diff options
Diffstat (limited to 'lib/libm/common')
-rw-r--r-- | lib/libm/common/atan2.c | 284 | ||||
-rw-r--r-- | lib/libm/common/sincos.c | 101 | ||||
-rw-r--r-- | lib/libm/common/tan.c | 77 | ||||
-rw-r--r-- | lib/libm/common/trig.h | 215 |
4 files changed, 0 insertions, 677 deletions
diff --git a/lib/libm/common/atan2.c b/lib/libm/common/atan2.c deleted file mode 100644 index 20a4e46..0000000 --- a/lib/libm/common/atan2.c +++ /dev/null @@ -1,284 +0,0 @@ -/* - * 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. - */ - -#include <sys/cdefs.h> -__FBSDID("$FreeBSD$"); - -#ifndef lint -static char sccsid[] = "@(#)atan2.c 8.1 (Berkeley) 6/4/93"; -#endif /* not lint */ - -/* ATAN2(Y,X) - * RETURN ARG (X+iY) - * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) - * CODED IN C BY K.C. NG, 1/8/85; - * REVISED BY K.C. NG on 2/7/85, 2/13/85, 3/7/85, 3/30/85, 6/29/85. - * - * Required system supported functions : - * copysign(x,y) - * scalb(x,y) - * logb(x) - * - * Method : - * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). - * 2. Reduce x to positive by (if x and y are unexceptional): - * ARG (x+iy) = arctan(y/x) ... if x > 0, - * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, - * 3. According to the integer k=4t+0.25 truncated , t=y/x, the argument - * is further reduced to one of the following intervals and the - * arctangent of y/x is evaluated by the corresponding formula: - * - * [0,7/16] atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) - * [7/16,11/16] atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) ) - * [11/16.19/16] atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) ) - * [19/16,39/16] atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) ) - * [39/16,INF] atan(y/x) = atan(INF) + atan( -x/y ) - * - * Special cases: - * Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y). - * - * ARG( NAN , (anything) ) is NaN; - * ARG( (anything), NaN ) is NaN; - * ARG(+(anything but NaN), +-0) is +-0 ; - * ARG(-(anything but NaN), +-0) is +-PI ; - * ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2; - * ARG( +INF,+-(anything but INF and NaN) ) is +-0 ; - * ARG( -INF,+-(anything but INF and NaN) ) is +-PI; - * ARG( +INF,+-INF ) is +-PI/4 ; - * ARG( -INF,+-INF ) is +-3PI/4; - * ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2; - * - * Accuracy: - * atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded, - * where - * - * 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 356,000 random argument on [-1,1] * [-1,1] on a - * VAX, the maximum observed error was 1.41 ulps (units of the last place) - * compared with (PI/pi)*(the exact ARG(x+iy)). - * - * Note: - * We use machine PI (the true pi rounded) in place of the actual - * value of pi for all the trig and inverse trig functions. In general, - * if trig is one of sin, cos, tan, then computed trig(y) returns the - * exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig - * returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the - * trig functions have period PI, and trig(arctrig(x)) returns x for - * all critical values x. - * - * 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(athfhi, 4.6364760900080611433E-1 ,6338,3fed,da7b,2b0d, -1, .ED63382B0DDA7B) -vc(athflo, 1.9338828231967579916E-19 ,5005,2164,92c0,9cfe, -62, .E450059CFE92C0) -vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2) -vc(at1fhi, 9.8279372324732906796E-1 ,985e,407b,b4d9,940f, 