x33222168 */
|
|
3.4473217170e-08f, /* atan(1.5)lo 0x33140fb4 */
|
|
7.5497894159e-08f, /* atan(inf)lo 0x33a22168 */
|
|
};
|
|
|
|
static const float susan_aT[ ] = {
|
|
3.3333334327e-01f, /* 0x3eaaaaaa */
|
|
-2.0000000298e-01f, /* 0xbe4ccccd */
|
|
1.4285714924e-01f, /* 0x3e124925 */
|
|
-1.1111110449e-01f, /* 0xbde38e38 */
|
|
9.0908870101e-02f, /* 0x3dba2e6e */
|
|
-7.6918758452e-02f, /* 0xbd9d8795 */
|
|
6.6610731184e-02f, /* 0x3d886b35 */
|
|
-5.8335702866e-02f, /* 0xbd6ef16b */
|
|
4.9768779427e-02f, /* 0x3d4bda59 */
|
|
-3.6531571299e-02f, /* 0xbd15a221 */
|
|
1.6285819933e-02f, /* 0x3c8569d7 */
|
|
};
|
|
|
|
float susan___atanf( float x )
|
|
{
|
|
float w, s1, s2, z;
|
|
int32_t ix, hx, id;
|
|
|
|
GET_FLOAT_WORD( hx, x );
|
|
ix = hx & 0x7fffffff;
|
|
if ( ix >= 0x50800000 ) { /* if |x| >= 2^34 */
|
|
if ( ix > 0x7f800000 )
|
|
return x + x; /* NaN */
|
|
if ( hx > 0 ) return susan_atanhi[ 3 ] + susan_atanlo[ 3 ];
|
|
else return -susan_atanhi[ 3 ] - susan_atanlo[ 3 ];
|
|
}
|
|
if ( ix < 0x3ee00000 ) { /* |x| < 0.4375 */
|
|
if ( ix < 0x31000000 ) { /* |x| < 2^-29 */
|
|
if ( susan_huge + x > susan_one ) return x; /* raise inexact */
|
|
}
|
|
id = -1;
|
|
} else {
|
|
x = fabsf( x );
|
|
if ( ix < 0x3f980000 ) { /* |x| < 1.1875 */
|
|
if ( ix < 0x3f300000 ) { /* 7/16 <=|x|<11/16 */
|
|
id = 0;
|
|
x = ( ( float )2.0f * x - susan_one ) / ( ( float )2.0f + x );
|
|
} else { /* 11/16<=|x|< 19/16 */
|
|
id = 1;
|
|
x = ( x - susan_one ) / ( x + susan_one );
|
|
}
|
|
} else {
|
|
if ( ix < 0x401c0000 ) { /* |x| < 2.4375 */
|
|
id = 2;
|
|
x = ( x - ( float )1.5f ) / ( susan_one + ( float )1.5f * x );
|
|
} else { /* 2.4375 <= |x| < 2^66 */
|
|
id = 3;
|
|
x = -( float )1.0f / x;
|
|
}
|
|
}
|
|
}
|
|
/* end of argument reduction */
|
|
z = x * x;
|
|
w = z * z;
|
|
/* break sum from i=0 to 10 aT[ i ]z**(i+1) into odd and even poly */
|
|
s1 = z * ( susan_aT[ 0 ] + w * ( susan_aT[ 2 ] + w * ( susan_aT[ 4 ] + w *
|
|
( susan_aT[ 6 ] + w * ( susan_aT[ 8 ] + w * susan_aT[ 10 ] ) ) ) ) );
|
|
s2 = w * ( susan_aT[ 1 ] + w * ( susan_aT[ 3 ] + w * ( susan_aT[ 5 ] + w *
|
|
( susan_aT[ 7 ] + w * susan_aT[ 9 ] ) ) ) );
|
|
if ( id < 0 ) return x - x * ( s1 + s2 );
|
|
else {
|
|
z = susan_atanhi[ id ] - ( ( x * ( s1 + s2 ) - susan_atanlo[ id ] ) - x );
|
|
return ( hx < 0 ) ? -z : z;
|
|
}
|
|
}
|
|
|
|
/* s_cosf.c -- float version of s_cos.c.
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
float susan___cosf( float x )
|
|
{
|
|
float y[ 2 ], z = 0.0f;
|
|
int32_t n, ix;
|
|
|
|
GET_FLOAT_WORD( ix, x );
|
|
|
|
/* |x| ~< pi/4 */
|
|
ix &= 0x7fffffff;
|
|
if ( ix <= 0x3f490fd8 ) return susan___kernel_cosf( x, z );
|
|
|
|
/* cos(Inf or NaN) is NaN */
|
|
else
|
|
if ( ix >= 0x7f800000 ) return x - x;
|
|
|
|
/* argument reduction needed */
|
|
else {
|
|
n = susan___ieee754_rem_pio2f( x, y );
|
|
switch ( n & 3 ) {
|
|
case 0:
|
|
return susan___kernel_cosf( y[ 0 ], y[ 1 ] );
|
|
case 1:
|
|
return -susan___kernel_sinf( y[ 0 ], y[ 1 ], 1 );
|
|
case 2:
|
|
return -susan___kernel_cosf( y[ 0 ], y[ 1 ] );
|
|
default:
|
|
return susan___kernel_sinf( y[ 0 ], y[ 1 ], 1 );
|
|
}
|
|
}
|
|
}
|
|
|
|
/* s_sinf.c -- float version of s_sin.c.
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
float susan___sinf( float x )
|
|
{
|
|
float y[ 2 ], z = 0.0;
|
|
int32_t n, ix;
|
|
|
|
GET_FLOAT_WORD( ix, x );
|
|
|
|
/* |x| ~< pi/4 */
|
|
ix &= 0x7fffffff;
|
|
if ( ix <= 0x3f490fd8 ) return susan___kernel_sinf( x, z, 0 );
|
|
|
|
/* sin(Inf or NaN) is NaN */
|
|
else
|
|
if ( ix >= 0x7f800000 ) return x - x;
|
|
|
|
/* argument reduction needed */
|
|
else {
|
|
n = susan___ieee754_rem_pio2f( x, y );
|
|
switch ( n & 3 ) {
|
|
case 0:
|
|
return susan___kernel_sinf( y[ 0 ], y[ 1 ], 1 );
|
|
case 1:
|
|
return susan___kernel_cosf( y[ 0 ], y[ 1 ] );
|
|
case 2:
|
|
return -susan___kernel_sinf( y[ 0 ], y[ 1 ], 1 );
|
|
default:
|
|
return -susan___kernel_cosf( y[ 0 ], y[ 1 ] );
|
|
}
|
|
}
|
|
}
|
|
|
|
/* s_fabsf.c -- float version of s_fabs.c.
|
|
Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
|
|
/*
|
|
====================================================
|
|
Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
|
|
Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
Permission to use, copy, modify, and distribute this
|
|
software is freely granted, provided that this notice
|
|
is preserved.
|
|
====================================================
|
|
*/
|
|
|
|
/*
|
|
fabsf(x) returns the absolute value of x.
|
|
*/
|
|
|
|
|
|
float susan___fabsf( float x )
|
|
{
|
|
u_int32_t ix;
|
|
GET_FLOAT_WORD( ix, x );
|
|
SET_FLOAT_WORD( x, ix & 0x7fffffff );
|
|
return x;
|
|
}
|