diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/math/exp.c | 20 | ||||
| -rw-r--r-- | src/math/expf.c | 98 |
2 files changed, 55 insertions, 63 deletions
diff --git a/src/math/exp.c b/src/math/exp.c index 5c0edee4..5ec8f8a7 100644 --- a/src/math/exp.c +++ b/src/math/exp.c @@ -80,7 +80,7 @@ P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ double exp(double x) { - double hi, lo, c, z; + double hi, lo, c, xx; int k, sign; uint32_t hx; @@ -92,24 +92,26 @@ double exp(double x) if (hx >= 0x40862e42) { /* if |x| >= 709.78... */ if (isnan(x)) return x; + if (hx == 0x7ff00000 && sign) /* -inf */ + return 0; if (x > 709.782712893383973096) { /* overflow if x!=inf */ STRICT_ASSIGN(double, x, 0x1p1023 * x); return x; } if (x < -745.13321910194110842) { - /* underflow if x!=-inf */ - STRICT_ASSIGN(double, x, 0x1p-1000 / -x * 0x1p-1000); + /* underflow */ + STRICT_ASSIGN(double, x, 0x1p-1000 * 0x1p-1000); return x; } } /* argument reduction */ if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ - if (hx < 0x3ff0a2b2) /* if |x| < 1.5 ln2 */ - k = 1 - sign - sign; /* optimization */ - else + if (hx >= 0x3ff0a2b2) /* if |x| >= 1.5 ln2 */ k = (int)(invln2*x + half[sign]); + else + k = 1 - sign - sign; hi = x - k*ln2hi; /* k*ln2hi is exact here */ lo = k*ln2lo; STRICT_ASSIGN(double, x, hi - lo); @@ -124,9 +126,9 @@ double exp(double x) } /* x is now in primary range */ - z = x*x; - c = x - z*(P1+z*(P2+z*(P3+z*(P4+z*P5)))); - x = 1 + ((x*c/(2-c) - lo) + hi); + xx = x*x; + c = x - xx*(P1+xx*(P2+xx*(P3+xx*(P4+xx*P5)))); + x = 1 + (x*c/(2-c) - lo + hi); if (k == 0) return x; return scalbn(x, k); diff --git a/src/math/expf.c b/src/math/expf.c index 3c3e2ab9..8aefc917 100644 --- a/src/math/expf.c +++ b/src/math/expf.c @@ -16,79 +16,69 @@ #include "libm.h" static const float -halF[2] = {0.5,-0.5,}, -huge = 1.0e+30, -o_threshold = 8.8721679688e+01, /* 0x42b17180 */ -u_threshold = -1.0397208405e+02, /* 0xc2cff1b5 */ -ln2HI[2] = { 6.9314575195e-01, /* 0x3f317200 */ - -6.9314575195e-01,},/* 0xbf317200 */ -ln2LO[2] = { 1.4286067653e-06, /* 0x35bfbe8e */ - -1.4286067653e-06,},/* 0xb5bfbe8e */ -invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ +half[2] = {0.5,-0.5}, +ln2hi = 6.9314575195e-1f, /* 0x3f317200 */ +ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */ +invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */ /* * Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]: * |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74 */ -P1 = 1.6666625440e-1, /* 0xaaaa8f.0p-26 */ -P2 = -2.7667332906e-3; /* -0xb55215.0p-32 */ - -static const volatile float twom100 = 7.8886090522e-31; /* 2**-100=0x0d800000 */ +P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */ +P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */ float expf(float x) { - float y,hi=0.0,lo=0.0,c,t,twopk; - int32_t k=0,xsb; + float hi, lo, c, xx; + int k, sign; uint32_t hx; GET_FLOAT_WORD(hx, x); - xsb = (hx>>31)&1; /* sign bit of x */ + sign = hx >> 31; /* sign bit of x */ hx &= 0x7fffffff; /* high word of |x| */ - /* filter out non-finite argument */ - if (hx >= 0x42b17218) { /* if |x|>=88.721... */ + /* special cases */ + if (hx >= 0x42b17218) { /* if |x| >= 88.722839f or NaN */ if (hx > 0x7f800000) /* NaN */ - return x+x; - if (hx == 0x7f800000) /* exp(+-inf)={inf,0} */ - return xsb==0 ? x : 0.0; - if (x > o_threshold) - return huge*huge; /* overflow */ - if (x < u_threshold) - return twom100*twom100; /* underflow */ + return x; + if (!sign) { + /* overflow if x!=inf */ + STRICT_ASSIGN(float, x, x * 0x1p127f); + return x; + } + if (hx == 0x7f800000) /* -inf */ + return 0; + if (hx >= 0x42cff1b5) { /* x <= -103.972084f */ + /* underflow */ + STRICT_ASSIGN(float, x, 0x1p-100f*0x1p-100f); + return x; + } } /* argument reduction */ - if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ - if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ - hi = x-ln2HI[xsb]; - lo = ln2LO[xsb]; - k = 1 - xsb - xsb; - } else { - k = invln2*x + halF[xsb]; - t = k; - hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ - lo = t*ln2LO[0]; - } + if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */ + k = invln2*x + half[sign]; + else + k = 1 - sign - sign; + hi = x - k*ln2hi; /* k*ln2hi is exact here */ + lo = k*ln2lo; STRICT_ASSIGN(float, x, hi - lo); - } else if(hx < 0x39000000) { /* |x|<2**-14 */ - /* raise inexact */ - if (huge+x > 1.0f) - return 1.0f + x; - } else + } else if (hx > 0x39000000) { /* |x| > 2**-14 */ k = 0; + hi = x; + lo = 0; + } else { + /* raise inexact */ + FORCE_EVAL(0x1p127f + x); + return 1 + x; + } /* x is now in primary range */ - t = x*x; - if (k >= -125) - SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23)); - else - SET_FLOAT_WORD(twopk, 0x3f800000+((k+100)<<23)); - c = x - t*(P1+t*P2); + xx = x*x; + c = x - xx*(P1+xx*P2); + x = 1 + (x*c/(2-c) - lo + hi); if (k == 0) - return 1.0f - ((x*c)/(c - 2.0f) - x); - y = 1.0f - ((lo - (x*c)/(2.0f - c)) - hi); - if (k < -125) - return y*twopk*twom100; - if (k == 128) - return y*2.0f*0x1p127f; - return y*twopk; + return x; + return scalbnf(x, k); } |