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Diffstat (limited to 'sysdeps/ieee754/support.c')
| -rw-r--r-- | sysdeps/ieee754/support.c | 524 |
1 files changed, 524 insertions, 0 deletions
diff --git a/sysdeps/ieee754/support.c b/sysdeps/ieee754/support.c new file mode 100644 index 0000000000..e976839421 --- /dev/null +++ b/sysdeps/ieee754/support.c @@ -0,0 +1,524 @@ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by the University of + * California, Berkeley and its contributors. + * 4. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)support.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* + * Some IEEE standard 754 recommended functions and remainder and sqrt for + * supporting the C elementary functions. + ****************************************************************************** + * WARNING: + * These codes are developed (in double) to support the C elementary + * functions temporarily. They are not universal, and some of them are very + * slow (in particular, drem and sqrt is extremely inefficient). Each + * computer system should have its implementation of these functions using + * its own assembler. + ****************************************************************************** + * + * IEEE 754 required operations: + * drem(x,p) + * returns x REM y = x - [x/y]*y , where [x/y] is the integer + * nearest x/y; in half way case, choose the even one. + * sqrt(x) + * returns the square root of x correctly rounded according to + * the rounding mod. + * + * IEEE 754 recommended functions: + * (a) copysign(x,y) + * returns x with the sign of y. + * (b) scalb(x,N) + * returns x * (2**N), for integer values N. + * (c) logb(x) + * returns the unbiased exponent of x, a signed integer in + * double precision, except that logb(0) is -INF, logb(INF) + * is +INF, and logb(NAN) is that NAN. + * (d) finite(x) + * returns the value TRUE if -INF < x < +INF and returns + * FALSE otherwise. + * + * + * CODED IN C BY K.C. NG, 11/25/84; + * REVISED BY K.C. NG on 1/22/85, 2/13/85, 3/24/85. + */ + +#include "mathimpl.h" + +#if defined(vax)||defined(tahoe) /* VAX D format */ +#include <errno.h> + static const unsigned short msign=0x7fff , mexp =0x7f80 ; + static const short prep1=57, gap=7, bias=129 ; + static const double novf=1.7E38, nunf=3.0E-39, zero=0.0 ; +#else /* defined(vax)||defined(tahoe) */ + static const unsigned short msign=0x7fff, mexp =0x7ff0 ; + static const short prep1=54, gap=4, bias=1023 ; + static const double novf=1.7E308, nunf=3.0E-308,zero=0.0; +#endif /* defined(vax)||defined(tahoe) */ + +double scalb(x,N) +double x; int N; +{ + int k; + +#ifdef national + unsigned short *px=(unsigned short *) &x + 3; +#else /* national */ + unsigned short *px=(unsigned short *) &x; +#endif /* national */ + + if( x == zero ) return(x); + +#if defined(vax)||defined(tahoe) + if( (k= *px & mexp ) != ~msign ) { + if (N < -260) + return(nunf*nunf); + else if (N > 260) { + return(copysign(infnan(ERANGE),x)); + } +#else /* defined(vax)||defined(tahoe) */ + if( (k= *px & mexp ) != mexp ) { + if( N<-2100) return(nunf*nunf); else if(N>2100) return(novf+novf); + if( k == 0 ) { + x *= scalb(1.0,(int)prep1); N -= prep1; return(scalb(x,N));} +#endif /* defined(vax)||defined(tahoe) */ + + if((k = (k>>gap)+ N) > 0 ) + if( k < (mexp>>gap) ) *px = (*px&~mexp) | (k<<gap); + else x=novf+novf; /* overflow */ + else + if( k > -prep1 ) + /* gradual underflow */ + {*px=(*px&~mexp)|(short)(1<<gap); x *= scalb(1.0,k-1);} + else + return(nunf*nunf); + } + return(x); +} + + +double copysign(x,y) +double x,y; +{ +#ifdef national + unsigned short *px=(unsigned