s_expm1f.c revision 352835
12116Sjkh/* s_expm1f.c -- float version of s_expm1.c. 22116Sjkh * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 32116Sjkh */ 42116Sjkh 52116Sjkh/* 62116Sjkh * ==================================================== 72116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 82116Sjkh * 92116Sjkh * Developed at SunPro, a Sun Microsystems, Inc. business. 102116Sjkh * Permission to use, copy, modify, and distribute this 118870Srgrimes * software is freely granted, provided that this notice 122116Sjkh * is preserved. 132116Sjkh * ==================================================== 142116Sjkh */ 152116Sjkh 16176082Sbde#include <sys/cdefs.h> 17176082Sbde__FBSDID("$FreeBSD: stable/10/lib/msun/src/s_expm1f.c 352835 2019-09-28 08:57:29Z dim $"); 182116Sjkh 19226596Sdas#include <float.h> 20226596Sdas 212116Sjkh#include "math.h" 222116Sjkh#include "math_private.h" 232116Sjkh 242116Sjkhstatic const float 252116Sjkhone = 1.0, 262116Sjkhtiny = 1.0e-30, 272116Sjkho_threshold = 8.8721679688e+01,/* 0x42b17180 */ 282116Sjkhln2_hi = 6.9313812256e-01,/* 0x3f317180 */ 292116Sjkhln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ 302116Sjkhinvln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ 31176132Sbde/* 32176132Sbde * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: 33176132Sbde * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 34176132Sbde * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): 35176132Sbde */ 36176132SbdeQ1 = -3.3333212137e-2, /* -0x888868.0p-28 */ 37176132SbdeQ2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ 382116Sjkh 39251024Sdasstatic volatile float huge = 1.0e+30; 40251024Sdas 4197413Salfredfloat 4297413Salfredexpm1f(float x) 432116Sjkh{ 44176082Sbde float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; 452116Sjkh int32_t k,xsb; 462116Sjkh u_int32_t hx; 472116Sjkh 482116Sjkh GET_FLOAT_WORD(hx,x); 492116Sjkh xsb = hx&0x80000000; /* sign bit of x */ 502116Sjkh hx &= 0x7fffffff; /* high word of |x| */ 512116Sjkh 522116Sjkh /* filter out huge and non-finite argument */ 532116Sjkh if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ 542116Sjkh if(hx >= 0x42b17218) { /* if |x|>=88.721... */ 552116Sjkh if(hx>0x7f800000) 562116Sjkh return x+x; /* NaN */ 572116Sjkh if(hx==0x7f800000) 582116Sjkh return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ 592116Sjkh if(x > o_threshold) return huge*huge; /* overflow */ 602116Sjkh } 612116Sjkh if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ 622116Sjkh if(x+tiny<(float)0.0) /* raise inexact */ 632116Sjkh return tiny-one; /* return -1 */ 642116Sjkh } 652116Sjkh } 662116Sjkh 672116Sjkh /* argument reduction */ 688870Srgrimes if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ 692116Sjkh if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ 702116Sjkh if(xsb==0) 712116Sjkh {hi = x - ln2_hi; lo = ln2_lo; k = 1;} 722116Sjkh else 732116Sjkh {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} 742116Sjkh } else { 752116Sjkh k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); 762116Sjkh t = k; 772116Sjkh hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ 782116Sjkh lo = t*ln2_lo; 792116Sjkh } 80226596Sdas STRICT_ASSIGN(float, x, hi - lo); 812116Sjkh c = (hi-x)-lo; 828870Srgrimes } 832116Sjkh else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ 842116Sjkh t = huge+x; /* return x with inexact flags when x!=0 */ 858870Srgrimes return x - (t-(huge+x)); 862116Sjkh } 872116Sjkh else k = 0; 882116Sjkh 892116Sjkh /* x is now in primary range */ 902116Sjkh hfx = (float)0.5*x; 912116Sjkh hxs = x*hfx; 92176132Sbde r1 = one+hxs*(Q1+hxs*Q2); 932116Sjkh t = (float)3.0-r1*hfx; 942116Sjkh e = hxs*((r1-t)/((float)6.0 - x*t)); 952116Sjkh if(k==0) return x - (x*e-hxs); /* c is 0 */ 962116Sjkh else { 97352835Sdim SET_FLOAT_WORD(twopk,((u_int32_t)(0x7f+k))<<23); /* 2^k */ 982116Sjkh e = (x*(e-c)-c); 992116Sjkh e -= hxs; 1002116Sjkh if(k== -1) return (float)0.5*(x-e)-(float)0.5; 101177711Sdas if(k==1) { 1022116Sjkh if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); 1032116Sjkh else return one+(float)2.0*(x-e); 104177711Sdas } 1052116Sjkh if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ 1062116Sjkh y = one-(e-x); 107176082Sbde if (k == 128) y = y*2.0F*0x1p127F; 108176082Sbde else y = y*twopk; 1092116Sjkh return y-one; 1102116Sjkh } 1112116Sjkh t = one; 1122116Sjkh if(k<23) { 1132116Sjkh SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ 1142116Sjkh y = t-(e-x); 115176082Sbde y = y*twopk; 1162116Sjkh } else { 1172116Sjkh SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ 1182116Sjkh y = x-(e+t); 1192116Sjkh y += one; 120176082Sbde y = y*twopk; 1212116Sjkh } 1222116Sjkh } 1232116Sjkh return y; 1242116Sjkh} 125