| 1 | /* @(#)s_tan.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 | #ifndef lint
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| 14 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tan.c,v 1.9 2003/07/23 04:53:47 peter Exp $";
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| 15 | #endif
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| 16 |
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| 17 | /* tan(x)
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| 18 | * Return tangent function of x.
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| 19 | *
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| 20 | * kernel function:
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| 21 | * __kernel_tan ... tangent function on [-pi/4,pi/4]
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| 22 | * __ieee754_rem_pio2 ... argument reduction routine
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| 23 | *
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| 24 | * Method.
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| 25 | * Let S,C and T denote the sin, cos and tan respectively on
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| 26 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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| 27 | * in [-pi/4 , +pi/4], and let n = k mod 4.
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| 28 | * We have
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| 29 | *
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| 30 | * n sin(x) cos(x) tan(x)
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| 31 | * ----------------------------------------------------------
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| 32 | * 0 S C T
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| 33 | * 1 C -S -1/T
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| 34 | * 2 -S -C T
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| 35 | * 3 -C S -1/T
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| 36 | * ----------------------------------------------------------
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| 37 | *
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| 38 | * Special cases:
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| 39 | * Let trig be any of sin, cos, or tan.
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| 40 | * trig(+-INF) is NaN, with signals;
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| 41 | * trig(NaN) is that NaN;
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| 42 | *
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| 43 | * Accuracy:
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| 44 | * TRIG(x) returns trig(x) nearly rounded
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| 45 | */
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| 46 |
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| 47 | #include "math.h"
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| 48 | #include "math_private.h"
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| 49 |
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| 50 | double
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| 51 | tan(double x)
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| 52 | {
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| 53 | double y[2],z=0.0;
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| 54 | int32_t n, ix;
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| 55 |
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| 56 | /* High word of x. */
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| 57 | GET_HIGH_WORD(ix,x);
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| 58 |
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| 59 | /* |x| ~< pi/4 */
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| 60 | ix &= 0x7fffffff;
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| 61 | if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
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| 62 |
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| 63 | /* tan(Inf or NaN) is NaN */
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| 64 | else if (ix>=0x7ff00000) return x-x; /* NaN */
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| 65 |
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| 66 | /* argument reduction needed */
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| 67 | else {
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| 68 | n = __ieee754_rem_pio2(x,y);
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| 69 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
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| 70 | -1 -- n odd */
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| 71 | }
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| 72 | }
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