a5de509e4e
Follow the ordinary gentype conventions for the log implementation, instead of using a plain header. This doesn't quite yet enable vectorization, due to how the table is currently indexed. This should make it easier for targets to selectively overload the function for a subset of types.
244 lines
7.2 KiB
C++
244 lines
7.2 KiB
C++
//===----------------------------------------------------------------------===//
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//
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// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
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// See https://llvm.org/LICENSE.txt for license information.
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// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
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//
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//===----------------------------------------------------------------------===//
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/*
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Algorithm:
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Based on:
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Ping-Tak Peter Tang
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"Table-driven implementation of the logarithm function in IEEE
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floating-point arithmetic"
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ACM Transactions on Mathematical Software (TOMS)
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Volume 16, Issue 4 (December 1990)
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x very close to 1.0 is handled differently, for x everywhere else
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a brief explanation is given below
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x = (2^m)*A
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x = (2^m)*(G+g) with (1 <= G < 2) and (g <= 2^(-8))
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x = (2^m)*2*(G/2+g/2)
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x = (2^m)*2*(F+f) with (0.5 <= F < 1) and (f <= 2^(-9))
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Y = (2^(-1))*(2^(-m))*(2^m)*A
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Now, range of Y is: 0.5 <= Y < 1
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F = 0x80 + (first 7 mantissa bits) + (8th mantissa bit)
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Now, range of F is: 128 <= F <= 256
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F = F / 256
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Now, range of F is: 0.5 <= F <= 1
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f = -(Y-F), with (f <= 2^(-9))
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log(x) = m*log(2) + log(2) + log(F-f)
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log(x) = m*log(2) + log(2) + log(F) + log(1-(f/F))
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log(x) = m*log(2) + log(2*F) + log(1-r)
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r = (f/F), with (r <= 2^(-8))
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r = f*(1/F) with (1/F) precomputed to avoid division
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log(x) = m*log(2) + log(G) - poly
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log(G) is precomputed
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poly = (r + (r^2)/2 + (r^3)/3 + (r^4)/4) + (r^5)/5))
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log(2) and log(G) need to be maintained in extra precision
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to avoid losing precision in the calculations
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For x close to 1.0, we employ the following technique to
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ensure faster convergence.
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log(x) = log((1+s)/(1-s)) = 2*s + (2/3)*s^3 + (2/5)*s^5 + (2/7)*s^7
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x = ((1+s)/(1-s))
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x = 1 + r
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s = r/(2+r)
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*/
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#ifdef __CLC_SCALAR
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#if __CLC_FPSIZE == 32
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_CLC_OVERLOAD _CLC_DEF __CLC_FLOATN
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#if defined(COMPILING_LOG2)
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__clc_log2(__CLC_FLOATN x)
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#elif defined(COMPILING_LOG10)
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__clc_log10(__CLC_FLOATN x)
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#else
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__clc_log(__CLC_FLOATN x)
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#endif
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{
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#if defined(COMPILING_LOG2)
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const __CLC_FLOATN LOG2E = 0x1.715476p+0f; // 1.4426950408889634
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const __CLC_FLOATN LOG2E_HEAD = 0x1.700000p+0f; // 1.4375
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const __CLC_FLOATN LOG2E_TAIL = 0x1.547652p-8f; // 0.00519504072
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#elif defined(COMPILING_LOG10)
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const __CLC_FLOATN LOG10E = 0x1.bcb7b2p-2f; // 0.43429448190325182
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const __CLC_FLOATN LOG10E_HEAD = 0x1.bc0000p-2f; // 0.43359375
