[libc-commits] [libc] 5ee9787 - [libc][math] Improve the performance of sqrtf128. (#122578)
via libc-commits
libc-commits at lists.llvm.org
Thu Feb 13 14:49:55 PST 2025
Author: lntue
Date: 2025-02-13T17:49:52-05:00
New Revision: 5ee97877308e8617a2c42bb120f0a90e594eba31
URL: https://github.com/llvm/llvm-project/commit/5ee97877308e8617a2c42bb120f0a90e594eba31
DIFF: https://github.com/llvm/llvm-project/commit/5ee97877308e8617a2c42bb120f0a90e594eba31.diff
LOG: [libc][math] Improve the performance of sqrtf128. (#122578)
Use a combination of polynomial approximation and Newton-Raphson
iterations in 64-bit and 128-bit integers to improve the performance of
sqrtf128. The correct rounding is provided by squaring the result and
comparing it with the argument.
Performance improvement using the newly added perf test:
- My function = the improved implementation from this PR
- Other function = current implementation using
`libc/src/__support/FPUtil/generic/sqrt.h`
```
Performance tests with inputs in denormal range:
-- My function --
Total time : 1260765265 ns
Average runtime : 125.951 ns/op
Ops per second : 7939623 op/s
-- Other function --
Total time : 7160726518 ns
Average runtime : 715.357 ns/op
Ops per second : 1397902 op/s
-- Average runtime ratio --
Mine / Other's : 0.176067
Performance tests with inputs in normal range:
-- My function --
Total time : 373003808 ns
Average runtime : 37.2631 ns/op
Ops per second : 26836189 op/s
-- Other function --
Total time : 7353398916 ns
Average runtime : 734.605 ns/op
Ops per second : 1361275 op/s
-- Average runtime ratio --
Mine / Other's : 0.0507254
```
---------
Co-authored-by: Alexei Sibidanov <sibid at uvic.ca>
Added:
libc/test/src/math/performance_testing/sqrtf128_perf.cpp
Modified:
libc/src/__support/big_int.h
libc/src/math/generic/CMakeLists.txt
libc/src/math/generic/sqrtf128.cpp
libc/test/UnitTest/FPMatcher.h
libc/test/src/math/SqrtTest.h
libc/test/src/math/performance_testing/CMakeLists.txt
libc/test/src/math/smoke/SqrtTest.h
libc/test/src/math/smoke/generic_sqrt_test.cpp
libc/test/src/math/smoke/generic_sqrtf128_test.cpp
libc/test/src/math/smoke/generic_sqrtf_test.cpp
libc/test/src/math/smoke/generic_sqrtl_test.cpp
libc/test/src/math/smoke/sqrt_test.cpp
libc/test/src/math/smoke/sqrtf128_test.cpp
libc/test/src/math/smoke/sqrtf16_test.cpp
libc/test/src/math/smoke/sqrtf_test.cpp
libc/test/src/math/smoke/sqrtl_test.cpp
Removed:
################################################################################
diff --git a/libc/src/__support/big_int.h b/libc/src/__support/big_int.h
index f591b41df037b..fb5ad99d53e7b 100644
--- a/libc/src/__support/big_int.h
+++ b/libc/src/__support/big_int.h
@@ -241,7 +241,7 @@ LIBC_INLINE constexpr void quick_mul_hi(cpp::array<word, N> &dst,
}
template <typename word, size_t N>
-LIBC_INLINE constexpr bool is_negative(cpp::array<word, N> &array) {
+LIBC_INLINE constexpr bool is_negative(const cpp::array<word, N> &array) {
using signed_word = cpp::make_signed_t<word>;
return cpp::bit_cast<signed_word>(array.back()) < 0;
}
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index 2bda741b453f5..537d5b5ad94ed 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -2978,6 +2978,11 @@ add_entrypoint_object(
HDRS
../sqrtf128.h
DEPENDS
+ libc.src.__support.CPP.bit
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.rounding_mode
+ libc.src.__support.macros.optimization
libc.src.__support.macros.properties.types
libc.src.__support.FPUtil.sqrt
)
diff --git a/libc/src/math/generic/sqrtf128.cpp b/libc/src/math/generic/sqrtf128.cpp
index f87066b6f6403..c844d3afa11c8 100644
--- a/libc/src/math/generic/sqrtf128.cpp
+++ b/libc/src/math/generic/sqrtf128.cpp
@@ -7,14 +7,431 @@
//===----------------------------------------------------------------------===//
#include "src/math/sqrtf128.h"
-#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/CPP/bit.h"
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/rounding_mode.h"
#include "src/__support/common.h"
-#include "src/__support/macros/config.h"
+#include "src/__support/macros/optimization.h"
+#include "src/__support/uint128.h"
+
+// Compute sqrtf128 with correct rounding for all rounding modes using integer
+// arithmetic by Alexei Sibidanov (sibid at uvic.ca):
+// https://github.com/sibidanov/llvm-project/tree/as_sqrt_v2
+// https://github.com/sibidanov/llvm-project/tree/as_sqrt_v3
+// TODO: Update the reference once Alexei's implementation is in the CORE-MATH
+// project. https://github.com/llvm/llvm-project/issues/126794
+
+// Let the input be expressed as x = 2^e * m_x,
+// - Step 1: Range reduction
+// Let x_reduced = 2^(e % 2) * m_x,
+// Then sqrt(x) = 2^(e / 2) * sqrt(x_reduced), with
+// 1 <= x_reduced < 4.
+// - Step 2: Polynomial approximation
+// Approximate 1/sqrt(x_reduced) using polynomial approximation with the
+// result errors bounded by:
+// |r0 - 1/sqrt(x_reduced)| < 2^-32.
+// The computations are done in uint64_t.
+// - Step 3: First Newton iteration
+// Let the scaled error defined by:
+// h0 = r0^2 * x_reduced - 1.
+// Then we compute the first Newton iteration:
+// r1 = r0 - r0 * h0 / 2.
+// The result is then bounded by:
+// |r1 - 1 / sqrt(x_reduced)| < 2^-62.
+// - Step 4: Second Newton iteration
+// We calculate the scaled error from Step 3:
+// h1 = r1^2 * x_reduced - 1.
+// Then the second Newton iteration is computed by:
+// r2 = x_reduced * (r1 - r1 * h0 / 2)
+// ~ x_reduced * (1/sqrt(x_reduced)) = sqrt(x_reduced)
+// - Step 5: Perform rounding test and correction if needed.
