/* float.c floating-point constant support for the Netwide Assembler * * The Netwide Assembler is copyright (C) 1996 Simon Tatham and * Julian Hall. All rights reserved. The software is * redistributable under the licence given in the file "Licence" * distributed in the NASM archive. * * initial version 13/ix/96 by Simon Tatham */ #include "compiler.h" #include #include #include #include #include #include "nasm.h" #include "float.h" /* * ----------------- * local variables * ----------------- */ static efunc error; static bool daz = false; /* denormals as zero */ static enum float_round rc = FLOAT_RC_NEAR; /* rounding control */ /* * ----------- * constants * ----------- */ /* 112 bits + 64 bits for accuracy + 16 bits for rounding */ #define MANT_WORDS 12 /* 52 digits fit in 176 bits because 10^53 > 2^176 > 10^52 */ #define MANT_DIGITS 52 /* the format and the argument list depend on MANT_WORDS */ #define MANT_FMT "%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x_%04x%04x" #define MANT_ARG SOME_ARG(mant, 0) #define SOME_ARG(a,i) (a)[(i)+0], (a)[(i)+1], (a)[(i)+2], (a)[(i)+3], \ (a)[(i)+4], (a)[(i)+5], (a)[(i)+6], (a)[(i)+7], (a)[(i)+8], \ (a)[(i)+9], (a)[(i)+10], (a)[(i)+11] /* * --------------------------------------------------------------------------- * emit a printf()-like debug message... but only if DEBUG_FLOAT was defined * --------------------------------------------------------------------------- */ #ifdef DEBUG_FLOAT #define dprintf(x) printf x #else /* */ #define dprintf(x) do { } while (0) #endif /* */ /* * --------------------------------------------------------------------------- * multiply * --------------------------------------------------------------------------- */ static int float_multiply(uint16_t * to, uint16_t * from) { uint32_t temp[MANT_WORDS * 2]; int32_t i, j; /* * guaranteed that top bit of 'from' is set -- so we only have * to worry about _one_ bit shift to the left */ dprintf(("%s=" MANT_FMT "\n", "mul1", SOME_ARG(to, 0))); dprintf(("%s=" MANT_FMT "\n", "mul2", SOME_ARG(from, 0))); memset(temp, 0, sizeof temp); for (i = 0; i < MANT_WORDS; i++) { for (j = 0; j < MANT_WORDS; j++) { uint32_t n; n = (uint32_t) to[i] * (uint32_t) from[j]; temp[i + j] += n >> 16; temp[i + j + 1] += n & 0xFFFF; } } for (i = MANT_WORDS * 2; --i;) { temp[i - 1] += temp[i] >> 16; temp[i] &= 0xFFFF; } dprintf(("%s=" MANT_FMT "_" MANT_FMT "\n", "temp", SOME_ARG(temp, 0), SOME_ARG(temp, MANT_WORDS))); if (temp[0] & 0x8000) { for (i = 0; i < MANT_WORDS; i++) { to[i] = temp[i] & 0xFFFF; } dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), 0)); return 0; } else { for (i = 0; i < MANT_WORDS; i++) { to[i] = (temp[i] << 1) + !!(temp[i + 1] & 0x8000); } dprintf(("%s=" MANT_FMT " (%i)\n", "prod", SOME_ARG(to, 0), -1)); return -1; } } /* * --------------------------------------------------------------------------- * read an exponent; returns INT32_MAX on error * --------------------------------------------------------------------------- */ static int32_t read_exponent(const char *string, int32_t max) { int32_t i = 0; bool neg = false; if (*string == '+') { string++; } else if (*string == '-') { neg = true; string++; } while (*string) { if (*string >= '0' && *string <= '9') { i = (i * 10) + (*string - '0'); /* * To ensure that underflows and overflows are * handled properly we must avoid wraparounds of * the signed integer value that is used to hold * the exponent. Therefore we cap the exponent at * +/-5000, which is slightly more/less than * what's required for normal and denormal numbers * in single, double, and extended precision, but * sufficient to avoid signed