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Add floating point parsing playground.
This commit is contained in:
Olaf Seibert
parent
e86f0bd4d5
commit
bb56fc33f1
968
tests/float.c
Executable file
968
tests/float.c
Executable file
@ -0,0 +1,968 @@
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# /*
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gcc float.c -o float -lm
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./float
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exit $?
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*/
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/*
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* Parsing PDP-11 floating point literals.
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* Testing ground for different implementations.
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*/
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#include <stdlib.h>
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#include <stdint.h>
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#include <stdio.h>
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#include <string.h>
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#include <ctype.h>
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#include <math.h>
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#include <float.h>
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#include <ieeefp.h>
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#define DEBUG_FLOAT 1
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void
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printflt(unsigned *flt, int size)
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{
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printf("%06o: ", flt[0]);
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printf("sign: %d ", (flt[0] & 0x8000) >> 15);
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printf("uexp: %x ", (flt[0] & 0x7F80) >> 7);
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printf("ufrac: %02x", flt[0] & 0x007F);
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for (int i = 1; i < size; i++) {
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printf(" %04x", flt[i]);
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}
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printf("\n");
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}
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#if DEBUG_FLOAT
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#define DF(...) printf(__VA_ARGS__)
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#else
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#define DF(...)
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#endif
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/*
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* We need 56 bits of mantissa.
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*
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* Try to detect if it is needed, possible and useful to use
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* long double instead of double, when parsing floating point numbers.
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*/
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#if DBL_MANT_DIG >= 56
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/* plain double seems big enough */
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# define USE_LONG_DOUBLE 0
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/* long double exists and seems big enough */
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#elif LDBL_MANT_DIG >= 56
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# define USE_LONG_DOUBLE 1
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#elif defined(LDBL_MANT_DIG)
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/* long double exists but is probably still too small */
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# define USE_LONG_DOUBLE 1
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#else
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/* long double does not exist and plain double is too small */
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# define USE_LONG_DOUBLE 0
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#endif
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#if USE_LONG_DOUBLE
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# define DOUBLE long double
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# define SCANF_FMT "%Lf"
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# define FREXP frexpl
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#else
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# define DOUBLE double
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# define SCANF_FMT "%lf"
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# define FREXP frexp
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#endif
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/* Parse PDP-11 64-bit floating point format. */
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/* Give a pointer to "size" words to receive the result. */
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/* Note: there are probably degenerate cases that store incorrect
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results. For example, I think rounding up a FLT2 might cause
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exponent overflow. Sorry. */
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/* Note also that the full 56 bits of precision probably aren't always
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available on the source platform, given the widespread application
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of IEEE floating point formats, so expect some differences. Sorry
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again. */
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int parse_float(
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char *cp,
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int size,
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unsigned *flt)
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{
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DOUBLE d; /* value */
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DOUBLE frac; /* fractional value */
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uint64_t ufrac; /* fraction converted to 56 bit
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unsigned integer */
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uint64_t onehalf; /* one half of the smallest bit
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(used for rounding) */
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int i; /* Number of fields converted by sscanf */
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int n; /* Number of characters converted by sscanf */
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int sexp; /* Signed exponent */
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unsigned uexp; /* Unsigned excess-128 exponent */
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unsigned sign = 0; /* Sign mask */
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i = sscanf(cp, SCANF_FMT "%n", &d, &n);
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if (i == 0)
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return 0; /* Wasn't able to convert */
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DF("LDBL_MANT_DIG: %d\n", LDBL_MANT_DIG);
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DF("%Lf input: %s\n", d, cp);
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cp += n;
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if (d == 0.0) {
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for (i = 0; i < size; i++) {
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flt[i] = 0; /* All-bits-zero equals zero */
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}
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return 1; /* Good job. */
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}
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frac = FREXP(d, &sexp); /* Separate into exponent and mantissa */
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DF("frac: %Lf %La sexp: %d\n", frac, frac, sexp);
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if (sexp < -127 || sexp > 127)
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return 0; /* Exponent out of range. */
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uexp = sexp + 128; /* Make excess-128 mode */
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uexp &= 0xff; /* express in 8 bits */
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DF("uexp: %02x\n", uexp);
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/*
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* frexp guarantees its fractional return value is
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* abs(frac) >= 0.5 and abs(frac) < 1.0
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* Another way to think of this is that:
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* abs(frac) >= 2**-1 and abs(frac) < 2**0
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*/
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if (frac < 0) {
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sign = (1 << 15); /* Negative sign */
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frac = -frac; /* fix the mantissa */
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}
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/*
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* For the PDP-11 floating point representation the
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* fractional part is 7 bits (for 16-bit floating point
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* literals), 23 bits (for 32-bit floating point values),
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* or 55 bits (for 64-bit floating point values).
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* However the bit immediately above the MSB is always 1
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* because the value is normalized. So it's actually
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* 8 bits, 24 bits, or 56 bits.
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* We effectively multiply the fractional part of our value by
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* 2**56 to fully expose all of those bits (including
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* the MSB which is 1).
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* However as an intermediate step, we really multiply by
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* 2**57, so we get one lsb for possible later rounding
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* purposes. After that, we divide by 2 again.
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*/
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/* The following big literal is 2 to the 57th power: */
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ufrac = (uint64_t) (frac * 144115188075855872.0); /* Align fraction bits */
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DF("ufrac: %016lx\n", ufrac);
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DF("56 : %016lx\n", (1UL<<57) - 2);
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/*
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* ufrac is now >= 2**56 and < 2**57.
