+++ /dev/null
-/*
- * Copyright (c) 1985, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * 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. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``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 THE REGENTS OR CONTRIBUTORS 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.
- */
-
-#ifndef lint
-static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93";
-#endif /* not lint */
-
-/* ASIN(X)
- * RETURNS ARC SINE OF X
- * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
- * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
- *
- * Required system supported functions:
- * copysign(x,y)
- * sqrt(x)
- *
- * Required kernel function:
- * atan2(y,x)
- *
- * Method :
- * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is
- * computed as follows
- * 1-x*x if x < 0.5,
- * 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5.
- *
- * Special cases:
- * if x is NaN, return x itself;
- * if |x|>1, return NaN.
- *
- * Accuracy:
- * 1) If atan2() uses machine PI, then
- *
- * asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded;
- * and PI is the exact pi rounded to machine precision (see atan2 for
- * details):
- *
- * in decimal:
- * pi = 3.141592653589793 23846264338327 .....
- * 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
- *
- * in hexadecimal:
- * pi = 3.243F6A8885A308D313198A2E....
- * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
- * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
- *
- * In a test run with more than 200,000 random arguments on a VAX, the
- * maximum observed error in ulps (units in the last place) was
- * 2.06 ulps. (comparing against (PI/pi)*(exact asin(x)));
- *
- * 2) If atan2() uses true pi, then
- *
- * asin(x) returns the exact asin(x) with error below about 2 ulps.
- *
- * In a test run with more than 1,024,000 random arguments on a VAX, the
- * maximum observed error in ulps (units in the last place) was
- * 1.99 ulps.
- */
-
-double asin(x)
-double x;
-{
- double s,t,copysign(),atan2(),sqrt(),one=1.0;
-#if !defined(vax)&&!defined(tahoe)
- if(x!=x) return(x); /* x is NaN */
-#endif /* !defined(vax)&&!defined(tahoe) */
- s=copysign(x,one);
- if(s <= 0.5)
- return(atan2(x,sqrt(one-x*x)));
- else
- { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); }
-
-}
-
-/* ACOS(X)
- * RETURNS ARC COS OF X
- * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits)
- * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85.
- *
- * Required system supported functions:
- * copysign(x,y)
- * sqrt(x)
- *
- * Required kernel function:
- * atan2(y,x)
- *
- * Method :
- * ________
- * / 1 - x
- * acos(x) = 2*atan2( / -------- , 1 ) .
- * \/ 1 + x
- *
- * Special cases:
- * if x is NaN, return x itself;
- * if |x|>1, return NaN.
- *
- * Accuracy:
- * 1) If atan2() uses machine PI, then
- *
- * acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded;
- * and PI is the exact pi rounded to machine precision (see atan2 for
- * details):
- *
- * in decimal:
- * pi = 3.141592653589793 23846264338327 .....
- * 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
- *
- * in hexadecimal:
- * pi = 3.243F6A8885A308D313198A2E....
- * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps
- * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps
- *
- * In a test run with more than 200,000 random arguments on a VAX, the
- * maximum observed error in ulps (units in the last place) was
- * 2.07 ulps. (comparing against (PI/pi)*(exact acos(x)));
- *
- * 2) If atan2() uses true pi, then
- *
- * acos(x) returns the exact acos(x) with error below about 2 ulps.
- *
- * In a test run with more than 1,024,000 random arguments on a VAX, the
- * maximum observed error in ulps (units in the last place) was
- * 2.15 ulps.
- */
-
-double acos(x)
-double x;
-{
- double t,copysign(),atan2(),sqrt(),one=1.0;
-#if !defined(vax)&&!defined(tahoe)
- if(x!=x) return(x);
-#endif /* !defined(vax)&&!defined(tahoe) */
- if( x != -1.0)
- t=atan2(sqrt((one-x)/(one+x)),one);
- else
- t=atan2(one,0.0); /* t = PI/2 */
- return(t+t);
-}
+++ /dev/null
-/*
- * Copyright (c) 1985, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * 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. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``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 THE REGENTS OR CONTRIBUTORS 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.
