diff --git a/libc/docs/math/index.rst b/libc/docs/math/index.rst
--- a/libc/docs/math/index.rst
+++ b/libc/docs/math/index.rst
@@ -210,63 +210,63 @@
table below, using the system library as reference (such as the `GNU C library `_
on Linux). Fmod performance results obtained with "differential_testing".
-+--------------+-------------------------------+-------------------------------+-------------------------------------+---------------------------------------------------------------------+
-| | Reciprocal throughput (ns) | Latency (ns) | Testing ranges | Testing configuration |
-| +-----------+-------------------+-----------+-------------------+ +------------+-------------------------+--------------+---------------+
-| | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) | | CPU | OS | Compiler | Special flags |
-+==============+===========+===================+===========+===================+=====================================+============+=========================+==============+===============+
-| acosf | 24 | 29 | 62 | 77 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| acoshf | 18 | 26 | 73 | 74 | :math:`[1, 21]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| asinf | 23 | 27 | 62 | 62 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| asinhf | 21 | 39 | 77 | 91 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| atanf | 27 | 29 | 79 | 68 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| atanhf | 18 | 66 | 68 | 133 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| cosf | 13 | 32 | 53 | 59 | :math:`[0, 2\pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| coshf | 14 | 20 | 50 | 48 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| expf | 9 | 7 | 44 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| exp10f | 10 | 8 | 40 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| exp2f | 9 | 6 | 35 | 31 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| expm1f | 9 | 44 | 42 | 121 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| fmodf | 73 | 263 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
-| +-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| | 9 | 11 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| fmod | 595 | 3297 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
-| +-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| | 14 | 13 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| hypotf | 25 | 15 | 64 | 49 | :math:`[-10, 10] \times [-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| logf | 12 | 10 | 56 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| log10f | 13 | 25 | 57 | 72 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| log1pf | 16 | 33 | 61 | 97 | :math:`[e^{-0.5} - 1, e^{0.5} - 1]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| log2f | 13 | 10 | 57 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| sinf | 12 | 25 | 51 | 57 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| sincosf | 19 | 30 | 57 | 68 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| sinhf | 13 | 63 | 48 | 137 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| tanf | 16 | 50 | 61 | 107 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
-| tanhf | 13 | 55 | 57 | 123 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
-+--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+------------+-------------------------+--------------+---------------+
