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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 | 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 | DESCRIPTION |
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| 31 | <<tan>> computes the tangent of the argument <[x]>. |
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| 32 | Angles are specified in radians. |
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| 33 | |
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| 34 | <<tanf>> is identical, save that it takes and returns <<float>> values. |
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| 35 | |
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| 36 | RETURNS |
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| 37 | The tangent of <[x]> is returned. |
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| 38 | |
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| 39 | PORTABILITY |
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| 40 | <<tan>> is ANSI. <<tanf>> is an extension. |
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| 41 | */ |
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| 42 | |
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| 43 | /* tan(x) |
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| 44 | * Return tangent function of x. |
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| 45 | * |
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| 46 | * kernel function: |
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| 47 | * __kernel_tan ... tangent function on [-pi/4,pi/4] |
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| 48 | * __ieee754_rem_pio2 ... argument reduction routine |
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| 49 | * |
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| 50 | * Method. |
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| 51 | * Let S,C and T denote the sin, cos and tan respectively on |
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| 52 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
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| 53 | * in [-pi/4 , +pi/4], and let n = k mod 4. |
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| 54 | * We have |
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| 55 | * |
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| 56 | * n sin(x) cos(x) tan(x) |
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| 57 | * ---------------------------------------------------------- |
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| 58 | * 0 S C T |
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| 59 | * 1 C -S -1/T |
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| 60 | * 2 -S -C T |
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| 61 | * 3 -C S -1/T |
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| 62 | * ---------------------------------------------------------- |
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| 63 | * |
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| 64 | * Special cases: |
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| 65 | * Let trig be any of sin, cos, or tan. |
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| 66 | * trig(+-INF) is NaN, with signals; |
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| 67 | * trig(NaN) is that NaN; |
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| 68 | * |
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| 69 | * Accuracy: |
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| 70 | * TRIG(x) returns trig(x) nearly rounded |
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| 71 | */ |
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| 72 | |
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| 73 | #include "fdlibm.h" |
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| 74 | |
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| 75 | #ifndef _DOUBLE_IS_32BITS |
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| 76 | |
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| 77 | #ifdef __STDC__ |
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| 78 | double tan(double x) |
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| 79 | #else |
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| 80 | double tan(x) |
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| 81 | double x; |
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| 82 | #endif |
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| 83 | { |
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| 84 | double y[2],z=0.0; |
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| 85 | __int32_t n,ix; |
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| 86 | |
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| 87 | /* High word of x. */ |
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| 88 | GET_HIGH_WORD(ix,x); |
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| 89 | |
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| 90 | /* |x| ~< pi/4 */ |
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| 91 | ix &= 0x7fffffff; |
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| 92 | if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); |
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| 93 | |
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| 94 | /* tan(Inf or NaN) is NaN */ |
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| 95 | else if (ix>=0x7ff00000) return x-x; /* NaN */ |
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| 96 | |
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| 97 | /* argument reduction needed */ |
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| 98 | else { |
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| 99 | n = __ieee754_rem_pio2(x,y); |
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| 100 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
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| 101 | -1 -- n odd */ |
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| 102 | } |
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| 103 | } |
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| 104 | |
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| 105 | #endif /* _DOUBLE_IS_32BITS */ |
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