| 1 | /* s_tanl.c -- long double version of s_tan.c. |
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| 2 | */ |
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| 3 | |
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| 4 | /* @(#)s_tan.c 5.1 93/09/24 */ |
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| 5 | /* |
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| 6 | * ==================================================== |
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| 7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 8 | * |
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| 9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 10 | * Permission to use, copy, modify, and distribute this |
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| 11 | * software is freely granted, provided that this notice |
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| 12 | * is preserved. |
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| 13 | * ==================================================== |
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| 14 | */ |
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| 15 | |
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| 16 | /* tanl(x) |
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| 17 | * Return tangent function of x. |
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| 18 | * |
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| 19 | * kernel function: |
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| 20 | * __kernel_tanl ... tangent function on [-pi/4,pi/4] |
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| 21 | * __ieee754_rem_pio2l ... argument reduction routine |
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| 22 | * |
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| 23 | * Method. |
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| 24 | * Let S,C and T denote the sin, cos and tan respectively on |
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| 25 | * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
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| 26 | * in [-pi/4 , +pi/4], and let n = k mod 4. |
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| 27 | * We have |
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| 28 | * |
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| 29 | * n sin(x) cos(x) tan(x) |
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| 30 | * ---------------------------------------------------------- |
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| 31 | * 0 S C T |
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| 32 | * 1 C -S -1/T |
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| 33 | * 2 -S -C T |
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| 34 | * 3 -C S -1/T |
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| 35 | * ---------------------------------------------------------- |
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| 36 | * |
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| 37 | * Special cases: |
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| 38 | * Let trig be any of sin, cos, or tan. |
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| 39 | * trig(+-INF) is NaN, with signals; |
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| 40 | * trig(NaN) is that NaN; |
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| 41 | * |
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| 42 | * Accuracy: |
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| 43 | * TRIG(x) returns trig(x) nearly rounded |
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| 44 | */ |
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| 45 | |
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| 46 | #include <errno.h> |
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| 47 | #include <math.h> |
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| 48 | #include <math_private.h> |
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| 49 | #include <math_ldbl_opt.h> |
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| 50 | |
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| 51 | long double __tanl(long double x) |
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| 52 | { |
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| 53 | long double y[2],z=0.0L; |
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| 54 | int64_t n, ix; |
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| 55 | double xhi; |
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| 56 | |
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| 57 | /* High word of x. */ |
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| 58 | xhi = ldbl_high (x); |
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| 59 | EXTRACT_WORDS64 (ix, xhi); |
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| 60 | |
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| 61 | /* |x| ~< pi/4 */ |
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| 62 | ix &= 0x7fffffffffffffffLL; |
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| 63 | if(ix <= 0x3fe921fb54442d10LL) return __kernel_tanl(x,z,1); |
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| 64 | |
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| 65 | /* tanl(Inf or NaN) is NaN */ |
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| 66 | else if (ix>=0x7ff0000000000000LL) { |
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| 67 | if (ix == 0x7ff0000000000000LL) |
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| 68 | __set_errno (EDOM); |
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| 69 | return x-x; /* NaN */ |
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| 70 | } |
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| 71 | /* argument reduction needed */ |
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| 72 | else { |
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| 73 | n = __ieee754_rem_pio2l(x,y); |
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| 74 | return __kernel_tanl(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even |
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| 75 | -1 -- n odd */ |
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| 76 | } |
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| 77 | } |
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| 78 | long_double_symbol (libm, __tanl, tanl); |
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| 79 | |
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