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1 | /* @(#)k_sin.c 5.1 93/09/24 */\r |
| 2 | /*\r |
| 3 | * ====================================================\r |
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r |
| 5 | *\r |
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business.\r |
| 7 | * Permission to use, copy, modify, and distribute this\r |
| 8 | * software is freely granted, provided that this notice\r |
| 9 | * is preserved.\r |
| 10 | * ====================================================\r |
| 11 | */\r |
| 12 | #include <LibConfig.h>\r |
| 13 | #include <sys/EfiCdefs.h>\r |
| 14 | #if defined(LIBM_SCCS) && !defined(lint)\r |
| 15 | __RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $");\r |
| 16 | #endif\r |
| 17 | \r |
| 18 | /* __kernel_sin( x, y, iy)\r |
| 19 | * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854\r |
| 20 | * Input x is assumed to be bounded by ~pi/4 in magnitude.\r |
| 21 | * Input y is the tail of x.\r |
| 22 | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).\r |
| 23 | *\r |
| 24 | * Algorithm\r |
| 25 | * 1. Since sin(-x) = -sin(x), we need only to consider positive x.\r |
| 26 | * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.\r |
| 27 | * 3. sin(x) is approximated by a polynomial of degree 13 on\r |
| 28 | * [0,pi/4]\r |
| 29 | * 3 13\r |
| 30 | * sin(x) ~ x + S1*x + ... + S6*x\r |
| 31 | * where\r |
| 32 | *\r |
| 33 | * |sin(x) 2 4 6 8 10 12 | -58\r |
| 34 | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2\r |
| 35 | * | x |\r |
| 36 | *\r |
| 37 | * 4. sin(x+y) = sin(x) + sin'(x')*y\r |
| 38 | * ~ sin(x) + (1-x*x/2)*y\r |
| 39 | * For better accuracy, let\r |
| 40 | * 3 2 2 2 2\r |
| 41 | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))\r |
| 42 | * then 3 2\r |
| 43 | * sin(x) = x + (S1*x + (x *(r-y/2)+y))\r |
| 44 | */\r |
| 45 | \r |
| 46 | #include "math.h"\r |
| 47 | #include "math_private.h"\r |
| 48 | \r |
| 49 | static const double\r |
| 50 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */\r |
| 51 | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */\r |
| 52 | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */\r |
| 53 | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */\r |
| 54 | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */\r |
| 55 | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */\r |
| 56 | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */\r |
| 57 | \r |
| 58 | double\r |
| 59 | __kernel_sin(double x, double y, int iy)\r |
| 60 | {\r |
| 61 | double z,r,v;\r |
| 62 | int32_t ix;\r |
| 63 | GET_HIGH_WORD(ix,x);\r |
| 64 | ix &= 0x7fffffff; /* high word of x */\r |
| 65 | if(ix<0x3e400000) /* |x| < 2**-27 */\r |
| 66 | {if((int)x==0) return x;} /* generate inexact */\r |
| 67 | z = x*x;\r |
| 68 | v = z*x;\r |
| 69 | r = S2+z*(S3+z*(S4+z*(S5+z*S6)));\r |
| 70 | if(iy==0) return x+v*(S1+z*r);\r |
| 71 | else return x-((z*(half*y-v*r)-y)-v*S1);\r |
| 72 | }\r |
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