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📄 abs.go(366 B)
📄 acos_s390x.s(3.73 KB)
📄 acosh.go(1.71 KB)
📄 acosh_s390x.s(4.32 KB)
📄 all_test.go(86.77 KB)
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📄 arith_s390x_test.go(10.78 KB)
📄 asin.go(1.09 KB)
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📄 atan2.go(1.52 KB)
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📄 cbrt.go(2.31 KB)
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📄 const.go(2.76 KB)
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📄 exp.go(5.38 KB)
📄 exp2_asm.go(252 B)
📄 exp2_noasm.go(284 B)
📄 exp_amd64.go(261 B)
📄 exp_amd64.s(4.24 KB)
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📄 exp_asm.go(268 B)
📄 exp_noasm.go(302 B)
📄 exp_s390x.s(4.65 KB)
📄 expm1.go(7.91 KB)
📄 expm1_s390x.s(5.29 KB)
📄 export_s390x_test.go(732 B)
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📄 floor.go(3.29 KB)
📄 floor_386.s(1.47 KB)
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📄 fma.go(4.61 KB)
📄 frexp.go(929 B)
📄 gamma.go(5.53 KB)
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📄 hypot_386.s(1.81 KB)
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📄 jn.go(7.18 KB)
📄 ldexp.go(1.05 KB)
📄 lgamma.go(11.03 KB)
📄 log.go(3.86 KB)
📄 log10.go(873 B)
📄 log10_s390x.s(4.73 KB)
📄 log1p.go(6.34 KB)
📄 log1p_s390x.s(5.15 KB)
📄 log_amd64.s(3.66 KB)
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📄 pow.go(3.65 KB)
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📄 remainder.go(2.04 KB)
📄 signbit.go(302 B)
📄 sin.go(6.35 KB)
📄 sin_s390x.s(8.57 KB)
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📄 tan.go(3.68 KB)
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📄 tanh_s390x.s(4.57 KB)
📄 trig_reduce.go(3.34 KB)
📄 unsafe.go(1.27 KB)

Editing: exp.go

// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package math

// Exp returns e**x, the base-e exponential of x.
//
// Special cases are:
//
//	Exp(+Inf) = +Inf
//	Exp(NaN) = NaN
//
// Very large values overflow to 0 or +Inf.
// Very small values underflow to 1.
func Exp(x float64) float64 {
	if haveArchExp {
		return archExp(x)
	}
	return exp(x)
}

// The original C code, the long comment, and the constants
// below are from FreeBSD's /usr/src/lib/msun/src/e_exp.c
// and came with this notice. The go code is a simplified
// version of the original C.
//
// ====================================================
// Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved.
//
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
//
//
// exp(x)
// Returns the exponential of x.
//
// Method
//   1. Argument reduction:
//      Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
//      Given x, find r and integer k such that
//
//               x = k*ln2 + r,  |r| <= 0.5*ln2.
//
//      Here r will be represented as r = hi-lo for better
//      accuracy.
//
//   2. Approximation of exp(r) by a special rational function on
//      the interval [0,0.34658]:
//      Write
//          R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
//      We use a special Remez algorithm on [0,0.34658] to generate
//      a polynomial of degree 5 to approximate R. The maximum error
//      of this polynomial approximation is bounded by 2**-59. In
//      other words,
//          R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
//      (where z=r*r, and the values of P1 to P5 are listed below)
//      and
//          |                  5          |     -59
//          | 2.0+P1*z+...+P5*z   -  R(z) | <= 2
//          |                             |
//      The computation of exp(r) thus becomes
//                             2*r
//              exp(r) = 1 + -------
//                            R - r
//                                 r*R1(r)
//                     = 1 + r + ----------- (for better accuracy)
//                                2 - R1(r)
//      where
//                               2       4             10
//              R1(r) = r - (P1*r  + P2*r  + ... + P5*r   ).
//
//   3. Scale back to obtain exp(x):
//      From step 1, we have
//         exp(x) = 2**k * exp(r)
//
// Special cases:
//      exp(INF) is INF, exp(NaN) is NaN;
//      exp(-INF) is 0, and
//      for finite argument, only exp(0)=1 is exact.
//
// Accuracy:
//      according to an error analysis, the error is always less than
//      1 ulp (unit in the last place).
//
// Misc. info.
//      For IEEE double
//          if x >  7.09782712893383973096e+02 then exp(x) overflow
//          if x < -7.45133219101941108420e+02 then exp(x) underflow
//
// Constants:
// The hexadecimal values are the intended ones for the following
// constants. The decimal values may be used, provided that the
// compiler will convert from decimal to binary accurately enough
// to produce the hexadecimal values shown.