+// Rounding correction is done by computing the exact rounding errors:
+// x_reduced - r2^2.
namespace LIBC_NAMESPACE_DECL {
+using FPBits = fputil::FPBits<float128>;
+
+namespace {
+
+template <typename T, typename U = T> static inline constexpr T prod_hi(T, U);
+
+// Get high part of integer multiplications.
+// Use template to prevent implicit conversion.
+template <>
+inline constexpr uint64_t prod_hi<uint64_t>(uint64_t x, uint64_t y) {
+ return static_cast<uint64_t>(
+ (static_cast<UInt128>(x) * static_cast<UInt128>(y)) >> 64);
+}
+
+// Get high part of unsigned 128x64 bit multiplication.
+template <>
+inline constexpr UInt128 prod_hi<UInt128, uint64_t>(UInt128 x, uint64_t y) {
+ uint64_t x_lo = static_cast<uint64_t>(x);
+ uint64_t x_hi = static_cast<uint64_t>(x >> 64);
+ UInt128 xyl = static_cast<UInt128>(x_lo) * static_cast<UInt128>(y);
+ UInt128 xyh = static_cast<UInt128>(x_hi) * static_cast<UInt128>(y);
+ return xyh + (xyl >> 64);
+}
+
+// Get high part of signed 64x64 bit multiplication.
+template <> inline constexpr int64_t prod_hi<int64_t>(int64_t x, int64_t y) {
+ return static_cast<int64_t>(
+ (static_cast<Int128>(x) * static_cast<Int128>(y)) >> 64);
+}
+
+// Get high 128-bit part of unsigned 128x128 bit multiplication.
+template <> inline constexpr UInt128 prod_hi<UInt128>(UInt128 x, UInt128 y) {
+ uint64_t x_lo = static_cast<uint64_t>(x);
+ uint64_t x_hi = static_cast<uint64_t>(x >> 64);
+ uint64_t y_lo = static_cast<uint64_t>(y);
+ uint64_t y_hi = static_cast<uint64_t>(y >> 64);
+
+ UInt128 xh_yh = static_cast<UInt128>(x_hi) * static_cast<UInt128>(y_hi);
+ UInt128 xh_yl = static_cast<UInt128>(x_hi) * static_cast<UInt128>(y_lo);
+ UInt128 xl_yh = static_cast<UInt128>(x_lo) * static_cast<UInt128>(y_hi);
+
+ xh_yh += xh_yl >> 64;
+
+ return xh_yh + (xl_yh >> 64);
+}
+
+// Get high 128-bit part of mixed sign 128x128 bit multiplication.
+template <>
+inline constexpr Int128 prod_hi<Int128, UInt128>(Int128 x, UInt128 y) {
+ UInt128 mask = static_cast<UInt128>(x >> 127);
+ UInt128 negative_part = y & mask;
+ UInt128 prod = prod_hi(static_cast<UInt128>(x), y);
+ return static_cast<Int128>(prod - negative_part);
+}
+
+// Newton-Raphson first order step to improve accuracy of the result.
+// For the initial approximation r0 ~ 1/sqrt(x), let
+// h = r0^2 * x - 1
+// be its scaled error. Then the first-order Newton-Raphson iteration is:
+// r1 = r0 - r0 * h / 2
+// which has error bounded by:
+// |r1 - 1/sqrt(x)| < h^2 / 2.
+LIBC_INLINE uint64_t rsqrt_newton_raphson(uint64_t m, uint64_t r) {
+ uint64_t r2 = prod_hi(r, r);
+ // h = r0^2*x - 1.
+ int64_t h = static_cast<int64_t>(prod_hi(m, r2) + r2);
+ // hr = r * h / 2
+ int64_t hr = prod_hi(h, static_cast<int64_t>(r >> 1));
+ return r - hr;
+}
+
+#ifdef LIBC_MATH_HAS_SMALL_TABLES
+// Degree-12 minimax polynomials for 1/sqrt(x) on [1, 2].
+constexpr uint32_t RSQRT_COEFFS[12] = {
+ 0xb5947a4a, 0x2d651e32, 0x9ad50532, 0x2d28d093, 0x0d8be653, 0x04239014,
+ 0x01492449, 0x0066ff7d, 0x001e74a1, 0x000984cc, 0x00049abc, 0x00018340,
+};
+
+LIBC_INLINE uint64_t rsqrt_approx(uint64_t m) {
+ int64_t x = static_cast<uint64_t>(m) ^ (uint64_t(1) << 63);
+ int64_t x_26 = x >> 2;
+ int64_t z = x >> 31;
+
+ if (LIBC_UNLIKELY(z <= -4294967296))
+ return ~(m >> 1);
+
+ uint64_t x2 = static_cast<uint64_t>(z) * static_cast<uint64_t>(z);
+ uint64_t x2_26 = x2 >> 5;
+ x2 >>= 32;
+ // Calculate the odd part of the polynomial using Horner's method.
+ uint64_t c0 = RSQRT_COEFFS[8] + ((x2 * RSQRT_COEFFS[10]) >> 32);
+ uint64_t c1 = RSQRT_COEFFS[6] + ((x2 * c0) >> 32);
+ uint64_t c2 = RSQRT_COEFFS[4] + ((x2 * c1) >> 32);
+ uint64_t c3 = RSQRT_COEFFS[2] + ((x2 * c2) >> 32);
+ uint64_t c4 = RSQRT_COEFFS[0] + ((x2 * c3) >> 32);
+ uint64_t odd =
+ static_cast<uint64_t>((x >> 34) * static_cast<int64_t>(c4 >> 3)) + x_26;
+ // Calculate the even part of the polynomial using Horner's method.
+ uint64_t d0 = RSQRT_COEFFS[9] + ((x2 * RSQRT_COEFFS[11]) >> 32);
+ uint64_t d1 = RSQRT_COEFFS[7] + ((x2 * d0) >> 32);
+ uint64_t d2 = RSQRT_COEFFS[5] + ((x2 * d1) >> 32);
+ uint64_t d3 = RSQRT_COEFFS[3] + ((x2 * d2) >> 32);
+ uint64_t d4 = RSQRT_COEFFS[1] + ((x2 * d3) >> 32);
+ uint64_t even = 0xd105eb806655d608ul + ((x2 * d4) >> 6) + x2_26;
+
+ uint64_t r = even - odd; // error < 1.5e-10
+ // Newton-Raphson first order step to improve accuracy of the result to almost
+ // 64 bits.