integer wraparound. */ if (i > max) i = max; } else if (*string == '_') { /* do nothing */ } else { error(ERR_NONFATAL, "invalid character in floating-point constant %s: '%c'", "exponent", *string); return INT32_MAX; } string++; } return neg ? -i : i; } /* * --------------------------------------------------------------------------- * convert * --------------------------------------------------------------------------- */ static bool ieee_flconvert(const char *string, uint16_t * mant, int32_t * exponent) { char digits[MANT_DIGITS]; char *p, *q, *r; uint16_t mult[MANT_WORDS], bit; uint16_t *m; int32_t tenpwr, twopwr; int32_t extratwos; bool started, seendot, warned; p = digits; tenpwr = 0; started = seendot = false; warned = (pass0 != 1); while (*string && *string != 'E' && *string != 'e') { if (*string == '.') { if (!seendot) { seendot = true; } else { error(ERR_NONFATAL, "too many periods in floating-point constant"); return false; } } else if (*string >= '0' && *string <= '9') { if (*string == '0' && !started) { if (seendot) { tenpwr--; } } else { started = true; if (p < digits + sizeof(digits)) { *p++ = *string - '0'; } else { if (!warned) { error(ERR_WARNING|ERR_WARN_FL_TOOLONG, "floating-point constant significand contains " "more than %i digits", MANT_DIGITS); warned = true; } } if (!seendot) { tenpwr++; } } } else if (*string == '_') { /* do nothing */ } else { error(ERR_NONFATAL, "invalid character in floating-point constant %s: '%c'", "significand", *string); return false; } string++; } if (*string) { int32_t e; string++; /* eat the E */ e = read_exponent(string, 5000); if (e == INT32_MAX) return false; tenpwr += e; } /* * At this point, the memory interval [digits,p) contains a * series of decimal digits zzzzzzz, such that our number X * satisfies X = 0.zzzzzzz * 10^tenpwr. */ q = digits; dprintf(("X = 0.")); while (q < p) { dprintf(("%c", *q + '0')); q++; } dprintf((" * 10^%i\n", tenpwr)); /* * Now convert [digits,p) to our internal representation. */ bit = 0x8000; for (m = mant; m < mant + MANT_WORDS; m++) { *m = 0; } m = mant; q = digits; started = false; twopwr = 0; while (m < mant + MANT_WORDS) { uint16_t carry = 0; while (p > q && !p[-1]) { p--; } if (p <= q) { break; } for (r = p; r-- > q;) { int32_t i; i = 2 * *r + carry; if (i >= 10) { carry = 1; i -= 10; } else { carry = 0; } *r = i; } if (carry) { *m |= bit; started = true; } if (started) { if (bit == 1) { bit = 0x8000; m++; } else { bit >>= 1; } } else { twopwr--; } } twopwr += tenpwr; /* * At this point, the 'mant' array contains the first frac- * tional places of a base-2^16 real number which when mul- * tiplied by 2^twopwr and 5^tenpwr gives X. */ dprintf(("X = " MANT_FMT " * 2^%i * 5^%i\n", MANT_ARG, twopwr, tenpwr)); /* * Now multiply 'mant' by 5^tenpwr. */ if (tenpwr < 0) { /* mult = 5^-1 = 0.2 */ for (m = mult; m < mult + MANT_WORDS - 1; m++) { *m = 0xCCCC; } mult[MANT_WORDS - 1] = 0xCCCD; extratwos = -2; tenpwr = -tenpwr; /* * If tenpwr was 1000...000b, then it becomes 1000...000b. See * the "ANSI C" comment below for more details on that case. * * Because we already truncated tenpwr to +5000...-5000 inside * the exponent parsing code, this shouldn't happen though. */ } else if (tenpwr > 0) { /* mult = 5^+1 = 5.0 */ mult[0] = 0xA000; for (m = mult + 1; m < mult + MANT_WORDS; m++) { *m = 0; } extratwos = 3; } else { extratwos = 0; } while (tenpwr) { dprintf(("loop=" MANT_FMT " * 2^%i * 5^%i (%i)\n", MANT_ARG, twopwr, tenpwr, extratwos)); if (tenpwr & 1) { dprintf(("mant*mult\n")); twopwr += extratwos + float_multiply(mant, mult); } dprintf(("mult*mult\n")); extratwos = extratwos * 2 + float_multiply(mult, mult); tenpwr >>= 1; /* * In ANSI C, the result of right-shifting a signed integer is * considered implementation-specific. To ensure that the loop * terminates even if tenpwr was 1000...000b to begin with, we * manually clear the MSB, in case a 1 was shifted in. * * Because we already truncated tenpwr to +5000...