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