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* This means it's normalized: bit [56] is 1
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* and all higher bits are 0.
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*/
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/* Round from 57-bits to 56, 24, or 8.
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* We do this by:
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* + first adding a value equal to one half of the
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* least significant bit (the value 'onehalf')
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* + (possibly) dealing with any carrying that
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* causes the value to no longer be normalized
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* (with bit [56] = 1 and all higher bits = 0)
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* + shifting right by 1 bit (which throws away
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* the 0 bit). Note this step could be rolled
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* into the next step.
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* + taking the remaining highest order 8,
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* 24, or 56 bits.
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*
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* +--+--------+-------+ +--------+--------+
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* |15|14 7|6 0| |15 | 0|
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* +--+--------+-------+ +--------+--------+
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* | S|EEEEEEEE|MMMMMMM| |MMMMMMMM|MMMMMMMM| ...maybe 2 more words...
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* +--+--------+-------+ +--------+--------+
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* Sign (1 bit)
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* Exponent (8 bits)
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* Mantissa (7 bits)
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*/
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onehalf = 1ULL << (16 * (4-size));
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ufrac += onehalf;
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DF("onehalf=%016lx, ufrac+onehalf: %016lx\n", onehalf, ufrac);
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/* Did it roll up to a value 2**56? */
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if ((ufrac >> 57) > 0) { /* Overflow? */
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if (uexp < 0xFF) {
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ufrac >>= 1; /* Normalize */
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uexp++;
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DF("ufrac: %016lx uexp: %02x (normalized)\n", ufrac, uexp);
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} else {
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/*
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* If rounding and then normalisation would cause the exponent to
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* overflow, just don't round: the cure is worse than the disease.
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* We could detect ahead of time but the conditions for all size
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* values may be a bit complicated, and so rare, that it is more
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* readable to just undo it here.
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*/
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ufrac -= onehalf;
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DF("don't round: exponent overflow\n");
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}
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}
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ufrac >>= 1; /* Go from 57 bits to 56 */
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flt[0] = (unsigned) (sign | (uexp << 7) | ((ufrac >> 48) & 0x7F));
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if (size > 1) {
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flt[1] = (unsigned) ((ufrac >> 32) & 0xffff);
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if (size > 2) {
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flt[2] = (unsigned) ((ufrac >> 16) & 0xffff);
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flt[3] = (unsigned) ((ufrac >> 0) & 0xffff);
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}
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}
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return 1;
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}
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/*
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* Several of these functions assume that "unsigned" contains more
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* than 16 bits. Bit 16 is sometimes used to store a carry.
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*/
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#define DUMP DF("exp: %d. %d %04x %04x %04x %04x\n", \
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float_dec_exponent, float_bin_exponent, \
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float_buf[0], float_buf[1], float_buf[2], float_buf[3])
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#define DUMP4(b, t) DF("%04x %04x %04x %04x%s", \
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b[0], b[1], b[2], b[3], t)
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void float_copy( /* XMIT4 at FLTGSV, more or less */
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unsigned *to,
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unsigned *from)
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{
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to[0] = from[0] & 0xFFFF;
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to[1] = from[1] & 0xFFFF;
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to[2] = from[2] & 0xFFFF;
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to[3] = from[3] & 0xFFFF;
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}
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int float_right_shift( /* FLTGRS */
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unsigned *buf)
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{
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int carry1, carry2;
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carry1 = buf[0] & 0x0001; buf[0] >>= 1;
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carry2 = buf[1] & 0x0001; buf[1] >>= 1; buf[1] |= (carry1 << 15);
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carry1 = buf[2] & 0x0001; buf[2] >>= 1; buf[2] |= (carry2 << 15);
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carry2 = buf[3] & 0x0001; buf[3] >>= 1; buf[3] |= (carry1 << 15);
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return carry2;
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}
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int float_left_shift( /* FLTGLS */
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unsigned *buf)
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{
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int carry1, carry2;
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carry1 = buf[3] >> 15; buf[3] <<= 1;
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carry2 = buf[2] >> 15; buf[2] <<= 1; buf[2] |= (carry1 & 0x0001);
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carry1 = buf[1] >> 15; buf[1] <<= 1; buf[1] |= (carry2 & 0x0001);
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carry2 = buf[0] >> 15; buf[0] <<= 1; buf[0] |= (carry1 & 0x0001);
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float_copy(buf, buf); /* Clean up carries */
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return carry2 & 0x01;
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}
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void float_add( /* FLTGAD */
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unsigned *to,
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unsigned *from)
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{
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//DF("float_add: "); DUMP4(to, ""); DF(" += "); DUMP4(from, "\n");
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to[3] += from[3];
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to[2] += from[2] + ((to[3] >> 16) & 0x0001);
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to[1] += from[1] + ((to[2] >> 16) & 0x0001);
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to[0] += from[0] + ((to[1] >> 16) & 0x0001);
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//DF(" = "); DUMP4(to, "\n");
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float_copy(to, to); /* Clean up carries */
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}
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void float_mult_by_5( /* FLTM50 */
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unsigned *buf,
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unsigned *workspace)
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{
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float_copy(workspace, buf); /* Save 1 x original value */
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float_left_shift(buf); /* 2 x */
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float_left_shift(buf); /* 4 x */
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float_add(buf, workspace); /* 5 x */
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}
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void float_mult_by_5_4th( /* FLTM54 */
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int *bin_exp,
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unsigned *buf,
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unsigned *workspace)
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{
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if (buf[0] >= 0146314) {
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float_right_shift(buf);
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++*bin_exp;
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}
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float_copy(workspace, buf);
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float_right_shift(buf); /* half of the original */
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float_right_shift(buf); /* a quarter */
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float_add(buf, workspace); /* add the original to the quarter */
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}
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int parse_float_m2(
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char *cp,
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int size,
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unsigned *flt)
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{
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int float_sign = 0;
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int float_dot = 0;
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int float_dec_exponent = 0;
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int float_bin_exponent = 0;
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unsigned float_buf[4] = { 0 };
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unsigned float_save[4];
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float_bin_exponent = 65;
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if (*cp == '+') {
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cp++;
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} else if (*cp == '-') {
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float_sign = 0100000;
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cp++;
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}
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DF("float_sign: %d\n", float_sign);
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for (;;) {
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if (isdigit(*cp)) {
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/* Can we multiply by 10? */
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DF("digit: %c\n", *cp);
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if (float_buf[0] & 0174000) {
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/* No, that would overflow */
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float_dec_exponent++; /* no, compensate for the snub */
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/*
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* Explanation of the above comment:
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* - after the decimal separator, we should ignore extra digits
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* completely. Since float_dot == -1, the exponent will be
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* decremented below, and compensate for that here.
