Further optimize the math library

The sincosf() function is now twice as fast, thanks to ARM Limited. The same might also be true of logf() and expm1f() which have been updated.
2025-05-28 08:12:28 +00:00 · 2023-04-28 01:17:28 -07:00 · 2023-04-28 01:17:28 -07:00 · 420f889ac3
commit 420f889ac3
parent e8b43903b2
22 changed files with 854 additions and 118 deletions
--- a/libc/tinymath/expm1f.c
+++ b/libc/tinymath/expm1f.c
@ -0,0 +1,103 @@
+/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:2;tab-width:8;coding:utf-8 -*-│
+│vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8                                :vi│
+╚──────────────────────────────────────────────────────────────────────────────╝
+│                                                                              │
+│  Optimized Routines                                                          │
+│  Copyright (c) 1999-2022, Arm Limited.                                       │
+│                                                                              │
+│  Permission is hereby granted, free of charge, to any person obtaining       │
+│  a copy of this software and associated documentation files (the             │
+│  "Software"), to deal in the Software without restriction, including         │
+│  without limitation the rights to use, copy, modify, merge, publish,         │
+│  distribute, sublicense, and/or sell copies of the Software, and to          │
+│  permit persons to whom the Software is furnished to do so, subject to       │
+│  the following conditions:                                                   │
+│                                                                              │
+│  The above copyright notice and this permission notice shall be              │
+│  included in all copies or substantial portions of the Software.             │
+│                                                                              │
+│  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
+│  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          │
+│  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      │
+│  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        │
+│  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        │
+│  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           │
+│  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      │
+│                                                                              │
+╚─────────────────────────────────────────────────────────────────────────────*/
+#include "libc/math.h"
+#include "libc/tinymath/hornerf.internal.h"
+#include "libc/tinymath/internal.h"
+#include "third_party/libcxx/math.h"
+
+asm(".ident\t\"\\n\\n\
+Optimized Routines (MIT License)\\n\
+Copyright 2022 ARM Limited\"");
+asm(".include \"libc/disclaimer.inc\"");
+/* clang-format off */
+
+#define Shift (0x1.8p23f)
+#define InvLn2 (0x1.715476p+0f)
+#define Ln2hi (0x1.62e4p-1f)
+#define Ln2lo (0x1.7f7d1cp-20f)
+#define AbsMask (0x7fffffff)
+#define InfLimit                                                               \
+  (0x1.644716p6) /* Smallest value of x for which expm1(x) overflows.  */
+#define NegLimit                                                               \
+  (-0x1.9bbabcp+6) /* Largest value of x for which expm1(x) rounds to 1.  */
+
+#define C(i) __expm1f_poly[i]
+
+/* Generated using fpminimax, see tools/expm1f.sollya for details.  */
+const float __expm1f_poly[] = {0x1.fffffep-2, 0x1.5554aep-3, 0x1.555736p-5,
+			       0x1.12287cp-7, 0x1.6b55a2p-10};
+
+/* Approximation for exp(x) - 1 using polynomial on a reduced interval.
+   The maximum error is 1.51 ULP:
+   expm1f(0x1.8baa96p-2) got 0x1.e2fb9p-2
+			want 0x1.e2fb94p-2.  */
+float
+expm1f (float x)
+{
+  uint32_t ix = asuint (x);
+  uint32_t ax = ix & AbsMask;
+
+  /* Tiny: |x| < 0x1p-23. expm1(x) is closely approximated by x.
+     Inf:  x == +Inf => expm1(x) = x.  */
+  if (ax <= 0x34000000 || (ix == 0x7f800000))
+    return x;
+
+  /* +/-NaN.  */
+  if (ax > 0x7f800000)
+    return __math_invalidf (x);
+
+  if (x >= InfLimit)
+    return __math_oflowf (0);
+
+  if (x <= NegLimit || ix == 0xff800000)
+    return -1;
+
+  /* Reduce argument to smaller range:
+     Let i = round(x / ln2)
+     and f = x - i * ln2, then f is in [-ln2/2, ln2/2].
+     exp(x) - 1 = 2^i * (expm1(f) + 1) - 1
+     where 2^i is exact because i is an integer.  */
+  float j = fmaf (InvLn2, x, Shift) - Shift;
+  int32_t i = j;
+  float f = fmaf (j, -Ln2hi, x);
+  f = fmaf (j, -Ln2lo, f);
+
+  /* Approximate expm1(f) using polynomial.
+     Taylor expansion for expm1(x) has the form:
+	 x + ax^2 + bx^3 + cx^4 ....
+     So we calculate the polynomial P(f) = a + bf + cf^2 + ...
+     and assemble the approximation expm1(f) ~= f + f^2 * P(f).  */
+  float p = fmaf (f * f, HORNER_4 (f, C), f);
+  /* Assemble the result, using a slight rearrangement to achieve acceptable
+     accuracy.
+     expm1(x) ~= 2^i * (p + 1) - 1
+     Let t = 2^(i - 1).  */
+  float t = ldexpf (0.5f, i);
+  /* expm1(x) ~= 2 * (p * t + (t - 1/2)).  */
+  return 2 * fmaf (p, t, t - 0.5f);
+}