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-rw-r--r--libc/src/__support/math/CMakeLists.txt14
-rw-r--r--libc/src/__support/math/asinf16.h146
-rw-r--r--libc/src/math/generic/CMakeLists.txt11
-rw-r--r--libc/src/math/generic/asinf16.cpp121
4 files changed, 163 insertions, 129 deletions
diff --git a/libc/src/__support/math/CMakeLists.txt b/libc/src/__support/math/CMakeLists.txt
index b096c61..1050938 100644
--- a/libc/src/__support/math/CMakeLists.txt
+++ b/libc/src/__support/math/CMakeLists.txt
@@ -157,6 +157,20 @@ add_header_library(
)
add_header_library(
+ asinf16
+ HDRS
+ asinf16.h
+ DEPENDS
+ libc.src.__support.FPUtil.fenv_impl
+ libc.src.__support.FPUtil.fp_bits
+ libc.src.__support.FPUtil.polyeval
+ libc.src.__support.FPUtil.cast
+ libc.src.__support.FPUtil.multiply_add
+ libc.src.__support.FPUtil.sqrt
+ libc.src.__support.macros.optimization
+)
+
+add_header_library(
erff
HDRS
erff.h
diff --git a/libc/src/__support/math/asinf16.h b/libc/src/__support/math/asinf16.h
new file mode 100644
index 0000000..3d032a4
--- /dev/null
+++ b/libc/src/__support/math/asinf16.h
@@ -0,0 +1,146 @@
+//===-- Implementation header for asinf16 -----------------------*- C++ -*-===//
+//
+// 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
+//
+//===----------------------------------------------------------------------===//
+
+#ifndef LLVM_LIBC_SRC___SUPPORT_MATH_ASINF16_H
+#define LLVM_LIBC_SRC___SUPPORT_MATH_ASINF16_H
+
+#include "include/llvm-libc-macros/float16-macros.h"
+
+#ifdef LIBC_TYPES_HAS_FLOAT16
+
+#include "src/__support/FPUtil/FEnvImpl.h"
+#include "src/__support/FPUtil/FPBits.h"
+#include "src/__support/FPUtil/PolyEval.h"
+#include "src/__support/FPUtil/cast.h"
+#include "src/__support/FPUtil/multiply_add.h"
+#include "src/__support/FPUtil/sqrt.h"
+#include "src/__support/macros/optimization.h"
+
+namespace LIBC_NAMESPACE_DECL {
+
+namespace math {
+
+LIBC_INLINE static constexpr float16 asinf16(float16 x) {
+
+ // Generated by Sollya using the following command:
+ // > round(pi/2, D, RN);
+ constexpr float PI_2 = 0x1.921fb54442d18p0f;
+
+ using FPBits = fputil::FPBits<float16>;
+ FPBits xbits(x);
+
+ uint16_t x_u = xbits.uintval();
+ uint16_t x_abs = x_u & 0x7fff;
+ float xf = x;
+
+ // |x| > 0x1p0, |x| > 1, or x is NaN.
+ if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
+ // asinf16(NaN) = NaN
+ if (xbits.is_nan()) {
+ if (xbits.is_signaling_nan()) {
+ fputil::raise_except_if_required(FE_INVALID);
+ return FPBits::quiet_nan().get_val();
+ }
+
+ return x;
+ }
+
+ // 1 < |x| <= +/-inf
+ fputil::raise_except_if_required(FE_INVALID);
+ fputil::set_errno_if_required(EDOM);
+
+ return FPBits::quiet_nan().get_val();
+ }
+
+ float xsq = xf * xf;
+
+ // |x| <= 0x1p-1, |x| <= 0.5
+ if (x_abs <= 0x3800) {
+ // asinf16(+/-0) = +/-0
+ if (LIBC_UNLIKELY(x_abs == 0))
+ return x;
+
+ // Exhaustive tests show that,
+ // for |x| <= 0x1.878p-9, when:
+ // x > 0, and rounding upward, or
+ // x < 0, and rounding downward, then,
+ // asin(x) = x * 2^-11 + x
+ // else, in other rounding modes,
+ // asin(x) = x
+ if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) {
+ int rounding = fputil::quick_get_round();
+
+ if ((xbits.is_pos() && rounding == FE_UPWARD) ||
+ (xbits.is_neg() && rounding == FE_DOWNWARD))
+ return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf));
+ return x;
+ }
+
+ // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
+ // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+ float result =
+ fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
+ 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+ return fputil::cast<float16>(xf * result);
+ }
+
+ // When |x| > 0.5, assume that 0.5 < |x| <= 1,
+ //
+ // Step-by-step range-reduction proof:
+ // 1: Let y = asin(x), such that, x = sin(y)
+ // 2: From complimentary angle identity:
+ // x = sin(y) = cos(pi/2 - y)
+ // 3: Let z = pi/2 - y, such that x = cos(z)
+ // 4: From double angle formula; cos(2A) = 1 - sin^2(A):
+ // z = 2A, z/2 = A
+ // cos(z) = 1 - 2 * sin^2(z/2)
+ // 5: Make sin(z/2) subject of the formula:
+ // sin(z/2) = sqrt((1 - cos(z))/2)
+ // 6: Recall [3]; x = cos(z). Therefore:
+ // sin(z/2) = sqrt((1 - x)/2)
+ // 7: Let u = (1 - x)/2
+ // 8: Therefore:
+ // asin(sqrt(u)) = z/2
+ // 2 * asin(sqrt(u)) = z
+ // 9: Recall [3], z = pi/2 - y. Therefore:
+ // y = pi/2 - z
+ // y = pi/2 - 2 * asin(sqrt(u))
+ // 10: Recall [1], y = asin(x). Therefore:
+ // asin(x) = pi/2 - 2 * asin(sqrt(u))
+ //
+ // WHY?