+ return rsqrt_newton_raphson(m, r);
+}
+
+#else
+// Cubic minimax polynomials for 1/sqrt(x) on [1 + k/64, 1 + (k + 1)/64]
+// for k = 0..63.
+constexpr uint32_t RSQRT_COEFFS[64][4] = {
+ {0xffffffff, 0xfffff780, 0xbff55815, 0x9bb5b6e7},
+ {0xfc0bd889, 0xfa1d6e7d, 0xb8a95a89, 0x938bf8f0},
+ {0xf82ec882, 0xf473bea9, 0xb1bf4705, 0x8bed0079},
+ {0xf467f280, 0xeefff2a1, 0xab309d4a, 0x84cdb431},
+ {0xf0b6848c, 0xe9bf46f4, 0xa4f76232, 0x7e24037b},
+ {0xed19b75e, 0xe4af2628, 0x9f0e1340, 0x77e6ca62},
+ {0xe990cdad, 0xdfcd2521, 0x996f9b96, 0x720db8df},
+ {0xe61b138e, 0xdb16ffde, 0x94174a00, 0x6c913cff},
+ {0xe2b7dddf, 0xd68a967b, 0x8f00c812, 0x676a6f92},
+ {0xdf6689b7, 0xd225ea80, 0x8a281226, 0x62930308},
+ {0xdc267bea, 0xcde71c63, 0x8589702c, 0x5e05343e},
+ {0xd8f7208e, 0xc9cc6948, 0x81216f2e, 0x59bbbcf8},
+ {0xd5d7ea91, 0xc5d428ee, 0x7cecdb76, 0x55b1c7d6},
+ {0xd2c8534e, 0xc1fccbc9, 0x78e8bb45, 0x51e2e592},
+ {0xcfc7da32, 0xbe44d94a, 0x75124a0a, 0x4e4b0369},
+ {0xccd6045f, 0xbaaaee41, 0x7166f40f, 0x4ae66284},
+ {0xc9f25c5c, 0xb72dbb69, 0x6de45288, 0x47b19045},
+ {0xc71c71c7, 0xb3cc040f, 0x6a882804, 0x44a95f5f},
+ {0xc453d90f, 0xb0849cd4, 0x67505d2a, 0x41cae1a0},
+ {0xc1982b2e, 0xad566a85, 0x643afdc8, 0x3f13625c},
+ {0xbee9056f, 0xaa406113, 0x6146361f, 0x3c806169},
+ {0xbc46092e, 0xa7418293, 0x5e70506d, 0x3a0f8e8e},
+ {0xb9aedba5, 0xa458de58, 0x5bb7b2b1, 0x37bec572},
+ {0xb72325b7, 0xa1859022, 0x591adc9a, 0x358c09e2},
+ {0xb4a293c2, 0x9ec6bf52, 0x569865a7, 0x33758476},
+ {0xb22cd56d, 0x9c1b9e36, 0x542efb6a, 0x31797f8a},
+ {0xafc19d86, 0x9983695c, 0x51dd5ffb, 0x2f96647a},
+ {0xad60a1d1, 0x96fd66f7, 0x4fa2687c, 0x2dcab91f},
+ {0xab099ae9, 0x9488e64b, 0x4d7cfbc9, 0x2c151d8a},
+ {0xa8bc441a, 0x92253f20, 0x4b6c1139, 0x2a7449ef},
+ {0xa6785b42, 0x8fd1d14a, 0x496eaf82, 0x28e70cc3},
+ {0xa43da0ae, 0x8d8e042a, 0x4783eba7, 0x276c4900},
+ {0xa20bd701, 0x8b594648, 0x45aae80a, 0x2602f493},
+ {0x9fe2c315, 0x89330ce4, 0x43e2d382, 0x24aa16ec},
+ {0x9dc22be4, 0x871ad399, 0x422ae88c, 0x2360c7af},
+ {0x9ba9da6c, 0x85101c05, 0x40826c88, 0x22262d7b},
+ {0x99999999, 0x83126d70, 0x3ee8af07, 0x20f97cd2},
+ {0x97913630, 0x81215480, 0x3d5d0922, 0x1fd9f714},
+ {0x95907eb8, 0x7f3c62ef, 0x3bdedce0, 0x1ec6e994},
+ {0x93974369, 0x7d632f45, 0x3a6d94a9, 0x1dbfacbb},
+ {0x91a55615, 0x7b955498, 0x3908a2be, 0x1cc3a33b},
+ {0x8fba8a1c, 0x79d2724e, 0x37af80bf, 0x1bd23960},
+ {0x8dd6b456, 0x781a2be4, 0x3661af39, 0x1aeae458},
+ {0x8bf9ab07, 0x766c28ba, 0x351eb539, 0x1a0d21a2},
+ {0x8a2345cc, 0x74c813dd, 0x33e61feb, 0x19387676},
+ {0x88535d90, 0x732d9bdc, 0x32b7823a, 0x186c6f3e},
+ {0x8689cc7e, 0x719c7297, 0x3192747d, 0x17a89f21},
+ {0x84c66df1, 0x70144d19, 0x30769424, 0x16ec9f89},
+ {0x83091e6a, 0x6e94e36c, 0x2f63836f, 0x16380fbf},
+ {0x8151bb87, 0x6d1df079, 0x2e58e925, 0x158a9484},
+ {0x7fa023f1, 0x6baf31de, 0x2d567053, 0x14e3d7ba},
+ {0x7df43758, 0x6a4867d3, 0x2c5bc811, 0x1443880e},
+ {0x7c4dd664, 0x68e95508, 0x2b68a346, 0x13a958ab},
+ {0x7aace2b0, 0x6791be86, 0x2a7cb871, 0x131500ee},
+ {0x79113ebc, 0x66416b95, 0x2997c17a, 0x12863c29},
+ {0x777acde8, 0x64f825a1, 0x28b97b82, 0x11fcc95c},
+ {0x75e9746a, 0x63b5b822, 0x27e1a6b4, 0x11786b03},
+ {0x745d1746, 0x6279f081, 0x2710061d, 0x10f8e6da},
+ {0x72d59c46, 0x61449e06, 0x26445f86, 0x107e05ac},
+ {0x7152e9f4, 0x601591be, 0x257e7b4d, 0x10079327},
+ {0x6fd4e793, 0x5eec9e6b, 0x24be2445, 0x0f955da9},
+ {0x6e5b7d16, 0x5dc9986e, 0x24032795, 0x0f273620},
+ {0x6ce6931d, 0x5cac55b7, 0x234d5496, 0x0ebcefdb},
+ {0x6b7612ec, 0x5b94adb2, 0x229c7cbc, 0x0e56606e},
+};
+
+// Approximate rsqrt with cubic polynomials.
