src/libm/k_sin.c
 author Sam Lantinga Sat, 04 Nov 2017 15:53:19 -0700 changeset 11683 48bcba563d9c parent 6044 35448a5ea044 permissions -rw-r--r--
Updated math code from the uClibc 0.9.33 release
```     1 /*
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```     2  * ====================================================
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```     3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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```     4  *
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```     5  * Developed at SunPro, a Sun Microsystems, Inc. business.
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```     6  * Permission to use, copy, modify, and distribute this
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```     7  * software is freely granted, provided that this notice
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```     8  * is preserved.
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```     9  * ====================================================
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```    10  */
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```    11
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```    12 /* __kernel_sin( x, y, iy)
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```    13  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
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```    14  * Input x is assumed to be bounded by ~pi/4 in magnitude.
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```    15  * Input y is the tail of x.
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```    16  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
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```    17  *
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```    18  * Algorithm
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```    19  *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
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```    20  *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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```    21  *	3. sin(x) is approximated by a polynomial of degree 13 on
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```    22  *	   [0,pi/4]
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```    23  *		  	         3            13
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```    24  *	   	sin(x) ~ x + S1*x + ... + S6*x
```
```    25  *	   where
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```    26  *
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```    27  * 	|sin(x)         2     4     6     8     10     12  |     -58
```
```    28  * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
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```    29  * 	|  x 					           |
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```    30  *
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```    31  *	4. sin(x+y) = sin(x) + sin'(x')*y
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```    32  *		    ~ sin(x) + (1-x*x/2)*y
```
```    33  *	   For better accuracy, let
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```    34  *		     3      2      2      2      2
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```    35  *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
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```    36  *	   then                   3    2
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```    37  *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
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```    38  */
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```    39
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```    40 #include "math_libm.h"
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```    41 #include "math_private.h"
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```    42
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```    43 static const double
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```    44 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
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```    45 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
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```    46 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
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```    47 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
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```    48 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
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```    49 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
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```    50 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
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```    51
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```    52 double attribute_hidden __kernel_sin(double x, double y, int iy)
```
```    53 {
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```    54 	double z,r,v;
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```    55 	int32_t ix;
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```    56 	GET_HIGH_WORD(ix,x);
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```    57 	ix &= 0x7fffffff;			/* high word of x */
```
```    58 	if(ix<0x3e400000)			/* |x| < 2**-27 */
```
```    59 	   {if((int)x==0) return x;}		/* generate inexact */
```
```    60 	z	=  x*x;
```
```    61 	v	=  z*x;
```
```    62 	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
```
```    63 	if(iy==0) return x+v*(S1+z*r);
```
```    64 	else      return x-((z*(half*y-v*r)-y)-v*S1);
```
```    65 }
```