short *) &x+3, + *py=(unsigned short *) &y+3; +#else /* national */ + unsigned short *px=(unsigned short *) &x, + *py=(unsigned short *) &y; +#endif /* national */ + +#if defined(vax)||defined(tahoe) + if ( (*px & mexp) == 0 ) return(x); +#endif /* defined(vax)||defined(tahoe) */ + + *px = ( *px & msign ) | ( *py & ~msign ); + return(x); +} + +double logb(x) +double x; +{ + +#ifdef national + short *px=(short *) &x+3, k; +#else /* national */ + short *px=(short *) &x, k; +#endif /* national */ + +#if defined(vax)||defined(tahoe) + return (int)(((*px&mexp)>>gap)-bias); +#else /* defined(vax)||defined(tahoe) */ + if( (k= *px & mexp ) != mexp ) + if ( k != 0 ) + return ( (k>>gap) - bias ); + else if( x != zero) + return ( -1022.0 ); + else + return(-(1.0/zero)); + else if(x != x) + return(x); + else + {*px &= msign; return(x);} +#endif /* defined(vax)||defined(tahoe) */ +} + +finite(x) +double x; +{ +#if defined(vax)||defined(tahoe) + return(1); +#else /* defined(vax)||defined(tahoe) */ +#ifdef national + return( (*((short *) &x+3 ) & mexp ) != mexp ); +#else /* national */ + return( (*((short *) &x ) & mexp ) != mexp ); +#endif /* national */ +#endif /* defined(vax)||defined(tahoe) */ +} + +double drem(x,p) +double x,p; +{ + short sign; + double hp,dp,tmp; + unsigned short k; +#ifdef national + unsigned short + *px=(unsigned short *) &x +3, + *pp=(unsigned short *) &p +3, + *pd=(unsigned short *) &dp +3, + *pt=(unsigned short *) &tmp+3; +#else /* national */ + unsigned short + *px=(unsigned short *) &x , + *pp=(unsigned short *) &p , + *pd=(unsigned short *) &dp , + *pt=(unsigned short *) &tmp; +#endif /* national */ + + *pp &= msign ; + +#if defined(vax)||defined(tahoe) + if( ( *px & mexp ) == ~msign ) /* is x a reserved operand? */ +#else /* defined(vax)||defined(tahoe) */ + if( ( *px & mexp ) == mexp ) +#endif /* defined(vax)||defined(tahoe) */ + return (x-p)-(x-p); /* create nan if x is inf */ + if (p == zero) { +#if defined(vax)||defined(tahoe) + return(infnan(EDOM)); +#else /* defined(vax)||defined(tahoe) */ + return zero/zero; +#endif /* defined(vax)||defined(tahoe) */ + } + +#if defined(vax)||defined(tahoe) + if( ( *pp & mexp ) == ~msign ) /* is p a reserved operand? */ +#else /* defined(vax)||defined(tahoe) */ + if( ( *pp & mexp ) == mexp ) +#endif /* defined(vax)||defined(tahoe) */ + { if (p != p) return p; else return x;} + + else if ( ((*pp & mexp)>>gap) <= 1 ) + /* subnormal p, or almost subnormal p */ + { double b; b=scalb(1.0,(int)prep1); + p *= b; x = drem(x,p); x *= b; return(drem(x,p)/b);} + else if ( p >= novf/2) + { p /= 2 ; x /= 2; return(drem(x,p)*2);} + else + { + dp=p+p; hp=p/2; + sign= *px & ~msign ; + *px &= msign ; + while ( x > dp ) + { + k=(*px & mexp) - (*pd & mexp) ; + tmp = dp ; + *pt += k ; + +#if defined(vax)||defined(tahoe) + if( x < tmp ) *pt -= 128 ; +#else /* defined(vax)||defined(tahoe) */ + if( x < tmp ) *pt -= 16 ; +#endif /* defined(vax)||defined(tahoe) */ + + x -= tmp ; + } + if ( x > hp ) + { x -= p ; if ( x >= hp ) x -= p ; } + +#if defined(vax)||defined(tahoe) + if (x) +#endif /* defined(vax)||defined(tahoe) */ + *px ^= sign; + return( x); + + } +} + + +double sqrt(x) +double x; +{ + double q,s,b,r; + double t; + double const zero=0.0; + int m,n,i; +#if defined(vax)||defined(tahoe) + int k=54; +#else /* defined(vax)||defined(tahoe) */ + int k=51; +#endif /* defined(vax)||defined(tahoe) */ + + /* sqrt(NaN) is NaN, sqrt(+-0) = +-0 */ + if(x!