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const __CLC_FLOATN LOG10E_TAIL = 0x1.6f62a4p-11f; // 0.0007007319
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const __CLC_FLOATN LOG10_2_HEAD = 0x1.340000p-2f; // 0.30078125
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const __CLC_FLOATN LOG10_2_TAIL = 0x1.04d426p-12f; // 0.000248745637
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#else
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const __CLC_FLOATN LOG2_HEAD = 0x1.62e000p-1f; // 0.693115234
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const __CLC_FLOATN LOG2_TAIL = 0x1.0bfbe8p-15f; // 0.0000319461833
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#endif
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uint xi = __clc_as_uint(x);
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uint ax = xi & EXSIGNBIT_SP32;
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// Calculations for |x-1| < 2^-4
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__CLC_FLOATN r = x - 1.0f;
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int near1 = __clc_fabs(r) < 0x1.0p-4f;
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__CLC_FLOATN u2 = MATH_DIVIDE(r, 2.0f + r);
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__CLC_FLOATN corr = u2 * r;
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__CLC_FLOATN u = u2 + u2;
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__CLC_FLOATN v = u * u;
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__CLC_FLOATN znear1, z1, z2;
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// 2/(5 * 2^5), 2/(3 * 2^3)
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z2 = __clc_mad(u, __clc_mad(v, 0x1.99999ap-7f, 0x1.555556p-4f) * v, -corr);
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#if defined(COMPILING_LOG2)
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z1 = __CLC_AS_FLOATN(__CLC_AS_INTN(r) & 0xffff0000);
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z2 = z2 + (r - z1);
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znear1 = __clc_mad(
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z1, LOG2E_HEAD,
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__clc_mad(z2, LOG2E_HEAD, __clc_mad(z1, LOG2E_TAIL, z2 * LOG2E_TAIL)));
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#elif defined(COMPILING_LOG10)
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z1 = __CLC_AS_FLOATN(__clc_as_int(r) & 0xffff0000);
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z2 = z2 + (r - z1);
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znear1 = __clc_mad(
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z1, LOG10E_HEAD,
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__clc_mad(z2, LOG10E_HEAD, __clc_mad(z1, LOG10E_TAIL, z2 * LOG10E_TAIL)));
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#else
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znear1 = z2 + r;
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#endif
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// Calculations for x not near 1
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int m = (int)(xi >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
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// Normalize subnormal
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uint xis = __CLC_AS_UINTN(__CLC_AS_FLOATN(xi | 0x3f800000) - 1.0f);
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int ms = (int)(xis >> EXPSHIFTBITS_SP32) - 253;
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int c = m == -127;
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m = c ? ms : m;
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uint xin = c ? xis : xi;
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__CLC_FLOATN mf = (__CLC_FLOATN)m;
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uint indx = (xin & 0x007f0000) + ((xin & 0x00008000) << 1);
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// F - Y
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__CLC_FLOATN f = __CLC_AS_FLOATN(0x3f000000 | indx) -
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__CLC_AS_FLOATN(0x3f000000 | (xin & MANTBITS_SP32));
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indx = indx >> 16;
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r = f * __CLC_USE_TABLE(log_inv_tbl, indx);
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// 1/3, 1/2
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__CLC_FLOATN poly = __clc_mad(__clc_mad(r, 0x1.555556p-2f, 0.5f), r * r, r);
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#if defined(COMPILING_LOG2)
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float2 tv = __CLC_USE_TABLE(log2_tbl, indx);
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z1 = tv.s0 + mf;
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z2 = __clc_mad(poly, -LOG2E, tv.s1);
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#elif defined(COMPILING_LOG10)
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float2 tv = __CLC_USE_TABLE(log10_tbl, indx);
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z1 = __clc_mad(mf, LOG10_2_HEAD, tv.s0);
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z2 = __clc_mad(poly, -LOG10E, mf * LOG10_2_TAIL) + tv.s1;
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#else
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float2 tv = __CLC_USE_TABLE(log_tbl, indx);
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z1 = __clc_mad(mf, LOG2_HEAD, tv.s0);
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z2 = __clc_mad(mf, LOG2_TAIL, -poly) + tv.s1;
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#endif
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__CLC_FLOATN z = z1 + z2;
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z = near1 ? znear1 : z;
