diff options
Diffstat (limited to 'libgcc/config/libbid/bid64_to_uint32.c')
| -rw-r--r-- | libgcc/config/libbid/bid64_to_uint32.c | 1068 |
1 files changed, 534 insertions, 534 deletions
diff --git a/libgcc/config/libbid/bid64_to_uint32.c b/libgcc/config/libbid/bid64_to_uint32.c index 041cca68f6a..cf11e65748c 100644 --- a/libgcc/config/libbid/bid64_to_uint32.c +++ b/libgcc/config/libbid/bid64_to_uint32.c @@ -34,27 +34,27 @@ Software Foundation, 51 Franklin Street, Fifth Floor, Boston, MA #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_rnint (unsigned int *pres, UINT64 * px +bid64_to_uint32_rnint (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_rnint (UINT64 x +bid64_to_uint32_rnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -67,17 +67,17 @@ __bid64_to_uint32_rnint (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -91,56 +91,56 @@ __bid64_to_uint32_rnint (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag @@ -151,12 +151,12 @@ __bid64_to_uint32_rnint (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0x9fffffffbull * __bid_ten2k64[q - 11]; + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -171,11 +171,11 @@ __bid64_to_uint32_rnint (UINT64 x } // n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2 // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) // return 0 res = 0x00000000; BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) // res = 0 // else if x > 0 @@ -183,21 +183,21 @@ __bid64_to_uint32_rnint (UINT64 x // else // if x < 0 // invalid exc ind = q - 1; - if (C1 <= __bid_midpoint64[ind]) { - res = 0x00000000; // return 0 - } else if (x_sign) { // n < 0 + if (C1 <= midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // n > 0 - res = 0x00000001; // return +1 + } else { // n > 0 + res = 0x00000001; // return +1 } - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -206,25 +206,25 @@ __bid64_to_uint32_rnint (UINT64 x } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - C1 = C1 + __bid_midpoint64[ind - 1]; + C1 = C1 + midpoint64[ind - 1]; // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = (C1 + 1/2 * 10^x) * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // if (0 < f* < 10^(-x)) then the result is a midpoint // if floor(C*) is even then C* = floor(C*) - logical right // shift; C* has p decimal digits, correct by Prop. 1) @@ -235,31 +235,31 @@ __bid64_to_uint32_rnint (UINT64 x // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // if the result was a midpoint it was rounded away from zero, so // it will need a correction // check for midpoints if ((fstar.w[1] == 0) && fstar.w[0] && - (fstar.w[0] <= __bid_ten2mk128trunc[ind - 1].w[1])) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // the result is a midpoint; round to nearest - if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 - Cstar--; // Cstar is now even - } // else MP in [ODD, EVEN] + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] } - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -271,27 +271,27 @@ __bid64_to_uint32_rnint (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_xrnint (unsigned int *pres, UINT64 * px +bid64_to_uint32_xrnint (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_xrnint (UINT64 x +bid64_to_uint32_xrnint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -304,17 +304,17 @@ __bid64_to_uint32_xrnint (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -328,56 +328,56 @@ __bid64_to_uint32_xrnint (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag @@ -388,12 +388,12 @@ __bid64_to_uint32_xrnint (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0x9fffffffbull * __bid_ten2k64[q - 11]; + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -408,13 +408,13 @@ __bid64_to_uint32_xrnint (UINT64 x } // n is not too large to be converted to int32 if -1/2 <= n < 2^32 - 1/2 // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) // set inexact flag *pfpsf |= INEXACT_EXCEPTION; // return 0 res = 0x00000000; BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) // if 0.c(0)c(1)...c(q-1) <= 0.5 <=> c(0)c(1)...c(q-1) <= 5 * 10^(q-1) // res = 0 // else if x > 0 @@ -422,23 +422,23 @@ __bid64_to_uint32_xrnint (UINT64 x // else // if x < 0 // invalid exc ind = q - 1; - if (C1 <= __bid_midpoint64[ind]) { - res = 0x00000000; // return 0 - } else if (x_sign) { // n < 0 + if (C1 <= midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // n > 0 - res = 0x00000001; // return +1 + } else { // n > 0 + res = 0x00000001; // return +1 } // set inexact flag *pfpsf |= INEXACT_EXCEPTION; - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -447,25 +447,25 @@ __bid64_to_uint32_xrnint (UINT64 x } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - C1 = C1 + __bid_midpoint64[ind - 1]; + C1 = C1 + midpoint64[ind - 1]; // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = (C1 + 1/2 * 10^x) * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // if (0 < f* < 10^(-x)) then the result is a midpoint // if floor(C*) is even then C* = floor(C*) - logical right // shift; C* has p decimal digits, correct by Prop. 1) @@ -476,41 +476,41 @@ __bid64_to_uint32_xrnint (UINT64 x // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // determine inexactness of the rounding of C* // if (0 < f* - 1/2 < 10^(-x)) then // the result is exact // else // if (f* - 1/2 > T*) then // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (ind - 1 <= 2) { // fstar.w[1] is 0 if (fstar.w[0] > 0x8000000000000000ull) { // f* > 1/2 and the result may be exact - tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 - if ((tmp64 > __bid_ten2mk128trunc[ind - 1].w[1])) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // the result is inexact; f2* <= 1/2 + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; } - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] > __bid_one_half128[ind - 1] || - (fstar.w[1] == __bid_one_half128[ind - 1] && fstar.w[0])) { + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { // f2* > 1/2 and the result may be exact // Calculate f2* - 1/2 - tmp64 = fstar.w[1] - __bid_one_half128[ind - 1]; - if (tmp64 || fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // the result is inexact; f2* <= 1/2 + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; } @@ -520,23 +520,23 @@ __bid64_to_uint32_xrnint (UINT64 x // it will need a correction // check for midpoints if ((fstar.w[1] == 0) && fstar.w[0] && - (fstar.w[0] <= __bid_ten2mk128trunc[ind - 1].w[1])) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + (fstar.w[0] <= ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // the result is a midpoint; round to nearest - if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] + if (Cstar & 0x01) { // Cstar is odd; MP in [EVEN, ODD] // if floor(C*) is odd C = floor(C*) - 1; the result >= 1 - Cstar--; // Cstar is now even - } // else MP in [ODD, EVEN] + Cstar--; // Cstar is now even + } // else MP in [ODD, EVEN] } - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -548,27 +548,27 @@ __bid64_to_uint32_xrnint (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_floor (unsigned int *pres, UINT64 * px +bid64_to_uint32_floor (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_floor (UINT64 x +bid64_to_uint32_floor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 P128; // check for NaN or Infinity @@ -580,17 +580,17 @@ __bid64_to_uint32_floor (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -602,7 +602,7 @@ __bid64_to_uint32_floor (UINT64 x } // x is not special and is not zero - if (x_sign) { // if n < 0 the conversion is invalid + if (x_sign) { // if n < 0 the conversion is invalid // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -611,37 +611,37 @@ __bid64_to_uint32_floor (UINT64 x } // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit @@ -654,7 +654,7 @@ __bid64_to_uint32_floor (UINT64 x // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag @@ -665,12 +665,12 @@ __bid64_to_uint32_floor (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0xa00000000ull * __bid_ten2k64[q - 11]; + tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -684,45 +684,45 @@ __bid64_to_uint32_floor (UINT64 x } // n is not too large to be converted to int32 if -1 < n < 2^32 // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) + if ((q + exp) <= 0) { // n = +0.[0...0]c(0)c(1)...c(q-1) // return 0 res = 0x00000000; BID_RETURN (res); - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 fits in 64 bits // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = C1 * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -734,27 +734,27 @@ __bid64_to_uint32_floor (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_xfloor (unsigned int *pres, UINT64 * px +bid64_to_uint32_xfloor (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_xfloor (UINT64 x +bid64_to_uint32_xfloor (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -767,17 +767,17 @@ __bid64_to_uint32_xfloor (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -789,7 +789,7 @@ __bid64_to_uint32_xfloor (UINT64 x } // x is not special and is not zero - if (x_sign) { // if n < 0 the conversion is invalid + if (x_sign) { // if n < 0 the conversion is invalid // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -798,37 +798,37 @@ __bid64_to_uint32_xfloor (UINT64 x } // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit @@ -841,7 +841,7 @@ __bid64_to_uint32_xfloor (UINT64 x // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag @@ -852,12 +852,12 @@ __bid64_to_uint32_xfloor (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0xa00000000ull * __bid_ten2k64[q - 11]; + tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -871,39 +871,39 @@ __bid64_to_uint32_xfloor (UINT64 x } // n is not too large to be converted to int32 if -1 < n < 2^32 // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) // set inexact flag *pfpsf |= INEXACT_EXCEPTION; // return 0 res = 0x00000000; BID_RETURN (res); - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 fits in 64 bits // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = C1 * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // determine inexactness of the rounding of C* // if (0 < f* < 10^(-x)) then @@ -911,29 +911,29 @@ __bid64_to_uint32_xfloor (UINT64 x // else // if (f* > T*) then // the result is inexact if (ind - 1 <= 2) { - if (fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact + } // else the result is exact } - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -945,27 +945,27 @@ __bid64_to_uint32_xfloor (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_ceil (unsigned int *pres, UINT64 * px +bid64_to_uint32_ceil (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_ceil (UINT64 x +bid64_to_uint32_ceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -978,17 +978,17 @@ __bid64_to_uint32_ceil (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -1002,56 +1002,56 @@ __bid64_to_uint32_ceil (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n > 2^32 - 1 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 // <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 > 0x9fffffff6ull) { // set invalid flag @@ -1062,12 +1062,12 @@ __bid64_to_uint32_ceil (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) > 0x9fffffff6 <=> // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1 up) // Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0x9fffffff6ull * __bid_ten2k64[q - 11]; + tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; if (C1 > tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -1082,17 +1082,17 @@ __bid64_to_uint32_ceil (UINT64 x } // n is not too large to be converted to int32 if -1 < n < 2^32 // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) // return 0 or 1 if (x_sign) res = 0x00000000; else res = 0x00000001; BID_RETURN (res); - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x <= 2^32 - 1 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -1101,58 +1101,58 @@ __bid64_to_uint32_ceil (UINT64 x } // 1 <= x <= 2^32 - 1 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 fits in 64 bits // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = C1 * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // determine inexactness of the rounding of C* // if (0 < f* < 10^(-x)) then // the result is exact // else // if (f* > T*) then // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] Cstar++; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] Cstar++; - } // else the result is exact + } // else the result is exact } - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -1164,27 +1164,27 @@ __bid64_to_uint32_ceil (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_xceil (unsigned int *pres, UINT64 * px +bid64_to_uint32_xceil (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_xceil (UINT64 x +bid64_to_uint32_xceil (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -1197,17 +1197,17 @@ __bid64_to_uint32_xceil (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -1221,56 +1221,56 @@ __bid64_to_uint32_xceil (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n > 2^32 - 1 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) > 2^32 - 1 // <=> 0.c(0)c(1)...c(q-1) * 10^11 > 0x9fffffff6, 1<=q<=16 // <=> C * 10^(11-q) > 0x9fffffff6, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffff6 has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 > 0x9fffffff6ull) { // set invalid flag @@ -1281,12 +1281,12 @@ __bid64_to_uint32_xceil (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) > 0x9fffffff6 <=> // C > 0x9fffffff6 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1 up) // Note: 0x9fffffff6*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0x9fffffff6ull * __bid_ten2k64[q - 11]; + tmp64 = 0x9fffffff6ull * ten2k64[q - 11]; if (C1 > tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -1301,7 +1301,7 @@ __bid64_to_uint32_xceil (UINT64 x } // n is not too large to be converted to int32 if -1 < n < 2^32 // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) // set inexact flag *pfpsf |= INEXACT_EXCEPTION; // return 0 or 1 @@ -1310,10 +1310,10 @@ __bid64_to_uint32_xceil (UINT64 x else res = 0x00000001; BID_RETURN (res); - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x < 2^32 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -1322,62 +1322,62 @@ __bid64_to_uint32_xceil (UINT64 x } // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 fits in 64 bits // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = C1 * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // determine inexactness of the rounding of C* // if (0 < f* < 10^(-x)) then // the result is exact // else // if (f* > T*) then // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] Cstar++; // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] Cstar++; // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact + } // else the result is exact } - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -1389,27 +1389,27 @@ __bid64_to_uint32_xceil (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_int (unsigned int *pres, UINT64 * px +bid64_to_uint32_int (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_int (UINT64 x +bid64_to_uint32_int (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 P128; // check for NaN or Infinity @@ -1421,17 +1421,17 @@ __bid64_to_uint32_int (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -1445,56 +1445,56 @@ __bid64_to_uint32_int (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n >= 2^32 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag @@ -1505,12 +1505,12 @@ __bid64_to_uint32_int (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0xa00000000ull * __bid_ten2k64[q - 11]; + tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -1525,14 +1525,14 @@ __bid64_to_uint32_int (UINT64 x } // n is not too large to be converted to int32 if -1 < n < 2^32 // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) // return 0 res = 0x00000000; BID_RETURN (res); - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x < 2^32 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -1541,38 +1541,38 @@ __bid64_to_uint32_int (UINT64 x } // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 fits in 64 bits // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = C1 * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -1584,27 +1584,27 @@ __bid64_to_uint32_int (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_xint (unsigned int *pres, UINT64 * px +bid64_to_uint32_xint (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_xint (UINT64 x +bid64_to_uint32_xint (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -1617,17 +1617,17 @@ __bid64_to_uint32_xint (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -1641,56 +1641,56 @@ __bid64_to_uint32_xint (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n >= 2^32 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0xa00000000, 1<=q<=16 // <=> C * 10^(11-q) >= 0xa00000000, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0xa00000000 has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0xa00000000ull) { // set invalid flag @@ -1701,12 +1701,12 @@ __bid64_to_uint32_xint (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0xa00000000 <=> // C >= 0xa00000000 * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0xa00000000*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0xa00000000ull * __bid_ten2k64[q - 11]; + tmp64 = 0xa00000000ull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -1721,16 +1721,16 @@ __bid64_to_uint32_xint (UINT64 x } // n is not too large to be converted to int32 if -1 < n < 2^32 // Note: some of the cases tested for above fall through to this point - if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) + if ((q + exp) <= 0) { // n = +/-0.