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Implement ln based off FreeBSD's /usr/src/lib/msun/src/e_log.c
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gingerBill
@@ -96,18 +96,6 @@ fmuladd :: proc{
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fmuladd_f64, fmuladd_f64le, fmuladd_f64be,
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}
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ln_f16le :: proc "contextless" (x: f16le) -> f16le { return #force_inline f16le(ln_f16(f16(x))) }
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ln_f16be :: proc "contextless" (x: f16be) -> f16be { return #force_inline f16be(ln_f16(f16(x))) }
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ln_f32le :: proc "contextless" (x: f32le) -> f32le { return #force_inline f32le(ln_f32(f32(x))) }
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ln_f32be :: proc "contextless" (x: f32be) -> f32be { return #force_inline f32be(ln_f32(f32(x))) }
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ln_f64le :: proc "contextless" (x: f64le) -> f64le { return #force_inline f64le(ln_f64(f64(x))) }
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ln_f64be :: proc "contextless" (x: f64be) -> f64be { return #force_inline f64be(ln_f64(f64(x))) }
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ln :: proc{
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ln_f16, ln_f16le, ln_f16be,
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ln_f32, ln_f32le, ln_f32be,
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ln_f64, ln_f64le, ln_f64be,
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}
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exp_f16le :: proc "contextless" (x: f16le) -> f16le { return #force_inline f16le(exp_f16(f16(x))) }
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exp_f16be :: proc "contextless" (x: f16be) -> f16be { return #force_inline f16be(exp_f16(f16(x))) }
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exp_f32le :: proc "contextless" (x: f32le) -> f32le { return #force_inline f32le(exp_f32(f32(x))) }
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+117
-7
@@ -33,13 +33,6 @@ foreign _ {
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@(link_name="llvm.fmuladd.f64")
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fmuladd_f64 :: proc(a, b, c: f64) -> f64 ---
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@(link_name="llvm.log.f16")
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ln_f16 :: proc(x: f16) -> f16 ---
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@(link_name="llvm.log.f32")
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ln_f32 :: proc(x: f32) -> f32 ---
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@(link_name="llvm.log.f64")
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ln_f64 :: proc(x: f64) -> f64 ---
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@(link_name="llvm.exp.f16")
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exp_f16 :: proc(x: f16) -> f16 ---
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@(link_name="llvm.exp.f32")
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@@ -57,3 +50,120 @@ sqrt_f32 :: proc "contextless" (x: f32) -> f32 {
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sqrt_f64 :: proc "contextless" (x: f64) -> f64 {
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return intrinsics.sqrt(x)
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}
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ln_f64 :: proc "contextless" (x: f64) -> f64 {
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// The original C code, the long comment, and the constants
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// below are from FreeBSD's /usr/src/lib/msun/src/e_log.c
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// and came with this notice.
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//
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// ====================================================
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// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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//
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// Developed at SunPro, a Sun Microsystems, Inc. business.
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// Permission to use, copy, modify, and distribute this
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// software is freely granted, provided that this notice
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// is preserved.
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// ====================================================
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//
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// __ieee754_log(x)
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// Return the logarithm of x
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//
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// Method :
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// 1. Argument Reduction: find k and f such that
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// x = 2**k * (1+f),
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// where sqrt(2)/2 < 1+f < sqrt(2) .
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//
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// 2. Approximation of log(1+f).
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// Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
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// = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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// = 2s + s*R
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// We use a special Reme algorithm on [0,0.1716] to generate
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// a polynomial of degree 14 to approximate R. The maximum error
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// of this polynomial approximation is bounded by 2**-58.45. In
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// other words,
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// 2 4 6 8 10 12 14
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// R(z) ~ L1*s +L2*s +L3*s +L4*s +L5*s +L6*s +L7*s
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// (the values of L1 to L7 are listed in the program) and
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// | 2 14 | -58.45
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// | L1*s +...+L7*s - R(z) | <= 2
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// | |
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// Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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// In order to guarantee error in log below 1ulp, we compute log by
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// log(1+f) = f - s*(f - R) (if f is not too large)
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// log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy)
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//
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// 3. Finally, log(x) = k*Ln2 + log(1+f).