++--------------+-------------------------------+-------------------------------+-------------------------------------+----------------------------------------------------------------------+
+| | Reciprocal throughput (clk) | Latency (clk) | Testing ranges | Testing configuration |
+| +-----------+-------------------+-----------+-------------------+ +-------------+-------------------------+--------------+---------------+
+| | LLVM libc | Reference (glibc) | LLVM libc | Reference (glibc) | | CPU | OS | Compiler | Special flags |
++==============+===========+===================+===========+===================+=====================================+=============+=========================+==============+===============+
+| acosf | 24 | 29 | 62 | 77 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| acoshf | 18 | 26 | 73 | 74 | :math:`[1, 21]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| asinf | 23 | 27 | 62 | 62 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| asinhf | 21 | 39 | 77 | 91 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| atanf | 27 | 29 | 79 | 68 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| atanhf | 18 | 66 | 68 | 133 | :math:`[-1, 1]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| cosf | 13 | 32 | 53 | 59 | :math:`[0, 2\pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| coshf | 14 | 20 | 50 | 48 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| expf | 9 | 7 | 44 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| exp10f | 10 | 8 | 40 | 38 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| exp2f | 9 | 6 | 35 | 31 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| expm1f | 9 | 44 | 42 | 121 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| fmodf | 73 | 263 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
+| +-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| | 9 | 11 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| fmod | 595 | 3297 | - | - | [MIN_NORMAL, MAX_NORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
+| +-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| | 14 | 13 | - | - | [0, MAX_SUBNORMAL] | i5 mobile | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| hypotf | 25 | 15 | 64 | 49 | :math:`[-10, 10] \times [-10, 10]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| logf | 12 | 10 | 56 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| log10f | 9 | 17 | 35 | 48 | :math:`[e^{-1}, e]` | Ryzen 5900X | Ubuntu 22.04 LTS x86_64 | Clang 15.0.6 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| log1pf | 16 | 33 | 61 | 97 | :math:`[e^{-0.5} - 1, e^{0.5} - 1]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| log2f | 13 | 10 | 57 | 46 | :math:`[e^{-1}, e]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| sinf | 12 | 25 | 51 | 57 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| sincosf | 19 | 30 | 57 | 68 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 20.04 LTS x86_64 | Clang 12.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| sinhf | 13 | 63 | 48 | 137 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| tanf | 16 | 50 | 61 | 107 | :math:`[-\pi, \pi]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
+| tanhf | 13 | 55 | 57 | 123 | :math:`[-10, 10]` | Ryzen 1700 | Ubuntu 22.04 LTS x86_64 | Clang 14.0.0 | FMA |