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* - before the decimal separator, we don't add the digit
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* (which would overflow) so we lose some lesser significant
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* bits. float_dot == 0 in this case, and we do want the
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* exponent increased to compensate for the ignored digit.
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* So in both cases the right thing happens.
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*/
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} else {
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/* Multiply by 10 */
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float_mult_by_5(float_buf, float_save);
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float_left_shift(float_buf);
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/* Add digit */
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float_buf[3] += *cp - '0';
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/* Ripple carry */
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float_buf[2] += (float_buf[3] >> 16) & 0x0001;
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float_buf[1] += (float_buf[2] >> 16) & 0x0001;
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float_buf[0] += (float_buf[1] >> 16) & 0x0001;
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float_copy(float_buf, float_buf); /* Clean up carries */
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}
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float_dec_exponent += float_dot;
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DUMP;
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cp++;
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} else if (*cp == '.') {
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DF("dot: %c\n", *cp);
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if (float_dot < 0) {
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// error...
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printf("Error: repeated decimal separator\n");
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return 0;
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}
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float_dot = -1;
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||||||
|
cp++;
|
||||||
|
} else {
|
||||||
|
DF("Other char: %c\n", *cp);
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if (toupper(*cp) == 'E') {
|
||||||
|
cp++;
|
||||||
|
int exp = strtol(cp, &cp, 10);
|
||||||
|
|
||||||
|
float_dec_exponent += exp;
|
||||||
|
DF("E%d -> dec_exp %d\n", exp, float_dec_exponent);
|
||||||
|
}
|
||||||
|
|
||||||
|
/* FLTG3 */
|
||||||
|
if (float_buf[0] | float_buf[1] | float_buf[2] | float_buf[3]) {
|
||||||
|
/* Non-zero */
|
||||||
|
DF("Non-zero: decimal exponent: %d\n", float_dec_exponent);
|
||||||
|
while (float_dec_exponent > 0) { /* 31$ */
|
||||||
|
DUMP;
|
||||||
|
if (float_buf[0] <= 031426) { /* 13078, 0x3316, 65390 / 5 */
|
||||||
|
/* Multiply by 5 and 2 */
|
||||||
|
DF("Multiply by 5 and 2\n");
|
||||||
|
float_mult_by_5(float_buf, float_save);
|
||||||
|
float_bin_exponent++;
|
||||||
|
DUMP;
|
||||||
|
} else {
|
||||||
|
/* Multiply by 5/4 and 8 32$ */
|
||||||
|
DF("Multiply by 5/4 and 8\n");
|
||||||
|
float_mult_by_5_4th(&float_bin_exponent, float_buf, float_save);
|
||||||
|
float_bin_exponent += 3;
|
||||||
|
DUMP;
|
||||||
|
}
|
||||||
|
float_dec_exponent--;
|
||||||
|
}
|
||||||
|
|
||||||
|
while (float_dec_exponent < 0) { /* 41$ ish */
|
||||||
|
DUMP;
|
||||||
|
DF("Prepare for division by left-shifting the bits\n");
|
||||||
|
/* Prepare for division by left-shifting the bits */
|
||||||
|
while ((float_buf[0] & 0x8000) == 0) { /* 41$ */
|
||||||
|
float_bin_exponent--; /* 40$ */
|
||||||
|
float_left_shift(float_buf);
|
||||||
|
DUMP;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Divide by 2 */
|
||||||
|
float_right_shift(float_buf);
|
||||||
|
|
||||||
|
float_copy(float_save, float_buf);
|
||||||
|
DUMP;
|
||||||
|
DF("float_save: "); DUMP4(float_save, "\n");
|
||||||
|
|
||||||
|
/* Divide by 5:
|
||||||
|
* multiplying by (2**32 - 1) / 5 = 0x333333333
|
||||||
|
* while dropping the 32 least significant bits.
|
||||||
|
* This is nearly exact but exact enough?
|
||||||
|
* 2**32 - 1 is a multiple of 5.
