1 /* s_expm1f.c -- float version of s_expm1.c. 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) cygnus.com. 3 */ 4 5 /* 6 * ==================================================== 7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 8 * 9 * Developed at SunPro, a Sun Microsystems, Inc. business. 10 * Permission to use, copy, modify, and distribute this 11 * software is freely granted, provided that this notice 12 * is preserved. 13 * ==================================================== 14 */ 15 16 #include <sys/cdefs.h> 17 #if defined(LIBM_SCCS) && !defined(lint) 18 __RCSID("$NetBSD: s_expm1f.c,v 1.11 2017/02/09 22:11:09 maya Exp $"); 19 #endif 20 21 #include "math.h" 22 #include "math_private.h" 23 24 static const float huge = 1.0e+30, tiny = 1.0e-30; 25 26 static const float 27 one = 1.0, 28 o_threshold = 8.8721679688e+01,/* 0x42b17180 */ 29 ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 30 ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 31 invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 32 /* scaled coefficients related to expm1 */ 33 Q1 = -3.3333335072e-02, /* 0xbd088889 */ 34 Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ 35 Q3 = -7.9365076090e-05, /* 0xb8a670cd */ 36 Q4 = 4.0082177293e-06, /* 0x36867e54 */ 37 Q5 = -2.0109921195e-07; /* 0xb457edbb */ 38 39 float 40 expm1f(float x) 41 { 42 float y,hi,lo,c,t,e,hxs,hfx,r1; 43 int32_t k,xsb; 44 u_int32_t hx; 45 46 c = 0; 47 GET_FLOAT_WORD(hx,x); 48 xsb = hx&0x80000000; /* sign bit of x */ 49 #ifdef DEAD_CODE 50 if(xsb==0) y=x; else y= -x; /* y = |x| */ 51 #endif 52 hx &= 0x7fffffff; /* high word of |x| */ 53 54 /* filter out huge and non-finite argument */ 55 if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 56 if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 57 if(hx>0x7f800000) 58 return x+x; /* NaN */ 59 if(hx==0x7f800000) 60 return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 61 if(x > o_threshold) return huge*huge; /* overflow */ 62 } 63 if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 64 if(x+tiny<(float)0.0) /* raise inexact */ 65 return tiny-one; /* return -1 */ 66 } 67 } 68 69 /* argument reduction */ 70 if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 71 if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 72 if(xsb==0) 73 {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 74 else 75 {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 76 } else { 77 k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 78 t = k; 79 hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 80 lo = t*ln2_lo; 81 } 82 x = hi - lo; 83 c = (hi-x)-lo; 84 } 85 else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 86 t = huge+x; /* return x with inexact flags when x!=0 */ 87 return x - (t-(huge+x)); 88 } 89 else k = 0; 90 91 /* x is now in primary range */ 92 hfx = (float)0.5*x; 93 hxs = x*hfx; 94 r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); 95 t = (float)3.0-r1*hfx; 96 e = hxs*((r1-t)/((float)6.0 - x*t)); 97 if(k==0) return x - (x*e-hxs); /* c is 0 */ 98 else { 99 e = (x*(e-c)-c); 100 e -= hxs; 101 if(k== -1) return (float)0.5*(x-e)-(float)0.5; 102 if(k==1) { 103 if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 104 else return one+(float)2.0*(x-e); 105 } 106 if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 107 int32_t i; 108 y = one-(e-x); 109 GET_FLOAT_WORD(i,y); 110 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 111 return y-one; 112 } 113 t = one; 114 if(k<23) { 115 int32_t i; 116 SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 117 y = t-(e-x); 118 GET_FLOAT_WORD(i,y); 119 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 120 } else { 121 int32_t i; 122 SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 123 y = x-(e+t); 124 y += one; 125 GET_FLOAT_WORD(i,y); 126 SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ 127 } 128 } 129 return y; 130 } 131
Indexes created Sun Sep 21 15:09:59 GMT 2025