diff options
Diffstat (limited to 'sysdeps/libm-ieee754/s_exp2f.c')
| -rw-r--r-- | sysdeps/libm-ieee754/s_exp2f.c | 77 |
1 files changed, 41 insertions, 36 deletions
diff --git a/sysdeps/libm-ieee754/s_exp2f.c b/sysdeps/libm-ieee754/s_exp2f.c index 05e79c9f5a..11c5d55e2e 100644 --- a/sysdeps/libm-ieee754/s_exp2f.c +++ b/sysdeps/libm-ieee754/s_exp2f.c @@ -38,20 +38,22 @@ #include "t_exp2f.h" static const volatile float TWOM100 = 7.88860905e-31; -static const volatile float huge = 1e+30; +static const volatile float TWO127 = 1.7014118346e+38; float __ieee754_exp2f (float x) { - static const uint32_t a_inf = 0x7f800000; + static const uint32_t a_minf = 0xff800000; + static const float himark = (float) FLT_MAX_EXP; + static const float lomark = (float) (FLT_MIN_EXP - FLT_MANT_DIG - 1) - 1.0; + /* Check for usual case. */ - if (isless (x, (float) FLT_MAX_EXP) - && isgreater (x, (float) (FLT_MIN_EXP - 1))) + if (isless (x, himark) && isgreater (x, lomark)) { - static const float TWO16 = 65536.0; - int tval; - float rx, x22; - union ieee754_float ex2_u; + static const float TWO15 = 32768.0; + int tval, unsafe; + float rx, x22, result; + union ieee754_float ex2_u, scale_u; fenv_t oldenv; feholdexcept (&oldenv); @@ -68,13 +70,13 @@ __ieee754_exp2f (float x) First, calculate rx = ex + t/256. */ if (x >= 0) { - rx = x + TWO16; - rx -= TWO16; + rx = x + TWO15; + rx -= TWO15; } else { - rx = x - TWO16; - rx += TWO16; + rx = x - TWO15; ++ rx += TWO15; } x -= rx; /* Compute x=x1. */ /* Compute tval = (ex*256 + t)+128. @@ -92,40 +94,43 @@ __ieee754_exp2f (float x) /* 'tval & 255' is the same as 'tval%256' except that it's always positive. Compute x = x2. */ - x -= exp2_deltatable[tval & 255]; + x -= __exp2_deltatable[tval & 255]; /* 3. Compute ex2 = 2^(t/255+e+ex). */ - ex2_u.f = exp2_accuratetable[tval & 255]; - ex2_u.ieee.exponent += tval >> 8; + ex2_u.f = __exp2f_atable[tval & 255]; + tval >>= 8; + unsafe = abs(tval) >= -FLT_MIN_EXP - 1; + ex2_u.ieee.exponent += tval >> unsafe; + scale_u.f = 1.0; + scale_u.ieee.exponent += tval - (tval >> unsafe); /* 4. Approximate 2^x2 - 1, using a second-degree polynomial, - 2^x2 ~= sum(k=0..2 | (x2 * ln(2))^k / k! ) + - so - 2^x2 - 1 ~= sum(k=1..4 | (x2 * ln(2))^k / k! ) - with error less than 2^(1/512+7e-4) * (x2 * ln(2))^3 / 3! < 1.2e-18. */ + with maximum error in [-2^-9 - 2^-14, 2^-9 + 2^-14] + less than 1.3e-10. */ - x22 = (.240226507f * x + .6931471806f) * ex2_u.f; + x22 = (.24022656679f * x + .69314736128f) * ex2_u.f; /* 5. Return (2^x2-1) * 2^(t/512+e+ex) + 2^(t/512+e+ex). */ fesetenv (&oldenv); - /* Need to check: does this set FE_INEXACT correctly? */ - return x22 * x + ex2_u.f; + result = x22 * x + ex2_u.f; + + if (!unsafe) + return result; + else + return result * scale_u.f; } - /* 2^inf == inf, with no error. */ - else if (x == *(const float *)&a_inf) + /* Exceptional cases: */ + else if (isless (x, himark)) { - return x; + if (x == *(const float *) &a_minf) + /* e^-inf == 0, with no error. */ + return 0; + else + /* Underflow */ + return TWOM100 * TWOM100; } - /* Check for overflow. */ - else if (isgreaterequal (x, (float) FLT_MAX_EXP)) - return huge * huge; - /* And underflow (including -inf). */ - else if (isless (x, (float) (FLT_MIN_EXP - FLT_MANT_DIG))) - return TWOM100 * TWOM100; - /* Maybe the result needs to be a denormalised number... */ - else if (!isnan (x)) - return __ieee754_exp2f (x + 100.0) * TWOM100; - else /* isnan(x) */ - return x + x; + else + /* Return x, if x is a NaN or Inf; or overflow, otherwise. */ + return TWO127*x; } |