=x||x==zero) return(x); + + /* sqrt(negative) is invalid */ + if(x<zero) { +#if defined(vax)||defined(tahoe) + return (infnan(EDOM)); /* NaN */ +#else /* defined(vax)||defined(tahoe) */ + return(zero/zero); +#endif /* defined(vax)||defined(tahoe) */ + } + + /* sqrt(INF) is INF */ + if(!finite(x)) return(x); + + /* scale x to [1,4) */ + n=logb(x); + x=scalb(x,-n); + if((m=logb(x))!=0) x=scalb(x,-m); /* subnormal number */ + m += n; + n = m/2; + if((n+n)!=m) {x *= 2; m -=1; n=m/2;} + + /* generate sqrt(x) bit by bit (accumulating in q) */ + q=1.0; s=4.0; x -= 1.0; r=1; + for(i=1;i<=k;i++) { + t=s+1; x *= 4; r /= 2; + if(t<=x) { + s=t+t+2, x -= t; q += r;} + else + s *= 2; + } + + /* generate the last bit and determine the final rounding */ + r/=2; x *= 4; + if(x==zero) goto end; 100+r; /* trigger inexact flag */ + if(s<x) { + q+=r; x -=s; s += 2; s *= 2; x *= 4; + t = (x-s)-5; + b=1.0+3*r/4; if(b==1.0) goto end; /* b==1 : Round-to-zero */ + b=1.0+r/4; if(b>1.0) t=1; /* b>1 : Round-to-(+INF) */ + if(t>=0) q+=r; } /* else: Round-to-nearest */ + else { + s *= 2; x *= 4; + t = (x-s)-1; + b=1.0+3*r/4; if(b==1.0) goto end; + b=1.0+r/4; if(b>1.0) t=1; + if(t>=0) q+=r; } + +end: return(scalb(q,n)); +} + +#if 0 +/* DREM(X,Y) + * RETURN X REM Y =X-N*Y, N=[X/Y] ROUNDED (ROUNDED TO EVEN IN THE HALF WAY CASE) + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * INTENDED FOR ASSEMBLY LANGUAGE + * CODED IN C BY K.C. NG, 3/23/85, 4/8/85. + * + * Warning: this code should not get compiled in unless ALL of + * the following machine-dependent routines are supplied. + * + * Required machine dependent functions (not on a VAX): + * swapINX(i): save inexact flag and reset it to "i" + * swapENI(e): save inexact enable and reset it to "e" + */ + +double drem(x,y) +double x,y; +{ + +#ifdef national /* order of words in floating point number */ + static const n0=3,n1=2,n2=1,n3=0; +#else /* VAX, SUN, ZILOG, TAHOE */ + static const n0=0,n1=1,n2=2,n3=3; +#endif + + static const unsigned short mexp =0x7ff0, m25 =0x0190, m57 =0x0390; + static const double zero=0.0; + double hy,y1,t,t1; + short k; + long n; + int i,e; + unsigned short xexp,yexp, *px =(unsigned short *) &x , + nx,nf, *py =(unsigned short *) &y , + sign, *pt =(unsigned short *) &t , + *pt1 =(unsigned short *) &t1 ; + + xexp = px[n0] & mexp ; /* exponent of x */ + yexp = py[n0] & mexp ; /* exponent of y */ + sign = px[n0] &0x8000; /* sign of x */ + +/* return NaN if x is NaN, or y is NaN, or x is INF, or y is zero */ + if(x!=x) return(x); if(y!=y) return(y); /* x or y is NaN */ + if( xexp == mexp ) return(zero/zero); /* x is INF */ + if(y==zero) return(y/y); + +/* save the inexact flag and inexact enable in i and e respectively + * and reset them to zero + */ + i=swapINX(0); e=swapENI(0); + +/* subnormal number */ + nx=0; + if(yexp==0) {t=1.0,pt[n0]+=m57; y*=t; nx=m57;} + +/* if y is tiny (biased exponent <= 57), scale up y to y*2**57 */ + if( yexp <= m57 ) {py[n0]+=m57; nx+=m57; yexp+=m57;} + + nf=nx; + py[n0] &= 0x7fff; + px[n0] &= 0x7fff; + +/* mask off the least significant 27 bits of y */ + t=y; pt[n3]=0; pt[n2]&=0xf800; y1=t; + +/* LOOP: argument reduction on x whenever x > y */ +loop: + while ( x > y ) + { + t=y; + t1=y1; + xexp=px[n0]&mexp; /* exponent of x */ + k=xexp-yexp-m25; + if(k>0) /* if x/y >= 2**26, scale up y so that x/y < 2**26 */ + {pt[n0]+=k;pt1[n0]+=k;} + n=x/t; x=(x-n*t1)-n*(t-t1); + } + /* end while (x > y) */ + + if(nx!=0) {t=1.0; pt[n0]+=nx; x*=t; nx=0; goto loop;} + +/* final adjustment */ + + hy=y/2.0; + if(x>hy||((x==hy)&&n%2==1)) x-=y; + px[n0] ^= sign; + if(nf!