+ // 11: Recall [7], u = (1 - x)/2
+ // 12: Since 0.5 < x <= 1, therefore:
+ // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
+ //
+ // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
+ // Step [10] as `sqrt(u)` is in range.
+
+ // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0
+ float xf_abs = (xf < 0 ? -xf : xf);
+ float sign = (xbits.uintval() >> 15 == 1 ? -1.0 : 1.0);
+ float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
+ float u_sqrt = fputil::sqrt<float>(u);
+
+ // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
+ // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
+ float asin_sqrt_u =
+ u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
+ 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
+
+ return fputil::cast<float16>(sign *
+ fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2));
+}
+
+} // namespace math
+
+} // namespace LIBC_NAMESPACE_DECL
+
+#endif // LIBC_TYPES_HAS_FLOAT16
+
+#endif // LLVM_LIBC_SRC___SUPPORT_MATH_ASINF16_H
diff --git a/libc/src/math/generic/CMakeLists.txt b/libc/src/math/generic/CMakeLists.txt
index ecf0967..d4d268c 100644
--- a/libc/src/math/generic/CMakeLists.txt
+++ b/libc/src/math/generic/CMakeLists.txt
@@ -3968,16 +3968,7 @@ add_entrypoint_object(
HDRS
../asinf16.h
DEPENDS
- libc.hdr.errno_macros
- libc.hdr.fenv_macros
- libc.src.__support.FPUtil.cast
- libc.src.__support.FPUtil.fenv_impl
- libc.src.__support.FPUtil.fp_bits
- libc.src.__support.FPUtil.multiply_add
- libc.src.__support.FPUtil.polyeval
- libc.src.__support.FPUtil.sqrt
- libc.src.__support.macros.optimization
- libc.src.__support.macros.properties.types
+ libc.src.__support.math.asinf16
)
add_entrypoint_object(
diff --git a/libc/src/math/generic/asinf16.cpp b/libc/src/math/generic/asinf16.cpp
index 518c384..af8dbfe 100644
--- a/libc/src/math/generic/asinf16.cpp
+++ b/libc/src/math/generic/asinf16.cpp
@@ -7,127 +7,10 @@
//===----------------------------------------------------------------------===//
#include "src/math/asinf16.h"
-#include "hdr/errno_macros.h"
-#include "hdr/fenv_macros.h"
-#include "src/__support/FPUtil/FEnvImpl.h"
-#include "src/__support/FPUtil/FPBits.h"
-#include "src/__support/FPUtil/PolyEval.h"
-#include "src/__support/FPUtil/cast.h"
-#include "src/__support/FPUtil/multiply_add.h"
-#include "src/__support/FPUtil/sqrt.h"
-#include "src/__support/macros/optimization.h"
+#include "src/__support/math/asinf16.h"
namespace LIBC_NAMESPACE_DECL {
-// Generated by Sollya using the following command:
-// > round(pi/2, D, RN);
-static constexpr float PI_2 = 0x1.921fb54442d18p0f;
-
-LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) {
- using FPBits = fputil::FPBits<float16>;
- FPBits xbits(x);
-
- uint16_t x_u = xbits.uintval();
- uint16_t x_abs = x_u & 0x7fff;
- float xf = x;
-
- // |x| > 0x1p0, |x| > 1, or x is NaN.
