diff --git a/doc/index.rst b/doc/index.rst
index bbd64a5f67e52ea3a8fb8e933f32835350dcb843..b8d8e03e67ac059139481649a784cce7aa99e7a7 100644
--- a/doc/index.rst
+++ b/doc/index.rst
@@ -55,7 +55,6 @@ Some key features include:
library
simd_api
- simd_maths
profiler
sampling_api
diff --git a/doc/simd_api.rst b/doc/simd_api.rst
index be33e7a040ebaa0693adaad8af0ca926b4207750..f88c8f0859bc1bfd80307b34be14dfdf0d92ed87 100644
--- a/doc/simd_api.rst
+++ b/doc/simd_api.rst
@@ -1,5 +1,5 @@
-SIMD classes for Arbor
-======================
+SIMD Classes
+============
The purpose of the SIMD classes is to abstract and consolidate the use of
compiler intrinsics for the manipulation of architecture-specific vector
@@ -456,7 +456,7 @@ all SIMD value types, while the transcendental functions are only usable for
SIMD floating point types.
Vectorized implementations of some of the transcendental functions are provided:
-refer to :doc:`simd_maths` for details.
+refer to the `vector transcendental functions documentation <simd_maths_>`_ for details.
In the following:
@@ -948,3 +948,191 @@ of our generated mechanisms.
implementation API to support this would allow, for example, efficient use
of AVX512 masked arithmetic instructions.
+.. _simd_maths:
+
+Implementation of vector transcendental functions
+-------------------------------------------------
+
+When building with the Intel C++ compiler, transcendental
+functions on SIMD values in ``simd<double, 8, simd_detail::avx512>``
+wrap calls to the Intel scalar vector mathematics library (SVML).
+
+Outside of this case, the functions *exp*, *log*, *expm1* and
+*exprelr* use explicit approximations as detailed below. The
+algortihms follow those used in the
+`Cephes library <http://www.netlib.org/cephes/>`_, with
+some accommodations.
+
+.. default-role:: math
+
+Exponentials
+^^^^^^^^^^^^
+
+`\operatorname{exp}(x)`
+~~~~~~~~~~~~~~~~~~~~~~~
+
+The exponential is computed as
+
+.. math::
+
+ e^x = 2^n · e^g,
+
+with `|g| ≤ 0.5` and `n` an integer. The power of two
+is computed via direct manipulation of the exponent bits of the floating
+point representation, while `e^g` is approximated by a rational polynomial.
+
+`n` and `g` are computed by:
+
+.. math::
+
+ n &= \left\lfloor \frac{x}{\log 2} + 0.5 \right\rfloor
+
+ g &= x - n·\log 2
+
+where the subtraction in the calculation of `g` is performed in two stages,
+to limit cancellation error:
+
+.. math::
+
+ g &\leftarrow \operatorname{fl}(x - n · c_1)
+
+ g &\leftarrow \operatorname{fl}(g - n · c_2)
+
+where `c_1+c_2 = \log 2`, `c_1` comprising the first 32 bits of the mantissa.
+(In principle `c_1` might contain more bits of the logarithm, but this
+particular decomposition matches that used in the Cephes library.) This
+decomposition gives `|g|\leq \frac{1}{2}\log 2\approx 0.347`.
+
+The rational approximation for `e^g` is of the form
+
+.. math::
+
+ e^g \approx \frac{R(g)}{R(-g)}
+
+where `R(g)` is a polynomial of order 6. The coefficients are again those
+used by Cephes, and probably are derived via a Remez algorithm.
+`R(g)` is decomposed into even and odd terms
+
+.. math::
+
+ R(g) = Q(x^2) + xP(x^2)
+
+so that the ratio can be calculated by:
+
+.. math::
+
+ e^g \approx 1 + \frac{2gP(g^2)}{Q(g^2)-gP(g^2)}.
+
+Randomized testing indicates the approximation is accurate to 2 ulp.
+
+
+`\operatorname{expm1}(x)`
+~~~~~~~~~~~~~~~~~~~~~~~~~
+
+A similar decomposition of `x = g + n·\log 2` is performed so that
+`g≤0.5`, with the exception that `n` is always taken to
+be zero for `|x|≤0.5`, i.e.
+
+.. math::
+
+ n = \begin{cases}
+ 0&\text{if $|x|≤0.5$,}\\
+ \left\lfloor \frac{x}{\log 2} + 0.5 \right\rfloor
+ &\text{otherwise.}
+ \end{cases}
+
+
+`\operatorname{expm1}(x)` is then computed as
+
+.. math::
+
+ e^x - 1 = 2^n·(e^g - 1)+(2^n-1).