+// The range [1,2] is splitted into 64 equal sub-ranges and the reciprocal
+// square root is approximated by a cubic polynomial by the minimax method in
+// each subrange. The approximation accuracy fits into 32-33 bits and thus it is
+// natural to round coefficients into 32 bit. The constant coefficient can be
+// rounded to 33 bits since the most significant bit is always 1 and implicitly
+// assumed in the table.
+LIBC_INLINE uint64_t rsqrt_approx(uint64_t m) {
+ // ULP(m) = 2^-64.
+ // Use the top 6 bits as index for looking up polynomial coeffs.
+ uint64_t indx = m >> 58;
+
+ uint64_t c0 = static_cast<uint64_t>(RSQRT_COEFFS[indx][0]);
+ c0 <<= 31; // to 64 bit with the space for the implicit bit
+ c0 |= 1ull << 63; // add implicit bit
+
+ uint64_t c1 = static_cast<uint64_t>(RSQRT_COEFFS[indx][1]);
+ c1 <<= 25; // to 64 bit format
+
+ uint64_t c2 = static_cast<uint64_t>(RSQRT_COEFFS[indx][2]);
+ uint64_t c3 = static_cast<uint64_t>(RSQRT_COEFFS[indx][3]);
+
+ uint64_t d = (m << 6) >> 32; // local coordinate in the subrange [0, 2^32]
+ uint64_t d2 = (d * d) >> 32; // square of the local coordinate
+ uint64_t re = c0 + (d2 * c2 >> 13); // even part of the polynomial (positive)
+ uint64_t ro = d * ((c1 + ((d2 * c3) >> 19)) >> 26) >>
+ 6; // odd part of the polynomial (negative)
+ uint64_t r = re - ro; // maximal error < 1.55e-10 and it is less than 2^-32
+ // Newton-Raphson first order step to improve accuracy of the result to almost
+ // 64 bits.
+ r = rsqrt_newton_raphson(m, r);
+ // Adjust in the unlucky case x~1;
+ if (LIBC_UNLIKELY(!r))
+ --r;
+ return r;
+}
+#endif // LIBC_MATH_HAS_SMALL_TABLES
+
+} // anonymous namespace
+
LLVM_LIBC_FUNCTION(float128, sqrtf128, (float128 x)) {
- return fputil::sqrt<float128>(x);
+ using FPBits = fputil::FPBits<float128>;
+ // Get rounding mode.
+ uint32_t rm = fputil::get_round();
+
+ FPBits xbits(x);
+ UInt128 x_u = xbits.uintval();
+ // Bring leading bit of the mantissa to the highest bit.
+ // ulp(x_frac) = 2^-128.
+ UInt128 x_frac = xbits.get_mantissa() << (FPBits::EXP_LEN + 1);
+
+ int sign_exp = static_cast<int>(x_u >> FPBits::FRACTION_LEN);
+
+ if (LIBC_UNLIKELY(sign_exp == 0 || sign_exp >= 0x7fff)) {
+ // Special cases: NAN, inf, negative numbers
+ if (sign_exp >= 0x7fff) {
+ // x = -0 or x = inf
+ if (xbits.is_zero() || xbits == xbits.inf())
+ return x;
+ // x is nan
+ if (xbits.is_nan()) {
+ // pass through quiet nan
+ if (xbits.is_quiet_nan())
+ return x;
+ // transform signaling nan to quiet and return
+ return xbits.quiet_nan().get_val();
+ }
+ // x < 0 or x = -inf
+ fputil::set_errno_if_required(EDOM);
+ fputil::raise_except_if_required(FE_INVALID);
+ return xbits.quiet_nan().get_val();
+ }
+ // Now x is subnormal or x = +0.
+
+ // x is +0.
+ if (x_frac == 0)
+ return x;
+
+ // Normalize subnormal inputs.
+ sign_exp = -cpp::countl_zero(x_frac);
+ int normal_shifts = 1 - sign_exp;
+ x_frac <<= normal_shifts;
+ }
+
+ // For sign_exp = biased exponent of x = real_exponent + 16383,
+ // let f be the real exponent of the output:
+ // f = floor(real_exponent / 2)
+ // Then:
+ // floor((sign_exp + 1) / 2) = f + 8192
+ // Hence, the biased exponent of the final result is:
+ // f + 16383 = floor((sign_exp + 1) / 2) + 8191.
+ // Since the output mantissa will include the hidden bit, we can define the
+ // output exponent part:
+ // e2 = floor((sign_exp + 1) / 2) + 8190
+ unsigned i = static_cast<unsigned>(1 - (sign_exp & 1));
+ uint32_t q2 = (sign_exp + 1) >> 1;
+ // Exponent of the final result
+ uint32_t e2 = q2 + 8190;
+
+ constexpr uint64_t RSQRT_2[2] = {~0ull,
+ 0xb504f333f9de6484 /* 2^64/sqrt(2) */};
+
+ // Approximate 1/sqrt(1 + x_frac)
+ // Error: |r_1 - 1/sqrt(x)| < 2^-62.
+ uint64_t r1 = rsqrt_approx(static_cast<uint64_t>(x_frac >> 64));
+ // Adjust for the even/odd exponent.
+ uint64_t r2 = prod_hi(r1, RSQRT_2[i]);
+ unsigned shift = 2 - i;
+
+ // Normalized input:
+ // 1 <= x_reduced < 4
+ UInt128 x_reduced = (x_frac >> shift) | (UInt128(1) << (126 + i));
+ // With r2 ~ 1/sqrt(x) up to 2^-63, we perform another round of Newton-Raphson
+ // iteration:
+ // r3 = r2 - r2 * h / 2,
+ // for h = r2^2 * x - 1.
+ // Then:
+ // sqrt(x) = x * (1 / sqrt(x))
+ // ~ x * r3
+ // = x * (r2 - r2 * h / 2)
+ // = (x * r2) - (x * r2) * h / 2
+ UInt128 sx = prod_hi(x_reduced, r2);
+ UInt128 h = prod_hi(sx, r2) << 2;
+ UInt128 ds = static_cast<UInt128>(prod_hi(static_cast<Int128>(h), sx));
+ UInt128 v = (sx << 1) - ds;
+
+ uint32_t nrst = rm == FE_TONEAREST;
+ // The result lies within (-2,5) of true square root so we now
+ // test that we can correctly round the result taking into account
+ // the rounding mode.