++--------------+-----------+-------------------+-----------+-------------------+-------------------------------------+-------------+-------------------------+--------------+---------------+
Algorithms + Implementation Details
===================================
diff --git a/libc/src/math/generic/common_constants.h b/libc/src/math/generic/common_constants.h
--- a/libc/src/math/generic/common_constants.h
+++ b/libc/src/math/generic/common_constants.h
@@ -17,6 +17,9 @@
// Lookup table for log(f) = log(1 + n*2^(-7)) where n = 0..127.
extern const double LOG_F[128];
+// Lookup table for range reduction constants r for logarithms.
+extern const float R[128];
+
// Lookup table for exp(m) with m = -104, ..., 89.
// -104 = floor(log(single precision's min denormal))
// 89 = ceil(log(single precision's max normal))
diff --git a/libc/src/math/generic/common_constants.cpp b/libc/src/math/generic/common_constants.cpp
--- a/libc/src/math/generic/common_constants.cpp
+++ b/libc/src/math/generic/common_constants.cpp
@@ -102,6 +102,34 @@
0x1.58cadb5cd7989p-1, 0x1.5ad404c359f2cp-1, 0x1.5cdb1dc6c1764p-1,
0x1.5ee02a9241675p-1, 0x1.60e32f44788d8p-1};
+// Range reduction constants for logarithms.
+// r(0) = 1, r(127) = 0.5
+// r(k) = 2^-10 * ceil(2^10 * (1 - 2^-8) / (1 + k*2^-7))
+// The constants are chosen so that v = fma(r, m_x, -1) is exact in single
+// precision, and -2^-8 <= v < 2^-7.
+// TODO(lntue): Add reference to how the constants are derived after the
+// resulting paper is ready.
+const float R[128] = {
+ 0x1p0, 0x1.fcp-1, 0x1.f8p-1, 0x1.f4p-1, 0x1.fp-1, 0x1.ecp-1, 0x1.e8p-1,
+ 0x1.e4p-1, 0x1.ep-1, 0x1.dep-1, 0x1.dap-1, 0x1.d6p-1, 0x1.d4p-1, 0x1.dp-1,
+ 0x1.ccp-1, 0x1.cap-1, 0x1.c6p-1, 0x1.c4p-1, 0x1.cp-1, 0x1.bep-1, 0x1.bap-1,
+ 0x1.b8p-1, 0x1.b4p-1, 0x1.b2p-1, 0x1.aep-1, 0x1.acp-1, 0x1.a8p-1, 0x1.a6p-1,
+ 0x1.a4p-1, 0x1.ap-1, 0x1.9ep-1, 0x1.9cp-1, 0x1.98p-1, 0x1.96p-1, 0x1.94p-1,
+ 0x1.92p-1, 0x1.9p-1, 0x1.8cp-1, 0x1.8ap-1, 0x1.88p-1, 0x1.86p-1, 0x1.84p-1,
+ 0x1.8p-1, 0x1.7ep-1, 0x1.7cp-1, 0x1.7ap-1, 0x1.78p-1, 0x1.76p-1, 0x1.74p-1,
+ 0x1.72p-1, 0x1.7p-1, 0x1.6ep-1, 0x1.6cp-1, 0x1.6ap-1, 0x1.68p-1, 0x1.66p-1,
+ 0x1.64p-1, 0x1.62p-1, 0x1.6p-1, 0x1.5ep-1, 0x1.5cp-1, 0x1.5ap-1, 0x1.58p-1,
+ 0x1.56p-1, 0x1.54p-1, 0x1.54p-1, 0x1.52p-1, 0x1.5p-1, 0x1.4ep-1, 0x1.4cp-1,
+ 0x1.4ap-1, 0x1.4ap-1, 0x1.48p-1, 0x1.46p-1, 0x1.44p-1, 0x1.42p-1, 0x1.4p-1,
+ 0x1.4p-1, 0x1.3ep-1, 0x1.3cp-1, 0x1.3ap-1, 0x1.3ap-1, 0x1.38p-1, 0x1.36p-1,
+ 0x1.34p-1, 0x1.34p-1, 0x1.32p-1, 0x1.3p-1, 0x1.3p-1, 0x1.2ep-1, 0x1.2cp-1,
+ 0x1.2cp-1, 0x1.2ap-1, 0x1.28p-1, 0x1.28p-1, 0x1.26p-1, 0x1.24p-1, 0x1.24p-1,
+ 0x1.22p-1, 0x1.2p-1, 0x1.2p-1, 0x1.1ep-1, 0x1.1cp-1, 0x1.1cp-1, 0x1.1ap-1,
+ 0x1.1ap-1, 0x1.18p-1, 0x1.16p-1, 0x1.16p-1, 0x1.14p-1, 0x1.14p-1, 0x1.12p-1,
+ 0x1.1p-1, 0x1.1p-1, 0x1.0ep-1, 0x1.0ep-1, 0x1.0cp-1, 0x1.0cp-1, 0x1.0ap-1,
+ 0x1.0ap-1, 0x1.08p-1, 0x1.08p-1, 0x1.06p-1, 0x1.06p-1, 0x1.04p-1, 0x1.04p-1,
+ 0x1.02p-1, 0x1.0p-1};
+
// Lookup table for exp(m) with m = -104, ..., 89.
// -104 = floor(log(single precision's min denormal))
// 89 = ceil(log(single precision's max normal))
diff --git a/libc/src/math/generic/log10f.cpp b/libc/src/math/generic/log10f.cpp
--- a/libc/src/math/generic/log10f.cpp
+++ b/libc/src/math/generic/log10f.cpp
@@ -56,53 +56,51 @@
namespace __llvm_libc {
-// Exact power of 10 in float:
-
-// Lookup table for log10(f) = log10(1 + n*2^(-7)) where n = 0..127.
