2fe8fb192f
There is important information about booting non-ack images in docs/UPDATING. ack/aout-format images can't be built any more, and booting clang/ELF-format ones is a little different. Updating to the new boot monitor is recommended. Changes in this commit: . drop boot monitor -> allowing dropping ack support . facility to copy ELF boot files to /boot so that old boot monitor can still boot fairly easily, see UPDATING . no more ack-format libraries -> single-case libraries . some cleanup of OBJECT_FMT, COMPILER_TYPE, etc cases . drop several ack toolchain commands, but not all support commands (e.g. aal is gone but acksize is not yet). . a few libc files moved to netbsd libc dir . new /bin/date as minix date used code in libc/ . test compile fix . harmonize includes . /usr/lib is no longer special: without ack, /usr/lib plays no kind of special bootstrapping role any more and bootstrapping is done exclusively through packages, so releases depend even less on the state of the machine making them now. . rename nbsd_lib* to lib* . reduce mtree
157 lines
4.4 KiB
C
157 lines
4.4 KiB
C
/* @(#)k_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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#if defined(LIBM_SCCS) && !defined(lint)
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__RCSID("$NetBSD: k_tan.c,v 1.12 2004/07/22 18:24:09 drochner Exp $");
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#endif
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/* __kernel_tan( x, y, k )
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* kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854
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* Input x is assumed to be bounded by ~pi/4 in magnitude.
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* Input y is the tail of x.
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* Input k indicates whether tan (if k=1) or
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* -1/tan (if k= -1) is returned.
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*
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* Algorithm
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* 1. Since tan(-x) = -tan(x), we need only to consider positive x.
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* 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0.
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* 3. tan(x) is approximated by a odd polynomial of degree 27 on
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* [0,0.67434]
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* 3 27
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* tan(x) ~ x + T1*x + ... + T13*x
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* where
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*
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* |tan(x) 2 4 26 | -59.2
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* |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2
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* | x |
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*
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* Note: tan(x+y) = tan(x) + tan'(x)*y
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* ~ tan(x) + (1+x*x)*y
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* Therefore, for better accuracy in computing tan(x+y), let
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* 3 2 2 2 2
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* r = x *(T2+x *(T3+x *(...+x *(T12+x *T13))))
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* then
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* 3 2
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* tan(x+y) = x + (T1*x + (x *(r+y)+y))
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*
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* 4. For x in [0.67434,pi/4], let y = pi/4 - x, then
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* tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y))
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* = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y)))
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*/
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#include "math.h"
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#include "math_private.h"
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static const double xxx[] = {
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3.33333333333334091986e-01, /* 3FD55555, 55555563 */
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1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */
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5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */
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2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */
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8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */
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3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */
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1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */
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5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */
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2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */
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7.81794442939557092300e-05, /* 3F147E88, A03792A6 */
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7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */
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-1.85586374855275456654e-05, /* BEF375CB, DB605373 */
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2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */
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/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */
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/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */
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/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */
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};
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#define one xxx[13]
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#define pio4 xxx[14]
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#define pio4lo xxx[15]
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#define T xxx
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double
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__kernel_tan(double x, double y, int iy)
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{
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double z, r, v, w, s;
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int32_t ix, hx;
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GET_HIGH_WORD(hx, x); /* high word of x */
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ix = hx & 0x7fffffff; /* high word of |x| */
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if (ix < 0x3e300000) { /* x < 2**-28 */
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if ((int) x == 0) { /* generate inexact */
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u_int32_t low;
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GET_LOW_WORD(low, x);
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if(((ix | low) | (iy + 1)) == 0)
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return one / fabs(x);
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else {
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if (iy == 1)
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return x;
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else { /* compute -1 / (x+y) carefully */
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double a, t;
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z = w = x + y;
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SET_LOW_WORD(z, 0);
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v = y - (z - x);
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t = a = -one / w;
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SET_LOW_WORD(t, 0);
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s = one + t * z;
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return t + a * (s + t * v);
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}
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}
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}
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}
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if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */
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if (hx < 0) {
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x = -x;
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y = -y;
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}
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z = pio4 - x;
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w = pio4lo - y;
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x = z + w;
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y = 0.0;
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}
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z = x * x;
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w = z * z;
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/*
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* Break x^5*(T[1]+x^2*T[2]+...) into
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* x^5(T[1]+x^4*T[3]+...+x^20*T[11]) +
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* x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12]))
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*/
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r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] +
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w * T[11]))));
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v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] +
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w * T[12])))));
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s = z * x;
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r = y + z * (s * (r + v) + y);
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r += T[0] * s;
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w = x + r;
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if (ix >= 0x3FE59428) {
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v = (double) iy;
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return (double) (1 - ((hx >> 30) & 2)) *
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(v - 2.0 * (x - (w * w / (w + v) - r)));
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}
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if (iy == 1)
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return w;
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else {
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/*
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* if allow error up to 2 ulp, simply return
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* -1.0 / (x+r) here
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*/
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/* compute -1.0 / (x+r) accurately */
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double a, t;
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z = w;
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SET_LOW_WORD(z, 0);
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v = r - (z - x); /* z+v = r+x */
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t = a = -1.0 / w; /* a = -1.0/w */
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SET_LOW_WORD(t, 0);
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s = 1.0 + t * z;
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return t + a * (s + t * v);
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}
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}
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