|
||||||
|
*/
|
||||||
|
for (int i = 16 * 2; i > 0; i--) {
|
||||||
|
if ((i & 1) == 0) { /* 42$ */
|
||||||
|
float_right_shift(float_buf);
|
||||||
|
float_right_shift(float_buf);
|
||||||
|
}
|
||||||
|
float_right_shift(float_buf); /* 43$ */
|
||||||
|
float_add(float_buf, float_save);
|
||||||
|
DF("Loop i=%2d: ", i); DUMP;
|
||||||
|
}
|
||||||
|
|
||||||
|
float_bin_exponent -= 3;
|
||||||
|
float_dec_exponent++;
|
||||||
|
DUMP;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Normalize the mantissa: shift a single 1 out to the left */
|
||||||
|
DF("Normalize the mantissa: shift a single 1 out to the left\n");
|
||||||
|
int carry;
|
||||||
|
do {
|
||||||
|
/* FLTG5 */
|
||||||
|
float_bin_exponent--;
|
||||||
|
carry = float_left_shift(float_buf);
|
||||||
|
DUMP;
|
||||||
|
} while (carry == 0);
|
||||||
|
|
||||||
|
/* Set excess 128. */
|
||||||
|
DF("Set excess 128.\n");
|
||||||
|
float_bin_exponent += 0200;
|
||||||
|
DUMP;
|
||||||
|
|
||||||
|
if (float_bin_exponent & 0xFF00) {
|
||||||
|
/* Error N. Underflow. 2$ */
|
||||||
|
printf("Error N (underflow)\n");
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Shift right 9 positions to make room for sign and exponent 3$ */
|
||||||
|
DF("Shift right 9 positions to make room for sign and exponent\n");
|
||||||
|
int round = (float_buf[3] >> 8) & 0x0001;
|
||||||
|
float_buf[3] >>= 9; float_buf[3] |= (float_buf[2] << (16-9)) & 0xff80;
|
||||||
|
float_buf[2] >>= 9; float_buf[2] |= (float_buf[1] << (16-9)) & 0xff80;
|
||||||
|
float_buf[1] >>= 9; float_buf[1] |= (float_buf[0] << (16-9)) & 0xff80;
|
||||||
|
float_buf[0] >>= 9;
|
||||||
|
float_buf[0] |= float_bin_exponent << 7;
|
||||||
|
DUMP;
|
||||||
|
/*
|
||||||
|
* float_bin_exponent is included because of the location of
|
||||||
|
* FLTBEX ;BINARY EXPONENT (MUST PRECEED FLTBUF)
|
||||||
|
*/
|
||||||
|
|
||||||
|
/* Round (this is optional, really) */
|
||||||
|
if (1) {
|
||||||
|
if (size < 4) {
|
||||||
|
round = float_buf[size] & 0x8000;
|
||||||
|
}
|
||||||
|
/* The rounding bit is the lesser significant bit that's just
|
||||||
|
* outside the returned result. If we round, we add it to the
|
||||||
|
* returned value.
|
||||||
|
*
|
||||||
|
* If there is a carry-out of the mantissa, it gets added to
|
||||||
|
* the exponent (increasing it by 1).
|
||||||
|
*
|
||||||
|
* If that also overflows, we truely have overflow.
|
||||||
|
*/
|
||||||
|
|
||||||
|
if (round) {
|
||||||
|
for (int i = size - 1 ; round && i >= 0; i--) {
|
||||||
|
float_buf[i]++; /* 5$ */
|
||||||
|
round = float_buf[i] & 0x10000; /* carry */
|
||||||
|
DF("round, i=%d: ", i); DUMP;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
DF("After rounding\n");
|
||||||
|
DUMP;
|
||||||
|
}
|
||||||
|
|
||||||
|
if (float_buf[0] & 0x8000) {
|
||||||
|
// 6$ error T: exponent overflow
|
||||||
|
printf("Error T\n");
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* 7$ */
|
||||||
|
float_buf[0] |= float_sign;
|
||||||
|
DF("Put in float_sign: "); DUMP;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Now put together the result from the parts */
|
||||||
|
flt[0] = float_buf[0] & 0xFFFF;
|
||||||
|
if (size > 1) {
|
||||||
|
flt[1] = float_buf[1] & 0xFFFF;
|
||||||
|
if (size > 2) {
|
||||||
|
flt[2] = float_buf[2] & 0xFFFF;
|
||||||
|
flt[3] = float_buf[3] & 0xFFFF;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
static void
|
||||||
|
mult64to128(uint64_t op1, uint64_t op2, uint64_t *hi, uint64_t *lo)
|
||||||
|
{
|
||||||
|
#if defined(__SIZEOF_INT128__) && __SIZEOF_INT128__ >= 16
|
||||||
|
__uint128_t result = (__uint128_t)op1 * op2;
|
||||||
|
*lo = result;
|
||||||
|
*hi = result >> 64;
|
||||||
|
#else
|
||||||
|
uint64_t u1 = (op1 & 0xffffffff);
|
||||||
|
uint64_t v1 = (op2 & 0xffffffff);
|
||||||
|
uint64_t t = (u1 * v1);
|
||||||
|
uint64_t w3 = (t & 0xffffffff);
|
||||||
|
uint64_t k = (t >> 32);
|
||||||
|
|
||||||
|
op1 >>= 32;
|
||||||
|
t = (op1 * v1) + k;
|
||||||
|
k = (t & 0xffffffff);
|
||||||
|
uint64_t w1 = (t >> 32);
|
||||||
|
|
||||||
|
op2 >>= 32;
|
||||||
|
t = (u1 * op2) + k;
|
||||||
|
k = (t >> 32);
|
||||||
|
|
||||||
|