-5000 inside * the exponent parsing code, this shouldn't matter; neverthe- * less it is the right thing to do here. */ tenpwr &= (uint32_t) - 1 >> 1; } /* * At this point, the 'mant' array contains the first frac- * tional places of a base-2^16 real number in [0.5,1) that * when multiplied by 2^twopwr gives X. Or it contains zero * of course. We are done. */ *exponent = twopwr; return true; } /* * --------------------------------------------------------------------------- * round a mantissa off after i words * --------------------------------------------------------------------------- */ #define ROUND_COLLECT_BITS \ for (j = i; j < MANT_WORDS; j++) { \ m = m | mant[j]; \ } #define ROUND_ABS_DOWN \ for (j = i; j < MANT_WORDS; j++) { \ mant[j] = 0x0000; \ } #define ROUND_ABS_UP \ do { \ ++mant[--i]; \ mant[i] &= 0xFFFF; \ } while (i > 0 && !mant[i]); \ return (!i && !mant[i]); static bool ieee_round(int sign, uint16_t * mant, int32_t i) { uint16_t m = 0; int32_t j; if ((sign == 0x0000) || (sign == 0x8000)) { if (rc == FLOAT_RC_NEAR) { if (mant[i] & 0x8000) { mant[i] &= 0x7FFF; ROUND_COLLECT_BITS; mant[i] |= 0x8000; if (m) { ROUND_ABS_UP; } else { if (mant[i - 1] & 1) { ROUND_ABS_UP; } else { ROUND_ABS_DOWN; } } } else { ROUND_ABS_DOWN; } } else if (((sign == 0x0000) && (rc == FLOAT_RC_DOWN)) || ((sign == 0x8000) && (rc == FLOAT_RC_UP))) { ROUND_COLLECT_BITS; if (m) { ROUND_ABS_DOWN; } } else if (((sign == 0x0000) && (rc == FLOAT_RC_UP)) || ((sign == 0x8000) && (rc == FLOAT_RC_DOWN))) { ROUND_COLLECT_BITS; if (m) { ROUND_ABS_UP; } } else if (rc == FLOAT_RC_ZERO) { ROUND_ABS_DOWN; } else { error(ERR_PANIC, "float_round() can't handle rc=%i", rc); } } else { error(ERR_PANIC, "float_round() can't handle sign=%i", sign); } return false; } /* Returns a value >= 16 if not a valid hex digit */ static unsigned int hexval(char c) { unsigned int v = (unsigned char) c; if (v >= '0' && v <= '9') return v - '0'; else return (v|0x20) - 'a' + 10; } /* Handle floating-point numbers with radix 2^bits and binary exponent */ static bool ieee_flconvert_bin(const char *string, int bits, uint16_t * mant, int32_t * exponent) { static const int log2tbl[16] = { -1, 0, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3 }; uint16_t mult[MANT_WORDS + 1], *mp; int ms; int32_t twopwr; bool seendot, seendigit; unsigned char c; int radix = 1 << bits; unsigned int v; twopwr = 0; seendot = seendigit = false; ms = 0; mp = NULL; memset(mult, 0, sizeof mult); while ((c = *string++) != '\0') { if (c == '.') { if (!seendot) seendot = true; else { error(ERR_NONFATAL, "too many periods in floating-point constant"); return false; } } else if ((v = hexval(c)) < (unsigned int)radix) { if (!seendigit && v) { int l = log2tbl[v]; seendigit = 1; mp = mult; ms = 15-l; twopwr = seendot ? twopwr-bits+l : l+1-bits; } if (seendigit) { if (ms <= 0) { *mp |= v >> -ms; mp++; if (mp > &mult[MANT_WORDS]) mp = &mult[MANT_WORDS]; /* Guard slot */ ms += 16; } *mp |= v << ms; ms -= bits; if (!seendot) twopwr += bits; } else { if (seendot) twopwr -= bits; } } else if (c == 'p' || c == 'P') { int32_t e; e = read_exponent(string, 20000); if (e == INT32_MAX) return false; twopwr += e; break; } else if (c == '_') { /* ignore */ } else { error(ERR_NONFATAL, "floating-point constant: `%c' is invalid