+
+and the same rational polynomial is used to approximate `e^g-1`,
+
+.. math::
+
+ e^g - 1 \approx \frac{2gP(g^2)}{Q(g^2)-gP(g^2)}.
+
+The scaling by step for `n≠0` is in practice calculated as
+
+.. math::
+
+ e^x - 1 = 2·(2^{n-1}·(e^g - 1)+(2^{n-1}-0.5)).
+
+in order to avoid overflow at the upper end of the range.
+
+The order 6 rational polynomial approximation for small `x`
+is insufficiently accurate to maintain 1 ulp accuracy; randomized
+testing indicates a maximum error of up to 3 ulp.
+
+
+`\operatorname{exprelr}(x)`
+~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+The function is defined as
+
+.. math::
+
+ \operatorname{exprelr}(x) = x/(e^x-1),
+
+and is the reciprocal of the relative exponential function,
+
+.. math::
+
+ \operatorname{exprel}(x) &= {}_1F_1(1; 2; x)\\
+ &= \frac{e^x-1}{x}.
+
+This is computed in terms of expm1 by:
+
+.. math::
+
+ \operatorname{exprelr}(x) :=
+ \begin{cases}
+ 1&\text{if $\operatorname{fl}(1+x) = 1$,}\\
+ x/\operatorname{expm1}(x)&\text{otherwise.}
+ \end{cases}
+
+With the approximation for `\operatorname{expm1}` used above,
+randomized testing demonstrates a maximum error on the order
+of 4 ulp.
+
+
+Logarithms
+^^^^^^^^^^
+
+The natural logarithm is computed as
+
+.. math::
+
+ \log x = \log u + n·log 2
+
+where `n` is an integer and `u` is in the interval
+`[ \frac{1}{2}\sqrt 2, \sqrt 2]`. The logarithm of
+`u` is then approximated by the rational polynomial
+used in the Cephes implementation,
+
+.. math::
+
+ \log u &\approx R(u-1)
+
+ R(z) &= z - \frac{z^2}{2} + z^3·\frac{P(z)}{Q(z)},
+
+where `P` and `Q` are polynomials of degree 5, with
+`Q` monic.
+
+Cancellation error is minimized by computing the sum for
+`\log x` as:
+
+.. math::
+
+ s &\leftarrow \operatorname{fl}(z^3·P(z)/Q(z))\\
+ s &\leftarrow \operatorname{fl}(s + n·c_4)\\
+ s &\leftarrow \operatorname{fl}(s - 0.5·z^2)\\
+ s &\leftarrow \operatorname{fl}(s + z)\\
+ s &\leftarrow \operatorname{fl}(s + n·c_3)
+
+where `z=u-1` and `c_3+c_4=\log 2`, `c_3` comprising
+the first 9 bits of the mantissa.
+
+
diff --git a/doc/simd_maths.rst b/doc/simd_maths.rst
deleted file mode 100644
index b93b07e663973100949c6f885bea4dff6863bd78..0000000000000000000000000000000000000000
--- a/doc/simd_maths.rst
+++ /dev/null
@@ -1,185 +0,0 @@
-Implementation of vector transcendental functions
-=================================================
-
-When building with the Intel C++ compiler, transcendental
-functions on SIMD values in ``simd<double, 8, simd_detail::avx512>``
-wrap calls to the Intel scalar vector mathematics library (SVML).
-
-Outside of this case, the functions *exp*, *log*, *expm1* and
-*exprelr* use explicit approximations as detailed below. The
-algortihms follow those used in the
-`Cephes library <http://www.netlib.org/cephes/>`_, with
-some accommodations.
-
-.. default-role:: math
-
-Exponentials
-------------
-
-`\operatorname{exp}(x)`
-^^^^^^^^^^^^^^^^^^^^^^^
-
-The exponential is computed as
-
-.. math::
-
- e^x = 2^n · e^g,
-
-with `|g| ≤ 0.5` and `n` an integer. The power of two
-is computed via direct manipulation of the exponent bits of the floating
-point representation, while `e^g` is approximated by a rational polynomial.
-
-`n` and `g` are computed by:
-
-.. math::
-
- n &= \left\lfloor \frac{x}{\log 2} + 0.5 \right\rfloor
-
- g &= x - n·\log 2
-
-where the subtraction in the calculation of `g` is performed in two stages,
-to limit cancellation error:
-
-.. math::
-
- g &\leftarrow \operatorname{fl}(x - n · c_1)
-
- g &\leftarrow \operatorname{fl}(g - n · c_2)
-
-where `c_1+c_2 = \log 2`,`c_1` comprising the first 32 bits of the mantissa.