*hi = (op1 * op2) + w1 + k;
|
||||||
|
*lo = (t << 32) + w3;
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
#define DUMP3 DF("exp: %d. %d %016llx\n", \
|
||||||
|
float_dec_exponent, float_bin_exponent, float_buf)
|
||||||
|
|
||||||
|
int parse_float_m3(
|
||||||
|
char *cp,
|
||||||
|
int size,
|
||||||
|
unsigned *flt)
|
||||||
|
{
|
||||||
|
int float_sign = 0;
|
||||||
|
int float_dot = 0;
|
||||||
|
int float_dec_exponent = 0;
|
||||||
|
int float_bin_exponent = 0;
|
||||||
|
uint64_t float_buf = 0;
|
||||||
|
|
||||||
|
float_bin_exponent = 65;
|
||||||
|
|
||||||
|
if (*cp == '+') {
|
||||||
|
cp++;
|
||||||
|
} else if (*cp == '-') {
|
||||||
|
float_sign = 1;
|
||||||
|
cp++;
|
||||||
|
}
|
||||||
|
DF("float_sign: %d\n", float_sign);
|
||||||
|
|
||||||
|
for (;;) {
|
||||||
|
if (isdigit(*cp)) {
|
||||||
|
/* Can we multiply by 10? */
|
||||||
|
DF("digit: %c\n", *cp);
|
||||||
|
if (float_buf & 0xF800000000000000ULL) { /* [0] & 0174000, 0xF800 */
|
||||||
|
/* No, that would overflow */
|
||||||
|
float_dec_exponent++; /* no, compensate for the snub */
|
||||||
|
/*
|
||||||
|
* Explanation of the above comment:
|
||||||
|
* - after the decimal separator, we should ignore extra digits
|
||||||
|
* completely. Since float_dot == -1, the exponent will be
|
||||||
|
* decremented below, and compensate for that here.
|
||||||
|
* - before the decimal separator, we don't add the digit
|
||||||
|
* (which would overflow) so we lose some lesser significant
|
||||||
|
* bits. float_dot == 0 in this case, and we do want the
|
||||||
|
* exponent increased to compensate for the ignored digit.
|
||||||
|
* So in both cases the right thing happens.
|
||||||
|
*/
|
||||||
|
} else {
|
||||||
|
/* Multiply by 10 */
|
||||||
|
float_buf *= 10;
|
||||||
|
/* Add digit */
|
||||||
|
float_buf += *cp - '0';
|
||||||
|
}
|
||||||
|
float_dec_exponent -= float_dot;
|
||||||
|
DUMP3;
|
||||||
|
cp++;
|
||||||
|
} else if (*cp == '.') {
|
||||||
|
DF("dot: %c\n", *cp);
|
||||||
|
if (float_dot) {
|
||||||
|
// error...
|
||||||
|
printf("Error: repeated decimal separator\n");
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
float_dot = 1;
|
||||||
|
cp++;
|
||||||
|
} else {
|
||||||
|
DF("Other char: %c\n", *cp);
|
||||||
|
break;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
if (toupper(*cp) == 'E') {
|
||||||
|
cp++;
|
||||||
|
int exp = strtol(cp, &cp, 10);
|
||||||
|
|
||||||
|
float_dec_exponent += exp;
|
||||||
|
DF("E%d -> dec_exp %d\n", exp, float_dec_exponent);
|
||||||
|
}
|
||||||
|
|
||||||
|
/* FLTG3 */
|
||||||
|
if (float_buf) {
|
||||||
|
/* Non-zero */
|
||||||
|
DF("Non-zero: decimal exponent: %d\n", float_dec_exponent);
|
||||||
|
while (float_dec_exponent > 0) { /* 31$ */
|
||||||
|
DUMP3;
|
||||||
|
if (float_buf <= 0x3316000000000000ULL) { /* 031426, 13078, 0x3316, 65390 / 5 */
|
||||||
|
/* Multiply by 5 and 2 */
|
||||||
|
DF("Multiply by 5 and 2\n");
|
||||||
|
float_buf *= 5;
|
||||||
|
float_bin_exponent++;
|
||||||
|
DUMP3;
|
||||||
|
} else {
|
||||||
|
/* Multiply by 5/4 and 8 32$ */
|
||||||
|
DF("Multiply by 5/4 and 8\n");
|
||||||
|
if (float_buf >= 0xCCCC000000000000ULL) {
|
||||||
|
float_buf >>= 1;
|
||||||
|
float_bin_exponent++;
|
||||||
|
}
|
||||||
|
float_buf += (float_buf >> 2);
|
||||||
|
float_bin_exponent += 3;
|
||||||
|
DUMP3;
|
||||||
|
}
|
||||||
|
float_dec_exponent--;
|
||||||
|
}
|
||||||
|
|
||||||
|
while (float_dec_exponent < 0) { /* 41$ ish */
|
||||||
|
DUMP3;
|
||||||
|
DF("Prepare for division by left-shifting the bits\n");
|
||||||
|
/* Prepare for division by left-shifting the bits */
|
||||||
|
while (((float_buf >> 63) & 1) == 0) { /* 41$ */
|
||||||
|
float_bin_exponent--; /* 40$ */
|
||||||
|
float_buf <<= 1;
|
||||||
|
DUMP3;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Divide by 2 */
|
||||||
|
float_buf >>= 1;
|
||||||
|
|
||||||
|
uint64_t float_save = float_buf;
|
||||||
|
DUMP3;
|
||||||
|
DF("float_save: %016llx\n", float_save);
|
||||||
|
|
||||||
|
/* Divide by 5:
|
||||||
|
* multiplying by (2**66 - 4) / 5 = 0xCCCCCCCCCCCCCCCC
|
||||||
|
* while dropping the 64 least significant bits.