- */
-
-#ifndef lint
-static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93";
-#endif /* not lint */
-
-/* exp__E(x,c)
- * ASSUMPTION: c << x SO THAT fl(x+c)=x.
- * (c is the correction term for x)
- * exp__E RETURNS
- *
- * / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736
- * exp__E(x,c) = |
- * \ 0 , |x| < 1E-19.
- *
- * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS)
- * KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS
- * CODED IN C BY K.C. NG, 1/31/85;
- * REVISED BY K.C. NG on 3/16/85, 4/16/85.
- *
- * Required system supported function:
- * copysign(x,y)
- *
- * Method:
- * 1. Rational approximation. Let r=x+c.
- * Based on
- * 2 * sinh(r/2)
- * exp(r) - 1 = ---------------------- ,
- * cosh(r/2) - sinh(r/2)
- * exp__E(r) is computed using
- * x*x (x/2)*W - ( Q - ( 2*P + x*P ) )
- * --- + (c + x*[---------------------------------- + c ])
- * 2 1 - W
- * where P := p1*x^2 + p2*x^4,
- * Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6)
- * W := x/2-(Q-x*P),
- *
- * (See the listing below for the values of p1,p2,q1,q2,q3. The poly-
- * nomials P and Q may be regarded as the approximations to sinh
- * and cosh :
- * sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . )
- *
- * The coefficients were obtained by a special Remez algorithm.
- *
- * Approximation error:
- *
- * | exp(x) - 1 | 2**(-57), (IEEE double)
- * | ------------ - (exp__E(x,0)+x)/x | <=
- * | x | 2**(-69). (VAX D)
- *
- * Constants:
- * The hexadecimal values are the intended ones for the following constants.
- * The decimal values may be used, provided that the compiler will convert
- * from decimal to binary accurately enough to produce the hexadecimal values
- * shown.
- */
-
-#include "mathimpl.h"
-
-vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1, -6, .F83ABE67E1066A)
-vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173)
-vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2, -3, .E8B95A44A2EC45)
-vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4, -9, .A5790572E4F5E7)
-vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395)
-
-ic(p1, 1.3887401997267371720E-2, -7, 1.C70FF8B3CC2CF)
-ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4)
-ic(q1, 1.1110813732786649355E-1, -4, 1.C719538248597)
-ic(q2, 9.9176615021572857300E-4, -10, 1.03FC4CB8C98E8)
-
-#ifdef vccast
-#define p1 vccast(p1)
-#define p2 vccast(p2)
-#define q1 vccast(q1)
-#define q2 vccast(q2)
-#define q3 vccast(q3)
-#endif
-
-double __exp__E(x,c)
-double x,c;
-{
- const static double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19;
- double z,p,q,xp,xh,w;
- if(copysign(x,one)>small) {
- z = x*x ;
- p = z*( p1 +z* p2 );
-#if defined(vax)||defined(tahoe)
- q = z*( q1 +z*( q2 +z* q3 ));
-#else /* defined(vax)||defined(tahoe) */
- q = z*( q1 +z* q2 );
-#endif /* defined(vax)||defined(tahoe) */
- xp= x*p ;
- xh= x*half ;
- w = xh-(q-xp) ;
- p = p+p;
- c += x*((xh*w-(q-(p+xp)))/(one-w)+c);
- return(z*half+c);
- }
- /* end of |x| > small */
-
- else {
- if(x!=zero) one+small; /* raise the inexact flag */
- return(copysign(zero,x));
- }
-}
+++ /dev/null
-/*
- * Copyright (c) 1985, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * 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. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``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 THE REGENTS OR CONTRIBUTORS 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.