-(In principle `c_1` might contain more bits of the logarithm, but this
-particular decomposition matches that used in the Cephes library.) This
-decomposition gives `|g|\leq \frac{1}{2}\log 2\approx 0.347`.
-
-The rational approximation for `e^g` is of the form
-
-.. math::
-
- e^g \approx \frac{R(g)}{R(-g)}
-
-where `R(g)` is a polynomial of order 6. The coefficients are again those
-used by Cephes, and probably are derived via a Remez algorithm.
-`R(g)` is decomposed into even and odd terms
-
-.. math::
-
- R(g) = Q(x^2) + xP(x^2)
-
-so that the ratio can be calculated by:
-
-.. math::
-
- e^g \approx 1 + \frac{2gP(g^2)}{Q(g^2)-gP(g^2)}.
-
-Randomized testing indicates the approximation is accurate to 2 ulp.
-
-
-`\operatorname{expm1}(x)`
-^^^^^^^^^^^^^^^^^^^^^^^^^
-
-A similar decomposition of `x = g + n·\log 2` is performed so that
-`g≤0.5`, with the exception that `n` is always taken to
-be zero for `|x|≤0.5`, i.e.
-
-.. math::
-
- n = \begin{cases}
- 0&\text{if $|x|≤0.5$,}\\
- \left\lfloor \frac{x}{\log 2} + 0.5 \right\rfloor
- &\text{otherwise.}
- \end{cases}
-
-
-`\operatorname{expm1}(x)` is then computed as
-
-.. math::
-
- e^x - 1 = 2^n·(e^g - 1)+(2^n-1).
-
-and the same rational polynomial is used to approximate `e^g-1`,
-
-.. math::
-
- e^g - 1 \approx \frac{2gP(g^2)}{Q(g^2)-gP(g^2)}.
-
-The scaling by step for `n≠0` is in practice calculated as
-
-.. math::
-
- e^x - 1 = 2·(2^{n-1}·(e^g - 1)+(2^{n-1}-0.5)).
-
-in order to avoid overflow at the upper end of the range.
-
-The order 6 rational polynomial approximation for small `x`
-is insufficiently accurate to maintain 1 ulp accuracy; randomized
-testing indicates a maximum error of up to 3 ulp.
-
-
-`\operatorname{exprelr}(x)`
-^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-The function is defined as
-
-.. math::
-
- \operatorname{exprelr}(x) = x/(e^x-1),
-
-and is the reciprocal of the relative exponential function,
-
-.. math::
-
- \operatorname{exprel}(x) &= {}_1F_1(1; 2; x)\\
- &= \frac{e^x-1}{x}.
-
-This is computed in terms of expm1 by:
-
-.. math::
-
- \operatorname{exprelr}(x) :=
- \begin{cases}
- 1&\text{if $\operatorname{fl}(1+x) = 1$,}\\
- x/\operatorname{expm1}(x)&\text{otherwise.}
- \end{cases}
-
-With the approximation for `\operatorname{expm1}` used above,
-randomized testing demonstrates a maximum error on the order
-of 4 ulp.
-
-
-Logarithms
-----------
-
-The natural logarithm is computed as
-
-.. math::
-
- \log x = \log u + n·log 2
-
-where `n` is an integer and `u` is in the interval
-`[ \frac{1}{2}\sqrt 2, \sqrt 2]`. The logarithm of
-`u` is then approximated by the rational polynomial
-used in the Cephes implementation,
-
-.. math::
-
- \log u &\approx R(u-1)
-
- R(z) &= z - \frac{z^2}{2} + z^3·\frac{P(z)}{Q(z)},
-
-where `P` and `Q` are polynomials of degree 5, with
-`Q` monic.
-
-Cancellation error is minimized by computing the sum for
-`\log x` as:
-
-.. math::
-
- s &\leftarrow \operatorname{fl}(z^3·P(z)/Q(z))\\
- s &\leftarrow \operatorname{fl}(s + n·c_4)\\
- s &\leftarrow \operatorname{fl}(s - 0.5·z^2)\\
- s &\leftarrow \operatorname{fl}(s + z)\\
- s &\leftarrow \operatorname{fl}(s + n·c_3)
-
-where `z=u-1` and `c_3+c_4=\log 2`, `c_3` comprising
-the first 9 bits of the mantissa.
-