first commit of the new libm!

[musl] / src / math / expm1f.c

diff --git a/src/math/expm1f.c b/src/math/expm1f.c
new file mode 100644 (file)
index 0000000..cfab697
--- /dev/null
+++ b/src/math/expm1f.c
@@ -0,0 +1,125 @@
+/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
+/*
+ * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
+ */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include "libm.h"
+
+static const float
+one         = 1.0,
+huge        = 1.0e+30,
+tiny        = 1.0e-30,
+o_threshold = 8.8721679688e+01, /* 0x42b17180 */
+ln2_hi      = 6.9313812256e-01, /* 0x3f317180 */
+ln2_lo      = 9.0580006145e-06, /* 0x3717f7d1 */
+invln2      = 1.4426950216e+00, /* 0x3fb8aa3b */
+/*
+ * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
+ * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
+ * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
+ */
+Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
+Q2 =  1.5807170421e-3; /*  0xcf3010.0p-33 */
+
+float expm1f(float x)
+{
+       float y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
+       int32_t k,xsb;
+       uint32_t hx;
+
+       GET_FLOAT_WORD(hx, x);
+       xsb = hx&0x80000000;  /* sign bit of x */
+       hx &= 0x7fffffff;     /* high word of |x| */
+
+       /* filter out huge and non-finite argument */
+       if (hx >= 0x4195b844) {  /* if |x|>=27*ln2 */
+               if (hx >= 0x42b17218) {  /* if |x|>=88.721... */
+                       if (hx > 0x7f800000)  /* NaN */
+                               return x+x;
+                       if (hx == 0x7f800000) /* exp(+-inf)={inf,-1} */
+                               return xsb==0 ? x : -1.0;
+                       if (x > o_threshold)
+                               return huge*huge; /* overflow */
+               }
+               if (xsb != 0) {  /* x < -27*ln2 */
+                       /* raise inexact */
+                       if (x+tiny < (float)0.0)
+                               return tiny-one;  /* return -1 */
+               }
+       }
+
+       /* argument reduction */
+       if (hx > 0x3eb17218) {           /* if  |x| > 0.5 ln2 */
+               if (hx < 0x3F851592) {       /* and |x| < 1.5 ln2 */
+                       if (xsb == 0) {
+                               hi = x - ln2_hi;
+                               lo = ln2_lo;
+                               k =  1;
+                       } else {
+                               hi = x + ln2_hi;
+                               lo = -ln2_lo;
+                               k = -1;
+                       }
+               } else {
+                       k  = invln2*x+((xsb==0)?(float)0.5:(float)-0.5);
+                       t  = k;
+                       hi = x - t*ln2_hi;      /* t*ln2_hi is exact here */
+                       lo = t*ln2_lo;
+               }
+               STRICT_ASSIGN(float, x, hi - lo);
+               c = (hi-x)-lo;
+       } else if (hx < 0x33000000) {  /* when |x|<2**-25, return x */
+               t = huge+x; /* return x with inexact flags when x!=0 */
+               return x - (t-(huge+x));
+       } else
+               k = 0;
+
+       /* x is now in primary range */
+       hfx = (float)0.5*x;
+       hxs = x*hfx;
+       r1 = one+hxs*(Q1+hxs*Q2);
+       t  = (float)3.0 - r1*hfx;
+       e  = hxs*((r1-t)/((float)6.0 - x*t));
+       if (k == 0)  /* c is 0 */
+               return x - (x*e-hxs);
+       SET_FLOAT_WORD(twopk, 0x3f800000+(k<<23));   /* 2^k */
+       e  = x*(e-c) - c;
+       e -= hxs;
+       if (k == -1)
+               return (float)0.5*(x-e) - (float)0.5;
+       if (k == 1) {
+               if (x < (float)-0.25)
+                       return -(float)2.0*(e-(x+(float)0.5));
+               return one+(float)2.0*(x-e);
+       }
+       if (k <= -2 || k > 56) {   /* suffice to return exp(x)-1 */
+               y = one - (e - x);
+               if (k == 128)
+                       y = y*2.0F*0x1p127F;
+               else
+                       y = y*twopk;
+               return y - one;
+       }
+       t = one;
+       if (k < 23) {
+               SET_FLOAT_WORD(t, 0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */
+               y = t - (e - x);
+               y = y*twopk;
+       } else {
+               SET_FLOAT_WORD(t, ((0x7f-k)<<23));  /* 2^-k */
+               y = x - (e + t);
+               y += one;
+               y = y*twopk;
+       }
+       return y;
+}