- if (LIBC_UNLIKELY(x_abs > 0x3c00)) {
- // asinf16(NaN) = NaN
- if (xbits.is_nan()) {
- if (xbits.is_signaling_nan()) {
- fputil::raise_except_if_required(FE_INVALID);
- return FPBits::quiet_nan().get_val();
- }
-
- return x;
- }
-
- // 1 < |x| <= +/-inf
- fputil::raise_except_if_required(FE_INVALID);
- fputil::set_errno_if_required(EDOM);
-
- return FPBits::quiet_nan().get_val();
- }
-
- float xsq = xf * xf;
-
- // |x| <= 0x1p-1, |x| <= 0.5
- if (x_abs <= 0x3800) {
- // asinf16(+/-0) = +/-0
- if (LIBC_UNLIKELY(x_abs == 0))
- return x;
-
- // Exhaustive tests show that,
- // for |x| <= 0x1.878p-9, when:
- // x > 0, and rounding upward, or
- // x < 0, and rounding downward, then,
- // asin(x) = x * 2^-11 + x
- // else, in other rounding modes,
- // asin(x) = x
- if (LIBC_UNLIKELY(x_abs <= 0x1a1e)) {
- int rounding = fputil::quick_get_round();
-
- if ((xbits.is_pos() && rounding == FE_UPWARD) ||
- (xbits.is_neg() && rounding == FE_DOWNWARD))
- return fputil::cast<float16>(fputil::multiply_add(xf, 0x1.0p-11f, xf));
- return x;
- }
-
- // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
- // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
- float result =
- fputil::polyeval(xsq, 0x1.000002p0f, 0x1.554c2ap-3f, 0x1.3541ccp-4f,
- 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
- return fputil::cast<float16>(xf * result);
- }
-
- // When |x| > 0.5, assume that 0.5 < |x| <= 1,
- //
- // Step-by-step range-reduction proof:
- // 1: Let y = asin(x), such that, x = sin(y)
- // 2: From complimentary angle identity:
- // x = sin(y) = cos(pi/2 - y)
- // 3: Let z = pi/2 - y, such that x = cos(z)
- // 4: From double angle formula; cos(2A) = 1 - sin^2(A):
- // z = 2A, z/2 = A
- // cos(z) = 1 - 2 * sin^2(z/2)
- // 5: Make sin(z/2) subject of the formula:
- // sin(z/2) = sqrt((1 - cos(z))/2)
- // 6: Recall [3]; x = cos(z). Therefore:
- // sin(z/2) = sqrt((1 - x)/2)
- // 7: Let u = (1 - x)/2
- // 8: Therefore:
- // asin(sqrt(u)) = z/2
- // 2 * asin(sqrt(u)) = z
- // 9: Recall [3], z = pi/2 - y. Therefore:
- // y = pi/2 - z
- // y = pi/2 - 2 * asin(sqrt(u))
- // 10: Recall [1], y = asin(x). Therefore:
- // asin(x) = pi/2 - 2 * asin(sqrt(u))
- //
- // WHY?
- // 11: Recall [7], u = (1 - x)/2
- // 12: Since 0.5 < x <= 1, therefore:
- // 0 <= u <= 0.25 and 0 <= sqrt(u) <= 0.5
- //
- // Hence, we can reuse the same [0, 0.5] domain polynomial approximation for
- // Step [10] as `sqrt(u)` is in range.
-
- // 0x1p-1 < |x| <= 0x1p0, 0.5 < |x| <= 1.0
- float xf_abs = (xf < 0 ? -xf : xf);
- float sign = (xbits.uintval() >> 15 == 1 ? -1.0 : 1.0);
- float u = fputil::multiply_add(-0.5f, xf_abs, 0.5f);
- float u_sqrt = fputil::sqrt<float>(u);
-
- // Degree-6 minimax odd polynomial of asin(x) generated by Sollya with:
- // > P = fpminimax(asin(x)/x, [|0, 2, 4, 6, 8|], [|SG...|], [0, 0.5]);
- float asin_sqrt_u =
- u_sqrt * fputil::polyeval(u, 0x1.000002p0f, 0x1.554c2ap-3f,
- 0x1.3541ccp-4f, 0x1.43b2d6p-5f, 0x1.a0d73ep-5f);
-
- return fputil::cast<float16>(sign *
- fputil::multiply_add(-2.0f, asin_sqrt_u, PI_2));
-}
+LLVM_LIBC_FUNCTION(float16, asinf16, (float16 x)) { return math::asinf16(x); }
} // namespace LIBC_NAMESPACE_DECL
generated by cgit v1.1 at 2025-07-27 22:33:23 +0000