- */
-
-#ifndef lint
-static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93";
-#endif /* not lint */
-
-/* log__L(Z)
- * LOG(1+X) - 2S X
- * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294...
- * S 2 + X
- *
- * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS)
- * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS
- * CODED IN C BY K.C. NG, 1/19/85;
- * REVISED BY K.C. Ng, 2/3/85, 4/16/85.
- *
- * Method :
- * 1. Polynomial approximation: let s = x/(2+x).
- * Based on log(1+x) = log(1+s) - log(1-s)
- * = 2s + 2/3 s**3 + 2/5 s**5 + .....,
- *
- * (log(1+x) - 2s)/s is computed by
- *
- * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...)))
- *
- * where z=s*s. (See the listing below for Lk's values.) The
- * coefficients are obtained by a special Remez algorithm.
- *
- * Accuracy:
- * Assuming no rounding error, the maximum magnitude of the approximation
- * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63)
- * for VAX D format.
- *
- * Constants:
- * The hexadecimal values are the intended ones for the following constants.
- * The decimal values may be used, provided that the compiler will convert
- * from decimal to binary accurately enough to produce the hexadecimal values
- * shown.
- */
-
-#include "mathimpl.h"
-
-vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5)
-vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684)
-vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782)
-vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C)
-vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E)
-vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D)
-vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92)
-vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000)
-
-ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592)
-ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24)
-ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4)
-ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6)
-ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F)
-ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B)
-ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122)
-
-#ifdef vccast
-#define L1 vccast(L1)
-#define L2 vccast(L2)
-#define L3 vccast(L3)
-#define L4 vccast(L4)
-#define L5 vccast(L5)
-#define L6 vccast(L6)
-#define L7 vccast(L7)
-#define L8 vccast(L8)
-#endif
-
-double __log__L(z)
-double z;
-{
-#if defined(vax)||defined(tahoe)
- return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8))))))));
-#else /* defined(vax)||defined(tahoe) */
- return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7)))))));
-#endif /* defined(vax)||defined(tahoe) */
-}
+++ /dev/null
-/* This part here added by roland@prep.ai.mit.edu for the GNU C library. */
-
-#include <math.h> /* Done first so we can #undef. */
-#include <endian.h>
-#if __BYTE_ORDER == __LITTLE_ENDIAN
-#undef national
-#define national
-#endif
-
-#undef isinf
-#define isinf __isinf
-#undef isnan
-#define isnan __isnan
-#undef infnan
-#define infnan __infnan
-#undef copysign
-#define copysign __copysign
-#undef scalb
-#define scalb __scalb
-#undef drem
-#define drem __drem
-#undef logb
-#define logb __logb
-#undef __finite
-#undef finite
-#define finite __finite
-#undef expm1
-#define expm1 __expm1
-
-/*
- * Copyright (c) 1988, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * 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. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``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 THE REGENTS OR CONTRIBUTORS 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.
- *
- * @(#)mathimpl.h 8.1 (Berkeley) 6/4/93
- */
-
-#include <sys/cdefs.h>
-#include <math.h>
-
-#if defined(vax)||defined(tahoe)
-
-/* Deal with different ways to concatenate in cpp */
-# ifdef __STDC__
-# define cat3(a,b,c) a ## b ## c
-# else
-# define cat3(a,b,c) a/**/b/**/c
-# endif
-
-/* Deal with vax/tahoe byte order issues */
-# ifdef vax
-# define cat3t(a,b,c) cat3(a,b,c)
-# else
-# define cat3t(a,b,c) cat3(a,c,b)
-# endif
-
-# define vccast(name) (*(const double *)(cat3(name,,x)))
-
- /*
- * Define a constant to high precision on a Vax or Tahoe.
- *
- * Args are the name to define, the decimal floating point value,
- * four 16-bit chunks of the float value in hex
- * (because the vax and tahoe differ in float format!), the power
- * of 2 of the hex-float exponent, and the hex-float mantissa.
