| 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 | /* tan(x) |
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| 15 | * Return tangent function of x. |
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| 16 | * |
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| 17 | * kernel function: |
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| 18 | * __kernel_tan ... tangent function on [-pi/4,pi/4] |
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| 19 | * __ieee754_rem_pio2 ... argument reduction routine |
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| 20 | * |
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| 21 | * Method. |
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| 22 | * Let S,C and T denote the sin, cos and tan respectively on |
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| 23 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
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| 24 | * in [-pi/4 , +pi/4], and let n = k mod 4. |
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| 25 | * We have |
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| 26 | * |
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| 27 | * n sin(x) cos(x) tan(x) |
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| 28 | * ---------------------------------------------------------- |
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| 29 | * 0 S C T |
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| 30 | * 1 C -S -1/T |
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| 31 | * 2 -S -C T |
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| 32 | * 3 -C S -1/T |
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| 33 | * ---------------------------------------------------------- |
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| 34 | * |
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| 35 | * Special cases: |
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| 36 | * Let trig be any of sin, cos, or tan. |
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| 37 | * trig(+-INF) is NaN, with signals; |
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| 38 | * trig(NaN) is that NaN; |
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| 39 | * |
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| 40 | * Accuracy: |
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| 41 | * TRIG(x) returns trig(x) nearly rounded |
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| 42 | */ |
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| 43 | |
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| 44 | #include <libm/fdlibm.h> |
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| 45 | |
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| 46 | #ifdef __STDC__ |
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| 47 | static const double one=1.0; |
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| 48 | #else |
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| 49 | static double one=1.0; |
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| 50 | #endif |
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| 51 | |
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| 52 | #ifdef __STDC__ |
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| 53 | double tan(double x) |
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| 54 | #else |
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| 55 | double tan(x) |
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| 56 | double x; |
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| 57 | #endif |
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| 58 | { |
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| 59 | double y[2],z=0.0; |
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| 60 | int n, ix; |
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| 61 | |
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| 62 | /* High word of x. */ |
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| 63 | ix = *( (((*(int*)&one)>>29)^1) + (int*)&x); |
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| 64 | |
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| 65 | /* |x| ~< pi/4 */ |
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| 66 | ix &= 0x7fffffff; |
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| 67 | if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); |
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| 68 | |
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| 69 | /* tan(Inf or NaN) is NaN */ |
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| 70 | else if (ix>=0x7ff00000) return x-x; /* NaN */ |
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| 71 | |
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| 72 | /* argument reduction needed */ |
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| 73 | else { |
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| 74 | n = __ieee754_rem_pio2(x,y); |
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| 75 | return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
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| 76 | -1 -- n odd */ |
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| 77 | } |
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| 78 | } |
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