-static constexpr double LOG10_F[128] = {
- 0x0.0000000000000p+0, 0x1.bafd47221ed26p-9, 0x1.b9476a4fcd10fp-8,
- 0x1.49b0851443684p-7, 0x1.b5e908eb13790p-7, 0x1.10a83a8446c78p-6,
- 0x1.45f4f5acb8be0p-6, 0x1.7adc3df3b1ff8p-6, 0x1.af5f92b00e610p-6,
- 0x1.e3806acbd058fp-6, 0x1.0ba01a8170000p-5, 0x1.25502c0fc314cp-5,
- 0x1.3ed1199a5e425p-5, 0x1.58238eeb353dap-5, 0x1.71483427d2a99p-5,
- 0x1.8a3fadeb847f4p-5, 0x1.a30a9d609efeap-5, 0x1.bba9a058dfd84p-5,
- 0x1.d41d5164facb4p-5, 0x1.ec6647eb58808p-5, 0x1.02428c1f08016p-4,
- 0x1.0e3d29d81165ep-4, 0x1.1a23445501816p-4, 0x1.25f5215eb594ap-4,
- 0x1.31b3055c47118p-4, 0x1.3d5d335c53179p-4, 0x1.48f3ed1df48fbp-4,
- 0x1.5477731973e85p-4, 0x1.5fe80488af4fdp-4, 0x1.6b45df6f3e2c9p-4,
- 0x1.769140a2526fdp-4, 0x1.81ca63d05a44ap-4, 0x1.8cf183886480dp-4,
- 0x1.9806d9414a209p-4, 0x1.a30a9d609efeap-4, 0x1.adfd07416be07p-4,
- 0x1.b8de4d3ab3d98p-4, 0x1.c3aea4a5c6effp-4, 0x1.ce6e41e463da5p-4,
- 0x1.d91d5866aa99cp-4, 0x1.e3bc1ab0e19fep-4, 0x1.ee4aba610f204p-4,
- 0x1.f8c9683468191p-4, 0x1.019c2a064b486p-3, 0x1.06cbd67a6c3b6p-3,
- 0x1.0bf3d0937c41cp-3, 0x1.11142f0811357p-3, 0x1.162d082ac9d10p-3,
- 0x1.1b3e71ec94f7bp-3, 0x1.204881dee8777p-3, 0x1.254b4d35e7d3cp-3,
- 0x1.2a46e8ca7ba2ap-3, 0x1.2f3b691c5a001p-3, 0x1.3428e2540096dp-3,
- 0x1.390f6844a0b83p-3, 0x1.3def0e6dfdf85p-3, 0x1.42c7e7fe3fc02p-3,
- 0x1.479a07d3b6411p-3, 0x1.4c65807e93338p-3, 0x1.512a644296c3dp-3,
- 0x1.55e8c518b10f8p-3, 0x1.5aa0b4b0988fap-3, 0x1.5f52447255c92p-3,
- 0x1.63fd857fc49bbp-3, 0x1.68a288b60b7fcp-3, 0x1.6d415eaf0906bp-3,
- 0x1.71da17c2b7e80p-3, 0x1.766cc40889e85p-3, 0x1.7af97358b9e04p-3,
- 0x1.7f80354d952a0p-3, 0x1.84011944bcb75p-3, 0x1.887c2e605e119p-3,
- 0x1.8cf183886480dp-3, 0x1.9161276ba2978p-3, 0x1.95cb2880f45bap-3,
- 0x1.9a2f95085a45cp-3, 0x1.9e8e7b0c0d4bep-3, 0x1.a2e7e8618c2d2p-3,
- 0x1.a73beaaaa22f4p-3, 0x1.ab8a8f56677fcp-3, 0x1.afd3e3a23b680p-3,
- 0x1.b417f49ab8807p-3, 0x1.b856cf1ca3105p-3, 0x1.bc907fd5d1c40p-3,
- 0x1.c0c5134610e26p-3, 0x1.c4f495c0002a2p-3, 0x1.c91f1369eb7cap-3,
- 0x1.cd44983e9e7bdp-3, 0x1.d165300e333f7p-3, 0x1.d580e67edc43dp-3,
- 0x1.d997c70da9b47p-3, 0x1.dda9dd0f4a329p-3, 0x1.e1b733b0c7381p-3,
- 0x1.e5bfd5f83d342p-3, 0x1.e9c3cec58f807p-3, 0x1.edc328d3184afp-3,
- 0x1.f1bdeeb654901p-3, 0x1.f5b42ae08c407p-3, 0x1.f9a5e79f76ac5p-3,
- 0x1.fd932f1ddb4d6p-3, 0x1.00be05b217844p-2, 0x1.02b0432c96ff0p-2,
- 0x1.04a054e139004p-2, 0x1.068e3fa282e3dp-2, 0x1.087a0832fa7acp-2,
- 0x1.0a63b3456c819p-2, 0x1.0c4b457d3193dp-2, 0x1.0e30c36e71a7fp-2,
- 0x1.1014319e661bdp-2, 0x1.11f594839a5bdp-2, 0x1.13d4f0862b2e1p-2,
- 0x1.15b24a0004a92p-2, 0x1.178da53d1ee01p-2, 0x1.1967067bb94b8p-2,
- 0x1.1b3e71ec94f7bp-2, 0x1.1d13ebb32d7f9p-2, 0x1.1ee777e5f0dc3p-2,
- 0x1.20b91a8e76105p-2, 0x1.2288d7a9b2b64p-2, 0x1.2456b3282f786p-2,
- 0x1.2622b0ee3b79dp-2, 0x1.27ecd4d41eb67p-2, 0x1.29b522a64b609p-2,
- 0x1.2b7b9e258e422p-2, 0x1.2d404b073e27ep-2, 0x1.2f032cf56a5bep-2,
- 0x1.30c4478f0835fp-2, 0x1.32839e681fc62p-2};
+// Lookup table for -log10(r) where r is defined in common_constants.cpp.
