1 /* @(#)e_fmod.c 1.3 95/01/18 */ 2 /*- 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 #if 0 15 __FBSDID("$FreeBSD: src/lib/msun/src/e_fmodl.c,v 1.2 2008/07/31 20:09:47 das Exp $"); 16 #endif 17 18 #include <sys/types.h> 19 #include <machine/ieee.h> 20 21 #include <float.h> 22 #include <math.h> 23 #include <stdint.h> 24 25 #include "math_private.h" 26 27 #define BIAS (LDBL_MAX_EXP - 1) 28 29 /* 30 * These macros add and remove an explicit integer bit in front of the 31 * fractional mantissa, if the architecture doesn't have such a bit by 32 * default already. 33 */ 34 #ifdef LDBL_IMPLICIT_NBIT 35 #define LDBL_NBIT 0 36 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE)) 37 #define HFRAC_BITS EXT_FRACHBITS 38 #else 39 #define LDBL_NBIT 0x80000000 40 #define SET_NBIT(hx) (hx) 41 #define HFRAC_BITS (EXT_FRACHBITS - 1) 42 #endif 43 44 #define MANL_SHIFT (EXT_FRACLBITS - 1) 45 46 static const long double one = 1.0, Zero[] = {0.0, -0.0,}; 47 48 /* 49 * fmodl(x,y) 50 * Return x mod y in exact arithmetic 51 * Method: shift and subtract 52 * 53 * Assumptions: 54 * - The low part of the mantissa fits in a manl_t exactly. 55 * - The high part of the mantissa fits in an int64_t with enough room 56 * for an explicit integer bit in front of the fractional bits. 57 */ 58 long double 59 fmodl(long double x, long double y) 60 { 61 union { 62 long double e; 63 struct ieee_ext bits; 64 } ux, uy; 65 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */ 66 uint32_t hy; 67 uint32_t lx,ly,lz; 68 int ix,iy,n,sx; 69 70 ux.e = x; 71 uy.e = y; 72 sx = ux.bits.ext_sign; 73 74 /* purge off exception values */ 75 if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */ 76 (ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 77 (uy.bits.ext_exp == BIAS + LDBL_MAX_EXP && 78 ((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */ 79 return (x*y)/(x*y); 80 if(ux.bits.ext_exp<=uy.bits.ext_exp) { 81 if((ux.bits.ext_exp<uy.bits.ext_exp) || 82 (ux.bits.ext_frach<=uy.bits.ext_frach && 83 (ux.bits.ext_frach<uy.bits.ext_frach || 84 ux.bits.ext_fracl<uy.bits.ext_fracl))) { 85 return x; /* |x|<|y| return x or x-y */ 86 } 87 if(ux.bits.ext_frach==uy.bits.ext_frach && 88 ux.bits.ext_fracl==uy.bits.ext_fracl) { 89 return Zero[sx]; /* |x|=|y| return x*0*/ 90 } 91 } 92 93 /* determine ix = ilogb(x) */ 94 if(ux.bits.ext_exp == 0) { /* subnormal x */ 95 ux.e *= 0x1.0p512; 96 ix = ux.bits.ext_exp - (BIAS + 512); 97 } else { 98 ix = ux.bits.ext_exp - BIAS; 99 } 100 101 /* determine iy = ilogb(y) */ 102 if(uy.bits.ext_exp == 0) { /* subnormal y */ 103 uy.e *= 0x1.0p512; 104 iy = uy.bits.ext_exp - (BIAS + 512); 105 } else { 106 iy = uy.bits.ext_exp - BIAS; 107 } 108 109 /* set up {hx,lx}, {hy,ly} and align y to x */ 110 hx = SET_NBIT(ux.bits.ext_frach); 111 hy = SET_NBIT(uy.bits.ext_frach); 112 lx = ux.bits.ext_fracl; 113 ly = uy.bits.ext_fracl; 114 115 /* fix point fmod */ 116 n = ix - iy; 117 118 while(n--) { 119 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 120 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 121 else { 122 if ((hz|lz)==0) /* return sign(x)*0 */ 123 return Zero[sx]; 124 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; 125 } 126 } 127 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 128 if(hz>=0) {hx=hz;lx=lz;} 129 130 /* convert back to floating value and restore the sign */ 131 if((hx|lx)==0) /* return sign(x)*0 */ 132 return Zero[sx]; 133 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */ 134 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 135 iy -= 1; 136 } 137 ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */ 138 ux.bits.ext_fracl = lx; 139 if (iy < LDBL_MIN_EXP) { 140 ux.bits.ext_exp = iy + (BIAS + 512); 141 ux.e *= 0x1p-512; 142 } else { 143 ux.bits.ext_exp = iy + BIAS; 144 } 145 x = ux.e * one; /* create necessary signal */ 146 return x; /* exact output */ 147 } 148