From: Dale Weiler Date: Wed, 7 Jan 2015 01:30:17 +0000 (-0500) Subject: Fix the soft float implementation. Comment it as well. X-Git-Tag: xonotic-v0.8.1~8 X-Git-Url: https://git.xonotic.org/?p=xonotic%2Fgmqcc.git;a=commitdiff_plain;h=e3577912c86755592035786a8fdceedf5331f9e0 Fix the soft float implementation. Comment it as well. --- diff --git a/fold.c b/fold.c index b519831..4f6ca5f 100644 --- a/fold.c +++ b/fold.c @@ -34,15 +34,16 @@ #define FOLD_TINYNESS SFLOAT_TBEFORE /* - * The constant folder is also responsible for validating if the constant - * expressions produce valid results. We cannot trust the FPU control - * unit for these exceptions because setting FPU control words might not - * work. Systems can set and enforce FPU modes of operation. It's also valid - * for libc's to simply ignore FPU exceptions. For instance ARM CPUs in - * glibc. We implement some trivial and IEE 754 conformant functions which - * emulate those operations. This is an entierly optional compiler feature - * which shouldn't be enabled for anything other than performing strict - * passes on constant expressions since it's quite slow. + * Comparing float values is an unsafe operation when the operands to the + * comparison are floating point values that are inexact. For instance 1/3 is an + * inexact value. The FPU is meant to raise exceptions when these sorts of things + * happen, including division by zero, underflows and overflows. The C standard + * library provides us with the header to gain access to the floating- + * point environment and lets us set the rounding mode and check for these exceptions. + * The problem is the standard C library allows an implementation to leave these + * stubbed out and does not require they be implemented. Furthermore, depending + * on implementations there is no control over the FPU. This is an IEE 754 + * conforming implementation in software to compensate. */ typedef uint32_t sfloat_t; @@ -78,7 +79,7 @@ typedef struct { sfloat_tdetect_t tiny; } sfloat_state_t; -/* Count of leading zero bits before the most-significand 1 bit. */ +/* Counts the number of leading zero bits before the most-significand one bit. */ #ifdef _MSC_VER /* MSVC has an intrinsic for this */ static GMQCC_INLINE uint32_t sfloat_clz(uint32_t x) { @@ -115,7 +116,7 @@ typedef struct { #endif /* The value of a NaN */ -#define SFLOAT_NAN 0xFFC00000 +#define SFLOAT_NAN 0xFFFFFFFF /* Test if NaN */ #define SFLOAT_ISNAN(A) \ (0xFF000000 < (uint32_t)((A) << 1)) @@ -126,8 +127,12 @@ typedef struct { #define SFLOAT_RAISE(STATE, FLAGS) \ ((STATE)->exceptionflags = (sfloat_exceptionflags_t)((STATE)->exceptionflags | (FLAGS))) /* - * Shifts `A' right `COUNT' bits. Non-zero bits are stored in LSB. Size - * sets the arbitrarly-large limit. + * Shifts `A' right by the number of bits given in `COUNT'. If any non-zero bits + * are shifted off they are forced into the least significand bit of the result + * by setting it to one. As a result of this, the value of `COUNT' can be + * arbitrarily large; if `COUNT' is greater than 32, the result will be either + * zero or one, depending on whether `A' is a zero or non-zero. The result is + * stored into the value pointed by `Z'. */ #define SFLOAT_SHIFT(SIZE, A, COUNT, Z) \ *(Z) = ((COUNT) == 0) \ @@ -135,6 +140,7 @@ typedef struct { : (((COUNT) < (SIZE)) \ ? ((A) >> (COUNT)) | (((A) << ((-(COUNT)) & ((SIZE) - 1))) != 0) \ : ((A) != 0)) + /* Extract fractional component */ #define SFLOAT_EXTRACT_FRAC(X) \ ((uint32_t)((X) & 0x007FFFFF)) @@ -144,21 +150,32 @@ typedef struct { /* Extract sign bit */ #define SFLOAT_EXTRACT_SIGN(X) \ ((X) >> 31) -/* Normalize a subnormal */ +/* + * Normalizes the subnormal value represented by the denormalized significand + * `SA'. The normalized exponent and significand are stored at the locations + * pointed by `Z' and `SZ' respectively. + */ #define SFLOAT_SUBNORMALIZE(SA, Z, SZ) \ - (void)(*(SZ) = (SA) << SFLOAT_CLZ((SA), 8), *(SZ) = 1 - SFLOAT_CLZ((SA), 8)) + (void)(*(SZ) = (SA) << SFLOAT_CLZ((SA), 8), *(Z) = 1 - SFLOAT_CLZ((SA), 8)) /* - * Pack sign, exponent and significand and produce a float. + * Packs the sign `SIGN', exponent `EXP' and significand `SIG' into the value + * giving the result. * - * Integer portions of the significand are added to the exponent. The - * exponent input should be one less than the result exponent whenever - * the significand is normalized since normalized significand will - * always have an integer portion of value one. + * After the shifting into their proper positions, the fields are added together + * to form the result. This means any integer portion of `SIG' will be added + * to the exponent. Similarly, because a properly normalized significand will + * always have an integer portion equal to one, the exponent input `EXP' should + * be one less than the desired result exponent whenever the significant input + * `SIG' is a complete, normalized significand. */ #define SFLOAT_PACK(SIGN, EXP, SIG) \ (sfloat_t)((((uint32_t)(SIGN)) << 31) + (((uint32_t)(EXP)) << 23) + (SIG)) -/* Calculate NaN. If either operands are signaling then raise invalid */ +/* + * Takes two values `a' and `b', one of which is a NaN, and returns the appropriate + * NaN result. If either `a' or `b' is a signaling NaN than an invalid exception is + * raised. + */ static sfloat_t sfloat_propagate_nan(sfloat_state_t *state, sfloat_t a, sfloat_t b) { bool isnan_a = SFLOAT_ISNAN(a); bool issnan_a = SFLOAT_ISSNAN(a); @@ -169,23 +186,33 @@ static sfloat_t sfloat_propagate_nan(sfloat_state_t *state, sfloat_t a, sfloat_t b |= 0x00400000; if (issnan_a | issnan_b) - SFLOAT_RAISE(state, SFLOAT_INEXACT); - if (issnan_a) { - if (issnan_b) - goto larger; - return isnan_b ? b : a; - } else if (isnan_a) { - if (issnan_b | !isnan_b) - return a; -larger: - if ((uint32_t)(a << 1) < (uint32_t)(b << 1)) return b; - if ((uint32_t)(b << 1) < (uint32_t)(a << 1)) return a; - return (a < b) ? a : b; - } + SFLOAT_RAISE(state, SFLOAT_INVALID); + if (isnan_a) + return (issnan_a & isnan_b) ? b : a; return b; } -/* Round and pack */ +/* + * Takes an abstract value having sign `sign_z', exponent `exp_z', and significand + * `sig_z' and returns the appropriate value corresponding to the abstract input. + * + * The abstract value is simply rounded and packed into the format. If the abstract + * input cannot be represented exactly an inexact exception is raised. If the + * abstract input is too large, the overflow and inexact exceptions are both raised + * and an infinity or maximal finite value is returned. If the abstract value is + * too small, the value is rounded to a subnormal and the underflow and inexact + * exceptions are only raised if the value cannot be represented exactly with + * a subnormal. + * + * The input significand `sig_z' has it's binary point between bits 30 and 29, + * this is seven bits to the left of its usual location. The shifted significand + * must be normalized or smaller than this. If it's not normalized then the exponent + * `exp_z' must be zero; in that case, the result returned is a subnormal number + * and is must not require rounding. In the more usual case where the significand + * is normalized, the exponent must be one less than the *true* exponent. + * + * The handling of underflow and overflow is otherwise in alignment with IEC/IEEE. + */ static sfloat_t SFLOAT_PACK_round(sfloat_state_t *state, bool sign_z, int16_t exp_z, uint32_t sig_z) { sfloat_roundingmode_t mode = state->roundingmode; bool even = !!(mode == SFLOAT_ROUND_NEAREST_EVEN); @@ -222,13 +249,6 @@ static sfloat_t SFLOAT_PACK_round(sfloat_state_t *state, bool sign_z, int16_t ex SFLOAT_RAISE(state, SFLOAT_UNDERFLOW); } } - - /* - * Significand has point between bits 30 and 29, 7 bits to the left of - * the usual place. This shifted significand has to be normalized - * or smaller, if it isn't the exponent must be zero, in which case - * no rounding occurs since the result will be a subnormal. - */ if (bits) SFLOAT_RAISE(state, SFLOAT_INEXACT); sig_z = (sig_z + increment) >> 7; @@ -238,12 +258,24 @@ static sfloat_t SFLOAT_PACK_round(sfloat_state_t *state, bool sign_z, int16_t ex return SFLOAT_PACK(sign_z, exp_z, sig_z); } -/* Normalized round and pack */ +/* + * Takes an abstract value having sign `sign_z', exponent `exp_z' and significand + * `sig_z' and returns the appropriate value corresponding to the abstract input. + * This function is exactly like `PACK_round' except the significand does not have + * to be normalized. + * + * Bit 31 of the significand must be zero and the exponent must be one less than + * the *true* exponent. + */ static sfloat_t SFLOAT_PACK_normal(sfloat_state_t *state, bool sign_z, int16_t exp_z, uint32_t sig_z) { unsigned char c = SFLOAT_CLZ(sig_z, 1); return SFLOAT_PACK_round(state, sign_z, exp_z - c, sig_z << c); } +/* + * Returns the result of adding the absolute values of `a' and `b'. The sign + * `sign_z' is ignored if the result is a NaN. + */ static sfloat_t sfloat_add_impl(sfloat_state_t *state, sfloat_t a, sfloat_t b, bool sign_z) { int16_t exp_a = SFLOAT_EXTRACT_EXP(a); int16_t exp_b = SFLOAT_EXTRACT_EXP(b); @@ -291,6 +323,11 @@ end: return SFLOAT_PACK_round(state, sign_z, exp_z, sig_z); } +/* + * Returns the result of subtracting the absolute values of `a' and `b'. If the + * sign `sign_z' is one, the difference is negated before being returned. The + * sign is ignored if the result is a NaN. + */ static sfloat_t sfloat_sub_impl(sfloat_state_t *state, sfloat_t a, sfloat_t b, bool sign_z) { int16_t exp_a = SFLOAT_EXTRACT_EXP(a); int16_t exp_b = SFLOAT_EXTRACT_EXP(b);