0, .FB985E940FB4D9) -vc(at1flo,-3.5540295636764633916E-18 ,1edc,a383,eaea,34d6, -57,-.831EDC34D6EAEA) -vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2) -vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2) -vc(a1, 3.3333333333333473730E-1 ,aaaa,3faa,ab75,aaaa, -1, .AAAAAAAAAAAB75) -vc(a2, -2.0000000000017730678E-1 ,cccc,bf4c,946e,cccd, -2,-.CCCCCCCCCD946E) -vc(a3, 1.4285714286694640301E-1 ,4924,3f12,4262,9274, -2, .92492492744262) -vc(a4, -1.1111111135032672795E-1 ,8e38,bee3,6292,ebc6, -3,-.E38E38EBC66292) -vc(a5, 9.0909091380563043783E-2 ,2e8b,3eba,d70c,b31b, -3, .BA2E8BB31BD70C) -vc(a6, -7.6922954286089459397E-2 ,89c8,be9d,7f18,27c3, -3,-.9D89C827C37F18) -vc(a7, 6.6663180891693915586E-2 ,86b4,3e88,9e58,ae37, -3, .8886B4AE379E58) -vc(a8, -5.8772703698290408927E-2 ,bba5,be70,a942,8481, -4,-.F0BBA58481A942) -vc(a9, 5.2170707402812969804E-2 ,b0f3,3e55,13ab,a1ab, -4, .D5B0F3A1AB13AB) -vc(a10, -4.4895863157820361210E-2 ,e4b9,be37,048f,7fd1, -4,-.B7E4B97FD1048F) -vc(a11, 3.3006147437343875094E-2 ,3174,3e07,2d87,3cf7, -4, .8731743CF72D87) -vc(a12, -1.4614844866464185439E-2 ,731a,bd6f,76d9,2f34, -6,-.EF731A2F3476D9) - -ic(athfhi, 4.6364760900080609352E-1 , -2, 1.DAC670561BB4F) -ic(athflo, 4.6249969567426939759E-18 , -58, 1.5543B8F253271) -ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18) -ic(at1fhi, 9.8279372324732905408E-1 , -1, 1.F730BD281F69B) -ic(at1flo,-2.4407677060164810007E-17 , -56, -1.C23DFEFEAE6B5) -ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18) -ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18) -ic(a1, 3.3333333333333942106E-1 , -2, 1.55555555555C3) -ic(a2, -1.9999999999979536924E-1 , -3, -1.9999999997CCD) -ic(a3, 1.4285714278004377209E-1 , -3, 1.24924921EC1D7) -ic(a4, -1.1111110579344973814E-1 , -4, -1.C71C7059AF280) -ic(a5, 9.0908906105474668324E-2 , -4, 1.745CE5AA35DB2) -ic(a6, -7.6919217767468239799E-2 , -4, -1.3B0FA54BEC400) -ic(a7, 6.6614695906082474486E-2 , -4, 1.10DA924597FFF) -ic(a8, -5.8358371008508623523E-2 , -5, -1.DE125FDDBD793) -ic(a9, 4.9850617156082015213E-2 , -5, 1.9860524BDD807) -ic(a10, -3.6700606902093604877E-2 , -5, -1.2CA6C04C6937A) -ic(a11, 1.6438029044759730479E-2 , -6, 1.0D52174A1BB54) - -#ifdef vccast -#define athfhi vccast(athfhi) -#define athflo vccast(athflo) -#define PIo4 vccast(PIo4) -#define at1fhi vccast(at1fhi) -#define at1flo vccast(at1flo) -#define PIo2 vccast(PIo2) -#define PI vccast(PI) -#define a1 vccast(a1) -#define a2 vccast(a2) -#define a3 vccast(a3) -#define a4 vccast(a4) -#define a5 vccast(a5) -#define a6 vccast(a6) -#define a7 vccast(a7) -#define a8 vccast(a8) -#define a9 vccast(a9) -#define a10 vccast(a10) -#define a11 vccast(a11) -#define a12 vccast(a12) -#endif - -double atan2(y,x) -double y,x; -{ - static const double zero=0, one=1, small=1.0E-9, big=1.0E18; - double t,z,signy,signx,hi,lo; - int k,m; - -#if !defined(vax)&&!defined(tahoe) - /* if x or y is NAN */ - if(x!=x) return(x); if(y!=y) return(y); -#endif /* !defined(vax)&&!defined(tahoe) */ - - /* copy down the sign of y and x */ - signy = copysign(one,y) ; - signx = copysign(one,x) ; - - /* if x is 1.0, goto begin */ - if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;} - - /* when y = 0 */ - if(y==zero) return((signx==one)?y:copysign(PI,signy)); - - /* when x = 0 */ - if(x==zero) return(copysign(PIo2,signy)); - - /* when x is INF */ - if(!finite(x)) - if(!finite(y)) - return(copysign((signx==one)?PIo4:3*PIo4,signy)); - else - return(copysign((signx==one)?zero:PI,signy)); - - /* when y is INF */ - if(!finite(y)) return(copysign(PIo2,signy)); - - /* compute y/x */ - x=copysign(x,one); - y=copysign(y,one); - if((m=(k=logb(y))-logb(x)) > 60) t=big+big; - else if(m < -80 ) t=y/x; - else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); } - - /* begin argument reduction */ -begin: - if (t < 2.4375) { - - /* truncate 4(t+1/16) to integer for branching */ - k = 4 * (t+0.0625); - switch (k) { - - /* t is in [0,7/16] */ - case 0: - case 1: - if (t < small) - { big + small ; /* raise inexact flag */ - return (copysign((signx>zero)?t:PI-t,signy)); } - - hi = zero; lo = zero; break; - - /* t is in [7/16,11/16] */ - case 2: - hi = athfhi; lo = athflo; - z = x+x; - t = ( (y+y) - x ) / ( z + y ); break; - - /* t is in [11/16,19/16] */ - case 3: - case 4: - hi = PIo4; lo = zero; - t = ( y - x ) / ( x + y ); break; - - /* t is in [19/16,39/16] */ - default: - hi = at1fhi; lo = at1flo; - z = y-x; y=y+y+y; t = x+x; - t = ( (z+z)-x ) / ( t + y ); break; - } - } - /* end of if (t < 2.4375) */ - - else - { - hi = PIo2; lo = zero; - - /* t is in [2.4375, big] */ - if (t <= big) t = - x / y; - - /* t is in [big, INF] */ - else - { big+small; /* raise inexact flag */ - t = zero; } - } - /* end of argument reduction */ - - /* compute atan(t) for t in [-.4375, .4375] */ - z = t*t; -#if defined(vax)||defined(tahoe) - z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+ - z*(a9+z*(a10+z*(a11+z*a12)))))))))))); -#else /* defined(vax)||defined(tahoe) */ - z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+ - z*(a9+z*(a10+z*a11))))))))))); -#endif /* defined(vax)||defined(tahoe) */ - z = lo - z; z += t; z += hi; - - return(copysign((signx>zero)?z:PI-z,signy)); -} diff --git a/lib/libm/common/sincos.c b/lib/libm/common/sincos.c deleted file mode 100644 index af7d635..0000000 --- a/lib/libm/common/sincos.c +++ /dev/null @@ -1,101 +0,0 @@ -/* - * 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. - */ - -#include <sys/cdefs.h> -__FBSDID("$FreeBSD$"); - -#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); -} diff --git a/lib/libm/common/tan.c b/lib/libm/common/tan.c deleted file mode 100644 index 2e87ec6..0000000 --- a/lib/libm/common/tan.c +++ /dev/null @@ -1,77 +0,0 @@ -/* - * 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. - */ - -#include <sys/cdefs.h> -__FBSDID("$FreeBSD$"); - -#ifndef lint -static char sccsid[] = "@(#)tan.c 8.1 (Berkeley) 6/4/93"; -#endif /* not lint */ - -#include "trig.h" -double -tan(x) -double x; -{ - double a,z,ss,cc,c; - int k; - - if(!finite(x)) /* tan(NaN) and tan(INF) must be NaN */ - return x-x; - x = drem(x,PI); /* reduce x into [-PI/2, PI/2] */ - a = copysign(x,one); /* ... = abs(x) */ - if (a >= PIo4) { - k = 1; - x = copysign(PIo2-a,x); - } - else { - k = 0; - if (a < small) { - big+a; - return x; - } - } - z = x*x; - cc = cos__C(z); - ss = sin__S(z); - z *= half; /* Next get c = cos(x) accurately */ - c = (z >= thresh ? half-((z-half)-cc) : one-(z-cc)); - if (k == 0) - return x+(x*(z-(cc-ss)))/c; /* ... sin/cos */ -#ifdef national - else if (x == zero) - return copysign(fmax,x); /* no inf on 32k */ -#endif /* national */ - else - return c/(x+x*ss); /* ... cos/sin */ -} diff --git a/lib/libm/common/trig.h b/lib/libm/common/trig.h deleted file mode 100644 index e31fb4c..0000000 --- a/lib/libm/common/trig.h +++ /dev/null @@ -1,215 +0,0 @@ -/* - * 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)))))) |