Mercurial > octave-nkf
view libcruft/misc/gen-d1mach.c @ 981:73cc20a6976b
[project @ 1994-12-14 03:46:24 by jwe]
Initial revision
author | jwe |
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date | Wed, 14 Dec 1994 03:48:48 +0000 |
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children | db38fe433efd |
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/* This file combines the single and double precision versions of machar, selected by cc -DSP or cc -DDP. This feature provided by D. G. Hough, August 3, 1988. */ #ifdef SP #define REAL float #define ZERO 0.0 #define ONE 1.0 #define PREC "Single " #define REALSIZE 1 #endif #ifdef DP #define REAL double #define ZERO 0.0e0 #define ONE 1.0e0 #define PREC "Double " #define REALSIZE 2 #endif #include <math.h> #include <stdio.h> #define ABS(xxx) ((xxx>ZERO)?(xxx):(-xxx)) void rmachar(ibeta,it,irnd,ngrd,machep,negep,iexp,minexp, maxexp,eps,epsneg,xmin,xmax) int *ibeta,*iexp,*irnd,*it,*machep,*maxexp,*minexp,*negep,*ngrd; REAL *eps,*epsneg,*xmax,*xmin; /* This subroutine is intended to determine the parameters of the floating-point arithmetic system specified below. The determination of the first three uses an extension of an algorithm due to M. Malcolm, CACM 15 (1972), pp. 949-951, incorporating some, but not all, of the improvements suggested by M. Gentleman and S. Marovich, CACM 17 (1974), pp. 276-277. An earlier version of this program was published in the book Software Manual for the Elementary Functions by W. J. Cody and W. Waite, Prentice-Hall, Englewood Cliffs, NJ, 1980. The present program is a translation of the Fortran 77 program in W. J. Cody, "MACHAR: A subroutine to dynamically determine machine parameters". TOMS (14), 1988. Parameter values reported are as follows: ibeta - the radix for the floating-point representation it - the number of base ibeta digits in the floating-point significand irnd - 0 if floating-point addition chops 1 if floating-point addition rounds, but not in the IEEE style 2 if floating-point addition rounds in the IEEE style 3 if floating-point addition chops, and there is partial underflow 4 if floating-point addition rounds, but not in the IEEE style, and there is partial underflow 5 if floating-point addition rounds in the IEEE style, and there is partial underflow ngrd - the number of guard digits for multiplication with truncating arithmetic. It is 0 if floating-point arithmetic rounds, or if it truncates and only it base ibeta digits participate in the post-normalization shift of the floating-point significand in multiplication; 1 if floating-point arithmetic truncates and more than it base ibeta digits participate in the post-normalization shift of the floating-point significand in multiplication. machep - the largest negative integer such that 1.0+FLOAT(ibeta)**machep .NE. 1.0, except that machep is bounded below by -(it+3) negeps - the largest negative integer such that 1.0-FLOAT(ibeta)**negeps .NE. 1.0, except that negeps is bounded below by -(it+3) iexp - the number of bits (decimal places if ibeta = 10) reserved for the representation of the exponent (including the bias or sign) of a floating-point number minexp - the largest in magnitude negative integer such that FLOAT(ibeta)**minexp is positive and normalized maxexp - the smallest positive power of BETA that overflows eps - the smallest positive floating-point number such that 1.0+eps .NE. 1.0. In particular, if either ibeta = 2 or IRND = 0, eps = FLOAT(ibeta)**machep. Otherwise, eps = (FLOAT(ibeta)**machep)/2 epsneg - A small positive floating-point number such that 1.0-epsneg .NE. 1.0. In particular, if ibeta = 2 or IRND = 0, epsneg = FLOAT(ibeta)**negeps. Otherwise, epsneg = (ibeta**negeps)/2. Because negeps is bounded below by -(it+3), epsneg may not be the smallest number that can alter 1.0 by subtraction. xmin - the smallest non-vanishing normalized floating-point power of the radix, i.e., xmin = FLOAT(ibeta)**minexp xmax - the largest finite floating-point number. In particular xmax = (1.0-epsneg)*FLOAT(ibeta)**maxexp Note - on some machines xmax will be only the second, or perhaps third, largest number, being too small by 1 or 2 units in the last digit of the significand. Latest revision - August 4, 1988 Author - W. J. Cody Argonne National Laboratory */ { int i,iz,j,k; int mx,itmp,nxres; REAL a,b,beta,betain,one,y,z,zero; REAL betah,t,tmp,tmpa,tmp1,two; (*irnd) = 1; one = (REAL)(*irnd); two = one + one; a = two; b = a; zero = 0.0e0; /* determine ibeta,beta ala malcolm */ tmp = ((a+one)-a)-one; while (tmp == zero) { a = a+a; tmp = a+one; tmp1 = tmp-a; tmp = tmp1-one; } tmp = a+b; itmp = (int)(tmp-a); while (itmp == 0) { b = b+b; tmp = a+b; itmp = (int)(tmp-a); } *ibeta = itmp; beta = (REAL)(*ibeta); /* determine irnd, it */ (*it) = 0; b = one; tmp = ((b+one)-b)-one; while (tmp == zero) { *it = *it+1; b = b*beta; tmp = b+one; tmp1 = tmp-b; tmp = tmp1-one; } *irnd = 0; betah = beta/two; tmp = a+betah; tmp1 = tmp-a; if (tmp1 != zero) *irnd = 1; tmpa = a+beta; tmp = tmpa+betah; if ((*irnd == 0) && (tmp-tmpa != zero)) *irnd = 2; /* determine negep, epsneg */ (*negep) = (*it) + 3; betain = one / beta; a = one; for (i = 1; i<=(*negep); i++) { a = a * betain; } b = a; tmp = (one-a); tmp = tmp-one; while (tmp == zero) { a = a*beta; *negep = *negep-1; tmp1 = one-a; tmp = tmp1-one; } (*negep) = -(*negep); (*epsneg) = a; /* determine machep, eps */ (*machep) = -(*it) - 3; a = b; tmp = one+a; while (tmp-one == zero) { a = a*beta; *machep = *machep+1; tmp = one+a; } *eps = a; /* determine ngrd */ (*ngrd) = 0; tmp = one+*eps; tmp = tmp*one; if (((*irnd) == 0) && (tmp-one) != zero) (*ngrd) = 1; /* determine iexp, minexp, xmin loop to determine largest i such that (1/beta) ** (2**(i)) does not underflow. exit from loop is signaled by an underflow. */ i = 0; k = 1; z = betain; t = one+*eps; nxres = 0; for (;;) { y = z; z = y * y; /* check for underflow */ a = z * one; tmp = z*t; if ((a+a == zero) || (ABS(z) > y)) break; tmp1 = tmp*betain; if (tmp1*beta == z) break; i = i + 1; k = k+k; } /* determine k such that (1/beta)**k does not underflow first set k = 2 ** i */ (*iexp) = i + 1; mx = k + k; if (*ibeta == 10) { /* for decimal machines only */ (*iexp) = 2; iz = *ibeta; while (k >= iz) { iz = iz * (*ibeta); (*iexp) = (*iexp) + 1; } mx = iz + iz - 1; } /* loop to determine minexp, xmin. exit from loop is signaled by an underflow. */ for (;;) { (*xmin) = y; y = y * betain; a = y * one; tmp = y*t; tmp1 = a+a; if ((tmp1 == zero) || (ABS(y) >= (*xmin))) break; k = k + 1; tmp1 = tmp*betain; tmp1 = tmp1*beta; if ((tmp1 == y) && (tmp != y)) { nxres = 3; *xmin = y; break; } } (*minexp) = -k; /* determine maxexp, xmax */ if ((mx <= k+k-3) && ((*ibeta) != 10)) { mx = mx + mx; (*iexp) = (*iexp) + 1; } (*maxexp) = mx + (*minexp); /* Adjust *irnd to reflect partial underflow. */ (*irnd) = (*irnd)+nxres; /* Adjust for IEEE style machines. */ if ((*irnd) >= 2) (*maxexp) = (*maxexp)-2; /* adjust for machines with implicit leading bit in binary significand and machines with radix point at extreme right of significand. */ i = (*maxexp) + (*minexp); if (((*ibeta) == 2) && (i == 0)) (*maxexp) = (*maxexp) - 1; if (i > 20) (*maxexp) = (*maxexp) - 1; if (a != y) (*maxexp) = (*maxexp) - 2; (*xmax) = one - (*epsneg); tmp = (*xmax)*one; if (tmp != (*xmax)) (*xmax) = one - beta * (*epsneg); (*xmax) = (*xmax) / (beta * beta * beta * (*xmin)); i = (*maxexp) + (*minexp) + 3; if (i > 0) { for (j = 1; j<=i; j++ ) { if ((*ibeta) == 2) (*xmax) = (*xmax) + (*xmax); if ((*ibeta) != 2) (*xmax) = (*xmax) * beta; } } return; } typedef union { double d; int i[2]; } equiv; int main (void) { /* Works for 32 bit machines with 32 bit ints and 64 bit doubles */ int ibeta, iexp, irnd, it, machep, maxexp, minexp, negep, ngrd; REAL eps, epsneg, xmax, xmin; int i; equiv flt_params[6]; rmachar (&ibeta, &it, &irnd, &ngrd, &machep, &negep, &iexp, &minexp, &maxexp, &eps, &epsneg, &xmin, &xmax); flt_params[1].d = xmin; flt_params[2].d = xmax; flt_params[3].d = epsneg; flt_params[4].d = eps; flt_params[5].d = log10 ((double) ibeta); printf ("* d1mach.f Do not edit. Generated automatically by gen-d1mach.c\n\ double precision function d1mach(i)\n\ integer i\n\ integer i1var (2)\n\ integer i2var (2)\n\ integer i3var (2)\n\ integer i4var (2)\n\ integer i5var (2)\n\ double precision dmach(5)\n\ equivalence (dmach(1), i1var(1))\n\ equivalence (dmach(2), i2var(1))\n\ equivalence (dmach(3), i3var(1))\n\ equivalence (dmach(4), i4var(1))\n\ equivalence (dmach(5), i5var(1))\n"); for (i = 1; i < 6; i++) printf (" data i%dvar(1), i%dvar(2) / %ld , %ld /\n", i, i, flt_params[i].i[0], flt_params[i].i[1]); printf (" if (i .lt. 1 .or. i .gt. 5) goto 999\n\ d1mach = dmach(i)\n\ return\n\ 999 write(*,1999) i\n\ 1999 format(' d1mach - i out of bounds', i10)\n\ call xstopx (' ')\n\ end\n"); return 0; }