+static constexpr double LOG10_R[128] = {
+ 0x0.0000000000000p+0, 0x1.be76bd77b4fc3p-9, 0x1.c03a80ae5e054p-8,
+ 0x1.51824c7587ebp-7, 0x1.c3d0837784c41p-7, 0x1.1b85d6044e9aep-6,
+ 0x1.559bd2406c3bap-6, 0x1.902c31d62a843p-6, 0x1.cb38fccd8bfdbp-6,
+ 0x1.e8eeb09f2f6cbp-6, 0x1.125d0432ea20ep-5, 0x1.30838cdc2fbfdp-5,
+ 0x1.3faf7c663060ep-5, 0x1.5e3966b7e9295p-5, 0x1.7d070145f4fd7p-5,
+ 0x1.8c878eeb05074p-5, 0x1.abbcebd84fcap-5, 0x1.bb7209d1e24e5p-5,
+ 0x1.db11ed766abf4p-5, 0x1.eafd05035bd3bp-5, 0x1.0585283764178p-4,
+ 0x1.0d966cc6500fap-4, 0x1.1dd5460c8b16fp-4, 0x1.2603072a25f82p-4,
+ 0x1.367ba3aaa1883p-4, 0x1.3ec6ad5407868p-4, 0x1.4f7aad9bbcbafp-4,
+ 0x1.57e3d47c3af7bp-4, 0x1.605735ee985f1p-4, 0x1.715d0ce367afcp-4,
+ 0x1.79efb57b0f803p-4, 0x1.828cfed29a215p-4, 0x1.93e7de0fc3e8p-4,
+ 0x1.9ca5aa1729f45p-4, 0x1.a56e8325f5c87p-4, 0x1.ae4285509950bp-4,
+ 0x1.b721cd17157e3p-4, 0x1.c902a19e65111p-4, 0x1.d204698cb42bdp-4,
+ 0x1.db11ed766abf4p-4, 0x1.e42b4c16caaf3p-4, 0x1.ed50a4a26eafcp-4,
+ 0x1.ffbfc2bbc7803p-4, 0x1.0484e4942aa43p-3, 0x1.093025a19976cp-3,
+ 0x1.0de1b56356b04p-3, 0x1.1299a4fb3e306p-3, 0x1.175805d1587c1p-3,
+ 0x1.1c1ce9955c0c6p-3, 0x1.20e8624038fedp-3, 0x1.25ba8215af7fcp-3,
+ 0x1.2a935ba5f1479p-3, 0x1.2f7301cf4e87bp-3, 0x1.345987bfeea91p-3,
+ 0x1.394700f7953fdp-3, 0x1.3e3b8149739d4p-3, 0x1.43371cde076c2p-3,
+ 0x1.4839e83506c87p-3, 0x1.4d43f8275a483p-3, 0x1.525561e9256eep-3,
+ 0x1.576e3b0bde0a7p-3, 0x1.5c8e998072fe2p-3, 0x1.61b6939983048p-3,
+ 0x1.66e6400da3f77p-3, 0x1.6c1db5f9bb336p-3, 0x1.6c1db5f9bb336p-3,
+ 0x1.715d0ce367afcp-3, 0x1.76a45cbb7e6ffp-3, 0x1.7bf3bde099f3p-3,