- * Most of these arguments are not used at compile time; they are
- * used in a post-check to make sure the constants were compiled
- * correctly.
- *
- * People who want to use the constant will have to do their own
- * #define foo vccast(foo)
- * since CPP cannot do this for them from inside another macro (sigh).
- * We define "vccast" if this needs doing.
- */
-# define vc(name, value, x1,x2,x3,x4, bexp, xval) \
- const static long cat3(name,,x)[] = {cat3t(0x,x1,x2), cat3t(0x,x3,x4)};
-
-# define ic(name, value, bexp, xval) ;
-
-#else /* vax or tahoe */
-
- /* Hooray, we have an IEEE machine */
-# undef vccast
-# define vc(name, value, x1,x2,x3,x4, bexp, xval) ;
-
-# define ic(name, value, bexp, xval) \
- const static double name = value;
-
-#endif /* defined(vax)||defined(tahoe) */
-
-
-/*
- * Functions internal to the math package, yet not static.
- */
-extern double __exp__E();
-extern double __log__L();
-
-struct Double {double a, b;};
-double __exp__D __P((double, double));
-struct Double __log__D __P((double));
+++ /dev/null
-/*
- * Copyright (c) 1987, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * 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. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``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 THE REGENTS OR CONTRIBUTORS 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.
- */
-
-#ifndef lint
-static char sccsid[] = "@(#)sincos.c 8.1 (Berkeley) 6/4/93";
-#endif /* not lint */
-
-#include "trig.h"
-double
-sin(x)
-double x;
-{
- double a,c,z;
-
- if(!finite(x)) /* sin(NaN) and sin(INF) must be NaN */
- return x-x;
- x=drem(x,PI2); /* reduce x into [-PI,PI] */
- a=copysign(x,one);
- if (a >= PIo4) {
- if(a >= PI3o4) /* ... in [3PI/4,PI] */
- x = copysign((a = PI-a),x);
- else { /* ... in [PI/4,3PI/4] */
- a = PIo2-a; /* rtn. sign(x)*C(PI/2-|x|) */
- z = a*a;
- c = cos__C(z);
- z *= half;
- a = (z >= thresh ? half-((z-half)-c) : one-(z-c));
- return copysign(a,x);
- }
- }
-
- if (a < small) { /* rtn. S(x) */
- big+a;
- return x;
- }
- return x+x*sin__S(x*x);
-}
-
-double
-cos(x)
-double x;
-{
- double a,c,z,s = 1.0;
-
- if(!finite(x)) /* cos(NaN) and cos(INF) must be NaN */
- return x-x;
- x=drem(x,PI2); /* reduce x into [-PI,PI] */
- a=copysign(x,one);
- if (a >= PIo4) {
- if (a >= PI3o4) { /* ... in [3PI/4,PI] */
- a = PI-a;
- s = negone;
- }
- else { /* ... in [PI/4,3PI/4] */
- a = PIo2-a;
- return a+a*sin__S(a*a); /* rtn. S(PI/2-|x|) */
- }
- }
- if (a < small) {
- big+a;
- return s; /* rtn. s*C(a) */
- }
- z = a*a;
- c = cos__C(z);
- z *= half;
- a = (z >= thresh ? half-((z-half)-c) : one-(z-c));
- return copysign(a,s);
-}
+++ /dev/null
-/*
- * Copyright (c) 1987, 1993
- * The Regents of the University of California. All rights reserved.
- *
- * 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. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
- * may be used to endorse or promote products derived from this software
- * without specific prior written permission.
- *
- * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``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 THE REGENTS OR CONTRIBUTORS 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.
