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
205 lines
4.8 KiB
C
205 lines
4.8 KiB
C
/* e_jnf.c -- float version of e_jn.c.
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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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: e_jnf.c,v 1.11 2010/11/29 15:10:06 drochner Exp $");
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#endif
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#include "math.h"
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#include "math_private.h"
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static const float
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#if 0
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invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */
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#endif
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two = 2.0000000000e+00, /* 0x40000000 */
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one = 1.0000000000e+00; /* 0x3F800000 */
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static const float zero = 0.0000000000e+00;
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float
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__ieee754_jnf(int n, float x)
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{
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int32_t i,hx,ix, sgn;
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float a, b, temp, di;
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float z, w;
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/* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x)
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* Thus, J(-n,x) = J(n,-x)
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*/
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GET_FLOAT_WORD(hx,x);
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ix = 0x7fffffff&hx;
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/* if J(n,NaN) is NaN */
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if(ix>0x7f800000) return x+x;
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if(n<0){
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n = -n;
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x = -x;
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hx ^= 0x80000000;
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}
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if(n==0) return(__ieee754_j0f(x));
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if(n==1) return(__ieee754_j1f(x));
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sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */
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x = fabsf(x);
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if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */
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b = zero;
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else if((float)n<=x) {
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/* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */
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a = __ieee754_j0f(x);
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b = __ieee754_j1f(x);
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for(i=1;i<n;i++){
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temp = b;
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b = b*((float)(i+i)/x) - a; /* avoid underflow */
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a = temp;
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}
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} else {
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if(ix<0x30800000) { /* x < 2**-29 */
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/* x is tiny, return the first Taylor expansion of J(n,x)
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* J(n,x) = 1/n!*(x/2)^n - ...
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*/
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if(n>33) /* underflow */
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b = zero;
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else {
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temp = x*(float)0.5; b = temp;
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for (a=one,i=2;i<=n;i++) {
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a *= (float)i; /* a = n! */
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b *= temp; /* b = (x/2)^n */
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}
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b = b/a;
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}
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} else {
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/* use backward recurrence */
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/* x x^2 x^2
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* J(n,x)/J(n-1,x) = ---- ------ ------ .....
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* 2n - 2(n+1) - 2(n+2)
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*
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* 1 1 1
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* (for large x) = ---- ------ ------ .....
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* 2n 2(n+1) 2(n+2)
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* -- - ------ - ------ -
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* x x x
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*
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* Let w = 2n/x and h=2/x, then the above quotient
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* is equal to the continued fraction:
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* 1
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* = -----------------------
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* 1
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* w - -----------------
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* 1
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* w+h - ---------
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* w+2h - ...
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*
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* To determine how many terms needed, let
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* Q(0) = w, Q(1) = w(w+h) - 1,
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* Q(k) = (w+k*h)*Q(k-1) - Q(k-2),
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* When Q(k) > 1e4 good for single
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* When Q(k) > 1e9 good for double
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* When Q(k) > 1e17 good for quadruple
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*/
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/* determine k */
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float t,v;
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float q0,q1,h,tmp; int32_t k,m;
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w = (n+n)/(float)x; h = (float)2.0/(float)x;
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q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1;
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while(q1<(float)1.0e9) {
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k += 1; z += h;
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tmp = z*q1 - q0;
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q0 = q1;
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q1 = tmp;
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}
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m = n+n;
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for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t);
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a = t;
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b = one;
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/* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n)
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* Hence, if n*(log(2n/x)) > ...
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* single 8.8722839355e+01
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* double 7.09782712893383973096e+02
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* long double 1.1356523406294143949491931077970765006170e+04
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* then recurrent value may overflow and the result is
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* likely underflow to zero
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*/
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tmp = n;
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v = two/x;
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tmp = tmp*__ieee754_logf(fabsf(v*tmp));
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if(tmp<(float)8.8721679688e+01) {
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for(i=n-1,di=(float)(i+i);i>0;i--){
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temp = b;
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b *= di;
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b = b/x - a;
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a = temp;
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di -= two;
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}
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} else {
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for(i=n-1,di=(float)(i+i);i>0;i--){
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temp = b;
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b *= di;
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b = b/x - a;
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a = temp;
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di -= two;
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/* scale b to avoid spurious overflow */
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if(b>(float)1e10) {
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a /= b;
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t /= b;
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b = one;
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}
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}
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}
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z = __ieee754_j0f(x);
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w = __ieee754_j1f(x);
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if (fabsf(z) >= fabsf(w))
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b = (t*z/b);
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else
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b = (t*w/a);
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}
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}
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if(sgn==1) return -b; else return b;
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}
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float
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__ieee754_ynf(int n, float x)
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{
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int32_t i,hx,ix,ib;
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int32_t sign;
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float a, b, temp;
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GET_FLOAT_WORD(hx,x);
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ix = 0x7fffffff&hx;
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/* if Y(n,NaN) is NaN */
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if(ix>0x7f800000) return x+x;
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if(ix==0) return -one/zero;
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if(hx<0) return zero/zero;
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sign = 1;
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if(n<0){
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n = -n;
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sign = 1 - ((n&1)<<1);
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}
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if(n==0) return(__ieee754_y0f(x));
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if(n==1) return(sign*__ieee754_y1f(x));
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if(ix==0x7f800000) return zero;
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a = __ieee754_y0f(x);
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b = __ieee754_y1f(x);
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/* quit if b is -inf */
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GET_FLOAT_WORD(ib,b);
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for(i=1;i<n&&(uint32_t)ib!=0xff800000;i++){
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temp = b;
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b = ((float)(i+i)/x)*b - a;
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GET_FLOAT_WORD(ib,b);
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a = temp;
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}
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if(sign>0) return b; else return -b;
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}
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