diff options
| -rw-r--r-- | fpu/softfloat.c | 209 |
1 files changed, 125 insertions, 84 deletions
diff --git a/fpu/softfloat.c b/fpu/softfloat.c index 4abcd36..c63e011 100644 --- a/fpu/softfloat.c +++ b/fpu/softfloat.c @@ -3086,6 +3086,127 @@ static float16 packFloat16(flag zSign, int_fast16_t zExp, uint16_t zSig) (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig); } +/*---------------------------------------------------------------------------- +| Takes an abstract floating-point value having sign `zSign', exponent `zExp', +| and significand `zSig', and returns the proper half-precision floating- +| point value corresponding to the abstract input. Ordinarily, the abstract +| value is simply rounded and packed into the half-precision format, with +| the inexact exception raised if the abstract input cannot be represented +| exactly. However, if the abstract value is too large, the overflow and +| inexact exceptions are raised and an infinity or maximal finite value is +| returned. If the abstract value is too small, the input value is rounded to +| a subnormal number, and the underflow and inexact exceptions are raised if +| the abstract input cannot be represented exactly as a subnormal half- +| precision floating-point number. +| The `ieee' flag indicates whether to use IEEE standard half precision, or +| ARM-style "alternative representation", which omits the NaN and Inf +| encodings in order to raise the maximum representable exponent by one. +| The input significand `zSig' has its binary point between bits 22 +| and 23, which is 13 bits to the left of the usual location. This shifted +| significand must be normalized or smaller. If `zSig' is not normalized, +| `zExp' must be 0; in that case, the result returned is a subnormal number, +| and it must not require rounding. In the usual case that `zSig' is +| normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. +| Note the slightly odd position of the binary point in zSig compared with the +| other roundAndPackFloat functions. This should probably be fixed if we +| need to implement more float16 routines than just conversion. +| The handling of underflow and overflow follows the IEC/IEEE Standard for +| Binary Floating-Point Arithmetic. +*----------------------------------------------------------------------------*/ + +static float32 roundAndPackFloat16(flag zSign, int_fast16_t zExp, + uint32_t zSig, flag ieee STATUS_PARAM) +{ + int maxexp = ieee ? 29 : 30; + uint32_t mask; + uint32_t increment; + int8 roundingMode; + bool rounding_bumps_exp; + bool is_tiny = false; + + /* Calculate the mask of bits of the mantissa which are not + * representable in half-precision and will be lost. + */ + if (zExp < 1) { + /* Will be denormal in halfprec */ + mask = 0x00ffffff; + if (zExp >= -11) { + mask >>= 11 + zExp; + } + } else { + /* Normal number in halfprec */ + mask = 0x00001fff; + } + + roundingMode = STATUS(float_rounding_mode); + switch (roundingMode) { + case float_round_nearest_even: + increment = (mask + 1) >> 1; + if ((zSig & mask) == increment) { + increment = zSig & (increment << 1); + } + break; + case float_round_up: + increment = zSign ? 