|
||||||
|
* This is nearly exact but exact enough?
|
||||||
|
* Somehow there is another doubling in here, so the
|
||||||
|
* final result = start * 8 / 5.
|
||||||
|
*/
|
||||||
|
for (int i = 16 * 2; i > 0; i--) {
|
||||||
|
if ((i & 1) == 0) { /* 42$ */
|
||||||
|
float_buf >>= 2;
|
||||||
|
}
|
||||||
|
float_buf >>= 1; /* 43$ */
|
||||||
|
float_buf += float_save;
|
||||||
|
DF("Loop i=%2d: ", i); DUMP3;
|
||||||
|
}
|
||||||
|
#if 1
|
||||||
|
{ /* Method 3 */
|
||||||
|
uint64_t hi, lo;
|
||||||
|
mult64to128(float_save, 0x9999999999999999ULL, &hi, &lo);
|
||||||
|
/*
|
||||||
|
* Really multiply with the 65-bit number
|
||||||
|
* 0x19999999999999999
|
||||||
|
* 1 1001 1001 1001 ...
|
||||||
|
* which is 8 * 0011 0011 0011 ... aka 0x333...
|
||||||
|
* which is (2**64 - 1) / 5.
|
||||||
|
*/
|
||||||
|
uint64_t result = hi + float_save;
|
||||||
|
if (result == float_buf) {
|
||||||
|
printf("Same 333 loop and *9999: %016llx vs %016llx\n", float_buf, result);
|
||||||
|
printf(" was : %016llx\n", float_save);
|
||||||
|
} else {
|
||||||
|
printf("Difference between 333 loop and *3333: %016llx vs %016llx\n", float_buf, result);
|
||||||
|
printf(" : %016llx %016llx\n", hi, lo);
|
||||||
|
printf(" was : %016llx\n", float_save);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
#if 1 /* Try other methods to calculate the same thing more directly */
|
||||||
|
{
|
||||||
|
uint64_t result = float_save / 5 * 8;
|
||||||
|
/* Try to fill in some of the lesser significant bits */
|
||||||
|
int round = float_save % 5;
|
||||||
|
if (round) {
|
||||||
|
result += round * 8 / 5;
|
||||||
|
} else {
|
||||||
|
//result--;
|
||||||
|
}
|
||||||
|
# if 0
|
||||||
|
if (result == float_buf) {
|
||||||
|
printf("Same 333 loop and /5 *8: %016llx vs %016llx\n", float_buf, result);
|
||||||
|
} else {
|
||||||
|
printf("Difference between 333 loop and /5 *8: %016llx vs %016llx\n", float_buf, result);
|
||||||
|
printf(" was : %016llx %d %d\n", float_buf, float_save % 20, (float_save % 20) * 2 / 5);
|
||||||
|
}
|
||||||
|
# endif
|
||||||
|
float_buf = result;
|
||||||
|
printf("after / 5 * 8: ");
|
||||||
|
DUMP3;
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
#if 0
|
||||||
|
{
|
||||||
|
__uint128_t big = (__uint128_t)float_save << 3;
|
||||||
|
|
||||||
|
uint64_t result = big / 5;
|
||||||
|
|
||||||
|
if (float_save % 5 == 0)
|
||||||
|
result--;
|
||||||
|
|
||||||
|
if (result == float_buf) {
|
||||||
|
printf("Same 333 loop and *8 /5: %016llx vs %016llx\n", float_buf, result);
|
||||||
|
} else {
|
||||||
|
printf("Difference between 333 loop and *8 /5: %016llx vs %016llx\n", float_buf, result);
|
||||||
|
}
|
||||||
|
|
||||||
|
/*
|
||||||
|
* Rounding is slightly different, in particular for start
|
||||||
|
* values that are multiples of 5 but some other cases too.
|
||||||
|
*/
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
|
||||||
|
/* It's not simply dividing by 5, it also multiplies by 8,
|
||||||
|
* so we need to adjust the exponent here. */
|
||||||
|
float_bin_exponent -= 3;
|
||||||
|
float_dec_exponent++;
|
||||||
|
DUMP3;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Normalize the mantissa: shift a single 1 out to the left */
|
||||||
|
DF("Normalize the mantissa: shift a single 1 out to the left\n");
|
||||||
|
int carry;
|
||||||
|
do {
|
||||||
|
/* FLTG5 */
|
||||||
|
float_bin_exponent--;
|
||||||
|
carry = (float_buf >> 63) & 1;
|
||||||
|
float_buf <<= 1;
|
||||||
|
DUMP3;
|
||||||
|
} while (carry == 0);
|
||||||
|
|
||||||
|
/* Set excess 128. */
|
||||||
|
DF("Set excess 128.\n");
|
||||||
|
float_bin_exponent += 0200;
|
||||||
|
DUMP3;
|
||||||
|
|
||||||
|
if (float_bin_exponent & 0xFF00) {
|
||||||
|
/* Error N. Underflow. 2$ */
|
||||||
|
printf("Error N (underflow)\n");
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Shift right 9 positions to make room for sign and exponent 3$ */
|
||||||
|
DF("Shift right 9 positions to make room for sign and exponent\n");
|
||||||
|
int round = (float_buf >> 8) & 0x0001;
|
||||||
|
float_buf >>= 9;
|
||||||
|
float_buf |= (uint64_t)float_bin_exponent << (64-9);
|
||||||
|
DUMP3;
|
||||||
|
|
||||||
|
/*
|
||||||
|
* This rounding step seems always needed to make the result the same
|
||||||
|
* as the implementation with long doubles.
