I figured the approach I used to construct a well-tuned implementation of log1pf() might work well for plain old logf() as well, and indeed it does. On my Quadro K2200 (sm_50) I measure the following throughput with CUDA 7.5:

```
CUDA 7.5 logf() -ftz=false 14.8 billion function calls per second
CUDA 7.5 logf() -ftz=true 16.5 billion function calls per second
my_logf() 27.4 billion function calls per second
```

The accuracy is also improved, with the maximum error compared to the mathematical result reduced from 1.00366 ulps to 0.85089 ulps, which means my_logf() is faithfully rounded.

[code below updated 7/3/2016, 7/18/2016, 1/21/2017, 12/18/2017, 4/23/2018, 4/28/2018]

```
/*
Copyright (c) 2015-2018, Norbert Juffa
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.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 COPYRIGHT
HOLDER 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.
*/
/* compute natural logarithm. max ulp error = 0.85095 */
__device__ float my_logf (float a)
{
float i, m, r, s, t;
int e;
i = 0.0f;
if (a < 1.175494351e-38f){ // 0x1.0p-126
a = a * 8388608.0f; // 0x1.0p+23
i = -23.0f;
}
e = (__float_as_int (a) - __float_as_int (0.666666667f)) & 0xff800000;
m = __int_as_float (__float_as_int (a) - e);
i = fmaf ((float)e, 1.19209290e-7f, i); // 0x1.0p-23
/* m in [2/3, 4/3] */
m = m - 1.0f;
s = m * m;
/* Compute log1p(m) for m in [-1/3, 1/3] */
r = -0.130310059f; // -0x1.0ae000p-3
t = 0.140869141f; // 0x1.208000p-3
r = fmaf (r, s, -0.121483512f); // -0x1.f198b2p-4
t = fmaf (t, s, 0.139814854f); // 0x1.1e5740p-3
r = fmaf (r, s, -0.166846126f); // -0x1.55b36cp-3
t = fmaf (t, s, 0.200120345f); // 0x1.99d8b2p-3
r = fmaf (r, s, -0.249996200f); // -0x1.fffe02p-3
r = fmaf (t, m, r);
r = fmaf (r, m, 0.333331972f); // 0x1.5554fap-2
r = fmaf (r, m, -0.500000000f); // -0x1.000000p-1
r = fmaf (r, s, m);
r = fmaf (i, 0.693147182f, r); // 0x1.62e430p-1 // log(2)
if (!((a > 0.0f) && (a < __int_as_float (0x7f800000)))) { // +INF
asm ("lg2.approx.ftz.f32 %0,%1;" : "=f"(r) : "f"(a)); // handle NaN, INF
}
return r;
}
```