| /* e_fmodl.c -- long double version of e_fmod.c. |
| * Conversion to IEEE quad long double by Jakub Jelinek, jj@ultra.linux.cz. |
| */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| /* |
| * __ieee754_fmodl(x,y) |
| * Return x mod y in exact arithmetic |
| * Method: shift and subtract |
| */ |
| |
| #include "math.h" |
| #include "math_private.h" |
| #include <ieee754.h> |
| |
| #ifdef __STDC__ |
| static const long double one = 1.0, Zero[] = {0.0, -0.0,}; |
| #else |
| static long double one = 1.0, Zero[] = {0.0, -0.0,}; |
| #endif |
| |
| #ifdef __STDC__ |
| long double __ieee754_fmodl(long double x, long double y) |
| #else |
| long double __ieee754_fmodl(x,y) |
| long double x,y; |
| #endif |
| { |
| int64_t n,hx,hy,hz,ix,iy,sx,i; |
| u_int64_t lx,ly,lz; |
| int temp; |
| |
| GET_LDOUBLE_WORDS64(hx,lx,x); |
| GET_LDOUBLE_WORDS64(hy,ly,y); |
| sx = hx&0x8000000000000000ULL; /* sign of x */ |
| hx ^=sx; /* |x| */ |
| hy &= 0x7fffffffffffffffLL; /* |y| */ |
| |
| /* purge off exception values */ |
| if((hy|(ly&0x7fffffffffffffff))==0||(hx>=0x7ff0000000000000LL)|| /* y=0,or x not finite */ |
| (hy>0x7ff0000000000000LL)) /* or y is NaN */ |
| return (x*y)/(x*y); |
| if(hx<=hy) { |
| if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ |
| if(lx==ly) |
| return Zero[(u_int64_t)sx>>63]; /* |x|=|y| return x*0*/ |
| } |
| |
| /* determine ix = ilogb(x) */ |
| if(hx<0x0010000000000000LL) { /* subnormal x */ |
| if(hx==0) { |
| for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; |
| } else { |
| for (ix = -1022, i=hx<<19; i>0; i<<=1) ix -=1; |
| } |
| } else ix = (hx>>52)-0x3ff; |
| |
| /* determine iy = ilogb(y) */ |
| if(hy<0x0010000000000000LL) { /* subnormal y */ |
| if(hy==0) { |
| for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; |
| } else { |
| for (iy = -1022, i=hy<<19; i>0; i<<=1) iy -=1; |
| } |
| } else iy = (hy>>52)-0x3ff; |
| |
| /* Make the IBM extended format 105 bit mantissa look like the ieee854 112 |
| bit mantissa so the following operatations will give the correct |
| result. */ |
| ldbl_extract_mantissa(&hx, &lx, &temp, x); |
| ldbl_extract_mantissa(&hy, &ly, &temp, y); |
| |
| /* set up {hx,lx}, {hy,ly} and align y to x */ |
| if(ix >= -1022) |
| hx = 0x0001000000000000LL|(0x0000ffffffffffffLL&hx); |
| else { /* subnormal x, shift x to normal */ |
| n = -1022-ix; |
| if(n<=63) { |
| hx = (hx<<n)|(lx>>(64-n)); |
| lx <<= n; |
| } else { |
| hx = lx<<(n-64); |
| lx = 0; |
| } |
| } |
| if(iy >= -1022) |
| hy = 0x0001000000000000LL|(0x0000ffffffffffffLL&hy); |
| else { /* subnormal y, shift y to normal */ |
| n = -1022-iy; |
| if(n<=63) { |
| hy = (hy<<n)|(ly>>(64-n)); |
| ly <<= n; |
| } else { |
| hy = ly<<(n-64); |
| ly = 0; |
| } |
| } |
| |
| /* fix point fmod */ |
| n = ix - iy; |
| while(n--) { |
| hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
| if(hz<0){hx = hx+hx+(lx>>63); lx = lx+lx;} |
| else { |
| if((hz|(lz&0x7fffffffffffffff))==0) /* return sign(x)*0 */ |
| return Zero[(u_int64_t)sx>>63]; |
| hx = hz+hz+(lz>>63); lx = lz+lz; |
| } |
| } |
| hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
| if(hz>=0) {hx=hz;lx=lz;} |
| |
| /* convert back to floating value and restore the sign */ |
| if((hx|(lx&0x7fffffffffffffff))==0) /* return sign(x)*0 */ |
| return Zero[(u_int64_t)sx>>63]; |
| while(hx<0x0001000000000000LL) { /* normalize x */ |
| hx = hx+hx+(lx>>63); lx = lx+lx; |
| iy -= 1; |
| } |
| if(iy>= -1022) { /* normalize output */ |
| x = ldbl_insert_mantissa((sx>>63), iy, hx, lx); |
| } else { /* subnormal output */ |
| n = -1022 - iy; |
| if(n<=48) { |
| lx = (lx>>n)|((u_int64_t)hx<<(64-n)); |
| hx >>= n; |
| } else if (n<=63) { |
| lx = (hx<<(64-n))|(lx>>n); hx = sx; |
| } else { |
| lx = hx>>(n-64); hx = sx; |
| } |
| x = ldbl_insert_mantissa((sx>>63), iy, hx, lx); |
| x *= one; /* create necessary signal */ |
| } |
| return x; /* exact output */ |
| } |