|
||||||
|
* This may be because of the slight imprecision of the divisions by 10?
|
||||||
|
* However there is something to be said for the argument that when you
|
||||||
|
* want a 1 or 2 word result, rounding twice is wrong.
|
||||||
|
* The reference implementation omits this rounding for size != 4.
|
||||||
|
*/
|
||||||
|
float_buf += round;
|
||||||
|
DF("round: size = 4, round = %d\n", round);
|
||||||
|
|
||||||
|
/* Round (there is a truncation option to omit this step) */
|
||||||
|
if (1) {
|
||||||
|
if (size < 4) {
|
||||||
|
/* 1 << 31 or 1 << 47 */
|
||||||
|
uint64_t onehalf = 1ULL << ((16 * (4-size)) - 1);
|
||||||
|
DUMP3;
|
||||||
|
DF("round: size = %d, onehalf = %016llx\n", size, onehalf);
|
||||||
|
float_buf += onehalf;
|
||||||
|
DUMP3;
|
||||||
|
|
||||||
|
/* The rounding bit is the lesser significant bit that's just
|
||||||
|
* outside the returned result. If we round, we add it to the
|
||||||
|
* returned value.
|
||||||
|
*
|
||||||
|
* If there is a carry-out of the mantissa, it gets added to
|
||||||
|
* the exponent (increasing it by 1).
|
||||||
|
*
|
||||||
|
* If that also overflows, we truely have overflow.
|
||||||
|
*/
|
||||||
|
}
|
||||||
|
|
||||||
|
DF("After rounding\n");
|
||||||
|
DUMP3;
|
||||||
|
}
|
||||||
|
|
||||||
|
if (float_buf & 0x8000000000000000ULL) {
|
||||||
|
// 6$ error T: exponent overflow
|
||||||
|
printf("Error T: exponent overflow\n");
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* 7$ */
|
||||||
|
float_buf |= (uint64_t)float_sign << 63;
|
||||||
|
DF("Put in float_sign: "); DUMP3;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* Now put together the result from the parts */
|
||||||
|
flt[0] = (float_buf >> 48) & 0xFFFF;
|
||||||
|
if (size > 1) {
|
||||||
|
flt[1] = (float_buf >> 32) & 0xFFFF;
|
||||||
|
if (size > 2) {
|
||||||
|
flt[2] = (float_buf >> 16) & 0xFFFF;
|
||||||
|
flt[3] = (float_buf >> 0) & 0xFFFF;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
return 1;
|
||||||
|
}
|
||||||
|
|
||||||
|
void
|
||||||
|
test_one(char *input, unsigned expected0, unsigned expected1, unsigned expected2, unsigned expected3)
|
||||||
|
{
|
||||||
|
unsigned result[4];
|
||||||
|
unsigned result2[4];
|
||||||
|
|
||||||
|
printf("------------------------\n");
|
||||||
|
parse_float_m3(input, 4, result);
|
||||||
|
|
||||||
|
if (result[0] != expected0 ||
|
||||||
|
result[1] != expected1 ||
|
||||||
|
result[2] != expected2 ||
|
||||||
|
result[3] != expected3) {
|
||||||
|
printf("Unexpected result: %04x %04x %04x %04x from %s\n", result[0], result[1], result[2], result[3], input);
|
||||||
|
printf(" expected : %04x %04x %04x %04x\n", expected0, expected1, expected2, expected3);
|
||||||
|
printflt(result, 4);
|
||||||
|
}
|
||||||
|
|
||||||
|
#if 0
|
||||||
|
parse_float_m2(input, 4, result2);
|
||||||
|
if (result2[0] != expected0 ||
|
||||||
|
result2[1] != expected1 ||
|
||||||
|
result2[2] != expected2 ||
|
||||||
|
result2[3] != expected3) {
|
||||||
|
printf("Unexpected result2: %04x %04x %04x %04x from %s\n", result2[0], result2[1], result2[2], result2[3], input);
|
||||||
|
printf(" expected : %04x %04x %04x %04x\n", expected0, expected1, expected2, expected3);
|
||||||
|
printflt(result2, 4);
|
||||||
|
}
|
||||||
|
#endif
|
||||||
|
}
|
||||||
|
|
||||||
|
int
|
||||||
|
main(int argc, char **argv)
|
||||||
|
{
|
||||||
|
/* Should print 64 */
|
||||||
|
DF("LDBL_MANT_DIG: %d\n", LDBL_MANT_DIG);
|
||||||
|
|
||||||
|
test_one("100E-2", 040200, 0000000, 0000000, 0000000);
|
||||||
|
#if 1
|
||||||
|
test_one("10000000000E-10", 040200, 0000000, 0000000, 0000000);
|
||||||
|
test_one("1.0", 040200, 0000000, 0000000, 0000000);
|
||||||
|
test_one("0.1", 037314, 0146314, 0146314, 0146315);
|
||||||
|
test_one("1.0E5", 0044303, 0050000, 0000000, 0000000);
|
||||||
|
test_one("1.0E10", 0050425, 0001371, 0000000, 0000000);
|
||||||
|
test_one("1.0E20", 0060655, 0074353, 0142654, 0061000);
|
||||||
|
