author | William Roberts <williamr@symbian.org> |
Thu, 22 Jul 2010 16:48:56 +0100 | |
branch | GCC_SURGE |
changeset 45 | 4b03adbd26ca |
parent 0 | e4d67989cc36 |
permissions | -rw-r--r-- |
0
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/*-------------------------------------------------------------------- |
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*© Portions copyright (c) 2006 Nokia Corporation. All rights reserved. |
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*-------------------------------------------------------------------- |
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*/ |
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/*- |
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* Copyright (c) 2005 David Schultz <das@FreeBSD.ORG> |
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* All rights reserved. |
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* |
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* Redistribution and use in source and binary forms, with or without |
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* modification, are permitted provided that the following conditions |
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* are met: |
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* 1. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the distribution. |
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* |
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
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* SUCH DAMAGE. |
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*/ |
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|
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#include <sys/cdefs.h> |
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#ifndef __SYMBIAN32__ |
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__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.1 2005/04/05 02:57:15 das Exp $"); |
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#endif //__SYMBIAN32__ |
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#include <math.h> |
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#include "math_private.h" |
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|
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#define TBLBITS 4 |
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#define TBLSIZE (1 << TBLBITS) |
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|
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#ifndef __SYMBIAN32__ |
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static const float |
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huge = 0x1p100f, |
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twom100 = 0x1p-100f, |
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redux = 0x1.8p23f / TBLSIZE, |
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P1 = 0x1.62e430p-1f, |
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P2 = 0x1.ebfbe0p-3f, |
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P3 = 0x1.c6b348p-5f, |
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P4 = 0x1.3b2c9cp-7f; |
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|
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static const double exp2ft[TBLSIZE] = { |
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0x1.6a09e667f3bcdp-1, |
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0x1.7a11473eb0187p-1, |
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0x1.8ace5422aa0dbp-1, |
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0x1.9c49182a3f090p-1, |
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0x1.ae89f995ad3adp-1, |
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0x1.c199bdd85529cp-1, |
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0x1.d5818dcfba487p-1, |
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0x1.ea4afa2a490dap-1, |
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0x1.0000000000000p+0, |
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0x1.0b5586cf9890fp+0, |
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0x1.172b83c7d517bp+0, |
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0x1.2387a6e756238p+0, |
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0x1.306fe0a31b715p+0, |
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0x1.3dea64c123422p+0, |
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0x1.4bfdad5362a27p+0, |
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0x1.5ab07dd485429p+0, |
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}; |
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|
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#else |
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static const float |
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huge = 1.26765e+30f, |
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twom100 = 7.88861e-31f, |
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redux = 12582912/ TBLSIZE, |
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P1 = 0.6931472f, |
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P2 = 0.2402265f, |
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P3 = 0.05550541f, |
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P4 = 0.009618355; |
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|
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static const double exp2ft[TBLSIZE] = { |
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0.70710677, |
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0.7384131, |
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0.7711054, |
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0.80524516, |
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0.8408964, |
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0.8781261, |
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0.91700405, |
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0.9576033, |
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1.000000, |
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1.0442737, |
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1.0905077, |
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1.1387886, |
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1.1892071, |
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1.2418578, |
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1.2968396, |
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1.3542556, |
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}; |
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#endif //__SYMBIAN32__ |
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/* |
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* exp2f(x): compute the base 2 exponential of x |
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104 |
* |
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* Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927. |
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106 |
* |
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* Method: (equally-spaced tables) |
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108 |
* |
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* Reduce x: |
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* x = 2**k + y, for integer k and |y| <= 1/2. |
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* Thus we have exp2f(x) = 2**k * exp2(y). |
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112 |
* |
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* Reduce y: |
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* y = i/TBLSIZE + z for integer i near y * TBLSIZE. |
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* Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), |
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* with |z| <= 2**-(TBLSIZE+1). |
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* |
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* We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a |
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* degree-4 minimax polynomial with maximum error under 1.4 * 2**-33. |
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* Using double precision in the final calculation avoids roundoff error. |
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121 |
* |
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* This method is due to Tang, but I do not use his suggested parameters: |
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123 |
* |
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* Tang, P. Table-driven Implementation of the Exponential Function |
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* in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989). |
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*/ |
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EXPORT_C float exp2f(float x) |
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128 |
{ |
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double tv; |
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float r, z; |
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volatile float t; /* prevent gcc from using too much precision */ |
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uint32_t hx, hr, ix, i0; |
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int32_t k; |
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134 |
|
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/* Filter out exceptional cases. */ |
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GET_FLOAT_WORD(hx,x); |
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ix = hx & 0x7fffffff; /* high word of |x| */ |
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if(ix >= 0x43000000) { /* |x| >= 128 */ |
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if(ix >= 0x7f800000) { |
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if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0) |
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return (x); /* x is NaN or +Inf */ |
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else |
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return (0.0); /* x is -Inf */ |
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} |
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#ifdef __SYMBIAN32__ |
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if(x >= 128.0f) |
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#else |
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if(x >= 0x1.0p7f) |
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#endif //__SYMBIAN32__ |
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return (huge * huge); /* overflow */ |
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#ifdef __SYMBIAN32__ |
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if(x <= -150.0f) |
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#else |
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if(x <= -0x1.2cp7f) |
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#endif //__SYMBIAN32__ |
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return (twom100 * twom100); /* underflow */ |
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} else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */ |
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return (1.0f + x); |
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} |
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160 |
|
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/* Reduce x, computing z, i0, and k. */ |
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t = x + redux; |
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GET_FLOAT_WORD(i0, t); |
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i0 += TBLSIZE / 2; |
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k = (i0 >> TBLBITS) << 23; |
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i0 &= TBLSIZE - 1; |
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t -= redux; |
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z = x - t; |
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169 |
|
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/* Compute r = exp2(y) = exp2ft[i0] * p(z). */ |
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tv = exp2ft[i0]; |
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r = tv + tv * (z * (P1 + z * (P2 + z * (P3 + z * P4)))); |
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173 |
|
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/* Scale by 2**(k>>23). */ |
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if(k >= -125 << 23) { |
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if (k != 0) { |
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GET_FLOAT_WORD(hr, r); |
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SET_FLOAT_WORD(r, hr + k); |
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} |
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return (r); |
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} else { |
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GET_FLOAT_WORD(hr, r); |
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SET_FLOAT_WORD(r, hr + (k + (100 << 23))); |
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return (r * twom100); |
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} |
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} |