- *
- * @(#)trig.h 8.1 (Berkeley) 6/4/93
- */
-
-#include "mathimpl.h"
-
-vc(thresh, 2.6117239648121182150E-1 ,b863,3f85,6ea0,6b02, -1, .85B8636B026EA0)
-vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2)
-vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2)
-vc(PI3o4, 2.3561944901923449203E0 ,cbe3,4116,0e92,f999, 2, .96CBE3F9990E92)
-vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2)
-vc(PI2, 6.2831853071795864540E0 ,0fda,41c9,68c2,a221, 3, .C90FDAA22168C2)
-
-ic(thresh, 2.6117239648121182150E-1 , -2, 1.0B70C6D604DD4)
-ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18)
-ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18)
-ic(PI3o4, 2.3561944901923448370E0 , 1, 1.2D97C7F3321D2)
-ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18)
-ic(PI2, 6.2831853071795862320E0 , 2, 1.921FB54442D18)
-
-#ifdef vccast
-#define thresh vccast(thresh)
-#define PIo4 vccast(PIo4)
-#define PIo2 vccast(PIo2)
-#define PI3o4 vccast(PI3o4)
-#define PI vccast(PI)
-#define PI2 vccast(PI2)
-#endif
-
-#ifdef national
-static long fmaxx[] = { 0xffffffff, 0x7fefffff};
-#define fmax (*(double*)fmaxx)
-#endif /* national */
-
-static const double
- zero = 0,
- one = 1,
- negone = -1,
- half = 1.0/2.0,
- small = 1E-10, /* 1+small**2 == 1; better values for small:
- * small = 1.5E-9 for VAX D
- * = 1.2E-8 for IEEE Double
- * = 2.8E-10 for IEEE Extended
- */
- big = 1E20; /* big := 1/(small**2) */
-
-/* sin__S(x*x) ... re-implemented as a macro
- * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
- * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X)
- * CODED IN C BY K.C. NG, 1/21/85;
- * REVISED BY K.C. NG on 8/13/85.
- *
- * sin(x*k) - x
- * RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded
- * x
- * value of pi in machine precision:
- *
- * Decimal:
- * pi = 3.141592653589793 23846264338327 .....
- * 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
- *
- * Hexadecimal:
- * pi = 3.243F6A8885A308D313198A2E....
- * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18
- * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2
- *
- * Method:
- * 1. Let z=x*x. Create a polynomial approximation to
- * (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5).
- * Then
- * sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5)
- *
- * The coefficient S's are obtained by a special Remez algorithm.
- *
- * Accuracy:
- * In the absence of rounding error, the approximation has absolute error
- * less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE.
- *
- * Constants:
- * The hexadecimal values are the intended ones for the following constants.
- * The decimal values may be used, provided that the compiler will convert
- * from decimal to binary accurately enough to produce the hexadecimal values
- * shown.
- *
- */
-
-vc(S0, -1.6666666666666646660E-1 ,aaaa,bf2a,aa71,aaaa, -2, -.AAAAAAAAAAAA71)
-vc(S1, 8.3333333333297230413E-3 ,8888,3d08,477f,8888, -6, .8888888888477F)
-vc(S2, -1.9841269838362403710E-4 ,0d00,ba50,1057,cf8a, -12, -.D00D00CF8A1057)
-vc(S3, 2.7557318019967078930E-6 ,ef1c,3738,bedc,a326, -18, .B8EF1CA326BEDC)
-vc(S4, -2.5051841873876551398E-8 ,3195,b3d7,e1d3,374c, -25, -.D73195374CE1D3)
-vc(S5, 1.6028995389845827653E-10 ,3d9c,3030,cccc,6d26, -32, .B03D9C6D26CCCC)
-vc(S6, -6.2723499671769283121E-13 ,8d0b,ac30,ea82,7561, -40, -.B08D0B7561EA82)
-
-ic(S0, -1.6666666666666463126E-1 , -3, -1.555555555550C)
-ic(S1, 8.3333333332992771264E-3 , -7, 1.111111110C461)
-ic(S2, -1.9841269816180999116E-4 , -13, -1.A01A019746345)
-ic(S3, 2.7557309793219876880E-6 , -19, 1.71DE3209CDCD9)
-ic(S4, -2.5050225177523807003E-8 , -26, -1.AE5C0E319A4EF)
-ic(S5, 1.5868926979889205164E-10 , -33, 1.5CF61DF672B13)
-
-#ifdef vccast
-#define S0 vccast(S0)
-#define S1 vccast(S1)
-#define S2 vccast(S2)
-#define S3 vccast(S3)
-#define S4 vccast(S4)
-#define S5 vccast(S5)
-#define S6 vccast(S6)
-#endif
-
-#if defined(vax)||defined(tahoe)
-# define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*(S5+z*S6)))))))
-#else /* defined(vax)||defined(tahoe) */
-# define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*S5))))))
-#endif /* defined(vax)||defined(tahoe) */
-
-/* cos__C(x*x) ... re-implemented as a macro
- * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS)
- * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X)
- * CODED IN C BY K.C. NG, 1/21/85;
- * REVISED BY K.C. NG on 8/13/85.
