The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 1 | /* s_expm1f.c -- float version of s_expm1.c. |
| 2 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@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 | |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 16 | #include <sys/cdefs.h> |
| 17 | __FBSDID("$FreeBSD$"); |
| 18 | |
| 19 | #include <float.h> |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 20 | |
| 21 | #include "math.h" |
| 22 | #include "math_private.h" |
| 23 | |
| 24 | static const float |
| 25 | one = 1.0, |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 26 | tiny = 1.0e-30, |
| 27 | o_threshold = 8.8721679688e+01,/* 0x42b17180 */ |
| 28 | ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ |
| 29 | ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ |
| 30 | invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 31 | /* |
| 32 | * Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]: |
| 33 | * |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04 |
| 34 | * Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c): |
| 35 | */ |
| 36 | Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */ |
| 37 | Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */ |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 38 | |
Elliott Hughes | 7841946 | 2013-06-12 16:37:58 -0700 | [diff] [blame] | 39 | static volatile float huge = 1.0e+30; |
| 40 | |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 41 | float |
| 42 | expm1f(float x) |
| 43 | { |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 44 | float y,hi,lo,c,t,e,hxs,hfx,r1,twopk; |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 45 | int32_t k,xsb; |
| 46 | u_int32_t hx; |
| 47 | |
| 48 | GET_FLOAT_WORD(hx,x); |
| 49 | xsb = hx&0x80000000; /* sign bit of x */ |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 50 | hx &= 0x7fffffff; /* high word of |x| */ |
| 51 | |
| 52 | /* filter out huge and non-finite argument */ |
| 53 | if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ |
| 54 | if(hx >= 0x42b17218) { /* if |x|>=88.721... */ |
| 55 | if(hx>0x7f800000) |
| 56 | return x+x; /* NaN */ |
| 57 | if(hx==0x7f800000) |
| 58 | return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ |
| 59 | if(x > o_threshold) return huge*huge; /* overflow */ |
| 60 | } |
| 61 | if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ |
| 62 | if(x+tiny<(float)0.0) /* raise inexact */ |
| 63 | return tiny-one; /* return -1 */ |
| 64 | } |
| 65 | } |
| 66 | |
| 67 | /* argument reduction */ |
| 68 | if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ |
| 69 | if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ |
| 70 | if(xsb==0) |
| 71 | {hi = x - ln2_hi; lo = ln2_lo; k = 1;} |
| 72 | else |
| 73 | {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} |
| 74 | } else { |
| 75 | k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); |
| 76 | t = k; |
| 77 | hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ |
| 78 | lo = t*ln2_lo; |
| 79 | } |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 80 | STRICT_ASSIGN(float, x, hi - lo); |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 81 | c = (hi-x)-lo; |
| 82 | } |
| 83 | else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ |
| 84 | t = huge+x; /* return x with inexact flags when x!=0 */ |
| 85 | return x - (t-(huge+x)); |
| 86 | } |
| 87 | else k = 0; |
| 88 | |
| 89 | /* x is now in primary range */ |
| 90 | hfx = (float)0.5*x; |
| 91 | hxs = x*hfx; |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 92 | r1 = one+hxs*(Q1+hxs*Q2); |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 93 | t = (float)3.0-r1*hfx; |
| 94 | e = hxs*((r1-t)/((float)6.0 - x*t)); |
| 95 | if(k==0) return x - (x*e-hxs); /* c is 0 */ |
| 96 | else { |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 97 | SET_FLOAT_WORD(twopk,0x3f800000+(k<<23)); /* 2^k */ |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 98 | e = (x*(e-c)-c); |
| 99 | e -= hxs; |
| 100 | if(k== -1) return (float)0.5*(x-e)-(float)0.5; |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 101 | if(k==1) { |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 102 | if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); |
| 103 | else return one+(float)2.0*(x-e); |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 104 | } |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 105 | if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 106 | y = one-(e-x); |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 107 | if (k == 128) y = y*2.0F*0x1p127F; |
| 108 | else y = y*twopk; |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 109 | return y-one; |
| 110 | } |
| 111 | t = one; |
| 112 | if(k<23) { |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 113 | SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ |
| 114 | y = t-(e-x); |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 115 | y = y*twopk; |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 116 | } else { |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 117 | SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ |
| 118 | y = x-(e+t); |
| 119 | y += one; |
Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame] | 120 | y = y*twopk; |
The Android Open Source Project | 1dc9e47 | 2009-03-03 19:28:35 -0800 | [diff] [blame] | 121 | } |
| 122 | } |
| 123 | return y; |
| 124 | } |