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386 lines
9.8 KiB
386 lines
9.8 KiB
page ,132
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subttl emfprem.asm - fprem
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;***
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;emfprem.asm - FPREM emulation
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;
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; Copyright (c) 1987, Microsoft Corporation
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;
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;Purpose:
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; To emulate the 8087/80287 FPREM instruction.
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;
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;Revision History:
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; 08-12-86 JMB Initial version
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;
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; 09-23-86 JMB Changed from unsigned (jnc) to signed branch
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; (jge) on lc < 0 comparison
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;
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; 10-24-86 BCM Fixed a problem with large quotients that
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; caused a signed comparison (cmp bp,2) to
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; behave in an undesired manner when bp (quotient)
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; becomes larger than 32767; we now use bigquot
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; to indicate a quotients overflowing an unsigned word
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; Also, the quotient is now enregistered in bp
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; through most of the FPREM algorithm.
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;
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; 11-14-86 BCM Fixed a problem with the 4-word comparison of
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; numerator and denominator mantissas by substituting
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; unsigned-compare jumps (JB and JA) for signed-compare
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; jumps (JL and JG).
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;
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; Also see emulator.hst
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;
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;*******************************************************************************
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; The following is a working C program which was used to simulate
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; floating point numbers and to test the algorithm used in the
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; fprem emulation.
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;#include <math.h>
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;#include <stdio.h>
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;
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;typedef struct floating {
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; unsigned long man;
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; unsigned int expo;
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; } FLOAT_NUM;
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;
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;double fprem(double,double,unsigned int *);
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;
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;#define normalize(n) while (n&0x8000==0) { \
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; if (lc == 0) \
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; return(ldexp((double)(num.man)/65536,den.expo)); \
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; n <<= 1; \
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; lc--; \
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; *pq <<=1; \
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; }
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;
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;
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;main() {
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; unsigned int qv,qt;
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; double n,d,rv,rt;
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; FILE *fpinp;
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;
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; fpinp = fopen("fprem.dat","r");
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; if (fpinp) {
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; while (fscanf(fpinp,"%E %E",&n,&d) != EOF) {
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; qv=(unsigned int)(n/d);
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; rv=n-(d*qv);
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; printf(" \nnumerator is %f\n denominator is %f",n,d);
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; printf(" \nquotient is %x\n remainder is %f",qv,rv);
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; rt = fprem(n,d,&qt);
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; printf(" \nquotient is %x\n remainder is %f\n\n",qt,rt);
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; }
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; fclose(fpinp);
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; }
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; else
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; printf(" \nerror opening fprem.dat");
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; }
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;
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;double fprem(n,d,pq)
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; double n,d;
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; unsigned int *pq; {
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; int lc;
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; FLOAT_NUM num;
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; FLOAT_NUM den;
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;
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; num.man = (unsigned long)(65536*frexp(n,&num.expo));
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; den.man = (unsigned long)(65536*frexp(d,&den.expo));
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;
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; printf(" \nnumerator mantissa: %lx",num.man);
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; printf(" \nnumerator exponent: %x",num.expo);
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; printf(" \ndenominator mantissa: %lx",den.man);
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; printf(" \ndenominator exponent: %x",den.expo);
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;
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; *pq=0;
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; lc = num.expo - den.expo;
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; if (lc < 0) { /* then the numerator is the remainder */
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; return(ldexp((double)(num.man)/65536,num.expo));
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; }
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; while(1) {
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; if (den.man <= num.man) { /* do subtraction */
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; num.man -= den.man;
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; (*pq)++;
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; if (lc == 0) {
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; /* normalize(num.man) */
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; return(ldexp((double)(num.man)/65536,den.expo));
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; }
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; normalize(num.man)
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; }
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; else { /* don't do the subtraction */
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; if (lc == 0) {
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; /* normalize(num.man) */
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; return(ldexp((double)(num.man)/65536,den.expo));
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; }
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;
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; num.man <<= 1;
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; lc--;
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; (*pq) <<= 1;
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;
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; num.man -= den.man;
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; (*pq)++;
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;
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; normalize(num.man)
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; }
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; }
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; }
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;***
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;eFPREM - entry point for FPREM emulation
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;Purpose:
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;
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;Entry:
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;
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;Exit:
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;
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;Uses:
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;
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;Exceptions:
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;*******************************************************************************
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ProfBegin FPREM
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pub eFPREM
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; NOTE: The C program excerpts interspersed below are from the C program
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; shown in its entirety above.