test_one("1.0E30", 0071111, 0171311, 0146404, 0063517);
|
||||||
|
test_one("1.0E38", 0077626, 0073231, 0050265, 0006611);
|
||||||
|
test_one("1.701411834604692307e+38", 077777, 0177777, 0177777, 0177777);
|
||||||
|
#endif
|
||||||
|
test_one("0.994140625", 0040176, 0100000, 000000, 000000);
|
||||||
|
// 407e 8000 0000 0000
|
||||||
|
#if 1
|
||||||
|
test_one("0.998046875", 0040177, 0100000, 000000, 000000);
|
||||||
|
test_one("1.00390625", 0040200, 0100000, 000000, 000000);
|
||||||
|
test_one("1.01171875", 0040201, 0100000, 000000, 000000);
|
||||||
|
test_one("0.999999910593032836914062", 0040177, 0177776, 0100000, 0000000);
|
||||||
|
test_one("0.999999970197677612304687", 0040177, 0177777, 0100000, 0000000);
|
||||||
|
test_one("1.00000005960464477539062", 0040200, 0000000, 0100000, 0000000);
|
||||||
|
test_one("1.000000178813934326171875", 0040200, 0000001, 0100000, 0000000);
|
||||||
|
test_one("1.0000000000000000138777878078144567552953958511353", 0040200, 0000000, 0000000, 0000000);
|
||||||
|
test_one("1.0000000000000000416333634234433702658861875534058", 0040200, 0000000, 0000000, 0000001);
|
||||||
|
test_one("0.99999999999999997918331828827831486705690622329712", 0040177, 0177777, 0177777, 0177776);
|
||||||
|
test_one("0.99999999999999999306110609609277162235230207443237", 0040177, 0177777, 0177777, 0177777);
|
||||||
|
//test_one("", 0, 0, 0, 0);
|
||||||
|
test_one("6.66666", 040725, 052507, 055061, 0122276);
|
||||||
|
test_one("170141183460469230846243588177825628160", 0100000, 0000000, 0000000, 0000000); // T error
|
||||||
|
test_one("170141183460469230564930741053754966016", 0077777, 0177777, 0177777, 0177777);
|
||||||
|
//test_one("3.1415926535897932384626433", 0, 0, 0, 0);
|
||||||
|
//test_one("", 0, 0, 0, 0);
|
||||||
|
//
|
||||||
|
/* First a number that should just fit in a 56 bit mantissa. */
|
||||||
|
/* 1 << 56 */
|
||||||
|
test_one("72057594037927936", 056200, 000000, 000000, 000000);
|
||||||
|
/* A bit more requires more precision, so they are rounded. */
|
||||||
|
test_one("72057594037927937", 056200, 000000, 000000, 000001);
|
||||||
|
test_one("72057594037927938", 056200, 000000, 000000, 000001);
|
||||||
|
|
||||||
|
/* Lower numbers should all be represented exactly */
|
||||||
|
test_one("72057594037927935", 056177, 0177777, 0177777, 0177777);
|
||||||
|
test_one("72057594037927934", 056177, 0177777, 0177777, 0177776);
|
||||||
|
test_one("72057594037927933", 056177, 0177777, 0177777, 0177775);
|
||||||
|
|
||||||
|
/* 1 << 57 should also be exactly representable */
|
||||||
|
test_one("144115188075855872", 056400, 000000, 000000, 000000);
|
||||||
|
|
||||||
|
/* 1 less lacks one significant bit so will be rounded up */
|
||||||
|
test_one("144115188075855871", 056400, 000000, 000000, 000000);
|
||||||
|
|
||||||
|
/* Same for 1 more, rounded down */
|
||||||
|
test_one("144115188075855873", 056400, 000000, 000000, 000000);
|
||||||
|
|
||||||
|
/* but 2 more should show up in the lsb */
|
||||||
|
/* This one seems most clearly problematic */
|
||||||
|
test_one("144115188075855874", 056400, 000000, 000000, 000001);
|
||||||
|
|
||||||
|
// Some numbers around some of the magic numbers in the parser
|
||||||
|
test_one("3681129745421959167", 0057514, 0054000, 0, 0);
|
||||||
|
test_one("3681129745421959168", 0057514, 0054000, 0, 0); // 0x3316000000000000
|
||||||
|
test_one("3681129745421959169", 0057514, 0054000, 0, 0);
|
||||||
|
test_one("3681129745421959170", 0057514, 0054000, 0, 0);
|
||||||
|
|
||||||
|
test_one("14757170078986272767", 0060114, 0146000, 0000000, 0000000);
|
||||||
|
test_one("14757170078986272768", 0060114, 0146000, 0000000, 0000000); // 0xCCCC000000000000
|
||||||
|
test_one("14757170078986272769", 0060114, 0146000, 0000000, 0000000);
|
||||||
|
test_one("14757170078986272780", 0060114, 0146000, 0000000, 0000000);
|
||||||
|
|
||||||
|
#endif
|
||||||
|
|
||||||
|
return 0;
|
||||||
|
}
|
||||||
Loading…
x
Reference in New Issue
Block a user