src/libm/k_sin.c
changeset 2756 a98604b691c8
child 3162 dc1eb82ffdaa
equal deleted inserted replaced
2755:2a3ec308d995 2756:a98604b691c8
       
     1 /* @(#)k_sin.c 5.1 93/09/24 */
       
     2 /*
       
     3  * ====================================================
       
     4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
       
     5  *
       
     6  * Developed at SunPro, a Sun Microsystems, Inc. business.
       
     7  * Permission to use, copy, modify, and distribute this
       
     8  * software is freely granted, provided that this notice
       
     9  * is preserved.
       
    10  * ====================================================
       
    11  */
       
    12 
       
    13 #if defined(LIBM_SCCS) && !defined(lint)
       
    14 static char rcsid[] = "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $";
       
    15 #endif
       
    16 
       
    17 /* __kernel_sin( x, y, iy)
       
    18  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
       
    19  * Input x is assumed to be bounded by ~pi/4 in magnitude.
       
    20  * Input y is the tail of x.
       
    21  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
       
    22  *
       
    23  * Algorithm
       
    24  *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
       
    25  *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
       
    26  *	3. sin(x) is approximated by a polynomial of degree 13 on
       
    27  *	   [0,pi/4]
       
    28  *		  	         3            13
       
    29  *	   	sin(x) ~ x + S1*x + ... + S6*x
       
    30  *	   where
       
    31  *
       
    32  * 	|sin(x)         2     4     6     8     10     12  |     -58
       
    33  * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
       
    34  * 	|  x 					           |
       
    35  *
       
    36  *	4. sin(x+y) = sin(x) + sin'(x')*y
       
    37  *		    ~ sin(x) + (1-x*x/2)*y
       
    38  *	   For better accuracy, let
       
    39  *		     3      2      2      2      2
       
    40  *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
       
    41  *	   then                   3    2
       
    42  *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
       
    43  */
       
    44 
       
    45 #include "math.h"
       
    46 #include "math_private.h"
       
    47 
       
    48 #ifdef __STDC__
       
    49 static const double
       
    50 #else
       
    51 static double
       
    52 #endif
       
    53   half = 5.00000000000000000000e-01,    /* 0x3FE00000, 0x00000000 */
       
    54     S1 = -1.66666666666666324348e-01,   /* 0xBFC55555, 0x55555549 */
       
    55     S2 = 8.33333333332248946124e-03,    /* 0x3F811111, 0x1110F8A6 */
       
    56     S3 = -1.98412698298579493134e-04,   /* 0xBF2A01A0, 0x19C161D5 */
       
    57     S4 = 2.75573137070700676789e-06,    /* 0x3EC71DE3, 0x57B1FE7D */
       
    58     S5 = -2.50507602534068634195e-08,   /* 0xBE5AE5E6, 0x8A2B9CEB */
       
    59     S6 = 1.58969099521155010221e-10;    /* 0x3DE5D93A, 0x5ACFD57C */
       
    60 
       
    61 #ifdef __STDC__
       
    62 double attribute_hidden
       
    63 __kernel_sin(double x, double y, int iy)
       
    64 #else
       
    65 double attribute_hidden
       
    66 __kernel_sin(x, y, iy)
       
    67      double x, y;
       
    68      int iy;                    /* iy=0 if y is zero */
       
    69 #endif
       
    70 {
       
    71     double z, r, v;
       
    72     int32_t ix;
       
    73     GET_HIGH_WORD(ix, x);
       
    74     ix &= 0x7fffffff;           /* high word of x */
       
    75     if (ix < 0x3e400000) {      /* |x| < 2**-27 */
       
    76         if ((int) x == 0)
       
    77             return x;
       
    78     }                           /* generate inexact */
       
    79     z = x * x;
       
    80     v = z * x;
       
    81     r = S2 + z * (S3 + z * (S4 + z * (S5 + z * S6)));
       
    82     if (iy == 0)
       
    83         return x + v * (S1 + z * r);
       
    84     else
       
    85         return x - ((z * (half * y - v * r) - y) - v * S1);
       
    86 }