+ 0x1.814b4921bd52bp-3, 0x1.86ab17c10bc7fp-3, 0x1.86ab17c10bc7fp-3,
+ 0x1.8c13437695532p-3, 0x1.9183e673394fap-3, 0x1.96fd1b639fc09p-3,
+ 0x1.9c7efd734a2f9p-3, 0x1.a209a84fbcff8p-3, 0x1.a209a84fbcff8p-3,
+ 0x1.a79d382bc21d9p-3, 0x1.ad39c9c2c608p-3, 0x1.b2df7a5c50299p-3,
+ 0x1.b2df7a5c50299p-3, 0x1.b88e67cf9798p-3, 0x1.be46b087354bcp-3,
+ 0x1.c4087384f4f8p-3, 0x1.c4087384f4f8p-3, 0x1.c9d3d065c5b42p-3,
+ 0x1.cfa8e765cbb72p-3, 0x1.cfa8e765cbb72p-3, 0x1.d587d96494759p-3,
+ 0x1.db70c7e96e7f3p-3, 0x1.db70c7e96e7f3p-3, 0x1.e163d527e68cfp-3,
+ 0x1.e76124046b3f3p-3, 0x1.e76124046b3f3p-3, 0x1.ed68d819191fcp-3,
+ 0x1.f37b15bab08d1p-3, 0x1.f37b15bab08d1p-3, 0x1.f99801fdb749dp-3,
+ 0x1.ffbfc2bbc7803p-3, 0x1.ffbfc2bbc7803p-3, 0x1.02f93f4c87101p-2,
+ 0x1.06182e84fd4acp-2, 0x1.06182e84fd4acp-2, 0x1.093cc32c90f84p-2,
+ 0x1.093cc32c90f84p-2, 0x1.0c6711d6abd7ap-2, 0x1.0f972f87ff3d6p-2,
+ 0x1.0f972f87ff3d6p-2, 0x1.12cd31b9c99ffp-2, 0x1.12cd31b9c99ffp-2,
+ 0x1.16092e5d3a9a6p-2, 0x1.194b3bdef6b9ep-2, 0x1.194b3bdef6b9ep-2,
+ 0x1.1c93712abc7ffp-2, 0x1.1c93712abc7ffp-2, 0x1.1fe1e5af2c141p-2,
+ 0x1.1fe1e5af2c141p-2, 0x1.2336b161b3337p-2, 0x1.2336b161b3337p-2,
+ 0x1.2691ecc29f042p-2, 0x1.2691ecc29f042p-2, 0x1.29f3b0e15584bp-2,
+ 0x1.29f3b0e15584bp-2, 0x1.2d5c1760b86bbp-2, 0x1.2d5c1760b86bbp-2,
+ 0x1.30cb3a7bb3625p-2, 0x1.34413509f79ffp-2};
LLVM_LIBC_FUNCTION(float, log10f, (float x)) {
constexpr double LOG10_2 = 0x1.34413509f79ffp-2;
@@ -112,39 +110,52 @@
uint32_t x_u = xbits.uintval();
// Exact powers of 10 and other hard-to-round cases.
