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Diffstat (limited to 'sysdeps/generic/trig.h')
| -rw-r--r-- | sysdeps/generic/trig.h | 215 |
1 files changed, 0 insertions, 215 deletions
diff --git a/sysdeps/generic/trig.h b/sysdeps/generic/trig.h deleted file mode 100644 index 9e05b0ea0d..0000000000 --- a/sysdeps/generic/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)))))) |