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Diffstat (limited to 'src/math/s_expm1f.c')
| -rw-r--r-- | src/math/s_expm1f.c | 122 |
1 files changed, 122 insertions, 0 deletions
diff --git a/src/math/s_expm1f.c b/src/math/s_expm1f.c new file mode 100644 index 00000000..b22cf0f9 --- /dev/null +++ b/src/math/s_expm1f.c @@ -0,0 +1,122 @@ +/* s_expm1f.c -- float version of s_expm1.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 <math.h> +#include "math_private.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 */ + /* scaled coefficients related to expm1 */ +Q1 = -3.3333335072e-02, /* 0xbd088889 */ +Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ +Q3 = -7.9365076090e-05, /* 0xb8a670cd */ +Q4 = 4.0082177293e-06, /* 0x36867e54 */ +Q5 = -2.0109921195e-07; /* 0xb457edbb */ + +float +expm1f(float x) +{ + float y,hi,lo,c=0.0,t,e,hxs,hfx,r1; + int32_t k,xsb; + uint32_t hx; + + GET_FLOAT_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |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) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ + if(x+tiny<(float)0.0) /* raise inexact */ + 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; + } + 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+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = (float)3.0-r1*hfx; + e = hxs*((r1-t)/((float)6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + 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)); + else return one+(float)2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + int32_t i; + y = one-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<23) { + int32_t i; + SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } else { + int32_t i; + SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } + } + return y; +} |