+ // Check the lowest 14 bits (by clearing and sign-extending the top
+ // 32 - 14 = 18 bits).
+ int dd = (static_cast<int>(v) << 18) >> 18;
+
+ if (LIBC_UNLIKELY(dd < 4 && dd >= -8)) { // can round correctly?
+ // m is almost the final result it can be only 1 ulp off so we
+ // just need to test both possibilities. We square it and
+ // compare with the initial argument.
+ UInt128 m = v >> 15;
+ UInt128 m2 = m * m;
+ // The
diff erence of the squared result and the argument
+ Int128 t0 = static_cast<Int128>(m2 - (x_reduced << 98));
+ if (t0 == 0) {
+ // the square root is exact
+ v = m << 15;
+ } else {
+ // Add +-1 ulp to m depend on the sign of the
diff erence. Here
+ // we do not need to square again since (m+1)^2 = m^2 + 2*m +
+ // 1 so just need to add shifted m and 1.
+ Int128 t1 = t0;
+ Int128 sgn = t0 >> 127; // sign of the
diff erence
+ t1 -= (m << 1) ^ sgn;
+ t1 += 1 + sgn;
+
+ Int128 sgn1 = t1 >> 127;
+ if (LIBC_UNLIKELY(sgn == sgn1)) {
+ t0 = t1;
+ v -= sgn << 15;
+ t1 -= (m << 1) ^ sgn;
+ t1 += 1 + sgn;
+ }
+
+ if (t1 == 0) {
+ // 1 ulp offset brings again an exact root
+ v = (m - (2 * sgn + 1)) << 15;
+ } else {
+ t1 += t0;
+ Int128 side = t1 >> 127; // select what is closer m or m+-1
+ v &= ~UInt128(0) << 15; // wipe the fractional bits
+ v -= ((sgn & side) | (~sgn & 1)) << (15 + side);
+ v |= 1; // add sticky bit since we cannot have an exact mid-point
+ // situation
+ }
+ }
+ }
+
+ unsigned frac = static_cast<unsigned>(v) & 0x7fff; // fractional part
+ unsigned rnd; // round bit
+ if (LIBC_LIKELY(nrst != 0)) {
+ rnd = frac >> 14; // round to nearest tie to even
+ } else if (rm == FE_UPWARD) {
+ rnd = !!frac; // round up
+ } else {
+ rnd = 0; // round down or round to zero
+ }
+
+ v >>= 15; // position mantissa
+ v += rnd; // round
+
+ // Set inexact flag only if square root is inexact
+ // TODO: We will have to raise FE_INEXACT most of the time, but this
+ // operation is very costly, especially in x86-64, since technically, it
+ // needs to synchronize both SSE and x87 flags. Need to investigate
+ // further to see how we can make this performant.
+ // https://github.com/llvm/llvm-project/issues/126753
+
+ // if(frac) fputil::raise_except_if_required(FE_INEXACT);
+
+ v += static_cast<UInt128>(e2) << FPBits::FRACTION_LEN; // place exponent
+ return cpp::bit_cast<float128>(v);
}
} // namespace LIBC_NAMESPACE_DECL
diff --git a/libc/test/UnitTest/FPMatcher.h b/libc/test/UnitTest/FPMatcher.h
index 53e0c16f22101..21b8a45b0726f 100644
--- a/libc/test/UnitTest/FPMatcher.h
+++ b/libc/test/UnitTest/FPMatcher.h
@@ -330,27 +330,6 @@ struct ModifyMXCSR {
EXPECT_FP_EXCEPTION(expected_except); \
} while (0)
-#define EXPECT_FP_EQ_ALL_ROUNDING(expected, actual) \
- do { \
- using namespace LIBC_NAMESPACE::fputil::testing; \
- ForceRoundingMode __r1(RoundingMode::Nearest); \
- if (__r1.success) { \
- EXPECT_FP_EQ((expected), (actual)); \
- } \
- ForceRoundingMode __r2(RoundingMode::Upward); \
- if (__r2.success) { \
- EXPECT_FP_EQ((expected), (actual)); \
- } \
- ForceRoundingMode __r3(RoundingMode::Downward); \
- if (__r3.success) { \
- EXPECT_FP_EQ((expected), (actual)); \
- } \
- ForceRoundingMode __r4(RoundingMode::TowardZero); \
- if (__r4.success) { \
- EXPECT_FP_EQ((expected), (actual)); \
- } \
- } while (0)
-
#define EXPECT_FP_EQ_ROUNDING_MODE(expected, actual, rounding_mode) \
do { \
using namespace LIBC_NAMESPACE::fputil::testing; \
@@ -372,6 +351,61 @@ struct ModifyMXCSR {
#define EXPECT_FP_EQ_ROUNDING_TOWARD_ZERO(expected, actual) \
EXPECT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::TowardZero)
+#define EXPECT_FP_EQ_ALL_ROUNDING_1(expected, actual) \
+ do { \
+ EXPECT_FP_EQ_ROUNDING_NEAREST((expected), (actual)); \
+ EXPECT_FP_EQ_ROUNDING_UPWARD((expected), (actual)); \
+ EXPECT_FP_EQ_ROUNDING_DOWNWARD((expected), (actual)); \
+ EXPECT_FP_EQ_ROUNDING_TOWARD_ZERO((expected), (actual)); \
+ } while (0)
+
+#define EXPECT_FP_EQ_ALL_ROUNDING_4(expected_nearest, expected_upward, \
+ expected_downward, expected_toward_zero, \
+ actual) \
+ do { \
+ EXPECT_FP_EQ_ROUNDING_NEAREST((expected_nearest), (actual)); \
+ EXPECT_FP_EQ_ROUNDING_UPWARD((expected_upward), (actual)); \
+ EXPECT_FP_EQ_ROUNDING_DOWNWARD((expected_downward), (actual)); \
+ EXPECT_FP_EQ_ROUNDING_TOWARD_ZERO((expected_toward_zero), (actual)); \
