--- /dev/null
+//
+// Floating point to IEEE-754 conversion routines
+//
+// by James Hammons
+// (C) 2018 Underground Software
+//
+// Since there are no guarantees vis-a-vis floating point numbers in C, we have
+// to utilize routines like the following in order to guarantee that the thing
+// we get out of the C compiler is an honest-to-God IEEE-754 style floating
+// point number (since that's what the Motorola processors that we target
+// expect).
+//
+
+#include "fltpoint.h"
+#include <float.h>
+#include <math.h>
+
+//
+// Check for IEEE-754 conformance (C99 compilers should be OK here)
+//
+// The reason we do this is mainly to ensure consistency across all platforms,
+// even those that still haven't implemented C99 compliance after other
+// compilers have had them for decades. The long and the short of it is, there
+// are no guarantees for floating point implementations across platforms the
+// way there is for ints (in <stdint.h>, for example) and so we have to be
+// careful that bad assumptions vis-a-vis floating point numbers don't creep
+// into the codebase and cause problems similar to the ones we had when adding
+// proper 64-bit support. Hence, the following ugliness...
+//
+// IEEE-745 expects the following for floats and doubles:
+// float: exponent is 8 bits, mantissa is 24 bits
+// double: exponent is 11 bits, mantissa is 53 bits
+// FLT_RADIX should be 2
+#ifdef FLT_RADIX
+ #if FLT_RADIX != 2
+ #error "FLT_RADIX: Your compiler sucks. Get a real one."
+ #endif
+#endif
+#ifdef FLT_MANT_DIG
+ #if FLT_MANT_DIG != 24
+ #error "FLT_MANT_DIG: Your compiler sucks. Get a real one."
+ #endif
+#endif
+#ifdef DBL_MANT_DIG
+ #if DBL_MANT_DIG != 53
+ #error "DBL_MANT_DIG: Your compiler sucks. Get a real one."
+ #endif
+#endif
+#ifdef FLT_MAX_EXP
+ #if FLT_MAX_EXP != 128
+ #error "FLT_MAX_EXP: Your compiler sucks. Get a real one."
+ #endif
+#endif
+#ifdef DBL_MAX_EXP
+ #if DBL_MAX_EXP != 1024
+ #error "DBL_MAX_EXP: Your compiler sucks. Get a real one."
+ #endif
+#endif
+//
+// So if we get here, we can be pretty sure that a float is 4 bytes and a
+// double is 8. IEEE-754? Maaaaaaaaybe. But we don't have to worry about that
+// so much, as long as the token stream is OK (floats are 4 bytes, doubles are
+// 8).
+//
+
+
+uint32_t FloatToIEEE754(float f)
+{
+ uint32_t sign = (f < 0 ? 0x80000000 : 0);
+
+ // Split the float into normalized mantissa (range: (-1, -0.5], 0,
+ // [+0.5, +1)) and base-2 exponent
+ // d = mantissa * (2 ^ exponent) *exactly* for FLT_RADIX=2
+ // Also, since we want the mantissa to be non-inverted (2's complemented),
+ // we make sure to pass in a positive number (floats/doubles are not 2's
+ // complemented) as we already captured the sign bit above.
+ int32_t exponent;
+ float mantissa = frexpf((f < 0 ? -f : f), &exponent);
+
+ // Set the exponent bias for IEEE-754 floats
+ exponent += 0x7E;
+
+ // Check for zero, set the proper exponent if so (zero exponent means no
+ // implied leading one)
+ if (f == 0)
+ exponent = 0;
+
+ // Extract most significant 24 bits of mantissa
+ mantissa = ldexpf(mantissa, 24);
+
+ // Convert to an unsigned int
+ uint32_t ieeeVal = truncf(mantissa);
+
+ // ieeeVal now has the mantissa in binary format, *including* the leading 1
+ // bit; so we have to strip that bit out, since in IEEE-754, it's implied.
+ ieeeVal &= 0x007FFFFF;
+
+ // Finally, add in the other parts to make a proper IEEE-754 float
+ ieeeVal |= sign | ((exponent & 0xFF) << 23);
+
+ return ieeeVal;
+}
+
+
+uint64_t DoubleToIEEE754(double d)
+{
+ uint64_t sign = (d < 0 ? 0x8000000000000000LL : 0);
+ int32_t exponent;
+
+ // Split double into normalized mantissa (range: (-1, -0.5], 0, [+0.5, +1))
+ // and base-2 exponent
+ // d = mantissa * (2 ^ exponent) *exactly* for FLT_RADIX=2
+ // Also, since we want the mantissa to be non-inverted (2's complemented),
+ // we make sure to pass in a positive number (floats/doubles are not 2's
+ // complemented) as we already captured the sign bit above.
+ double mantissa = frexp((d < 0 ? -d : d), &exponent);
+
+ // Set the exponent bias for IEEE-754 doubles
+ exponent += 0x3FE;
+
+ // Check for zero, set the proper exponent if so
+ if (d == 0)
+ exponent = 0;
+
+ // Extract most significant 53 bits of mantissa
+ mantissa = ldexp(mantissa, 53);
+
+ // Convert to an unsigned int
+ uint64_t ieeeVal = trunc(mantissa);
+
+ // ieeeVal now has the mantissa in binary format, *including* the leading 1
+ // bit; so we have to strip that bit out, since in IEEE-754, it's implied.
+ ieeeVal &= 0x000FFFFFFFFFFFFF;
+
+ // Finally, add in the other parts to make a proper IEEE-754 double
+ ieeeVal |= sign | ((uint64_t)(exponent & 0x7FF) << 52);
+
+ return ieeeVal;
+}
+
+
+void DoubleToExtended(double d, uint8_t out[])
+{
+ int32_t exponent;
+ double mantissa = frexp((d < 0 ? -d : d), &exponent);
+ exponent += 0x3FFF;
+
+ if (d == 0)
+ exponent = 0;
+
+ mantissa = ldexp(mantissa, 64);
+ uint64_t intMant = trunc(mantissa);
+
+ // Motorola extended floating point is 96 bits, so we pack it into the
+ // 12-byte array that's passed in. The format is as follows: 1 bit (sign),
+ // 15 bits (exponent w/$3FFF bias), 16 bits of zero, 64 bits of mantissa.
+ out[0] = (d < 0 ? 0x80 : 0x00) | ((exponent >> 8) & 0x7F);
+ out[1] = exponent & 0xFF;
+ out[2] = 0;
+ out[3] = 0;
+ out[4] = (intMant >> 56) & 0xFF;
+ out[5] = (intMant >> 48) & 0xFF;
+ out[6] = (intMant >> 40) & 0xFF;
+ out[7] = (intMant >> 32) & 0xFF;
+ out[8] = (intMant >> 24) & 0xFF;
+ out[9] = (intMant >> 16) & 0xFF;
+ out[10] = (intMant >> 8) & 0xFF;
+ out[11] = intMant & 0xFF;
+}
+
projects / rmac / blobdiff