[0...0]c(0)c(1)...c(q-1) // set inexact flag *pfpsf |= INEXACT_EXCEPTION; // return 0 res = 0x00000000; BID_RETURN (res); - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // x <= -1 or 1 <= x < 2^32 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -1739,60 +1739,60 @@ __bid64_to_uint32_xint (UINT64 x } // 1 <= x < 2^32 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 fits in 64 bits // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = C1 * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // determine inexactness of the rounding of C* // if (0 < f* < 10^(-x)) then // the result is exact // else // if (f* > T*) then // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 - if (fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] || fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + } // else the result is exact + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact + } // else the result is exact } - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -1804,27 +1804,27 @@ __bid64_to_uint32_xint (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_rninta (unsigned int *pres, UINT64 * px +bid64_to_uint32_rninta (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_rninta (UINT64 x +bid64_to_uint32_rninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 P128; // check for NaN or Infinity @@ -1836,17 +1836,17 @@ __bid64_to_uint32_rninta (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -1860,56 +1860,56 @@ __bid64_to_uint32_rninta (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag @@ -1920,12 +1920,12 @@ __bid64_to_uint32_rninta (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0x9fffffffbull * __bid_ten2k64[q - 11]; + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -1940,11 +1940,11 @@ __bid64_to_uint32_rninta (UINT64 x } // n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2 // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) // return 0 res = 0x00000000; BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) // res = 0 // else if x > 0 @@ -1952,21 +1952,21 @@ __bid64_to_uint32_rninta (UINT64 x // else // if x < 0 // invalid exc ind = q - 1; - if (C1 < __bid_midpoint64[ind]) { - res = 0x00000000; // return 0 - } else if (x_sign) { // n < 0 + if (C1 < midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // n > 0 - res = 0x00000001; // return +1 + } else { // n > 0 + res = 0x00000001; // return +1 } - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -1975,40 +1975,40 @@ __bid64_to_uint32_rninta (UINT64 x } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - C1 = C1 + __bid_midpoint64[ind - 1]; + C1 = C1 + midpoint64[ind - 1]; // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = (C1 + 1/2 * 10^x) * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // if the result was a midpoint it was rounded away from zero - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); @@ -2020,27 +2020,27 @@ __bid64_to_uint32_rninta (UINT64 x #if DECIMAL_CALL_BY_REFERENCE void -__bid64_to_uint32_xrninta (unsigned int *pres, UINT64 * px +bid64_to_uint32_xrninta (unsigned int *pres, UINT64 * px _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { UINT64 x = *px; #else unsigned int -__bid64_to_uint32_xrninta (UINT64 x +bid64_to_uint32_xrninta (UINT64 x _EXC_FLAGS_PARAM _EXC_MASKS_PARAM _EXC_INFO_PARAM) { #endif unsigned int res; UINT64 x_sign; UINT64 x_exp; - int exp; // unbiased exponent + int exp; // unbiased exponent // Note: C1 represents x_significand (UINT64) UINT64 tmp64; BID_UI64DOUBLE tmp1; unsigned int x_nr_bits; int q, ind, shift; UINT64 C1; - UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits + UINT64 Cstar; // C* represents up to 16 decimal digits ~ 54 bits UINT128 fstar; UINT128 P128; @@ -2053,17 +2053,17 @@ __bid64_to_uint32_xrninta (UINT64 x BID_RETURN (res); } // unpack x - x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative + x_sign = x & MASK_SIGN; // 0 for positive, MASK_SIGN for negative // if steering bits are 11 (condition will be 0), then exponent is G[0:w+1] => if ((x & MASK_STEERING_BITS) == MASK_STEERING_BITS) { - x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased + x_exp = (x & MASK_BINARY_EXPONENT2) >> 51; // biased C1 = (x & MASK_BINARY_SIG2) | MASK_BINARY_OR2; - if (C1 > 9999999999999999ull) { // non-canonical + if (C1 > 9999999999999999ull) { // non-canonical x_exp = 0; C1 = 0; } } else { - x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased + x_exp = (x & MASK_BINARY_EXPONENT1) >> 53; // biased C1 = x & MASK_BINARY_SIG1; } @@ -2077,56 +2077,56 @@ __bid64_to_uint32_xrninta (UINT64 x // q = nr. of decimal digits in x (1 <= q <= 54) // determine first the nr. of bits in x - if (C1 >= 0x0020000000000000ull) { // x >= 2^53 + if (C1 >= 0x0020000000000000ull) { // x >= 2^53 // split the 64-bit value in two 32-bit halves to avoid rounding errors - if (C1 >= 0x0000000100000000ull) { // x >= 2^32 - tmp1.d = (double) (C1 >> 32); // exact conversion + if (C1 >= 0x0000000100000000ull) { // x >= 2^32 + tmp1.d = (double) (C1 >> 32); // exact conversion x_nr_bits = 33 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); - } else { // x < 2^32 - tmp1.d = (double) C1; // exact conversion + } else { // x < 2^32 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - } else { // if x < 2^53 - tmp1.d = (double) C1; // exact conversion + } else { // if x < 2^53 + tmp1.d = (double) C1; // exact conversion x_nr_bits = 1 + ((((unsigned int) (tmp1.ui64 >> 52)) & 0x7ff) - 0x3ff); } - q = __bid_nr_digits[x_nr_bits - 1].digits; + q = nr_digits[x_nr_bits - 1].digits; if (q == 0) { - q = __bid_nr_digits[x_nr_bits - 1].digits1; - if (C1 >= __bid_nr_digits[x_nr_bits - 1].threshold_lo) + q = nr_digits[x_nr_bits - 1].digits1; + if (C1 >= nr_digits[x_nr_bits - 1].threshold_lo) q++; } - exp = x_exp - 398; // unbiased exponent + exp = x_exp - 398; // unbiased exponent - if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) + if ((q + exp) > 10) { // x >= 10^10 ~= 2^33.2... (cannot fit in 32 bits) // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) + } else if ((q + exp) == 10) { // x = c(0)c(1)...c(9).c(10)...c(q-1) // in this case 2^29.89... ~= 10^9 <= x < 10^10 ~= 2^33.2... // so x rounded to an integer may or may not fit in an unsigned 32-bit int // the cases that do not fit are identified here; the ones that fit // fall through and will be handled with other cases further, // under '1 <= q + exp <= 10' - if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 + if (x_sign) { // if n < 0 and q + exp = 10 then x is much less than -1/2 // => set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // if n > 0 and q + exp = 10 + } else { // if n > 0 and q + exp = 10 // if n >= 2^32 - 1/2 then n is too large // too large if c(0)c(1)...c(9).c(10)...c(q-1) >= 2^32-1/2 // <=> 0.c(0)c(1)...c(q-1) * 10^11 >= 0x9fffffffb, 1<=q<=16 // <=> C * 10^(11-q) >= 0x9fffffffb, 1<=q<=16 if (q <= 11) { // Note: C * 10^(11-q) has 10 or 11 digits; 0x9fffffffb has 11 digits - tmp64 = C1 * __bid_ten2k64[11 - q]; // C scaled up to 11-digit int + tmp64 = C1 * ten2k64[11 - q]; // C scaled up to 11-digit int // c(0)c(1)...c(9)c(10) or c(0)c(1)...c(q-1)0...0 (11 digits) if (tmp64 >= 0x9fffffffbull) { // set invalid flag @@ -2137,12 +2137,12 @@ __bid64_to_uint32_xrninta (UINT64 x } // else cases that can be rounded to a 32-bit unsigned int fall through // to '1 <= q + exp <= 10' - } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 + } else { // if (q > 11), i.e. 12 <= q <= 16 and so -15 <= exp <= -2 // C * 10^(11-q) >= 0x9fffffffb <=> // C >= 0x9fffffffb * 10^(q-11) where 1 <= q - 11 <= 5 // (scale 2^32-1/2 up) // Note: 0x9fffffffb*10^(q-11) has q-1 or q digits, where q <= 16 - tmp64 = 0x9fffffffbull * __bid_ten2k64[q - 11]; + tmp64 = 0x9fffffffbull * ten2k64[q - 11]; if (C1 >= tmp64) { // set invalid flag *pfpsf |= INVALID_EXCEPTION; @@ -2157,13 +2157,13 @@ __bid64_to_uint32_xrninta (UINT64 x } // n is not too large to be converted to int32 if -1/2 < n < 2^32 - 1/2 // Note: some of the cases tested for above fall through to this point - if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) + if ((q + exp) < 0) { // n = +/-0.0...c(0)c(1)...c(q-1) // set inexact flag *pfpsf |= INEXACT_EXCEPTION; // return 0 res = 0x00000000; BID_RETURN (res); - } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) + } else if ((q + exp) == 0) { // n = +/-0.c(0)c(1)...c(q-1) // if 0.c(0)c(1)...c(q-1) < 0.5 <=> c(0)c(1)...c(q-1) < 5 * 10^(q-1) // res = 0 // else if x > 0 @@ -2171,23 +2171,23 @@ __bid64_to_uint32_xrninta (UINT64 x // else // if x < 0 // invalid exc ind = q - 1; - if (C1 < __bid_midpoint64[ind]) { - res = 0x00000000; // return 0 - } else if (x_sign) { // n < 0 + if (C1 < midpoint64[ind]) { + res = 0x00000000; // return 0 + } else if (x_sign) { // n < 0 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite res = 0x80000000; BID_RETURN (res); - } else { // n > 0 - res = 0x00000001; // return +1 + } else { // n > 0 + res = 0x00000001; // return +1 } // set inexact flag *pfpsf |= INEXACT_EXCEPTION; - } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) + } else { // if (1 <= q + exp <= 10, 1 <= q <= 16, -15 <= exp <= 9) // -2^32-1/2 <= x <= -1 or 1 <= x < 2^32-1/2 so if positive, x can be // rounded to nearest to a 32-bit unsigned integer - if (x_sign) { // x <= -1 + if (x_sign) { // x <= -1 // set invalid flag *pfpsf |= INVALID_EXCEPTION; // return Integer Indefinite @@ -2196,31 +2196,31 @@ __bid64_to_uint32_xrninta (UINT64 x } // 1 <= x < 2^32-1/2 so x can be rounded // to nearest to a 32-bit unsigned integer - if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 - ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' + if (exp < 0) { // 2 <= q <= 16, -15 <= exp <= -1, 1 <= q + exp <= 10 + ind = -exp; // 1 <= ind <= 15; ind is a synonym for 'x' // chop off ind digits from the lower part of C1 // C1 = C1 + 1/2 * 10^ind where the result C1 fits in 64 bits - C1 = C1 + __bid_midpoint64[ind - 1]; + C1 = C1 + midpoint64[ind - 1]; // calculate C* and f* // C* is actually floor(C*) in this case // C* and f* need shifting and masking, as shown by - // __bid_shiftright128[] and __bid_maskhigh128[] + // shiftright128[] and maskhigh128[] // 1 <= x <= 15 - // kx = 10^(-x) = __bid_ten2mk64[ind - 1] + // kx = 10^(-x) = ten2mk64[ind - 1] // C* = (C1 + 1/2 * 10^x) * 10^(-x) // the approximation of 10^(-x) was rounded up to 54 bits - __mul_64x64_to_128MACH (P128, C1, __bid_ten2mk64[ind - 1]); + __mul_64x64_to_128MACH (P128, C1, ten2mk64[ind - 1]); Cstar = P128.w[1]; - fstar.w[1] = P128.w[1] & __bid_maskhigh128[ind - 1]; + fstar.w[1] = P128.w[1] & maskhigh128[ind - 1]; fstar.w[0] = P128.w[0]; - // the top Ex bits of 10^(-x) are T* = __bid_ten2mk128trunc[ind].w[0], e.g. - // if x=1, T*=__bid_ten2mk128trunc[0].w[0]=0x1999999999999999 + // the top Ex bits of 10^(-x) are T* = ten2mk128trunc[ind].w[0], e.g. + // if x=1, T*=ten2mk128trunc[0].w[0]=0x1999999999999999 // C* = floor(C*) (logical right shift; C has p decimal digits, // correct by Property 1) // n = C* * 10^(e+x) - // shift right C* by Ex-64 = __bid_shiftright128[ind] - shift = __bid_shiftright128[ind - 1]; // 0 <= shift <= 39 + // shift right C* by Ex-64 = shiftright128[ind] + shift = shiftright128[ind - 1]; // 0 <= shift <= 39 Cstar = Cstar >> shift; // determine inexactness of the rounding of C* @@ -2228,47 +2228,47 @@ __bid64_to_uint32_xrninta (UINT64 x // the result is exact // else // if (f* - 1/2 > T*) then // the result is inexact - if (ind - 1 <= 2) { // fstar.w[1] is 0 + if (ind - 1 <= 2) { // fstar.w[1] is 0 if (fstar.w[0] > 0x8000000000000000ull) { // f* > 1/2 and the result may be exact - tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 - if ((tmp64 > __bid_ten2mk128trunc[ind - 1].w[1])) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + tmp64 = fstar.w[0] - 0x8000000000000000ull; // f* - 1/2 + if ((tmp64 > ten2mk128trunc[ind - 1].w[1])) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // the result is inexact; f2* <= 1/2 + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; } - } else { // if 3 <= ind - 1 <= 14 - if (fstar.w[1] > __bid_one_half128[ind - 1] || - (fstar.w[1] == __bid_one_half128[ind - 1] && fstar.w[0])) { + } else { // if 3 <= ind - 1 <= 14 + if (fstar.w[1] > onehalf128[ind - 1] || + (fstar.w[1] == onehalf128[ind - 1] && fstar.w[0])) { // f2* > 1/2 and the result may be exact // Calculate f2* - 1/2 - tmp64 = fstar.w[1] - __bid_one_half128[ind - 1]; - if (tmp64 || fstar.w[0] > __bid_ten2mk128trunc[ind - 1].w[1]) { - // __bid_ten2mk128trunc[ind -1].w[1] is identical to - // __bid_ten2mk128[ind -1].w[1] + tmp64 = fstar.w[1] - onehalf128[ind - 1]; + if (tmp64 || fstar.w[0] > ten2mk128trunc[ind - 1].w[1]) { + // ten2mk128trunc[ind -1].w[1] is identical to + // ten2mk128[ind -1].w[1] // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; - } // else the result is exact - } else { // the result is inexact; f2* <= 1/2 + } // else the result is exact + } else { // the result is inexact; f2* <= 1/2 // set the inexact flag *pfpsf |= INEXACT_EXCEPTION; } } // if the result was a midpoint it was rounded away from zero - res = Cstar; // the result is positive + res = Cstar; // the result is positive } else if (exp == 0) { // 1 <= q <= 10 // res = +C (exact) - res = C1; // the result is positive - } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 + res = C1; // the result is positive + } else { // if (exp > 0) => 1 <= exp <= 9, 1 <= q < 9, 2 <= q + exp <= 10 // res = +C * 10^exp (exact) - res = C1 * __bid_ten2k64[exp]; // the result is positive + res = C1 * ten2k64[exp]; // the result is positive } } BID_RETURN (res); |