38662c9698
optimization of about 10% for cos(x), sin(x) and tan(x) on |x| < 2**19*pi/2. We didn't do this before because __ieee754__rem_pio2() is too large and complicated for gcc-3.3 to inline very well. We don't do this for float precision because it interferes with optimization of the usual (?) case (|x| < 9pi/4) which is manually inlined for float precision only. This has some rough edges: - some static data is duplicated unnecessarily. There isn't much after the recent move of large tables to k_rem_pio2.c, and some static data is duplicated to good affect (all the data static const, so that the compiler can evaluate expressions like 2*pio2 at compile time and generate even more static data for the constant for this). - extern inline is used (for the same reason as in previous inlining of k_cosf.c etc.), but C99 apparently doesn't allow extern inline functions with static data, and gcc will eventually warn about this. Convert to __FBSDID(). Indent __ieee754_rem_pio2()'s declaration consistently (its style was made inconsistent with fdlibm a while ago, so complete this). Fix __ieee754_rem_pio2()'s return type to match its prototype. Someone changed too many ints to int32_t's when fixing the assumption that all ints are int32_t's.
84 lines
2.0 KiB
C
84 lines
2.0 KiB
C
/* @(#)s_tan.c 5.1 93/09/24 */
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD$");
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/* tan(x)
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* Return tangent function of x.
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*
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* kernel function:
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* __kernel_tan ... tangent function on [-pi/4,pi/4]
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* __ieee754_rem_pio2 ... argument reduction routine
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*
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* Method.
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* Let S,C and T denote the sin, cos and tan respectively on
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* [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
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* in [-pi/4 , +pi/4], and let n = k mod 4.
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* We have
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*
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* n sin(x) cos(x) tan(x)
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* ----------------------------------------------------------
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* 0 S C T
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* 1 C -S -1/T
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* 2 -S -C T
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* 3 -C S -1/T
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* ----------------------------------------------------------
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*
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* Special cases:
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* Let trig be any of sin, cos, or tan.
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* trig(+-INF) is NaN, with signals;
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* trig(NaN) is that NaN;
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*
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* Accuracy:
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* TRIG(x) returns trig(x) nearly rounded
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*/
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#include <float.h>
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#include "math.h"
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#define INLINE_REM_PIO2
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#include "math_private.h"
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#include "e_rem_pio2.c"
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double
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tan(double x)
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{
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double y[2],z=0.0;
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int32_t n, ix;
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/* High word of x. */
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GET_HIGH_WORD(ix,x);
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/* |x| ~< pi/4 */
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ix &= 0x7fffffff;
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if(ix <= 0x3fe921fb) {
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if(ix<0x3e300000) /* x < 2**-28 */
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if((int)x==0) return x; /* generate inexact */
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return __kernel_tan(x,z,1);
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}
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/* tan(Inf or NaN) is NaN */
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else if (ix>=0x7ff00000) return x-x; /* NaN */
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/* argument reduction needed */
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else {
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n = __ieee754_rem_pio2(x,y);
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return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even
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-1 -- n odd */
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}
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}
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#if (LDBL_MANT_DIG == 53)
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__weak_reference(tan, tanl);
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#endif
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