* Copyright (c) 1987 Regents of the University of California.
* Redistribution and use in source and binary forms are permitted
* provided that: (1) source distributions retain this entire copyright
* notice and comment, and (2) distributions including binaries display
* the following acknowledgement: ``This product includes software
* developed by the University of California, Berkeley and its contributors''
* in the documentation or other materials provided with the distribution
* and in all advertising materials mentioning features or use of this
* software. 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 ``AS IS'' AND WITHOUT ANY EXPRESS OR
* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
* All recipients should regard themselves as participants in an ongoing
* research project and hence should feel obligated to report their
* experiences (good or bad) with these elementary function codes, using
* the sendbug(8) program, to the authors.
* @(#)trig.h 5.5 (Berkeley) 6/1/90
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
)
#define thresh vccast(thresh)
#define PIo4 vccast(PIo4)
#define PIo2 vccast(PIo2)
#define PI3o4 vccast(PI3o4)
static long fmaxx
[] = { 0xffffffff, 0x7fefffff};
#define fmax (*(double*)fmaxx)
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.
* RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded
* value of pi in machine precision:
* pi = 3.141592653589793 23846264338327 .....
* 53 bits PI = 3.141592653589793 115997963 ..... ,
* 56 bits PI = 3.141592653589793 227020265 ..... ,
* pi = 3.243F6A8885A308D313198A2E....
* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18
* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2
* 1. Let z=x*x. Create a polynomial approximation to
* (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5).
* sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5)
* The coefficient S's are obtained by a special Remez algorithm.
* 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.
* 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
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
)
#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.
* RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI,
* PI is the rounded value of pi in machine precision :
* pi = 3.141592653589793 23846264338327 .....
* 53 bits PI = 3.141592653589793 115997963 ..... ,
* 56 bits PI = 3.141592653589793 227020265 ..... ,
* pi = 3.243F6A8885A308D313198A2E....
* 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18
* 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2
* 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)
* cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5)
* The coefficient C's are obtained by a special Remez algorithm.
* 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.
* 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
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
)
#define cos__C(z) (z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5))))))