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;
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; The correspondence between the C variables and the assembly
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; language version is as follows:
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;
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; C version masm version
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; *pq bp (quotient)
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; lc loopct
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; num.expo Expon[di]
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; den.expo Expon[si]
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; num.man MB0[di],MB2[di],MB4[di],MB6[di]
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; den.man MB0[si],MB2[si],MB4[si],MB6[si]
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; *pq=0;
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; lc = num.expo - den.expo;
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push ebp ;save bp; use bp as quotient
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mov edi,[CURSTK] ;point to ST(0), the numerator
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mov [RESULT],edi ;ST(0) is result (remainder)
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xor bp,bp ;begin with quotient = 0
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mov bigquot,0 ;quotient not > 65535 yet
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mov esi,edi ;si points to ST(0)
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sub esi,Reg87Len ;si points to ST(1), the denominator
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mov ax,word ptr Expon[edi] ;ax <== numerator exponent
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sub ax,word ptr Expon[esi] ;loopct = (num exponent - den exponent)
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mov loopct,ax
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mov dx,MB0[edi] ;move the mantissa of the
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mov cx,MB2[edi] ;numerator into
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mov bx,MB4[edi] ;ax:bx:cx:dx
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mov ax,MB6[edi]
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; if (lc < 0) { /* then the numerator is the remainder */
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; return(ldexp((double)(num.man)/65536,num.expo));
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; }
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jge short fpremLoop
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mov si,Expon[edi]
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jmp DoneEarly
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; while(1) {
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fpremLoop:
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; if (den.man <= num.man) { /* do subtraction */
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cmp ax,MB6[esi] ;compare msw of num to msw of den
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jb short NumLess ;numerator is less
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ja short NumMore ;numerator is more
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cmp bx,MB4[esi] ;compare word 2 of num to word 2 of den
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jb short NumLess ;numerator is less
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ja short NumMore ;numerator is more
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cmp cx,MB2[esi] ;compare word 4 of num to word 4 of den
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jb short NumLess ;numerator is less
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ja short NumMore ;numerator is more
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cmp dx,MB0[esi] ;compare lsw of num to lsw of den
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jb short NumLess ;numerator is less
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; num.man -= den.man;
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; (*pq)++;
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; if (lc == 0) {
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; /* normalize(num.man) */
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; return(ldexp((double)(num.man)/65536,den.expo));
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; }
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NumMore:
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call SubInc ;do subtraction, increment quotient
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cmp loopct,0 ;is expon diff zero?
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je short Done ;yes, then we're done
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; normalize(num.man)
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; }
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call fpremNorm ;normalize the numerator
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jnz fpremLoop ;do the next iteration
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jmp short Done ;loop counter is zero; we're done
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; else { /* don't do the subtraction */
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; if (lc == 0) {
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; /* normalize(num.man) */
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; return(ldexp((double)(num.man)/65536,den.expo));
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; }
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NumLess:
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cmp loopct,0 ;is expon diff zero?
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je short Done ;yes, then all done
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;
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; num.man <<= 1;
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; lc--;
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; (*pq) <<= 1;
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call ShiftDec ;shift quotient, numerator
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;
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; num.man -= den.man;
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; (*pq)++;
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call SubInc ;do subtraction, increment quotient
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;
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; normalize(num.man)
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; }
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call fpremNorm ;normalize for next iteration
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jnz fpremLoop ;do next iteration
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jmp short Done ;loop counter is zero; we're done
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; remainder: ax:bx:cx:dx is mantissa; Expon[si] is the exponent
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Done:
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;NOTE: the rounding routine wants the mantissa in di:bx:cx:dx:bp
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; the exponent in SI the sign and the old BP on the stack
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mov si,Expon[esi] ; mov exponent to si
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DoneEarly:
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mov di,Flag[edi] ; move sign of remainder to di
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xchg di,ax ; di becomes high mantissa word
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mov ah,al ; move sign to ah
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push ax ; put sign on stack
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; Except for bp which gets zeroed out later,
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; everything is now set up the way it needs to be for the normalization
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; routine, NODRQQ. Before we go there we need to set up the status
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; word as it should be set by fprem. For simplicity we did a complete
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; reduction of the dividend in one pass, so we will always clear C2
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; to indicate that the reduction is complete.
