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