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phunix/lib/libm/noieee_src/trig.h
Ben Gras 2fe8fb192f Full switch to clang/ELF. Drop ack. Simplify. 
There is important information about booting non-ack images in
docs/UPDATING. ack/aout-format images can't be built any more, and
booting clang/ELF-format ones is a little different. Updating to the
new boot monitor is recommended.

Changes in this commit:

	. drop boot monitor -> allowing dropping ack support
	. facility to copy ELF boot files to /boot so that old boot monitor
	  can still boot fairly easily, see UPDATING
	. no more ack-format libraries -> single-case libraries
	. some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases
	. drop several ack toolchain commands, but not all support
	  commands (e.g. aal is gone but acksize is not yet).
	. a few libc files moved to netbsd libc dir
	. new /bin/date as minix date used code in libc/
	. test compile fix
	. harmonize includes
	. /usr/lib is no longer special: without ack, /usr/lib plays no
	  kind of special bootstrapping role any more and bootstrapping
	  is done exclusively through packages, so releases depend even
	  less on the state of the machine making them now.
	. rename nbsd_lib* to lib*
	. reduce mtree
2012-02-14 14:52:02 +01:00

224 lines
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C
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/* $NetBSD: trig.h,v 1.6 2003/08/07 16:44:53 agc Exp $ */
/*
* 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. 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
*/
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 */
#ifdef _LIBM_DECLARE
const double
__zero = 0,
__one = 1,
__negone = -1,
__half = 1.0/2.0,
#ifdef __vax__
__small = 1E-9, /* 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 = 1E18; /* big := 1/(small**2) */
#else
__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) */
#endif
#else
extern const double __zero, __one, __negone, __half, __small, __big;
#endif
/* 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))))))
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