+ } while (0)
+
+#define EXPECT_FP_EQ_ALL_ROUNDING_UNSUPPORTED(...) \
+ static_assert(false, "Unsupported number of arguments")
+
+#define EXPECT_FP_EQ_ALL_ROUNDING_GET_6TH_ARG(ARG1, ARG2, ARG3, ARG4, ARG5, \
+ ARG6, ...) \
+ ARG6
+
+#define EXPECT_FP_EQ_ALL_ROUNDING_SELECTION(...) \
+ EXPECT_FP_EQ_ALL_ROUNDING_GET_6TH_ARG( \
+ __VA_ARGS__, EXPECT_FP_EQ_ALL_ROUNDING_4, \
+ EXPECT_FP_EQ_ALL_ROUNDING_UNSUPPORTED, \
+ EXPECT_FP_EQ_ALL_ROUNDING_UNSUPPORTED, EXPECT_FP_EQ_ALL_ROUNDING_1)
+
+#define EXPECT_FP_EQ_ALL_ROUNDING(...) \
+ EXPECT_FP_EQ_ALL_ROUNDING_SELECTION(__VA_ARGS__)(__VA_ARGS__)
+
+#define ASSERT_FP_EQ_ROUNDING_MODE(expected, actual, rounding_mode) \
+ do { \
+ using namespace LIBC_NAMESPACE::fputil::testing; \
+ ForceRoundingMode __r((rounding_mode)); \
+ if (__r.success) { \
+ ASSERT_FP_EQ((expected), (actual)); \
+ } \
+ } while (0)
+
+#define ASSERT_FP_EQ_ROUNDING_NEAREST(expected, actual) \
+ ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Nearest)
+
+#define ASSERT_FP_EQ_ROUNDING_UPWARD(expected, actual) \
+ ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Upward)
+
+#define ASSERT_FP_EQ_ROUNDING_DOWNWARD(expected, actual) \
+ ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::Downward)
+
+#define ASSERT_FP_EQ_ROUNDING_TOWARD_ZERO(expected, actual) \
+ ASSERT_FP_EQ_ROUNDING_MODE((expected), (actual), RoundingMode::TowardZero)
+
#define EXPECT_FP_EQ_WITH_EXCEPTION_ROUNDING_MODE( \
expected, actual, expected_except, rounding_mode) \
do { \
diff --git a/libc/test/src/math/SqrtTest.h b/libc/test/src/math/SqrtTest.h
index 770cc94b3b940..fdfc4f9bb9943 100644
--- a/libc/test/src/math/SqrtTest.h
+++ b/libc/test/src/math/SqrtTest.h
@@ -29,14 +29,14 @@ class SqrtTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
FPBits denormal(zero);
denormal.set_mantissa(mant);
InType x = denormal.get_val();
- EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
}
constexpr StorageType COUNT = 200'001;
constexpr StorageType STEP = HIDDEN_BIT / COUNT;
for (StorageType i = 0, v = 0; i <= COUNT; ++i, v += STEP) {
InType x = FPBits(i).get_val();
- EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
}
}
@@ -48,7 +48,7 @@ class SqrtTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
InType x = x_bits.get_val();
if (x_bits.is_nan() || (x < 0))
continue;
- EXPECT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
+ ASSERT_MPFR_MATCH_ALL_ROUNDING(mpfr::Operation::Sqrt, x, func(x), 0.5);
}
}
};
diff --git a/libc/test/src/math/performance_testing/CMakeLists.txt b/libc/test/src/math/performance_testing/CMakeLists.txt
index 60c074a248f72..838ed9e957ca7 100644
--- a/libc/test/src/math/performance_testing/CMakeLists.txt
+++ b/libc/test/src/math/performance_testing/CMakeLists.txt
@@ -500,3 +500,12 @@ add_perf_binary(
COMPILE_OPTIONS
-fno-builtin
)
+
+add_perf_binary(
+ sqrtf128_perf
+ SRCS
+ sqrtf128_perf.cpp
+ DEPENDS
+ .single_input_single_output_
diff
+ libc.src.math.sqrtf128
+)
diff --git a/libc/test/src/math/performance_testing/sqrtf128_perf.cpp b/libc/test/src/math/performance_testing/sqrtf128_perf.cpp
new file mode 100644
index 0000000000000..bc04e698b2439
--- /dev/null
+++ b/libc/test/src/math/performance_testing/sqrtf128_perf.cpp
@@ -0,0 +1,20 @@
+//===-- Differential test for sqrtf128
+//----------------------------------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "SingleInputSingleOutputPerf.h"
+
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/math/sqrtf128.h"
+
+float128 sqrtf128_placeholder(float128 x) {
+ return LIBC_NAMESPACE::fputil::sqrt<float128>(x);
+}
+
+SINGLE_INPUT_SINGLE_OUTPUT_PERF(float128, LIBC_NAMESPACE::sqrtf128,
+ ::sqrtf128_placeholder, "sqrtf128_perf.log")
diff --git a/libc/test/src/math/smoke/SqrtTest.h b/libc/test/src/math/smoke/SqrtTest.h
index b5eaee22fc79d..29666ad0d4e56 100644
--- a/libc/test/src/math/smoke/SqrtTest.h
+++ b/libc/test/src/math/smoke/SqrtTest.h
@@ -39,7 +39,8 @@ class SqrtTest : public LIBC_NAMESPACE::testing::FEnvSafeTest {
#define LIST_SQRT_TESTS(T, func) \
using LlvmLibcSqrtTest = SqrtTest<T, T>; \
- TEST_F(LlvmLibcSqrtTest, SpecialNumbers) { test_special_numbers(&func); }
+ TEST_F(LlvmLibcSqrtTest, SpecialNumbers) { test_special_numbers(&func); } \
+ static_assert(true, "Require semicolon.")