- switch (x_u) {
- case 0x4120'0000U: // x = 10
- return 1.0f;
- case 0x42c8'0000U: // x = 100
- return 2.0f;
- case 0x447a'0000U: // x = 1,000
- return 3.0f;
- case 0x461c'4000U: // x = 10,000
- return 4.0f;
- case 0x47c3'5000U: // x = 100,000
- return 5.0f;
- case 0x4974'2400U: // x = 1,000,000
- return 6.0f;
- case 0x4b18'9680U: // x = 10,000,000
- return 7.0f;
- case 0x4cbe'bc20U: // x = 100,000,000
- return 8.0f;
- case 0x4e6e'6b28U: // x = 1,000,000,000
- return 9.0f;
- case 0x5015'02f9U: // x = 10,000,000,000
- return 10.0f;
- case 0x4f13'4f83U: // x = 2471461632.0
- return fputil::round_result_slightly_down(0x1.2c9314p+3f);
- case 0x7956'ba5eU: // x = 69683218960000541503257137270226944.0
- return fputil::round_result_slightly_up(0x1.16bebap+5f);
+ if (LIBC_UNLIKELY((x_u & 0x3FF) == 0)) {
+ switch (x_u) {
+ case 0x3f80'0000U: // x = 1
+ return 0.0f;
+ case 0x4120'0000U: // x = 10
+ return 1.0f;
+ case 0x42c8'0000U: // x = 100
+ return 2.0f;
+ case 0x447a'0000U: // x = 1,000
+ return 3.0f;
+ case 0x461c'4000U: // x = 10,000
+ return 4.0f;
+ case 0x47c3'5000U: // x = 100,000
+ return 5.0f;
+ case 0x4974'2400U: // x = 1,000,000
+ return 6.0f;
+ }
+ } else {
+ switch (x_u) {
+ case 0x4b18'9680U: // x = 10,000,000
+ return 7.0f;
+ case 0x4cbe'bc20U: // x = 100,000,000
+ return 8.0f;
+ case 0x4e6e'6b28U: // x = 1,000,000,000
+ return 9.0f;
+ case 0x5015'02f9U: // x = 10,000,000,000
+ return 10.0f;
+ case 0x0efe'ee7aU: // x = 0x1.fddcf4p-98f
+ return fputil::round_result_slightly_up(-0x1.d33a46p+4f);
+ case 0x3f5f'de1bU: // x = 0x1.bfbc36p-1f
+ return fputil::round_result_slightly_up(-0x1.dd2c6ep-5f);
+ case 0x3f80'70d8U: // x = 0x1.00e1bp0f
+ return fputil::round_result_slightly_up(0x1.8762c4p-10f);
#ifndef LIBC_TARGET_CPU_HAS_FMA
- case 0x08ae'a356U: // x = 0x1.5d46acp-110f
- return fputil::round_result_slightly_up(-0x1.07d3b4p+5f);
- case 0x1c7d'a337U: // x = 0x1.fb466ep-71f
- return fputil::round_result_slightly_up(-0x1.5137dp+4f);
- case 0x69c8'c583U: // x = 0x1.918b06p+84f
- return fputil::round_result_slightly_down(0x1.97b652p+4f);
+ case 0x08ae'a356U: // x = 0x1.5d46acp-110f
+ return fputil::round_result_slightly_up(-0x1.07d3b4p+5f);
+ case 0x120b'93dcU: // x = 0x1.1727b8p-91f
+ return fputil::round_result_slightly_down(-0x1.b5b2aep+4f);
+ case 0x13ae'78d3U: // x = 0x1.5cf1a6p-88f
+ return fputil::round_result_slightly_down(-0x1.a5b2aep+4f);
+ case 0x4f13'4f83U: // x = 2471461632.0
+ return fputil::round_result_slightly_down(0x1.2c9314p+3f);
+ case 0x7956'ba5eU: // x = 69683218960000541503257137270226944.0
+ return fputil::round_result_slightly_up(0x1.16bebap+5f);
#endif // LIBC_TARGET_CPU_HAS_FMA
+ }
}
int m = -FPBits::EXPONENT_BIAS;
@@ -168,25 +179,36 @@
// Normalize denormal inputs.
xbits.set_val(xbits.get_val() * 0x1.0p23f);
m -= 23;
+ x_u = xbits.uintval();
}
- m += xbits.get_unbiased_exponent();
- int f_index = xbits.get_mantissa() >> 16;
+ // Add unbiased exponent.