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// Corner cases
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z = ax >= PINFBITPATT_SP32 ? x : z;
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z = xi != ax ? __CLC_AS_FLOATN(QNANBITPATT_SP32) : z;
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z = ax == 0 ? __CLC_AS_FLOATN(NINFBITPATT_SP32) : z;
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return z;
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}
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#elif __CLC_FPSIZE == 64
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_CLC_OVERLOAD _CLC_DEF __CLC_DOUBLEN
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#if defined(COMPILING_LOG2)
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__clc_log2(__CLC_DOUBLEN a)
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#elif defined(COMPILING_LOG10)
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__clc_log10(__CLC_DOUBLEN a)
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#else
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__clc_log(__CLC_DOUBLEN a)
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#endif
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{
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__CLC_INTN a_exp;
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__CLC_DOUBLEN m = __clc_frexp(a, &a_exp);
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__CLC_INTN b = m < (2.0 / 3.0);
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m = __clc_ldexp(m, b);
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__CLC_INTN e = a_exp - b;
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__CLC_EP_PAIR x = __clc_ep_div(m - 1.0, __clc_ep_fast_add(1.0, m));
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__CLC_DOUBLEN s = x.hi * x.hi;
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__CLC_DOUBLEN p = __clc_mad(s, __clc_mad(s, __clc_mad(s,
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__clc_mad(s, __clc_mad(s, __clc_mad(s, 0x1.3ab76bf559e2bp-3, 0x1.385386b47b09ap-3),
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0x1.7474dd7f4df2ep-3), 0x1.c71c016291751p-3),
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0x1.249249b27acf1p-2), 0x1.99999998ef7b6p-2), 0x1.5555555555780p-1);
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__CLC_EP_PAIR r =
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__clc_ep_fast_add(__clc_ep_ldexp(x, 1), s * x.hi * p);
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#if defined COMPILING_LOG2
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r = __clc_ep_add(
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__CLC_CONVERT_DOUBLEN(e),
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__clc_ep_mul(
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__clc_ep_make_pair(0x1.71547652b82fep+0, 0x1.777d0ffda0d24p-56), r));
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#elif defined COMPILING_LOG10
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r = __clc_ep_add(
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__clc_ep_mul(
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__clc_ep_make_pair(0x1.34413509f79ffp-2, -0x1.9dc1da994fd21p-59),
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__CLC_CONVERT_DOUBLEN(e)),
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__clc_ep_mul(
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__clc_ep_make_pair(0x1.bcb7b1526e50ep-2, 0x1.95355baaafad3p-57), r));
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#else
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r = __clc_ep_add(__clc_ep_mul(__clc_ep_make_pair(0x1.62e42fefa39efp-1,
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0x1.abc9e3b39803fp-56),
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__CLC_CONVERT_DOUBLEN(e)),
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r);
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#endif
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__CLC_DOUBLEN ret = r.hi;
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ret = __clc_isinf(a) ? a : ret;
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ret = a < 0.0 ? DBL_NAN : ret;
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ret = a == 0.0 ? -INFINITY : ret;
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return ret;
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}
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#elif __CLC_FPSIZE == 16
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_CLC_OVERLOAD _CLC_DEF __CLC_HALFN
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#if defined(COMPILING_LOG2)
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__clc_log2(__CLC_HALFN x) {
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return __CLC_CONVERT_HALFN(__clc_log2(__CLC_CONVERT_FLOATN(x)));
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}
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#elif defined(COMPILING_LOG10)
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__clc_log10(__CLC_HALFN x) {
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return __CLC_CONVERT_HALFN(__clc_log10(__CLC_CONVERT_FLOATN(x)));
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}
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#else
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__clc_log(__CLC_HALFN x) {
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return __CLC_CONVERT_HALFN(__clc_log(__CLC_CONVERT_FLOATN(x));
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}
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#endif
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#endif // __CLC_FPSIZE
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#endif // __CLC_SCALAR
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