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 __RCSID("$NetBSD: e_fmodl.c,v 1.3 2024/07/17 12:00:48 riastradh Exp $"); 15 #if 0 16 __FBSDID("$FreeBSD: head/lib/msun/src/e_fmodl.c 181063 2008-07-31 20:09:47Z das $"); 17 #endif 18 19 #include "namespace.h" 20 21 #include <float.h> 22 #include <stdint.h> 23 24 #include "math.h" 25 #include "math_private.h" 26 #include <machine/ieee.h> 27 28 #ifdef __HAVE_LONG_DOUBLE 29 30 #define BIAS (LDBL_MAX_EXP - 1) 31 32 #if EXT_FRACLBITS > 32 33 typedef uint64_t manl_t; 34 #else 35 typedef uint32_t manl_t; 36 #endif 37 38 #if EXT_FRACHBITS > 32 39 typedef uint64_t manh_t; 40 #else 41 typedef uint32_t manh_t; 42 #endif 43 44 /* 45 * These macros add and remove an explicit integer bit in front of the 46 * fractional significand, if the architecture doesn't have such a bit 47 * by default already. 48 */ 49 #ifdef LDBL_IMPLICIT_NBIT 50 #define SET_NBIT(hx) ((hx) | (1ULL << EXT_FRACHBITS)) 51 #define HFRAC_BITS EXT_FRACHBITS 52 #define LDBL_NBIT 0 53 #else 54 #define SET_NBIT(hx) (hx) 55 #define HFRAC_BITS (EXT_FRACHBITS - 1) 56 #endif 57 58 #define MANL_SHIFT (EXT_FRACLBITS - 1) 59 60 static const long double one = 1.0, Zero[] = {0.0, -0.0,}; 61 62 /* 63 * fmodl(x,y) 64 * Return x mod y in exact arithmetic 65 * Method: shift and subtract 66 * 67 * Assumptions: 68 * - The low part of the significand fits in a manl_t exactly. 69 * - The high part of the significand fits in an int64_t with enough 70 * room for an explicit integer bit in front of the fractional bits. 71 */ 72 long double 73 __ieee754_fmodl(long double x, long double y) 74 { 75 union ieee_ext_u ux = { .extu_ld = x, }; 76 union ieee_ext_u uy = { .extu_ld = y, }; 77 int64_t hx,hz; /* We need a carry bit even if EXT_FRACHBITS is 32. */ 78 manh_t hy; 79 manl_t lx,ly,lz; 80 int ix,iy,n,sx; 81 82 sx = ux.extu_sign; 83 84 /* purge off exception values */ 85 if((uy.extu_exp|uy.extu_frach|uy.extu_fracl)==0 || /* y=0 */ 86 (ux.extu_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */ 87 (uy.extu_exp == BIAS + LDBL_MAX_EXP && 88 ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)!=0)) /* or y is NaN */ 89 return (x*y)/(x*y); 90 if(ux.extu_exp<=uy.extu_exp) { 91 if((ux.extu_exp<uy.extu_exp) || 92 (ux.extu_frach<=uy.extu_frach && 93 (ux.extu_frach<uy.extu_frach || 94 ux.extu_fracl<uy.extu_fracl))) { 95 return x; /* |x|<|y| return x or x-y */ 96 } 97 if(ux.extu_frach==uy.extu_frach && ux.extu_fracl==uy.extu_fracl) { 98 return Zero[sx]; /* |x|=|y| return x*0*/ 99 } 100 } 101 102 /* determine ix = ilogb(x) */ 103 if(ux.extu_exp == 0) { /* subnormal x */ 104 ux.extu_ld *= 0x1.0p512; 105 ix = ux.extu_exp - (BIAS + 512); 106 } else { 107 ix = ux.extu_exp - BIAS; 108 } 109 110 /* determine iy = ilogb(y) */ 111 if(uy.extu_exp == 0) { /* subnormal y */ 112 uy.extu_ld *= 0x1.0p512; 113 iy = uy.extu_exp - (BIAS + 512); 114 } else { 115 iy = uy.extu_exp - BIAS; 116 } 117 118 /* set up {hx,lx}, {hy,ly} and align y to x */ 119 hx = SET_NBIT(ux.extu_frach); 120 hy = SET_NBIT(uy.extu_frach); 121 lx = ux.extu_fracl; 122 ly = uy.extu_fracl; 123 124 /* fix point fmod */ 125 n = ix - iy; 126 127 while(n--) { 128 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 129 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;} 130 else { 131 if ((hz|lz)==0) /* return sign(x)*0 */ 132 return Zero[sx]; 133 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; 134 } 135 } 136 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 137 if(hz>=0) {hx=hz;lx=lz;} 138 139 /* convert back to floating value and restore the sign */ 140 if((hx|lx)==0) /* return sign(x)*0 */ 141 return Zero[sx]; 142 while(hx<(1LL<<HFRAC_BITS)) { /* normalize x */ 143 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx; 144 iy -= 1; 145 } 146 ux.extu_frach = hx; /* The significand is truncated here if needed. */ 147 ux.extu_fracl = lx; 148 if (iy < LDBL_MIN_EXP) { 149 ux.extu_exp = iy + (BIAS + 512); 150 ux.extu_ld *= 0x1p-512; 151 } else { 152 ux.extu_exp = iy + BIAS; 153 } 154 x = ux.extu_ld * one; /* create necessary signal */ 155 return x; /* exact output */ 156 } 157 158 #endif /* __HAVE_LONG_DOUBLE */ 159