1 /* $NetBSD: trig.h,v 1.6 2003/08/07 16:44:53 agc Exp $ */ 2 /* 3 * Copyright (c) 1987, 1993 4 * The Regents of the University of California. All rights reserved. 5 * 6 * Redistribution and use in source and binary forms, with or without 7 * modification, are permitted provided that the following conditions 8 * are met: 9 * 1. Redistributions of source code must retain the above copyright 10 * notice, this list of conditions and the following disclaimer. 11 * 2. Redistributions in binary form must reproduce the above copyright 12 * notice, this list of conditions and the following disclaimer in the 13 * documentation and/or other materials provided with the distribution. 14 * 3. Neither the name of the University nor the names of its contributors 15 * may be used to endorse or promote products derived from this software 16 * without specific prior written permission. 17 * 18 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 19 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 20 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 21 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 22 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 23 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 24 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 25 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 26 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 27 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 28 * SUCH DAMAGE. 29 * 30 * @(#)trig.h 8.1 (Berkeley) 6/4/93 31 */ 32 33 vc(thresh, 2.6117239648121182150E-1 ,b863,3f85,6ea0,6b02, -1, .85B8636B026EA0) 34 vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2) 35 vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2) 36 vc(PI3o4, 2.3561944901923449203E0 ,cbe3,4116,0e92,f999, 2, .96CBE3F9990E92) 37 vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2) 38 vc(PI2, 6.2831853071795864540E0 ,0fda,41c9,68c2,a221, 3, .C90FDAA22168C2) 39 40 ic(thresh, 2.6117239648121182150E-1 , -2, 1.0B70C6D604DD4) 41 ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18) 42 ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18) 43 ic(PI3o4, 2.3561944901923448370E0 , 1, 1.2D97C7F3321D2) 44 ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18) 45 ic(PI2, 6.2831853071795862320E0 , 2, 1.921FB54442D18) 46 47 #ifdef vccast 48 #define thresh vccast(thresh) 49 #define PIo4 vccast(PIo4) 50 #define PIo2 vccast(PIo2) 51 #define PI3o4 vccast(PI3o4) 52 #define PI vccast(PI) 53 #define PI2 vccast(PI2) 54 #endif 55 56 #ifdef national 57 static long fmaxx[] = { 0xffffffff, 0x7fefffff}; 58 #define fmax (*(double*)fmaxx) 59 #endif /* national */ 60 61 #ifdef _LIBM_DECLARE 62 const double 63 __zero = 0, 64 __one = 1, 65 __negone = -1, 66 __half = 1.0/2.0, 67 #ifdef __vax__ 68 __small = 1E-9, /* 1+small**2 == 1; better values for small: 69 * small = 1.5E-9 for VAX D 70 * = 1.2E-8 for IEEE Double 71 * = 2.8E-10 for IEEE Extended 72 */ 73 __big = 1E18; /* big := 1/(small**2) */ 74 #else 75 __small = 1E-10, /* 1+small**2 == 1; better values for small: 76 * small = 1.5E-9 for VAX D 77 * = 1.2E-8 for IEEE Double 78 * = 2.8E-10 for IEEE Extended 79 */ 80 __big = 1E20; /* big := 1/(small**2) */ 81 #endif 82 #else 83 extern const double __zero, __one, __negone, __half, __small, __big; 84 #endif 85 86 /* sin__S(x*x) ... re-implemented as a macro 87 * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) 88 * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) 89 * CODED IN C BY K.C. NG, 1/21/85; 90 * REVISED BY K.C. NG on 8/13/85. 91 * 92 * sin(x*k) - x 93 * RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded 94 * x 95 * value of pi in machine precision: 96 * 97 * Decimal: 98 * pi = 3.141592653589793 23846264338327 ..... 99 * 53 bits PI = 3.141592653589793 115997963 ..... , 100 * 56 bits PI = 3.141592653589793 227020265 ..... , 101 * 102 * Hexadecimal: 103 * pi = 3.243F6A8885A308D313198A2E.... 104 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 105 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 106 * 107 * Method: 108 * 1. Let z=x*x. Create a polynomial approximation to 109 * (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5). 110 * Then 111 * sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5) 112 * 113 * The coefficient S's are obtained by a special Remez algorithm. 114 * 115 * Accuracy: 116 * In the absence of rounding error, the approximation has absolute error 117 * less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE. 118 * 119 * Constants: 120 * The hexadecimal values are the intended ones for the following constants. 