/* $OpenBSD: hdtoa.c,v 1.5 2020/05/31 12:27:19 mortimer Exp $ */ /*- * Copyright (c) 2004, 2005 David Schultz <das@FreeBSD.ORG> * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ #include <sys/types.h> #include <machine/ieee.h> #include <float.h> #include <limits.h> #include <math.h> #include "gdtoaimp.h" /* Strings values used by dtoa() */ #define INFSTR "Infinity" #define NANSTR "NaN" #define DBL_ADJ (DBL_MAX_EXP - 2 + ((DBL_MANT_DIG - 1) % 4)) #define LDBL_ADJ (LDBL_MAX_EXP - 2 + ((LDBL_MANT_DIG - 1) % 4)) /* * Round up the given digit string. If the digit string is fff...f, * this procedure sets it to 100...0 and returns 1 to indicate that * the exponent needs to be bumped. Otherwise, 0 is returned. */ static int roundup(char *s0, int ndigits) { char *s; for (s = s0 + ndigits - 1; *s == 0xf; s--) { if (s == s0) { *s = 1; return (1); } *s = 0; } ++*s; return (0); } /* * Round the given digit string to ndigits digits according to the * current rounding mode. Note that this could produce a string whose * value is not representable in the corresponding floating-point * type. The exponent pointed to by decpt is adjusted if necessary. */ static void dorounding(char *s0, int ndigits, int sign, int *decpt) { int adjust = 0; /* do we need to adjust the exponent? */ switch (FLT_ROUNDS) { case 0: /* toward zero */ default: /* implementation-defined */ break; case 1: /* to nearest, halfway rounds to even */ if ((s0[ndigits] > 8) || (s0[ndigits] == 8 && s0[ndigits + 1] & 1)) adjust = roundup(s0, ndigits); break; case 2: /* toward +inf */ if (sign == 0) adjust = roundup(s0, ndigits); break; case 3: /* toward -inf */ if (sign != 0) adjust = roundup(s0, ndigits); break; } if (adjust) *decpt += 4; } /* * This procedure converts a double-precision number in IEEE format * into a string of hexadecimal digits and an exponent of 2. Its * behavior is bug-for-bug compatible with dtoa() in mode 2, with the * following exceptions: * * - An ndigits < 0 causes it to use as many digits as necessary to * represent the number exactly. * - The additional xdigs argument should point to either the string * "0123456789ABCDEF" or the string "0123456789abcdef", depending on * which case is desired. * - This routine does not repeat dtoa's mistake of setting decpt * to 9999 in the case of an infinity or NaN. INT_MAX is used * for this purpose instead. * * Note that the C99 standard does not specify what the leading digit * should be for non-zero numbers. For instance, 0x1.3p3 is the same * as 0x2.6p2 is the same as 0x4.cp1. This implementation chooses the * first digit so that subsequent digits are aligned on nibble * boundaries (before rounding). * * Inputs: d, xdigs, ndigits * Outputs: decpt, sign, rve */ char * __hdtoa(double d, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve) { static const int sigfigs = (DBL_MANT_DIG + 3) / 4; struct ieee_double *p = (struct ieee_double *)&d; char *s, *s0; int bufsize; *sign = p->dbl_sign; switch (fpclassify(d)) { case FP_NORMAL: *decpt = p->dbl_exp - DBL_ADJ; break; case FP_ZERO: *decpt = 1; return (nrv_alloc("0", rve, 1)); case FP_SUBNORMAL: d *= 0x1p514; *decpt = p->dbl_exp - (514 + DBL_ADJ); break; case FP_INFINITE: *decpt = INT_MAX; return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); case FP_NAN: *decpt = INT_MAX; return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); default: abort(); } /* FP_NORMAL or FP_SUBNORMAL */ if (ndigits == 0) /* dtoa() compatibility */ ndigits = 1; /* * For simplicity, we generate all the digits even if the * caller has requested fewer. */ bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; s0 = rv_alloc(bufsize); if (s0 == NULL) return (NULL); /* * We work from right to left, first adding any requested zero * padding, then the least significant portion of the * mantissa, followed by the most significant. The buffer is * filled with the byte values 