character", c); return false; } } if (!seendigit) { memset(mant, 0, 2 * MANT_WORDS); /* Zero */ *exponent = 0; } else { memcpy(mant, mult, 2 * MANT_WORDS); *exponent = twopwr; } return true; } /* * Shift a mantissa to the right by i bits. */ static void ieee_shr(uint16_t * mant, int i) { uint16_t n, m; int j = 0; int sr, sl, offs; sr = i%16; sl = 16-sr; offs = i/16; if (sr == 0) { if (offs) for (j = MANT_WORDS-1; j >= offs; j--) mant[j] = mant[j-offs]; } else { n = mant[MANT_WORDS-1-offs] >> sr; for (j = MANT_WORDS-1; j > offs; j--) { m = mant[j-offs-1]; mant[j] = (m << sl) | n; n = m >> sr; } mant[j--] = n; } while (j >= 0) mant[j--] = 0; } #if defined(__i386__) || defined(__x86_64__) #define put(a,b) (*(uint16_t *)(a) = (b)) #else #define put(a,b) (((a)[0] = (b)), ((a)[1] = (b) >> 8)) #endif /* Set a bit, using *bigendian* bit numbering (0 = MSB) */ static void set_bit(uint16_t *mant, int bit) { mant[bit >> 4] |= 1 << (~bit & 15); } /* Test a single bit */ static int test_bit(const uint16_t *mant, int bit) { return (mant[bit >> 4] >> (~bit & 15)) & 1; } /* Report if the mantissa value is all zero */ static bool is_zero(const uint16_t *mant) { int i; for (i = 0; i < MANT_WORDS; i++) if (mant[i]) return false; return true; } /* Produce standard IEEE formats, with implicit or explicit integer bit; this makes the following assumptions: - the sign bit is the MSB, followed by the exponent, followed by the integer bit if present. - the sign bit plus exponent fit in 16 bits. - the exponent bias is 2^(n-1)-1 for an n-bit exponent */ struct ieee_format { int words; int mantissa; /* Fractional bits in the mantissa */ int explicit; /* Explicit integer */ int exponent; /* Bits in the exponent */ }; /* * The 16- and 128-bit formats are expected to be in IEEE 754r. * AMD SSE5 uses the 16-bit format. * * The 32- and 64-bit formats are the original IEEE 754 formats. * * The 80-bit format is x87-specific, but widely used. */ static const struct ieee_format ieee_16 = { 1, 10, 0, 5 }; static const struct ieee_format ieee_32 = { 2, 23, 0, 8 }; static const struct ieee_format ieee_64 = { 4, 52, 0, 11 }; static const struct ieee_format ieee_80 = { 5, 63, 1, 15 }; static const struct ieee_format ieee_128 = { 8, 112, 0, 15 }; /* Types of values we can generate */ enum floats { FL_ZERO, FL_DENORMAL, FL_NORMAL, FL_INFINITY, FL_QNAN, FL_SNAN }; static int to_float(const char *str, int sign, uint8_t * result, const struct ieee_format *fmt) { uint16_t mant[MANT_WORDS], *mp; int32_t exponent = 0; int32_t expmax = 1 << (fmt->exponent - 1); uint16_t one_mask = 0x8000 >> ((fmt->exponent+fmt->explicit) % 16); int one_pos = (fmt->exponent+fmt->explicit)/16; int i; int shift; enum floats type; bool ok; sign = (sign < 0 ? 0x8000 : 0); if (str[0] == '_') { /* Special tokens */ switch (str[2]) { case 'n': /* __nan__ */ case 'N': case 'q': /* __qnan__ */ case 'Q': type = FL_QNAN; break; case 's': /* __snan__ */ case 'S': type = FL_SNAN; break; case 'i': /* __infinity__ */ case 'I': type = FL_INFINITY; break; default: error(ERR_NONFATAL, "internal error: unknown FP constant token `%s'\n", str); type = FL_QNAN; break; } } else { if (str[0] == '0') { switch (str[1]) { case 'x': case 'X': case 'h': case 'H': ok = ieee_flconvert_bin(str+2, 4, mant, &exponent); break; case 'o': case 'O': case 'q': case 'Q': ok = ieee_flconvert_bin(str+2, 3, mant, &exponent); break; case 'b': case 'B': case 'y': case 'Y': ok = ieee_flconvert_bin(str+2, 1, mant, &exponent); break; case 'd': case 'D': case 't': case 'T': ok = ieee_flconvert(str+2, mant, &exponent); break; default: /* Leading zero was just a zero? */ ok = ieee_flconvert(str, mant, &exponent); break; } } else if (str[0] == '$') { ok = ieee_flconvert_bin(str+1, 4, mant, &exponent); } else { ok = ieee_flconvert(str, mant, &exponent); } if (!ok) { type = FL_QNAN; } else if (mant[0] & 0x8000) { /* * Non-zero. */ exponent--; if (exponent >= 2 - expmax && exponent <= expmax) { type = FL_NORMAL; } else if (exponent < 2 - expmax && exponent >= 2 - expmax - fmt->mantissa) { type = FL_DENORMAL; } else if (exponent > 0) { if (pass0 == 1) error(ERR_WARNING|ERR_WARN_FL_OVERFLOW, "overflow in floating-point constant"); type = FL_INFINITY; } else { /* underflow */ if (pass0 == 1) error(ERR_WARNING|ERR_WARN_FL_UNDERFLOW, "underflow in floating-point constant"); type = FL_ZERO; } } else { /* Zero */ type = FL_ZERO; } } switch (type) { case FL_ZERO: zero: memset(mant, 0, sizeof mant); break; case FL_DENORMAL: { shift = -(exponent + expmax - 2 - fmt->exponent) + fmt->explicit; ieee_shr(mant, shift); ieee_round(sign, mant, fmt->words); if (mant[one_pos] & one_mask) { /* One's position is set, we rounded up into normal range */ exponent = 1; if (!fmt->explicit) mant[one_pos] &= ~one_mask; /* remove explicit one */ mant[0] |= exponent << (15 - fmt->exponent); } else { if (daz || is_zero(mant)) { /* Flush denormals to zero */ if (pass0 == 1) error(ERR_WARNING|ERR_WARN_FL_UNDERFLOW, "underflow in floating-point constant"); goto zero; } else { if (pass0 == 1) error(ERR_WARNING|ERR_WARN_FL_DENORM, "denormal floating-point constant"); } } break; } case FL_NORMAL: exponent += expmax - 1; ieee_shr(mant, fmt->exponent+fmt->explicit); ieee_round(sign, mant, fmt->words); /* did we scale up by one? */ if (test_bit(mant, fmt->exponent+fmt->explicit-1)) { ieee_shr(mant, 1); exponent++; if (exponent >= (expmax << 1)-1) { if (pass0 == 1) error(ERR_WARNING|ERR_WARN_FL_OVERFLOW, "overflow in floating-point constant"); type = FL_INFINITY; goto overflow; } } if (!fmt->explicit) mant[one_pos] &= ~one_mask; /* remove explicit one */ mant[0] |= exponent << (15 - fmt->exponent); break; case FL_INFINITY: case FL_QNAN: case FL_SNAN: overflow: memset(mant, 0, sizeof mant); mant[0] = ((1 << fmt->exponent)-1) << (15 - fmt->exponent); if (fmt->explicit) mant[one_pos] |= one_mask; if (type == FL_QNAN) set_bit(mant, fmt->exponent+fmt->explicit+1); else if (type == FL_SNAN) set_bit(mant, fmt->exponent+fmt->explicit+fmt->mantissa); break; } mant[0] |= sign; for (mp = &mant[fmt->words], i = 0; i < fmt->words; i++) { uint16_t m = *--mp; put(result, m); result += 2; } return 1; /* success */ } int float_const(const char *number, int32_t sign, uint8_t * result, int bytes, efunc err) { error = err; switch (bytes) { case 2: return to_float(number, sign, result, &ieee_16); case 4: return to_float(number, sign, result, &ieee_32); case 8: return to_float(number, sign, result, &ieee_64); case 10: return to_float(number, sign, result, &ieee_80); case 16: return to_float(number, sign, result, &ieee_128); default: error(ERR_PANIC, "strange value %d passed to float_const", bytes); return 0; } } /* Set floating-point options */ int float_option(const char *option) { if (!nasm_stricmp(option, "daz")) { daz = true; return 0; } else if (!nasm_stricmp(option, "nodaz")) { daz = false; return 0; } else if (!nasm_stricmp(option, "near")) { rc = FLOAT_RC_NEAR; return 0; } else if (!nasm_stricmp(option, "down")) { rc = FLOAT_RC_DOWN; return 0; } else if (!nasm_stricmp(option, "up")) { rc = FLOAT_RC_UP; return 0; } else if (!nasm_stricmp(option, "zero")) { rc = FLOAT_RC_ZERO; return 0; } else if (!nasm_stricmp(option, "default")) { rc = FLOAT_RC_NEAR; daz = false; return 0; } else { return -1; /* Unknown option */ } }