- *
- * x*x
- * RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI,
- * 2
- * PI is the rounded value of pi in machine precision :
- *
- * Decimal:
- * pi = 3.141592653589793 23846264338327 .....
- * 53 bits PI = 3.141592653589793 115997963 ..... ,
- * 56 bits PI = 3.141592653589793 227020265 ..... ,
- *
- * Hexadecimal:
- * pi = 3.243F6A8885A308D313198A2E....
- * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18
- * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2
- *
- *
- * Method:
- * 1. Let z=x*x. Create a polynomial approximation to
- * cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5)
- * then
- * cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5)
- *
- * The coefficient C's are obtained by a special Remez algorithm.
- *
- * Accuracy:
- * In the absence of rounding error, the approximation has absolute error
- * less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE.
- *
- *
- * Constants:
- * The hexadecimal values are the intended ones for the following constants.
- * The decimal values may be used, provided that the compiler will convert
- * from decimal to binary accurately enough to produce the hexadecimal values
- * shown.
- */
-
-vc(C0, 4.1666666666666504759E-2 ,aaaa,3e2a,a9f0,aaaa, -4, .AAAAAAAAAAA9F0)
-vc(C1, -1.3888888888865302059E-3 ,0b60,bbb6,0cca,b60a, -9, -.B60B60B60A0CCA)
-vc(C2, 2.4801587285601038265E-5 ,0d00,38d0,098f,cdcd, -15, .D00D00CDCD098F)
-vc(C3, -2.7557313470902390219E-7 ,f27b,b593,e805,b593, -21, -.93F27BB593E805)
-vc(C4, 2.0875623401082232009E-9 ,74c8,320f,3ff0,fa1e, -28, .8F74C8FA1E3FF0)
-vc(C5, -1.1355178117642986178E-11 ,c32d,ae47,5a63,0a5c, -36, -.C7C32D0A5C5A63)
-
-ic(C0, 4.1666666666666504759E-2 , -5, 1.555555555553E)
-ic(C1, -1.3888888888865301516E-3 , -10, -1.6C16C16C14199)
-ic(C2, 2.4801587269650015769E-5 , -16, 1.A01A01971CAEB)
-ic(C3, -2.7557304623183959811E-7 , -22, -1.27E4F1314AD1A)
-ic(C4, 2.0873958177697780076E-9 , -29, 1.1EE3B60DDDC8C)
-ic(C5, -1.1250289076471311557E-11 , -37, -1.8BD5986B2A52E)
-
-#ifdef vccast
-#define C0 vccast(C0)
-#define C1 vccast(C1)
-#define C2 vccast(C2)
-#define C3 vccast(C3)
-#define C4 vccast(C4)
-#define C5 vccast(C5)
-#endif
-
-#define cos__C(z) (z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5))))))
projects / thirdparty / glibc.git / commitdiff
