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/* |
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* Copyright (C) 2004-2007 Anders Gavare. All rights reserved. |
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* |
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* Redistribution and use in source and binary forms, with or without |
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* modification, are permitted provided that the following conditions are met: |
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* |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the distribution. |
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* 3. The name of the author may not be used to endorse or promote products |
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* derived from this software without specific prior written permission. |
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* |
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
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* SUCH DAMAGE. |
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* |
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* $Id: float_emul.c,v 1.9 2006/12/30 13:30:52 debug Exp $ |
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* |
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* Floating point emulation routines. |
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*/ |
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|
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#include <stdio.h> |
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#include <stdlib.h> |
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#include <string.h> |
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#include <math.h> |
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|
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#include "float_emul.h" |
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#include "misc.h" |
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|
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|
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/* #define IEEE_DEBUG */ |
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|
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|
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/* |
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* ieee_interpret_float_value(): |
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* |
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* Interprets a float value from binary IEEE format into an ieee_float_value |
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* struct. |
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*/ |
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void ieee_interpret_float_value(uint64_t x, struct ieee_float_value *fvp, |
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int fmt) |
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{ |
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int n_frac = 0, n_exp = 0; |
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int i, nan, sign = 0, exponent; |
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double fraction; |
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|
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memset(fvp, 0, sizeof(struct ieee_float_value)); |
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|
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/* n_frac and n_exp: */ |
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switch (fmt) { |
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case IEEE_FMT_S: n_frac = 23; n_exp = 8; break; |
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case IEEE_FMT_W: n_frac = 31; n_exp = 0; break; |
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case IEEE_FMT_D: n_frac = 52; n_exp = 11; break; |
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case IEEE_FMT_L: n_frac = 63; n_exp = 0; break; |
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default:fatal("ieee_interpret_float_value(): " |
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"unimplemented format %i\n", fmt); |
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} |
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|
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/* exponent: */ |
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exponent = 0; |
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switch (fmt) { |
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case IEEE_FMT_W: |
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x &= 0xffffffffULL; |
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case IEEE_FMT_L: |
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break; |
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case IEEE_FMT_S: |
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x &= 0xffffffffULL; |
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case IEEE_FMT_D: |
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exponent = (x >> n_frac) & ((1 << n_exp) - 1); |
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exponent -= (1 << (n_exp-1)) - 1; |
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break; |
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default:fatal("ieee_interpret_float_value(): unimplemented " |
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"format %i\n", fmt); |
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} |
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|
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/* nan: */ |
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nan = 0; |
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switch (fmt) { |
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case IEEE_FMT_S: |
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if (x == 0x7fffffffULL || x == 0x7fbfffffULL) |
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nan = 1; |
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break; |
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case IEEE_FMT_D: |
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if (x == 0x7fffffffffffffffULL || |
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x == 0x7ff7ffffffffffffULL) |
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nan = 1; |
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break; |
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} |
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|
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if (nan) { |
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fvp->f = 1.0; |
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goto no_reasonable_result; |
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} |
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|
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/* fraction: */ |
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fraction = 0.0; |
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switch (fmt) { |
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case IEEE_FMT_W: |
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{ |
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int32_t r_int = x; |
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fraction = r_int; |
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} |
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break; |
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case IEEE_FMT_L: |
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{ |
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int64_t r_int = x; |
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fraction = r_int; |
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} |
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break; |
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case IEEE_FMT_S: |
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case IEEE_FMT_D: |
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/* sign: */ |
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sign = (x >> 31) & 1; |
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if (fmt == IEEE_FMT_D) |
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sign = (x >> 63) & 1; |
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|
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fraction = 0.0; |
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for (i=0; i<n_frac; i++) { |
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int bit = (x >> i) & 1; |
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fraction /= 2.0; |
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if (bit) |
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fraction += 1.0; |
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} |
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/* Add implicit bit 0: */ |
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fraction = (fraction / 2.0) + 1.0; |
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break; |
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default:fatal("ieee_interpret_float_value(): " |
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"unimplemented format %i\n", fmt); |
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} |
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|
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/* form the value: */ |
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fvp->f = fraction; |
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|
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#ifdef IEEE_DEBUG |
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fatal("{ ieee: x=%016"PRIx64" sign=%i exponent=%i frac=%f ", |
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(uint64_t) x, sign, exponent, fraction); |
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#endif |
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|
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/* TODO: this is awful for exponents of large magnitude. */ |
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if (exponent > 0) { |
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/* |
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* NOTE / TODO: |
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* |
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* This is an ulgy workaround on Alpha, where it seems that |
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* multiplying by 2, 1024 times causes a floating point |
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* exception. (Triggered by running for example NetBSD/pmax |