#define LIST_NARROWING_SQRT_TESTS(OutType, InType, func) \
using LlvmLibcSqrtTest = SqrtTest<OutType, InType>; \
diff --git a/libc/test/src/math/smoke/generic_sqrt_test.cpp b/libc/test/src/math/smoke/generic_sqrt_test.cpp
index d0ab31ffd0fe6..4451e5e82d2d4 100644
--- a/libc/test/src/math/smoke/generic_sqrt_test.cpp
+++ b/libc/test/src/math/smoke/generic_sqrt_test.cpp
@@ -10,4 +10,4 @@
#include "src/__support/FPUtil/generic/sqrt.h"
-LIST_SQRT_TESTS(double, LIBC_NAMESPACE::fputil::sqrt<double>)
+LIST_SQRT_TESTS(double, LIBC_NAMESPACE::fputil::sqrt<double>);
diff --git a/libc/test/src/math/smoke/generic_sqrtf128_test.cpp b/libc/test/src/math/smoke/generic_sqrtf128_test.cpp
index edba114adf06c..790ff0a47bd3a 100644
--- a/libc/test/src/math/smoke/generic_sqrtf128_test.cpp
+++ b/libc/test/src/math/smoke/generic_sqrtf128_test.cpp
@@ -10,4 +10,4 @@
#include "src/__support/FPUtil/generic/sqrt.h"
-LIST_SQRT_TESTS(float128, LIBC_NAMESPACE::fputil::sqrt<float128>)
+LIST_SQRT_TESTS(float128, LIBC_NAMESPACE::fputil::sqrt<float128>);
diff --git a/libc/test/src/math/smoke/generic_sqrtf_test.cpp b/libc/test/src/math/smoke/generic_sqrtf_test.cpp
index f22ac8829d5ac..e04d4c4f26d63 100644
--- a/libc/test/src/math/smoke/generic_sqrtf_test.cpp
+++ b/libc/test/src/math/smoke/generic_sqrtf_test.cpp
@@ -10,4 +10,4 @@
#include "src/__support/FPUtil/generic/sqrt.h"
-LIST_SQRT_TESTS(float, LIBC_NAMESPACE::fputil::sqrt<float>)
+LIST_SQRT_TESTS(float, LIBC_NAMESPACE::fputil::sqrt<float>);
diff --git a/libc/test/src/math/smoke/generic_sqrtl_test.cpp b/libc/test/src/math/smoke/generic_sqrtl_test.cpp
index ddc6a23695be4..ccb5054296115 100644
--- a/libc/test/src/math/smoke/generic_sqrtl_test.cpp
+++ b/libc/test/src/math/smoke/generic_sqrtl_test.cpp
@@ -10,4 +10,4 @@
#include "src/__support/FPUtil/generic/sqrt.h"
-LIST_SQRT_TESTS(long double, LIBC_NAMESPACE::fputil::sqrt<long double>)
+LIST_SQRT_TESTS(long double, LIBC_NAMESPACE::fputil::sqrt<long double>);
diff --git a/libc/test/src/math/smoke/sqrt_test.cpp b/libc/test/src/math/smoke/sqrt_test.cpp
index 1551b31d6f715..b41e06daf722e 100644
--- a/libc/test/src/math/smoke/sqrt_test.cpp
+++ b/libc/test/src/math/smoke/sqrt_test.cpp
@@ -10,4 +10,4 @@
#include "src/math/sqrt.h"
-LIST_SQRT_TESTS(double, LIBC_NAMESPACE::sqrt)
+LIST_SQRT_TESTS(double, LIBC_NAMESPACE::sqrt);
diff --git a/libc/test/src/math/smoke/sqrtf128_test.cpp b/libc/test/src/math/smoke/sqrtf128_test.cpp
index 23397b0623ce5..3b9686c4ea477 100644
--- a/libc/test/src/math/smoke/sqrtf128_test.cpp
+++ b/libc/test/src/math/smoke/sqrtf128_test.cpp
@@ -8,6 +8,130 @@
#include "SqrtTest.h"
+#include "src/__support/uint128.h"
#include "src/math/sqrtf128.h"
-LIST_SQRT_TESTS(float128, LIBC_NAMESPACE::sqrtf128)
+LIST_SQRT_TESTS(float128, LIBC_NAMESPACE::sqrtf128);
+
+TEST_F(LlvmLibcSqrtTest, HardToRound) {
+ using LIBC_NAMESPACE::fputil::testing::RoundingMode;
+ using FPBits = LIBC_NAMESPACE::fputil::FPBits<float128>;
+
+ // Since there is no exact half cases for square root I encode the
+ // round direction in the sign of the result. E.g. if the number is
+ // negative it means that the exact root is below the rounded value
+ // (the absolute value). Thus I can test not only hard to round
+ // cases for the round to nearest mode but also the directional
+ // modes.
+ float128 HARD_TO_ROUND[][2] = {
+ {0x0.000000dee2f5b6a26c8f07f05442p-16382q,
+ -0x1.ddbd8763a617cff753e2a31083p-8204q},
+ {0x0.000000c86d174c5ad8ae54a548e7p-16382q,
+ 0x1.c507bb538940719890851ec1ca88p-8204q},
+ {0x0.000020ab15cfe0b8e488e128f535p-16382q,
+ -0x1.6dccb402560213bc0d62d62e910bp-8201q},
+ {0x0.0000219e97732a9970f2511989bap-16382q,
+ 0x1.73163d28be706f4b5052791e28a5p-8201q},
+ {0x0.000026e477546ae99ef57066f9fdp-16382q,
+ -0x1.8f20dd0d0c570a23ea59bc2bf009p-8201q},
+ {0x0.00002d0f88d27a496b3e533f5067p-16382q,
+ 0x1.ad9d4abe9f047225a7352bcc52c1p-8201q},
+ {0x1.0000000000000000000000000001p+0q, 0x1p+0q},
+ {0x1.0000000000000000000000000002p+0q,
+ -0x1.0000000000000000000000000001p+0q},
+ {0x1.0000000000000000000000000003p+0q,
+ 0x1.0000000000000000000000000001p+0q},
+ {0x1.0000000000000000000000000005p+0q,
+ 0x1.0000000000000000000000000002p+0q},
+ {0x1.0000000000000000000000000006p+0q,
+ -0x1.0000000000000000000000000003p+0q},
+ {0x1.1d4c381cbf3a0aa15b9aee344892p+0q,
+ 0x1.0e408c3fadc5e64b449c63673f4bp+0q},
+ {0x1.2af17a4ae6f93d11310c49c11b59p+0q,