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mov ax,bp ; move quotient into ax
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and bp,0FFFCh ; check if quotient mod 64K < 4
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or bp,bigquot ; and quotient < 64K
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; bp is zero if and only if quotient < 4
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; (bp no longer holds the quotient itself)
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; al has low byte of quotient
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; ah will be for C0-C3 flags
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mov ah,SWcc ; move status word to ah
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and ah,not C2 ; clear C2 to indicate complete
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test al,01h ; is low bit of quotient set?
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jnz short SetC1 ; yes, go set C1
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and ah,not C1 ; low bit off, turn off C1
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jmp short DoC3 ; do the C3 bit
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SetC1:
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or ah,C1 ; low bit on, turn on C1
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DoC3:
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test al,02h ; is bit 1 of quotient set?
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jnz short SetC3 ; yes, go set C3
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or bp,bp ; is quotient less than 4?
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jz short QuotL2 ; then quotient < 2 (bit 1 off)
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; so don't set c0 or c3 from quotient
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; else if quotient >= 4
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and ah,not C3 ; bit 1 is off, so turn off C3
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jmp short DoC0 ; do the C0 bit
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SetC3:
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or ah,C3 ; bit 1 on, turn on C3
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DoC0:
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test al,04h ; is bit 2 of quotient set?
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jnz short SetC0 ; yes, go set C0
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or bp,bp ; is quotient less than 4?
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jz short QuotL4 ; yes, don't set c0 from quotient
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; else if quotient >= 4
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and ah,not C0 ; bit 2 off, turn off C0
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jmp short GoNormal ; we're done, go normalize
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SetC0:
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or ah,C0 ; bit 1 on, turn on C0
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GoNormal:
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mov SWcc,ah ; set new status word
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xor bp,bp ; clear low mantissa word
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jmp NODRQQ ; go normalize
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; (does pop ax, pop bp)
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; special case code if quotient is less than 2
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QuotL2:
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mov al,SWcc ; get old status word
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test al,C1 ; was C1 set
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jnz short SetC3toC1 ; yes, set C3
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and ah,not C3 ; clear C3
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jmp short QuotL4
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SetC3toC1:
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or ah,C3 ; set C3
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; special case code if quotient is less than 4
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QuotL4:
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mov al,SWcc ; get old status word
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test al,C3 ; was C3 set
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jnz short SetC0toC3 ; yes, set C0
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and ah,not C0 ; clear C0
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jmp short GoNormal ; go normalize the result
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SetC0toC3:
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or ah,C0 ; set C0
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jmp short GoNormal ; go normalize the result
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;#define normalize(n) while (n&0x8000==0) { \
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; if (lc == 0) \
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; return(ldexp((double)(num.man)/65536,den.expo)); \
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; n <<= 1; \
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; lc--; \
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; *pq <<=1; \
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; }
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;Inputs: ah contains high byte of numerator mantissa
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;Outputs: zero flag set indicates the loop counter is zero so we're finished
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; zero flag clear indicates the number was already normalized
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fpremNorm:
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test ah,80h ;is the numerator normalized?
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jnz short fpremIsNorm ;yes
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;no, normalize it
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cmp loopct,0 ;is expon diff zero?
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je short fpremIsNorm ;yes, then we're done
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call ShiftDec ;shift num, quotient
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;decrement loop ctr
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jmp short fpremNorm
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fpremIsNorm:
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ret
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ShiftDec:
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shl dx,1 ;numerator*2
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rcl cx,1
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rcl bx,1
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rcl ax,1
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dec loopct ;reduce exponent diff by one
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shl bp,1 ;quotient*2
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jc short QuotLarge ;carry out on quotient shift
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ret
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QuotLarge:
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mov bigquot,1 ;indicate large quotient > 65535
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ret
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SubInc:
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sub dx,MB0[esi] ;subtract lsw of den from lsw of num
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sbb cx,MB2[esi] ;subtract next word of den from num
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sbb bx,MB4[esi] ;subtract next word of den from num
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sbb ax,MB6[esi] ;subtract msw of den from msw of num
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inc bp ;add one to quotient
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ret
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ProfEnd FPREM
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