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* 2.0 emulated on an Alpha host.) |
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*/ |
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if (exponent == 1024) |
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exponent = 1023; |
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|
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while (exponent-- > 0) |
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fvp->f *= 2.0; |
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} else if (exponent < 0) { |
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while (exponent++ < 0) |
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fvp->f /= 2.0; |
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} |
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|
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if (sign) |
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fvp->f = -fvp->f; |
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|
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no_reasonable_result: |
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fvp->nan = nan; |
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|
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#ifdef IEEE_DEBUG |
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fatal("f=%f }\n", fvp->f); |
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#endif |
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} |
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|
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|
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/* |
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* ieee_store_float_value(): |
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* |
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* Generates a 64-bit IEEE-formated value in a specific format. |
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*/ |
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uint64_t ieee_store_float_value(double nf, int fmt, int nan) |
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{ |
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int n_frac = 0, n_exp = 0, signofs=0; |
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int i, exponent; |
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uint64_t r = 0, r2; |
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int64_t r3; |
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|
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/* n_frac and n_exp: */ |
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switch (fmt) { |
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case IEEE_FMT_S: n_frac = 23; n_exp = 8; signofs = 31; break; |
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case IEEE_FMT_W: n_frac = 31; n_exp = 0; signofs = 31; break; |
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case IEEE_FMT_D: n_frac = 52; n_exp = 11; signofs = 63; break; |
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case IEEE_FMT_L: n_frac = 63; n_exp = 0; signofs = 63; break; |
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default:fatal("ieee_store_float_value(): unimplemented format" |
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" %i\n", fmt); |
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} |
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|
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if ((fmt == IEEE_FMT_S || fmt == IEEE_FMT_D) && nan) |
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goto store_nan; |
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|
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/* fraction: */ |
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switch (fmt) { |
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case IEEE_FMT_W: |
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case IEEE_FMT_L: |
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/* |
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* This causes an implicit conversion of double to integer. |
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* If nf < 0.0, then r2 will begin with a sequence of binary |
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* 1's, which is ok. |
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*/ |
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r3 = nf; |
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r2 = r3; |
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r |= r2; |
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|
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if (fmt == IEEE_FMT_W) |
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r &= 0xffffffffULL; |
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break; |
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case IEEE_FMT_S: |
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case IEEE_FMT_D: |
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#ifdef IEEE_DEBUG |
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fatal("{ ieee store f=%f ", nf); |
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#endif |
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/* sign bit: */ |
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if (nf < 0.0) { |
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r |= ((uint64_t)1 << signofs); |
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nf = -nf; |
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} |
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|
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/* |
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* How to convert back from double to exponent + fraction: |
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* The fraction should be 1.xxx, that is |
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* 1.0 <= fraction < 2.0 |
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* |
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* This method is very slow but should work: |
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* (TODO: Fix the performance problem!) |
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*/ |
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exponent = 0; |
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while (nf < 1.0 && exponent > -1023) { |
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nf *= 2.0; |
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exponent --; |
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} |
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while (nf >= 2.0 && exponent < 1023) { |
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nf /= 2.0; |
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exponent ++; |
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} |
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|
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/* Here: 1.0 <= nf < 2.0 */ |
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#ifdef IEEE_DEBUG |
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fatal(" nf=%f", nf); |
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#endif |
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nf -= 1.0; /* remove implicit first bit */ |
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for (i=n_frac-1; i>=0; i--) { |
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nf *= 2.0; |
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if (nf >= 1.0) { |
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r |= ((uint64_t)1 << i); |
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nf -= 1.0; |
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} |
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} |
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|
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/* Insert the exponent into the resulting word: */ |
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/* (First bias, then make sure it's within range) */ |
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exponent += (((uint64_t)1 << (n_exp-1)) - 1); |
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if (exponent < 0) |
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exponent = 0; |
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if (exponent >= ((int64_t)1 << n_exp)) |
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exponent = ((int64_t)1 << n_exp) - 1; |
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r |= (uint64_t)exponent << n_frac; |
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|
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/* Special case for 0.0: */ |
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if (exponent == 0) |
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r = 0; |
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|
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#ifdef IEEE_DEBUG |
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fatal(" exp=%i, r = %016"PRIx64" }\n", exponent, (uint64_t) r); |
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#endif |
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break; |
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default:/* TODO */ |
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fatal("ieee_store_float_value(): unimplemented format %i\n", |
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fmt); |
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} |
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|
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store_nan: |
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if (nan) { |
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if (fmt == IEEE_FMT_S) |
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r = 0x7fffffffULL; |
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else if (fmt == IEEE_FMT_D) |
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r = 0x7fffffffffffffffULL; |
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else |
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r = 0x7fffffffULL; |
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} |
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|
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if (fmt == IEEE_FMT_S || fmt == IEEE_FMT_W) |
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r &= 0xffffffff; |
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|
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return r; |
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} |
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