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Diffstat (limited to 'source/luametatex/source/libraries/softposit/source/p16_sqrt.c')
| -rw-r--r-- | source/luametatex/source/libraries/softposit/source/p16_sqrt.c | 143 |
1 files changed, 143 insertions, 0 deletions
diff --git a/source/luametatex/source/libraries/softposit/source/p16_sqrt.c b/source/luametatex/source/libraries/softposit/source/p16_sqrt.c new file mode 100644 index 000000000..24d33f9c0 --- /dev/null +++ b/source/luametatex/source/libraries/softposit/source/p16_sqrt.c @@ -0,0 +1,143 @@ + +/*============================================================================ + +This C source file is part of the SoftPosit Posit Arithmetic Package +by S. H. Leong (Cerlane) and John Gustafson. + +Copyright 2017, 2018 A*STAR. All rights reserved. + +This C source file was based on SoftFloat IEEE Floating-Point Arithmetic +Package, Release 3d, by John R. Hauser. + +Copyright 2011, 2012, 2013, 2014, 2015, 2016 The Regents of the University of +California. All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are met: + + 1. Redistributions of source code must retain the above copyright notice, + this list of conditions, and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above copyright notice, + this list of conditions, and the following disclaimer in the documentation + and/or other materials provided with the distribution. + + 3. Neither the name of the University nor the names of its contributors may + be used to endorse or promote products derived from this software without + specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS "AS IS", AND ANY +EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE +DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY +DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES +(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; +LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND +ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS +SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + +=============================================================================*/ + +#include "platform.h" +#include "internals.h" + +extern const uint_fast16_t softposit_approxRecipSqrt0[]; +extern const uint_fast16_t softposit_approxRecipSqrt1[]; + +posit16_t p16_sqrt( posit16_t pA ) { + + union ui16_p16 uA; + uint_fast16_t expA, fracA, index, r0, shift, sigma0, uiA, uiZ; + uint_fast32_t eSqrR0, fracZ, negRem, recipSqrt, shiftedFracZ; + int_fast16_t kZ; + bool bitNPlusOne; + + uA.p = pA; + uiA = uA.ui; + + // If sign bit is set, return NaR. + if (uiA>>15) { + uA.ui = 0x8000; + return uA.p; + } + // If the argument is zero, return zero. + if (uiA==0) { + uA.ui = 0; + return uA.p; + } + // Compute the square root. Here, kZ is the net power-of-2 scaling of the result. + // Decode the regime and exponent bit; scale the input to be in the range 1 to 4: + if (uiA >> 14) { + kZ = -1; + while (uiA & 0x4000) { + kZ++; + uiA= (uiA<<1) & 0xFFFF; + } + } + else { + kZ = 0; + while (!(uiA & 0x4000)) { + kZ--; + uiA= (uiA<<1) & 0xFFFF; + } + + } + uiA &= 0x3fff; + expA = 1 - (uiA >> 13); + fracA = (uiA | 0x2000) >> 1; + + // Use table look-up of first four bits for piecewise linear approx. of 1/sqrt: + index = ((fracA >> 8) & 0xE) + expA; + + r0 = softposit_approxRecipSqrt0[index] + - (((uint_fast32_t) softposit_approxRecipSqrt1[index] + * (fracA & 0x1FF)) >> 13); + // Use Newton-Raphson refinement to get more accuracy for 1/sqrt: + eSqrR0 = ((uint_fast32_t) r0 * r0) >> 1; + + if (expA) eSqrR0 >>= 1; + sigma0 = 0xFFFF ^ (0xFFFF & (((uint64_t)eSqrR0 * (uint64_t)fracA) >> 18));//~(uint_fast16_t) ((eSqrR0 * fracA) >> 18); + recipSqrt = ((uint_fast32_t) r0 << 2) + (((uint_fast32_t) r0 * sigma0) >> 23); + + // We need 17 bits of accuracy for posit16 square root approximation. + // Multiplying 16 bits and 18 bits needs 64-bit scratch before the right shift: + fracZ = (((uint_fast64_t) fracA) * recipSqrt) >> 13; + + // Figure out the regime and the resulting right shift of the fraction: + if (kZ < 0) { + shift = (-1 - kZ) >> 1; + uiZ = 0x2000 >> shift; + } + else { + shift = kZ >> 1; + uiZ = 0x7fff - (0x7FFF >> (shift + 1)); + } + // Set the exponent bit in the answer, if it is nonzero: + if (kZ & 1) uiZ |= (0x1000 >> shift); + + // Right-shift fraction bits, accounting for 1 <= a < 2 versus 2 <= a < 4: + fracZ = fracZ >> (expA + shift); + + // Trick for eliminating off-by-one cases that only uses one multiply: + fracZ++; + if (!(fracZ & 7)) { + shiftedFracZ = fracZ >> 1; + negRem = (shiftedFracZ * shiftedFracZ) & 0x3FFFF; + if (negRem & 0x20000) { + fracZ |= 1; + } else { + if (negRem) fracZ--; + } + } + // Strip off the hidden bit and round-to-nearest using last 4 bits. + fracZ -= (0x10000 >> shift); + bitNPlusOne = (fracZ >> 3) & 1; + if (bitNPlusOne) { + if (((fracZ >> 4) & 1) | (fracZ & 7)) fracZ += 0x10; + } + // Assemble the result and return it. + uA.ui = uiZ | (fracZ >> 4); + return uA.p; + +} |