| 1 |
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| 2 | /* @(#)s_tan.c 5.1 93/09/24 */
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| 3 | /*
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| 4 | * ====================================================
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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| 6 | *
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business.
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| 8 | * Permission to use, copy, modify, and distribute this
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| 9 | * software is freely granted, provided that this notice
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| 10 | * is preserved.
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| 11 | * ====================================================
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| 12 | */
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| 13 |
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| 14 |
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| 15 | /*
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| 16 |
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| 17 | FUNCTION
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| 18 | <<tan>>, <<tanf>>---tangent
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| 19 |
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| 20 | INDEX
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| 21 | tan
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| 22 | INDEX
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| 23 | tanf
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| 24 |
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| 25 | ANSI_SYNOPSIS
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| 26 | #include <math.h>
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| 27 | double tan(double <[x]>);
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| 28 | float tanf(float <[x]>);
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| 29 |
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| 30 | TRAD_SYNOPSIS
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| 31 | #include <math.h>
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| 32 | double tan(<[x]>)
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| 33 | double <[x]>;
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| 34 |
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| 35 | float tanf(<[x]>)
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| 36 | float <[x]>;
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| 37 |
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| 38 |
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| 39 | DESCRIPTION
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| 40 | <<tan>> computes the tangent of the argument <[x]>.
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| 41 | Angles are specified in radians.
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| 42 |
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| 43 | <<tanf>> is identical, save that it takes and returns <<float>> values.
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| 44 |
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| 45 | RETURNS
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| 46 | The tangent of <[x]> is returned.
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| 47 |
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| 48 | PORTABILITY
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| 49 | <<tan>> is ANSI. <<tanf>> is an extension.
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| 50 | */
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| 51 |
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| 52 | /* tan(x)
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| 53 | * Return tangent function of x.
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| 54 | *
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| 55 | * kernel function:
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| 56 | * __kernel_tan ... tangent function on [-pi/4,pi/4]
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| 57 | * __ieee754_rem_pio2 ... argument reduction routine
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| 58 | *
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| 59 | * Method.
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| 60 | * Let S,C and T denote the sin, cos and tan respectively on
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| 61 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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| 62 | * in [-pi/4 , +pi/4], and let n = k mod 4.
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| 63 | * We have
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| 64 | *
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| 65 | * n sin(x) cos(x) tan(x)
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| 66 | * ----------------------------------------------------------
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| 67 | * 0 S C T
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| 68 | * 1 C -S -1/T
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| 69 | * 2 -S -C T
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| 70 | * 3 -C S -1/T
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| 71 | * ----------------------------------------------------------
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| 72 | *
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| 73 | * Special cases:
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| 74 | * Let trig be any of sin, cos, or tan.
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| 75 | * trig(+-INF) is NaN, with signals;
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| 76 | * trig(NaN) is that NaN;
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| 77 | *
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| 78 | * Accuracy:
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| 79 | * TRIG(x) returns trig(x) nearly rounded
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| 80 | */
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| 81 |
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| 82 | #include "fdlibm.h"
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| 83 |
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| 84 | #ifndef _DOUBLE_IS_32BITS
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| 85 |
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| 86 | #ifdef __STDC__
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| 87 | double tan(double x)
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| 88 | #else
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| 89 | double tan(x)
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| 90 | double x;
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| 91 | #endif
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| 92 | {
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| 93 | double y[2],z=0.0;
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| 94 | int32_t n,ix;
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| 95 |
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| 96 | /* High word of x. */
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| 97 | GET_HIGH_WORD(ix,x);
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| 98 |
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| 99 | /* |x| ~< pi/4 */
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| 100 | ix &= 0x7fffffff;
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| 101 | if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1);
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| 102 |
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| 103 | /* tan(Inf or NaN) is NaN */
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| 104 | else if (ix>=0x7ff00000) return x-x; /* NaN */
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| 105 |
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| 106 | /* argument reduction needed */
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| 107 | else {
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| 108 | n = __ieee754_rem_pio2(x,y);
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| 109 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
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| 110 | -1 -- n odd */
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| 111 | }
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| 112 | }
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| 113 |
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| 114 | #endif /* _DOUBLE_IS_32BITS */
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