diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/math_ldbl.h')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/math_ldbl.h | 291 |
1 files changed, 174 insertions, 117 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h b/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h index e7e1b963e8..d055d6597e 100644 --- a/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h +++ b/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h @@ -3,122 +3,179 @@ #endif #include <sysdeps/ieee754/ldbl-128/math_ldbl.h> +#include <ieee754.h> + +static inline void +ldbl_extract_mantissa (int64_t *hi64, u_int64_t *lo64, int *exp, long double x) +{ + /* We have 105 bits of mantissa plus one implicit digit. Since + 106 bits are representable we use the first implicit digit for + the number before the decimal point and the second implicit bit + as bit 53 of the mantissa. */ + unsigned long long hi, lo; + int ediff; + union ibm_extended_long_double eldbl; + eldbl.d = x; + *exp = eldbl.ieee.exponent - IBM_EXTENDED_LONG_DOUBLE_BIAS; -#define EXTRACT_IBM_EXTENDED_MANTISSA(hi64, lo64, expnt, ibm_ext_ldbl) \ - do \ - { \ - /* We have 105 bits of mantissa plus one implicit digit. Since \ - 106 bits are representable without the rest using hexadecimal \ - digits we use only the implicit digits for the number before \ - the decimal point. */ \ - unsigned long long hi, lo; \ - int ediff; \ - union ibm_extended_long_double eldbl; \ - eldbl.d = ibm_ext_ldbl; \ - expnt = eldbl.ieee.exponent - IBM_EXTENDED_LONG_DOUBLE_BIAS; \ - \ - lo = ((long long)eldbl.ieee.mantissa2 << 32) | eldbl.ieee.mantissa3; \ - hi = ((long long)eldbl.ieee.mantissa0 << 32) | eldbl.ieee.mantissa1; \ - /* If the lower double is not a denomal or zero then set the hidden \ - 53rd bit. */ \ - if (eldbl.ieee.exponent2 > 0x001) \ - { \ - lo |= (1ULL << 52); \ - lo = lo << 7; /* pre-shift lo to match ieee854. */ \ - /* The lower double is normalized separately from the upper. We \ - may need to adjust the lower manitissa to reflect this. */ \ - ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2; \ - if (ediff > 53) \ - lo = lo >> (ediff-53); \ - } \ - hi |= (1ULL << 52); \ - \ - if ((eldbl.ieee.negative != eldbl.ieee.negative2) \ - && ((eldbl.ieee.exponent2 != 0) && (lo != 0LL))) \ - { \ - hi--; \ - lo = (1ULL << 60) - lo; \ - if (hi < (1ULL << 52)) \ - { \ - /* we have a borrow from the hidden bit, so shift left 1. */ \ - hi = (hi << 1) | (lo >> 59); \ - lo = 0xfffffffffffffffLL & (lo << 1); \ - expnt--; \ - } \ - } \ - lo64 = (hi << 60) | lo; \ - hi64 = hi >> 4; \ - } \ - while (0) + lo = ((long long)eldbl.ieee.mantissa2 << 32) | eldbl.ieee.mantissa3; + hi = ((long long)eldbl.ieee.mantissa0 << 32) | eldbl.ieee.mantissa1; + /* If the lower double is not a denomal or zero then set the hidden + 53rd bit. */ + if (eldbl.ieee.exponent2 > 0x001) + { + lo |= (1ULL << 52); + lo = lo << 7; /* pre-shift lo to match ieee854. */ + /* The lower double is normalized separately from the upper. We + may need to adjust the lower manitissa to reflect this. */ + ediff = eldbl.ieee.exponent - eldbl.ieee.exponent2; + if (ediff > 53) + lo = lo >> (ediff-53); + } + hi |= (1ULL << 52); + + if ((eldbl.ieee.negative != eldbl.ieee.negative2) + && ((eldbl.ieee.exponent2 != 0) && (lo != 0LL))) + { + hi--; + lo = (1ULL << 60) - lo; + if (hi < (1ULL << 52)) + { + /* we have a borrow from the hidden bit, so shift left 1. */ + hi = (hi << 1) | (lo >> 59); + lo = 0xfffffffffffffffLL & (lo << 1); + *exp = *exp - 1; + } + } + *lo64 = (hi << 60) | lo; + *hi64 = hi >> 4; +} -#define INSERT_IBM_EXTENDED_MANTISSA(ibm_ext_ldbl, sign, expnt, hi64, lo64) \ - do \ - { \ - union ibm_extended_long_double u; \ - unsigned long hidden2, lzcount; \ - unsigned long long hi, lo; \ - \ - u.ieee.negative = sign; \ - u.ieee.negative2 = sign; \ - u.ieee.exponent = expnt + IBM_EXTENDED_LONG_DOUBLE_BIAS; \ - u.ieee.exponent2 = expnt-53 + IBM_EXTENDED_LONG_DOUBLE_BIAS; \ - /* Expect 113 bits (112 bits + hidden) right justified in two longs. \ - The low order 53 bits (52 + hidden) go into the lower double */ \ - lo = (lo64 >> 7)& ((1ULL << 53) - 1); \ - hidden2 = (lo64 >> 59) & 1ULL; \ - /* The high order 53 bits (52 + hidden) go into the upper double */ \ - hi = (lo64 >> 60) & ((1ULL << 11) - 1); \ - hi |= (hi64 << 4); \ - \ - if (lo != 0LL) \ - { \ - /* hidden2 bit of low double controls rounding of the high double. \ - If hidden2 is '1' then round up hi and adjust lo (2nd mantissa) \ - plus change the sign of the low double to compensate. */ \ - if (hidden2) \ - { \ - hi++; \ - u.ieee.negative2 = !sign; \ - lo = (1ULL << 53) - lo; \ - } \ - /* The hidden bit of the lo mantissa is zero so we need to \ - normalize the it for the low double. Shift it left until the \ - hidden bit is '1' then adjust the 2nd exponent accordingly. */ \ - \ - if (sizeof (lo) == sizeof (long)) \ - lzcount = __builtin_clzl (lo); \ - else if ((lo >> 32) != 0) \ - lzcount = __builtin_clzl ((long) (lo >> 32)); \ - else \ - lzcount = __builtin_clzl ((long) lo) + 32; \ - lzcount = lzcount - 11; \ - if (lzcount > 0) \ - { \ - int expnt2 = u.ieee.exponent2 - lzcount; \ - if (expnt2 >= 1) \ - { \ - /* Not denormal. Normalize and set low exponent. */ \ - lo = lo << lzcount; \ - u.ieee.exponent2 = expnt2; \ - } \ - else \ - { \ - /* Is denormal. */ \ - lo = lo << (lzcount + expnt2); \ - u.ieee.exponent2 = 0; \ - } \ - } \ - } \ - else \ - { \ - u.ieee.negative2 = 0; \ - u.ieee.exponent2 = 0; \ - } \ - \ - u.ieee.mantissa3 = lo & ((1ULL << 32) - 1); \ - u.ieee.mantissa2 = (lo >> 32) & ((1ULL << 20) - 1); \ - u.ieee.mantissa1 = hi & ((1ULL << 32) - 1); \ - u.ieee.mantissa0 = (hi >> 32) & ((1ULL << 20) - 1); \ - ibm_ext_ldbl = u.d; \ - } \ - while (0) +static inline long double +ldbl_insert_mantissa (int sign, int exp, int64_t hi64, u_int64_t lo64) +{ + union ibm_extended_long_double u; + unsigned long hidden2, lzcount; + unsigned long long hi, lo; + + u.ieee.negative = sign; + u.ieee.negative2 = sign; + u.ieee.exponent = exp + IBM_EXTENDED_LONG_DOUBLE_BIAS; + u.ieee.exponent2 = exp-53 + IBM_EXTENDED_LONG_DOUBLE_BIAS; + /* Expect 113 bits (112 bits + hidden) right justified in two longs. + The low order 53 bits (52 + hidden) go into the lower double */ + lo = (lo64 >> 7)& ((1ULL << 53) - 1); + hidden2 = (lo64 >> 59) & 1ULL; + /* The high order 53 bits (52 + hidden) go into the upper double */ + hi = (lo64 >> 60) & ((1ULL << 11) - 1); + hi |= (hi64 << 4); + + if (lo != 0LL) + { + /* hidden2 bit of low double controls rounding of the high double. + If hidden2 is '1' then round up hi and adjust lo (2nd mantissa) + plus change the sign of the low double to compensate. */ + if (hidden2) + { + hi++; + u.ieee.negative2 = !sign; + lo = (1ULL << 53) - lo; + } + /* The hidden bit of the lo mantissa is zero so we need to + normalize the it for the low double. Shift it left until the + hidden bit is '1' then adjust the 2nd exponent accordingly. */ + + if (sizeof (lo) == sizeof (long)) + lzcount = __builtin_clzl (lo); + else if ((lo >> 32) != 0) + lzcount = __builtin_clzl ((long) (lo >> 32)); + else + lzcount = __builtin_clzl ((long) lo) + 32; + lzcount = lzcount - 11; + if (lzcount > 0) + { + int expnt2 = u.ieee.exponent2 - lzcount; + if (expnt2 >= 1) + { + /* Not denormal. Normalize and set low exponent. */ + lo = lo << lzcount; + u.ieee.exponent2 = expnt2; + } + else + { + /* Is denormal. */ + lo = lo << (lzcount + expnt2); + u.ieee.exponent2 = 0; + } + } + } + else + { + u.ieee.negative2 = 0; + u.ieee.exponent2 = 0; + } + + u.ieee.mantissa3 = lo & ((1ULL << 32) - 1); + u.ieee.mantissa2 = (lo >> 32) & ((1ULL << 20) - 1); + u.ieee.mantissa1 = hi & ((1ULL << 32) - 1); + u.ieee.mantissa0 = (hi >> 32) & ((1ULL << 20) - 1); + return u.d; +} + +/* Handy utility functions to pack/unpack/cononicalize and find the nearbyint + of long double implemented as double double. */ +static inline long double +ldbl_pack (double a, double aa) +{ + union ibm_extended_long_double u; + u.dd[0] = a; + u.dd[1] = aa; + return u.d; +} + +static inline void +ldbl_unpack (long double l, double *a, double *aa) +{ + union ibm_extended_long_double u; + u.d = l; + *a = u.dd[0]; + *aa = u.dd[1]; +} + + +/* Convert a finite long double to canonical form. + Does not handle +/-Inf properly. */ +static inline void +ldbl_canonicalize (double *a, double *aa) +{ + double xh, xl; + + xh = *a + *aa; + xl = (*a - xh) + *aa; + *a = xh; + *aa = xl; +} + +/* Simple inline nearbyint (double) function . + Only works in the default rounding mode + but is useful in long double rounding functions. */ +static inline double +ldbl_nearbyint (double a) +{ + double two52 = 0x10000000000000LL; + + if (__builtin_expect ((__builtin_fabs (a) < two52), 1)) + { + if (__builtin_expect ((a > 0.0), 1)) + { + a += two52; + a -= two52; + } + else if (__builtin_expect ((a < 0.0), 1)) + { + a = two52 - a; + a = -(a - two52); + } + } + return a; +} |