+ m += static_cast(x_u >> 23);
+ // Extract 7 leading fractional bits of the mantissa
+ int index = (x_u >> 16) & 0x7F;
// Set bits to 1.m
xbits.set_unbiased_exponent(0x7F);
- FPBits f = xbits;
- f.bits &= ~0x0000'FFFF;
-
- double d = static_cast(xbits) - static_cast(f);
- d *= ONE_OVER_F[f_index];
-
- double extra_factor =
- fputil::multiply_add(static_cast(m), LOG10_2, LOG10_F[f_index]);
+ float u = static_cast(xbits);
+ double v;
+#ifdef LIBC_TARGET_CPU_HAS_FMA
+ v = static_cast(fputil::multiply_add(u, R[index], -1.0f)); // Exact.
+#else
+ v = fputil::multiply_add(static_cast(u),
+ static_cast(R[index]), -1.0); // Exact
+#endif // LIBC_TARGET_CPU_HAS_FMA
- double r = fputil::polyeval(d, extra_factor, 0x1.bcb7b1526e4c5p-2,
- -0x1.bcb7b1518a5e9p-3, 0x1.287a72a6f716p-3,
- -0x1.bcadb40b85565p-4, 0x1.5e0bc97f97e22p-4);
+ // Degree-5 polynomial approximation of log10 generated by:
+ // > P = fpminimax(log10(1 + x)/x, 4, [|D...|], [-2^-8, 2^-7]);
+ constexpr double COEFFS[5] = {0x1.bcb7b1526e2e5p-2, -0x1.bcb7b1528d43dp-3,
+ 0x1.287a77eb4ca0dp-3, -0x1.bcb8110a181b5p-4,
+ 0x1.60e7e3e747129p-4};
+ double v2 = v * v; // Exact
+ double p2 = fputil::multiply_add(v, COEFFS[4], COEFFS[3]);
+ double p1 = fputil::multiply_add(v, COEFFS[2], COEFFS[1]);
+ double p0 = fputil::multiply_add(v, COEFFS[0], LOG10_R[index]);
+ double r = fputil::multiply_add(static_cast(m), LOG10_2,
+ fputil::polyeval(v2, p0, p1, p2));
return static_cast(r);
}
diff --git a/libc/test/src/math/log10f_test.cpp b/libc/test/src/math/log10f_test.cpp
--- a/libc/test/src/math/log10f_test.cpp
+++ b/libc/test/src/math/log10f_test.cpp
@@ -28,12 +28,13 @@
EXPECT_FP_EQ_WITH_EXCEPTION(neg_inf, __llvm_libc::log10f(-0.0f),
FE_DIVBYZERO);
EXPECT_FP_IS_NAN_WITH_EXCEPTION(__llvm_libc::log10f(-1.0f), FE_INVALID);
- EXPECT_FP_EQ(zero, __llvm_libc::log10f(1.0f));
+ EXPECT_FP_EQ_ALL_ROUNDING(zero, __llvm_libc::log10f(1.0f));
}
TEST(LlvmLibcLog10fTest, TrickyInputs) {
- constexpr int N = 15;
+ constexpr int N = 21;
constexpr uint32_t INPUTS[N] = {
+ 0x3f800000U /*1.0f*/,
0x41200000U /*10.0f*/,
0x42c80000U /*100.0f*/,
0x447a0000U /*1,000.0f*/,
@@ -49,6 +50,11 @@
0x08ae'a356U /*0x1.5d46acp-110f*/,
0x1c7d'a337U /*0x1.fb466ep-71f*/,
0x69c8'c583U /*0x1.918b06p+84f*/,
+ 0x0efe'ee7aU /*0x1.fddcf4p-98f*/,
+ 0x3f5f'de1bU /*0x1.bfbc36p-1f*/,
+ 0x3f80'70d8U /*0x1.00e1bp0f*/,
+ 0x120b'93dcU /*0x1.1727b8p-91f*/,
+ 0x13ae'78d3U /*0x1.5cf1a6p-88f*/,
};
for (int i = 0; i < N; ++i) {