121 * The decimal values may be used, provided that the compiler will convert 122 * from decimal to binary accurately enough to produce the hexadecimal values 123 * shown. 124 * 125 */ 126 127 vc(S0, -1.6666666666666646660E-1 ,aaaa,bf2a,aa71,aaaa, -2, -.AAAAAAAAAAAA71) 128 vc(S1, 8.3333333333297230413E-3 ,8888,3d08,477f,8888, -6, .8888888888477F) 129 vc(S2, -1.9841269838362403710E-4 ,0d00,ba50,1057,cf8a, -12, -.D00D00CF8A1057) 130 vc(S3, 2.7557318019967078930E-6 ,ef1c,3738,bedc,a326, -18, .B8EF1CA326BEDC) 131 vc(S4, -2.5051841873876551398E-8 ,3195,b3d7,e1d3,374c, -25, -.D73195374CE1D3) 132 vc(S5, 1.6028995389845827653E-10 ,3d9c,3030,cccc,6d26, -32, .B03D9C6D26CCCC) 133 vc(S6, -6.2723499671769283121E-13 ,8d0b,ac30,ea82,7561, -40, -.B08D0B7561EA82) 134 135 ic(S0, -1.6666666666666463126E-1 , -3, -1.555555555550C) 136 ic(S1, 8.3333333332992771264E-3 , -7, 1.111111110C461) 137 ic(S2, -1.9841269816180999116E-4 , -13, -1.A01A019746345) 138 ic(S3, 2.7557309793219876880E-6 , -19, 1.71DE3209CDCD9) 139 ic(S4, -2.5050225177523807003E-8 , -26, -1.AE5C0E319A4EF) 140 ic(S5, 1.5868926979889205164E-10 , -33, 1.5CF61DF672B13) 141 142 #ifdef vccast 143 #define S0 vccast(S0) 144 #define S1 vccast(S1) 145 #define S2 vccast(S2) 146 #define S3 vccast(S3) 147 #define S4 vccast(S4) 148 #define S5 vccast(S5) 149 #define S6 vccast(S6) 150 #endif 151 152 #if defined(__vax__)||defined(tahoe) 153 # define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*(S5+z*S6))))))) 154 #else /* defined(__vax__)||defined(tahoe) */ 155 # define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*S5)))))) 156 #endif /* defined(__vax__)||defined(tahoe) */ 157 158 /* cos__C(x*x) ... re-implemented as a macro 159 * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) 160 * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) 161 * CODED IN C BY K.C. NG, 1/21/85; 162 * REVISED BY K.C. NG on 8/13/85. 163 * 164 * x*x 165 * RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI, 166 * 2 167 * PI is the rounded value of pi in machine precision : 168 * 169 * Decimal: 170 * pi = 3.141592653589793 23846264338327 ..... 171 * 53 bits PI = 3.141592653589793 115997963 ..... , 172 * 56 bits PI = 3.141592653589793 227020265 ..... , 173 * 174 * Hexadecimal: 175 * pi = 3.243F6A8885A308D313198A2E.... 176 * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 177 * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 178 * 179 * 180 * Method: 181 * 1. Let z=x*x. Create a polynomial approximation to 182 * cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5) 183 * then 184 * cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5) 185 * 186 * The coefficient C's are obtained by a special Remez algorithm. 187 * 188 * Accuracy: 189 * In the absence of rounding error, the approximation has absolute error 190 * less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE. 191 * 192 * 193 * Constants: 194 * The hexadecimal values are the intended ones for the following constants. 195 * The decimal values may be used, provided that the compiler will convert 196 * from decimal to binary accurately enough to produce the hexadecimal values 197 * shown. 198 */ 199 200 vc(C0, 4.1666666666666504759E-2 ,aaaa,3e2a,a9f0,aaaa, -4, .AAAAAAAAAAA9F0) 201 vc(C1, -1.3888888888865302059E-3 ,0b60,bbb6,0cca,b60a, -9, -.B60B60B60A0CCA) 202 vc(C2, 2.4801587285601038265E-5 ,0d00,38d0,098f,cdcd, -15, .D00D00CDCD098F) 203 vc(C3, -2.7557313470902390219E-7 ,f27b,b593,e805,b593, -21, -.93F27BB593E805) 204 vc(C4, 2.0875623401082232009E-9 ,74c8,320f,3ff0,fa1e, -28, .8F74C8FA1E3FF0) 205 vc(C5, -1.1355178117642986178E-11 ,c32d,ae47,5a63,0a5c, -36, -.C7C32D0A5C5A63) 206 207 ic(C0, 4.1666666666666504759E-2 , -5, 1.555555555553E) 208 ic(C1, -1.3888888888865301516E-3 , -10, -1.6C16C16C14199) 209 ic(C2, 2.4801587269650015769E-5 , -16, 1.A01A01971CAEB) 210 ic(C3, -2.7557304623183959811E-7 , -22, -1.27E4F1314AD1A) 211 ic(C4, 2.0873958177697780076E-9 , -29, 1.1EE3B60DDDC8C) 212 ic(C5, -1.1250289076471311557E-11 , -37, -1.8BD5986B2A52E) 213 214 #ifdef vccast 215 #define C0 vccast(C0) 216 #define C1 vccast(C1) 217 #define C2 vccast(C2) 218 #define C3 vccast(C3) 219 #define C4 vccast(C4) 220 #define C5 vccast(C5) 221 #endif 222 223 #define cos__C(z) (z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5)))))) 224
Indexes created Sat Sep 20 22:09:52 GMT 2025