=0) { t=1.0; pt[n0]-=nf; x*=t;} + +/* restore inexact flag and inexact enable */ + swapINX(i); swapENI(e); + + return(x); +} +#endif + +#if 0 +/* SQRT + * RETURN CORRECTLY ROUNDED (ACCORDING TO THE ROUNDING MODE) SQRT + * FOR IEEE DOUBLE PRECISION ONLY, INTENDED FOR ASSEMBLY LANGUAGE + * CODED IN C BY K.C. NG, 3/22/85. + * + * Warning: this code should not get compiled in unless ALL of + * the following machine-dependent routines are supplied. + * + * Required machine dependent functions: + * swapINX(i) ...return the status of INEXACT flag and reset it to "i" + * swapRM(r) ...return the current Rounding Mode and reset it to "r" + * swapENI(e) ...return the status of inexact enable and reset it to "e" + * addc(t) ...perform t=t+1 regarding t as a 64 bit unsigned integer + * subc(t) ...perform t=t-1 regarding t as a 64 bit unsigned integer + */ + +static const unsigned long table[] = { +0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, 29598, 36145, 43202, 50740, +58733, 67158, 75992, 85215, 83599, 71378, 60428, 50647, 41945, 34246, 27478, +21581, 16499, 12183, 8588, 5674, 3403, 1742, 661, 130, }; + +double newsqrt(x) +double x; +{ + double y,z,t,addc(),subc() + double const b54=134217728.*134217728.; /* b54=2**54 */ + long mx,scalx; + long const mexp=0x7ff00000; + int i,j,r,e,swapINX(),swapRM(),swapENI(); + unsigned long *py=(unsigned long *) &y , + *pt=(unsigned long *) &t , + *px=(unsigned long *) &x ; +#ifdef national /* ordering of word in a floating point number */ + const int n0=1, n1=0; +#else + const int n0=0, n1=1; +#endif +/* Rounding Mode: RN ...round-to-nearest + * RZ ...round-towards 0 + * RP ...round-towards +INF + * RM ...round-towards -INF + */ + const int RN=0,RZ=1,RP=2,RM=3; + /* machine dependent: work on a Zilog Z8070 + * and a National 32081 & 16081 + */ + +/* exceptions */ + if(x!=x||x==0.0) return(x); /* sqrt(NaN) is NaN, sqrt(+-0) = +-0 */ + if(x<0) return((x-x)/(x-x)); /* sqrt(negative) is invalid */ + if((mx=px[n0]&mexp)==mexp) return(x); /* sqrt(+INF) is +INF */ + +/* save, reset, initialize */ + e=swapENI(0); /* ...save and reset the inexact enable */ + i=swapINX(0); /* ...save INEXACT flag */ + r=swapRM(RN); /* ...save and reset the Rounding Mode to RN */ + scalx=0; + +/* subnormal number, scale up x to x*2**54 */ + if(mx==0) {x *= b54 ; scalx-=0x01b00000;} + +/* scale x to avoid intermediate over/underflow: + * if (x > 2**512) x=x/2**512; if (x < 2**-512) x=x*2**512 */ + if(mx>0x5ff00000) {px[n0] -= 0x20000000; scalx+= 0x10000000;} + if(mx<0x1ff00000) {px[n0] += 0x20000000; scalx-= 0x10000000;} + +/* magic initial approximation to almost 8 sig. bits */ + py[n0]=(px[n0]>>1)+0x1ff80000; + py[n0]=py[n0]-table[(py[n0]>>15)&31]; + +/* Heron's rule once with correction to improve y to almost 18 sig. bits */ + t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; + +/* triple to almost 56 sig. bits; now y approx. sqrt(x) to within 1 ulp */ + t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; + t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; + +/* twiddle last bit to force y correctly rounded */ + swapRM(RZ); /* ...set Rounding Mode to round-toward-zero */ + swapINX(0); /* ...clear INEXACT flag */ + swapENI(e); /* ...restore inexact enable status */ + t=x/y; /* ...chopped quotient, possibly inexact */ + j=swapINX(i); /* ...read and restore inexact flag */ + if(j==0) { if(t==y) goto end; else t=subc(t); } /* ...t=t-ulp */ + b54+0.1; /* ..trigger inexact flag, sqrt(x) is inexact */ + if(r==RN) t=addc(t); /* ...t=t+ulp */ + else if(r==RP) { t=addc(t);y=addc(y);}/* ...t=t+ulp;y=y+ulp; */ + y=y+t; /* ...chopped sum */ + py[n0]=py[n0]-0x00100000; /* ...correctly rounded sqrt(x) */ +end: py[n0]=py[n0]+scalx; /* ...scale back y */ + swapRM(r); /* ...restore Rounding Mode */ + return(y); +} +#endif |