func exp(x float64) float64 {
	const (
		Ln2Hi = 6.93147180369123816490e-01
		Ln2Lo = 1.90821492927058770002e-10
		Log2e = 1.44269504088896338700e+00

Overflow  = 7.09782712893383973096e+02
		Underflow = -7.45133219101941108420e+02
		NearZero  = 1.0 / (1 << 28) // 2**-28
	)

// special cases
	switch {
	case IsNaN(x) || IsInf(x, 1):
		return x
	case IsInf(x, -1):
		return 0
	case x > Overflow:
		return Inf(1)
	case x < Underflow:
		return 0
	case -NearZero < x && x < NearZero:
		return 1 + x
	}

// reduce; computed as r = hi - lo for extra precision.
	var k int
	switch {
	case x < 0:
		k = int(Log2e*x - 0.5)
	case x > 0:
		k = int(Log2e*x + 0.5)
	}
	hi := x - float64(k)*Ln2Hi
	lo := float64(k) * Ln2Lo

// compute
	return expmulti(hi, lo, k)
}

// Exp2 returns 2**x, the base-2 exponential of x.
//
// Special cases are the same as [Exp].
func Exp2(x float64) float64 {
	if haveArchExp2 {
		return archExp2(x)
	}
	return exp2(x)
}

func exp2(x float64) float64 {
	const (
		Ln2Hi = 6.93147180369123816490e-01
		Ln2Lo = 1.90821492927058770002e-10

Overflow  = 1.0239999999999999e+03
		Underflow = -1.0740e+03
	)

// special cases
	switch {
	case IsNaN(x) || IsInf(x, 1):
		return x
	case IsInf(x, -1):
		return 0
	case x > Overflow:
		return Inf(1)
	case x < Underflow:
		return 0
	}

// argument reduction; x = r×lg(e) + k with |r| ≤ ln(2)/2.
	// computed as r = hi - lo for extra precision.
	var k int
	switch {
	case x > 0:
		k = int(x + 0.5)
	case x < 0:
		k = int(x - 0.5)
	}
	t := x - float64(k)
	hi := t * Ln2Hi
	lo := -t * Ln2Lo

// compute
	return expmulti(hi, lo, k)
}

// exp1 returns e**r × 2**k where r = hi - lo and |r| ≤ ln(2)/2.
func expmulti(hi, lo float64, k int) float64 {
	const (
		P1 = 1.66666666666666657415e-01  /* 0x3FC55555; 0x55555555 */
		P2 = -2.77777777770155933842e-03 /* 0xBF66C16C; 0x16BEBD93 */
		P3 = 6.61375632143793436117e-05  /* 0x3F11566A; 0xAF25DE2C */
		P4 = -1.65339022054652515390e-06 /* 0xBEBBBD41; 0xC5D26BF1 */
		P5 = 4.13813679705723846039e-08  /* 0x3E663769; 0x72BEA4D0 */
	)

r := hi - lo
	t := r * r
	c := r - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))))
	y := 1 - ((lo - (r*c)/(2-c)) - hi)
	// TODO(rsc): make sure Ldexp can handle boundary k
	return Ldexp(y, k)
}

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