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// = k*Ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*Ln2_lo)))
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// Here Ln2 is split into two floating point number:
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// Ln2_hi + Ln2_lo,
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// where n*Ln2_hi is always exact for |n| < 2000.
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//
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// Special cases:
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// log(x) is NaN with signal if x < 0 (including -INF) ;
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// log(+INF) is +INF; log(0) is -INF with signal;
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// log(NaN) is that NaN with no signal.
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//
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// Accuracy:
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// according to an error analysis, the error is always less than
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// 1 ulp (unit in the last place).
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//
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// Constants:
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// The hexadecimal values are the intended ones for the following
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// constants. The decimal values may be used, provided that the
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// compiler will convert from decimal to binary accurately enough
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// to produce the hexadecimal values shown.
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LN2_HI :: 0h3fe62e42_fee00000 // 6.93147180369123816490e-01
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LN2_LO :: 0h3dea39ef_35793c76 // 1.90821492927058770002e-10
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L1 :: 0h3fe55555_55555593 // 6.666666666666735130e-01
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L2 :: 0h3fd99999_9997fa04 // 3.999999999940941908e-01
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L3 :: 0h3fd24924_94229359 // 2.857142874366239149e-01
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L4 :: 0h3fcc71c5_1d8e78af // 2.222219843214978396e-01
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L5 :: 0h3fc74664_96cb03de // 1.818357216161805012e-01
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L6 :: 0h3fc39a09_d078c69f // 1.531383769920937332e-01
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L7 :: 0h3fc2f112_df3e5244 // 1.479819860511658591e-01
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switch {
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case is_nan(x) || is_inf(x, 1):
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return x
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case x < 0:
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return nan_f64()
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case x == 0:
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return inf_f64(-1)
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}
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// reduce
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f1, ki := frexp(x)
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if f1 < SQRT_TWO/2 {
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f1 *= 2
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ki -= 1
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}
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f := f1 - 1
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k := f64(ki)
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// compute
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s := f / (2 + f)
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s2 := s * s
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s4 := s2 * s2
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t1 := s2 * (L1 + s4*(L3+s4*(L5+s4*L7)))
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t2 := s4 * (L2 + s4*(L4+s4*L6))
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R := t1 + t2
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hfsq := 0.5 * f * f
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return k*Ln2Hi_ - ((hfsq - (s*(hfsq+R) + k*LN2_LO)) - f)
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}
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ln_f16 :: proc "contextless" (x: f16) -> f16 { return #force_inline f16(ln_f64(f64(x))) }
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ln_f32 :: proc "contextless" (x: f32) -> f32 { return #force_inline f32(ln_f64(f64(x))) }
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ln_f16le :: proc "contextless" (x: f16le) -> f16le { return #force_inline f16le(ln_f64(f64(x))) }
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ln_f16be :: proc "contextless" (x: f16be) -> f16be { return #force_inline f16be(ln_f64(f64(x))) }
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ln_f32le :: proc "contextless" (x: f32le) -> f32le { return #force_inline f32le(ln_f64(f64(x))) }
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ln_f32be :: proc "contextless" (x: f32be) -> f32be { return #force_inline f32be(ln_f64(f64(x))) }
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ln_f64le :: proc "contextless" (x: f64le) -> f64le { return #force_inline f64le(ln_f64(f64(x))) }
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ln_f64be :: proc "contextless" (x: f64be) -> f64be { return #force_inline f64be(ln_f64(f64(x))) }
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ln :: proc{
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ln_f16, ln_f16le, ln_f16be,
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ln_f32, ln_f32le, ln_f32be,
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ln_f64, ln_f64le, ln_f64be,
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}
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