+ -0x1.14a3bdf0ea5231f12d421a5dbe33p+0q},
+ {0x1.96f893bf29fb91e0fbe19a46d0c8p+0q,
+ 0x1.42c6bf6202e66f2295807dee44d9p+0q},
+ {0x1.97fb3839925b66804c429289cce8p+0q,
+ -0x1.432d4049ac1c85a241f333d326e9p+0q},
+ {0x1.be1d900eaeb1533f0f19cc15c7e6p+0q,
+ 0x1.51f1715154da44f3bf11f3d96c2dp+0q},
+ {0x1.c4f5074269525063a26051a0ad27p+0q,
+ 0x1.54864e9b1daa4d9135ff00663366p+0q},
+ {0x1.035cb5f298a801dc4be9b1f8cd97p+1q,
+ -0x1.6c688775bffcb3f507ba11d0abb9p+0q},
+ {0x1.274be02380427e709beab4dedeb4p+1q,
+ -0x1.84d5763281f2318422392e506b1cp+0q},
+ {0x1.64e797cfdbaa3f7e2f33279dbc6p+1q,
+ 0x1.ab79b164e255b26eca00ff99cc99p+0q},
+ {0x1.693a741358c9dac44a570a7e9f6cp+1q,
+ 0x1.ae0e8eaeab25bb0c40ee0c2693d3p+0q},
+ {0x1.8275db3fc4d822596047adcb71b9p+1q,
+ -0x1.bcd2bfb653e37a5dbe0ccc2cd917p+0q},
+ {0x1.83280bb98c4a7b88bd6f535899d9p+1q,
+ 0x1.bd39409dfd1990dd6a7f8211bb27p+0q},
+ {0x1.d78d8352b48608b510bfd5c75315p+1q,
+ -0x1.eb5c420f15adce0ed2bde5a241cep+0q},
+ {0x1.e3e4774f564b526edff84ce46668p+1q,
+ 0x1.f1bf73c0523a19b4bb639c98c0b5p+0q},
+ {0x1.fffffffffffffffffffffffffffap+1q,
+ -0x1.fffffffffffffffffffffffffffdp+0q},
+ {0x1.fffffffffffffffffffffffffffbp+1q,
+ 0x1.fffffffffffffffffffffffffffdp+0q},
+ {0x1.fffffffffffffffffffffffffffdp+1q,
+ 0x1.fffffffffffffffffffffffffffep+0q},
+ {0x1.fffffffffffffffffffffffffffep+1q,
+ -0x1.ffffffffffffffffffffffffffffp+0q},
+ {0x1.ffffffffffffffffffffffffffffp+1q,
+ 0x1.ffffffffffffffffffffffffffffp+0q},
+ };
+
+ auto rnd = [](float128 x, RoundingMode rm) -> float128 {
+ bool is_neg = x < 0;
+ float128 y = is_neg ? -x : x;
+ FPBits ybits(y);
+
+ if (is_neg &&
+ (rm == RoundingMode::Downward || rm == RoundingMode::TowardZero))
+ return FPBits(ybits.uintval() - 1).get_val();
+ if (!is_neg && (rm == RoundingMode::Upward))
+ return FPBits(ybits.uintval() + 1).get_val();
+
+ return y;
+ };
+
+ for (auto &t : HARD_TO_ROUND) {
+ EXPECT_FP_EQ_ALL_ROUNDING(
+ rnd(t[1], RoundingMode::Nearest), rnd(t[1], RoundingMode::Upward),
+ rnd(t[1], RoundingMode::Downward), rnd(t[1], RoundingMode::TowardZero),
+ LIBC_NAMESPACE::sqrtf128(t[0]));
+ }
+
+ // Exact results for subnormal arguments
+ float128 EXACT_SUBNORMAL[][2] = {
+ {0x0.0000000000000000000000000001p-16382q, 0x1p-8247q},
+ {0x0.0000000000000000000000000004p-16382q, 0x1p-8246q},
+ {0x0.0000000000001000000000000000p-16382q, 0x1p-8217q},
+ {0x0.0000000000010000000000000000p-16382q, 0x1p-8215q},
+ {0x0.0000000000100000000000000000p-16382q, 0x1p-8213q},
+ };
+
+ for (auto t : EXACT_SUBNORMAL)
+ EXPECT_FP_EQ_ALL_ROUNDING(t[1], LIBC_NAMESPACE::sqrtf128(t[0]));
+
+ // Check exact cases starting from small numbers
+ for (unsigned k = 1; k < 100 * 100; ++k) {
+ unsigned k2 = k * k;
+ float128 x = static_cast<float128>(k2);
+ float128 y = static_cast<float128>(k);
+ EXPECT_FP_EQ_ALL_ROUNDING(y, LIBC_NAMESPACE::sqrtf128(x));
+ };
+
+ // Then from the largest number.
+ uint64_t k0 = 101904826760412362ULL;
+ for (uint64_t k = k0; k > k0 - 10000; --k) {
+ UInt128 k2 = static_cast<UInt128>(k) * static_cast<UInt128>(k);
+ float128 x = static_cast<float128>(k2);
+ float128 y = static_cast<float128>(k);
+ EXPECT_FP_EQ_ALL_ROUNDING(y, LIBC_NAMESPACE::sqrtf128(x));
+ }
+}
diff --git a/libc/test/src/math/smoke/sqrtf16_test.cpp b/libc/test/src/math/smoke/sqrtf16_test.cpp
index d62049661eecb..950abd28840f0 100644
--- a/libc/test/src/math/smoke/sqrtf16_test.cpp
+++ b/libc/test/src/math/smoke/sqrtf16_test.cpp
@@ -10,4 +10,4 @@
#include "src/math/sqrtf16.h"
-LIST_SQRT_TESTS(float16, LIBC_NAMESPACE::sqrtf16)
+LIST_SQRT_TESTS(float16, LIBC_NAMESPACE::sqrtf16);
diff --git a/libc/test/src/math/smoke/sqrtf_test.cpp b/libc/test/src/math/smoke/sqrtf_test.cpp
index 3f2e973325bd0..888b6cbdd643c 100644
--- a/libc/test/src/math/smoke/sqrtf_test.cpp
+++ b/libc/test/src/math/smoke/sqrtf_test.cpp
@@ -10,4 +10,4 @@
#include "src/math/sqrtf.h"
-LIST_SQRT_TESTS(float, LIBC_NAMESPACE::sqrtf)
+LIST_SQRT_TESTS(float, LIBC_NAMESPACE::sqrtf);
diff --git a/libc/test/src/math/smoke/sqrtl_test.cpp b/libc/test/src/math/smoke/sqrtl_test.cpp
index f80bcfb736078..4f4a64f81ab7f 100644
--- a/libc/test/src/math/smoke/sqrtl_test.cpp
+++ b/libc/test/src/math/smoke/sqrtl_test.cpp
@@ -10,4 +10,4 @@
#include "src/math/sqrtl.h"
-LIST_SQRT_TESTS(long double, LIBC_NAMESPACE::sqrtl)
+LIST_SQRT_TESTS(long double, LIBC_NAMESPACE::sqrtl);
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