Index: fusl/src/math/expm1.c |
diff --git a/fusl/src/math/expm1.c b/fusl/src/math/expm1.c |
index ac1e61e4f7f6a0d09651c814f7885cc6f25b163a..52cfc25b886b860e478192b6a9d753616b985968 100644 |
--- a/fusl/src/math/expm1.c |
+++ b/fusl/src/math/expm1.c |
@@ -106,96 +106,99 @@ |
#include "libm.h" |
-static const double |
-o_threshold = 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ |
-ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ |
-ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ |
-invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ |
-/* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: */ |
-Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ |
-Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ |
-Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ |
-Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ |
-Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ |
+static const double o_threshold = |
+ 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ |
+ ln2_hi = 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ |
+ ln2_lo = 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ |
+ invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ |
+ /* Scaled Q's: Qn_here = 2**n * Qn_above, for R(2*z) where z = hxs = x*x/2: |
+ */ |
+ Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ |
+ Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ |
+ Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ |
+ Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ |
+ Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ |
-double expm1(double x) |
-{ |
- double_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk; |
- union {double f; uint64_t i;} u = {x}; |
- uint32_t hx = u.i>>32 & 0x7fffffff; |
- int k, sign = u.i>>63; |
+double expm1(double x) { |
+ double_t y, hi, lo, c, t, e, hxs, hfx, r1, twopk; |
+ union { |
+ double f; |
+ uint64_t i; |
+ } u = {x}; |
+ uint32_t hx = u.i >> 32 & 0x7fffffff; |
+ int k, sign = u.i >> 63; |
- /* filter out huge and non-finite argument */ |
- if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */ |
- if (isnan(x)) |
- return x; |
- if (sign) |
- return -1; |
- if (x > o_threshold) { |
- x *= 0x1p1023; |
- return x; |
- } |
- } |
+ /* filter out huge and non-finite argument */ |
+ if (hx >= 0x4043687A) { /* if |x|>=56*ln2 */ |
+ if (isnan(x)) |
+ return x; |
+ if (sign) |
+ return -1; |
+ if (x > o_threshold) { |
+ x *= 0x1p1023; |
+ return x; |
+ } |
+ } |
- /* argument reduction */ |
- if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ |
- if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ |
- if (!sign) { |
- hi = x - ln2_hi; |
- lo = ln2_lo; |
- k = 1; |
- } else { |
- hi = x + ln2_hi; |
- lo = -ln2_lo; |
- k = -1; |
- } |
- } else { |
- k = invln2*x + (sign ? -0.5 : 0.5); |
- t = k; |
- hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ |
- lo = t*ln2_lo; |
- } |
- x = hi-lo; |
- c = (hi-x)-lo; |
- } else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */ |
- if (hx < 0x00100000) |
- FORCE_EVAL((float)x); |
- return x; |
- } else |
- k = 0; |
+ /* argument reduction */ |
+ if (hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ |
+ if (hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ |
+ if (!sign) { |
+ hi = x - ln2_hi; |
+ lo = ln2_lo; |
+ k = 1; |
+ } else { |
+ hi = x + ln2_hi; |
+ lo = -ln2_lo; |
+ k = -1; |
+ } |
+ } else { |
+ k = invln2 * x + (sign ? -0.5 : 0.5); |
+ t = k; |
+ hi = x - t * ln2_hi; /* t*ln2_hi is exact here */ |
+ lo = t * ln2_lo; |
+ } |
+ x = hi - lo; |
+ c = (hi - x) - lo; |
+ } else if (hx < 0x3c900000) { /* |x| < 2**-54, return x */ |
+ if (hx < 0x00100000) |
+ FORCE_EVAL((float)x); |
+ return x; |
+ } else |
+ k = 0; |
- /* x is now in primary range */ |
- hfx = 0.5*x; |
- hxs = x*hfx; |
- r1 = 1.0+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); |
- t = 3.0-r1*hfx; |
- e = hxs*((r1-t)/(6.0 - x*t)); |
- if (k == 0) /* c is 0 */ |
- return x - (x*e-hxs); |
- e = x*(e-c) - c; |
- e -= hxs; |
- /* exp(x) ~ 2^k (x_reduced - e + 1) */ |
- if (k == -1) |
- return 0.5*(x-e) - 0.5; |
- if (k == 1) { |
- if (x < -0.25) |
- return -2.0*(e-(x+0.5)); |
- return 1.0+2.0*(x-e); |
- } |
- u.i = (uint64_t)(0x3ff + k)<<52; /* 2^k */ |
- twopk = u.f; |
- if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ |
- y = x - e + 1.0; |
- if (k == 1024) |
- y = y*2.0*0x1p1023; |
- else |
- y = y*twopk; |
- return y - 1.0; |
- } |
- u.i = (uint64_t)(0x3ff - k)<<52; /* 2^-k */ |
- if (k < 20) |
- y = (x-e+(1-u.f))*twopk; |
- else |
- y = (x-(e+u.f)+1)*twopk; |
- return y; |
+ /* x is now in primary range */ |
+ hfx = 0.5 * x; |
+ hxs = x * hfx; |
+ r1 = 1.0 + hxs * (Q1 + hxs * (Q2 + hxs * (Q3 + hxs * (Q4 + hxs * Q5)))); |
+ t = 3.0 - r1 * hfx; |
+ e = hxs * ((r1 - t) / (6.0 - x * t)); |
+ if (k == 0) /* c is 0 */ |
+ return x - (x * e - hxs); |
+ e = x * (e - c) - c; |
+ e -= hxs; |
+ /* exp(x) ~ 2^k (x_reduced - e + 1) */ |
+ if (k == -1) |
+ return 0.5 * (x - e) - 0.5; |
+ if (k == 1) { |
+ if (x < -0.25) |
+ return -2.0 * (e - (x + 0.5)); |
+ return 1.0 + 2.0 * (x - e); |
+ } |
+ u.i = (uint64_t)(0x3ff + k) << 52; /* 2^k */ |
+ twopk = u.f; |
+ if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */ |
+ y = x - e + 1.0; |
+ if (k == 1024) |
+ y = y * 2.0 * 0x1p1023; |
+ else |
+ y = y * twopk; |
+ return y - 1.0; |
+ } |
+ u.i = (uint64_t)(0x3ff - k) << 52; /* 2^-k */ |
+ if (k < 20) |
+ y = (x - e + (1 - u.f)) * twopk; |
+ else |
+ y = (x - (e + u.f) + 1) * twopk; |
+ return y; |
} |