0 : mask; + break; + case float_round_down: + increment = zSign ? mask : 0; + break; + default: /* round_to_zero */ + increment = 0; + break; + } + + rounding_bumps_exp = (zSig + increment >= 0x01000000); + + if (zExp > maxexp || (zExp == maxexp && rounding_bumps_exp)) { + if (ieee) { + float_raise(float_flag_overflow | float_flag_inexact STATUS_VAR); + return packFloat16(zSign, 0x1f, 0); + } else { + float_raise(float_flag_invalid STATUS_VAR); + return packFloat16(zSign, 0x1f, 0x3ff); + } + } + + if (zExp < 0) { + /* Note that flush-to-zero does not affect half-precision results */ + is_tiny = + (STATUS(float_detect_tininess) == float_tininess_before_rounding) + || (zExp < -1) + || (!rounding_bumps_exp); + } + if (zSig & mask) { + float_raise(float_flag_inexact STATUS_VAR); + if (is_tiny) { + float_raise(float_flag_underflow STATUS_VAR); + } + } + + zSig += increment; + if (rounding_bumps_exp) { + zSig >>= 1; + zExp++; + } + + if (zExp < -10) { + return packFloat16(zSign, 0, 0); + } + if (zExp < 0) { + zSig >>= -zExp; + zExp = 0; + } + return packFloat16(zSign, zExp, zSig >> 13); +} + +static void normalizeFloat16Subnormal(uint32_t aSig, int_fast16_t *zExpPtr, + uint32_t *zSigPtr) +{ + int8_t shiftCount = countLeadingZeros32(aSig) - 21; + *zSigPtr = aSig << shiftCount; + *zExpPtr = 1 - shiftCount; +} + /* Half precision floats come in two formats: standard IEEE and "ARM" format. The latter gains extra exponent range by omitting the NaN/Inf encodings. */ @@ -3106,15 +3227,12 @@ float32 float16_to_float32(float16 a, flag ieee STATUS_PARAM) return packFloat32(aSign, 0xff, 0); } if (aExp == 0) { - int8 shiftCount; - if (aSig == 0) { return packFloat32(aSign, 0, 0); } - shiftCount = countLeadingZeros32( aSig ) - 21; - aSig = aSig << shiftCount; - aExp = -shiftCount; + normalizeFloat16Subnormal(aSig, &aExp, &aSig); + aExp--; } return packFloat32( aSign, aExp + 0x70, aSig << 13); } @@ -3124,12 +3242,6 @@ float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM) flag aSign; int_fast16_t aExp; uint32_t aSig; - uint32_t mask; - uint32_t increment; - int8 roundingMode; - int maxexp = ieee ? 15 : 16; - bool rounding_bumps_exp; - bool is_tiny = false; a = float32_squash_input_denormal(a STATUS_VAR); @@ -3164,80 +3276,9 @@ float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM) * codepath. */ aSig |= 0x00800000; - aExp -= 0x7f; - /* Calculate the mask of bits of the mantissa which are not - * representable in half-precision and will be lost. - */ - if (aExp < -14) { - /* Will be denormal in halfprec */ - mask = 0x00ffffff; - if (aExp >= -24) { - mask >>= 25 + aExp; - } - } else { - /* Normal number in halfprec */ - mask = 0x00001fff; - } + aExp -= 0x71; - roundingMode = STATUS(float_rounding_mode); - switch (roundingMode) { - case float_round_nearest_even: - increment = (mask + 1) >> 1; - if ((aSig & mask) == increment) { - increment = aSig & (increment << 1); - } - break; - case float_round_up: - increment = aSign ? 0 : mask; - break; - case float_round_down: - increment = aSign ? mask : 0; - break; - default: /* round_to_zero */ - increment = 0; - break; - } - - rounding_bumps_exp = (aSig + increment >= 0x01000000); - - if (aExp > maxexp || (aExp == maxexp && rounding_bumps_exp)) { - if (ieee) { - float_raise(float_flag_overflow | float_flag_inexact STATUS_VAR); - return packFloat16(aSign, 0x1f, 0); - } else { - float_raise(float_flag_invalid STATUS_VAR); - return packFloat16(aSign, 0x1f, 0x3ff); - } - } - - if (aExp < -14) { - /* Note that flush-to-zero does not affect half-precision results */ - is_tiny = - (STATUS(float_detect_tininess) == float_tininess_before_rounding) - || (aExp < -15) - || (!rounding_bumps_exp); - } - if (aSig & mask) { - float_raise(float_flag_inexact STATUS_VAR); - if (is_tiny) { - float_raise(float_flag_underflow STATUS_VAR); - } - } - - aSig += increment; - if (rounding_bumps_exp) { - aSig >>= 1; - aExp++; - } - - if (aExp < -24) { - return packFloat16(aSign, 0, 0); - } - if (aExp < -14) { - aSig >>= -14 - aExp; - aExp = -14; - } - return packFloat16(aSign, aExp + 14, aSig >> 13); + return roundAndPackFloat16(aSign, aExp, aSig, ieee STATUS_VAR); } /*---------------------------------------------------------------------------- |