0x0 through 0xf, which are * converted to xdigs[0x0] through xdigs[0xf] after the * rounding phase. */ for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) *s = 0; for (; s > s0 + sigfigs - (DBL_FRACLBITS / 4) - 1 && s > s0; s--) { *s = p->dbl_fracl & 0xf; p->dbl_fracl >>= 4; } for (; s > s0; s--) { *s = p->dbl_frach & 0xf; p->dbl_frach >>= 4; } /* * At this point, we have snarfed all the bits in the * mantissa, with the possible exception of the highest-order * (partial) nibble, which is dealt with by the next * statement. We also tack on the implicit normalization bit. */ *s = p->dbl_frach | (1U << ((DBL_MANT_DIG - 1) % 4)); /* If ndigits < 0, we are expected to auto-size the precision. */ if (ndigits < 0) { for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) ; } if (sigfigs > ndigits && s0[ndigits] != 0) dorounding(s0, ndigits, p->dbl_sign, decpt); s = s0 + ndigits; if (rve != NULL) *rve = s; *s-- = '\0'; for (; s >= s0; s--) *s = xdigs[(unsigned int)*s]; return (s0); } DEF_STRONG(__hdtoa); #if (LDBL_MANT_DIG > DBL_MANT_DIG) /* * This is the long double version of __hdtoa(). */ char * __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve) { static const int sigfigs = (LDBL_MANT_DIG + 3) / 4; struct ieee_ext *p = (struct ieee_ext *)&e; char *s, *s0; int bufsize; int fbits = 0; *sign = p->ext_sign; switch (fpclassify(e)) { case FP_NORMAL: *decpt = p->ext_exp - LDBL_ADJ; break; case FP_ZERO: *decpt = 1; return (nrv_alloc("0", rve, 1)); case FP_SUBNORMAL: e *= 0x1p514L; *decpt = p->ext_exp - (514 + LDBL_ADJ); break; case FP_INFINITE: *decpt = INT_MAX; return (nrv_alloc(INFSTR, rve, sizeof(INFSTR) - 1)); case FP_NAN: *decpt = INT_MAX; return (nrv_alloc(NANSTR, rve, sizeof(NANSTR) - 1)); default: abort(); } /* FP_NORMAL or FP_SUBNORMAL */ if (ndigits == 0) /* dtoa() compatibility */ ndigits = 1; /* * For simplicity, we generate all the digits even if the * caller has requested fewer. */ bufsize = (sigfigs > ndigits) ? sigfigs : ndigits; s0 = rv_alloc(bufsize); if (s0 == NULL) return (NULL); /* * We work from right to left, first adding any requested zero * padding, then the least significant portion of the * mantissa, followed by the most significant. The buffer is * filled with the byte values 0x0 through 0xf, which are * converted to xdigs[0x0] through xdigs[0xf] after the * rounding phase. */ for (s = s0 + bufsize - 1; s > s0 + sigfigs - 1; s--) *s = 0; for (fbits = EXT_FRACLBITS / 4; fbits > 0 && s > s0; s--, fbits--) { *s = p->ext_fracl & 0xf; p->ext_fracl >>= 4; } #ifdef EXT_FRACLMBITS for (fbits = EXT_FRACLMBITS / 4; fbits > 0 && s > s0; s--, fbits--) { *s = p->ext_fraclm & 0xf; p->ext_fraclm >>= 4; } #endif #ifdef EXT_FRACHMBITS for (fbits = EXT_FRACHMBITS / 4; fbits > 0 && s > s0; s--, fbits--) { *s = p->ext_frachm & 0xf; p->ext_frachm >>= 4; } #endif for (fbits = EXT_FRACHBITS / 4; fbits > 0 && s > s0; s--, fbits--) { *s = p->ext_frach & 0xf; p->ext_frach >>= 4; } /* * At this point, we have snarfed all the bits in the * mantissa, with the possible exception of the highest-order * (partial) nibble, which is dealt with by the next * statement. We also tack on the implicit normalization bit. */ *s = (p->ext_frach | (1U << ((LDBL_MANT_DIG - 1) % 4))) & 0xf; /* If ndigits < 0, we are expected to auto-size the precision. */ if (ndigits < 0) { for (ndigits = sigfigs; s0[ndigits - 1] == 0; ndigits--) ; } if (sigfigs > ndigits && s0[ndigits] != 0) dorounding(s0, ndigits, p->ext_sign, decpt); s = s0 + ndigits; if (rve != NULL) *rve = s; *s-- = '\0'; for (; s >= s0; s--) *s = xdigs[(unsigned int)*s]; return (s0); } DEF_STRONG(__hldtoa); #else /* (LDBL_MANT_DIG == DBL_MANT_DIG) */ char * __hldtoa(long double e, const char *xdigs, int ndigits, int *decpt, int *sign, char **rve) { return (__hdtoa((double)e, xdigs, ndigits, decpt, sign, rve)); } DEF_STRONG(__hldtoa); #endif /* (LDBL_MANT_DIG == DBL_MANT_DIG) */
